G := sub<Sym(6156)|(1, 3571)(2, 5297)(3, 1384)(4, 2270)(5, 1921)(6, 1762)(7, 4057)(8, 5716)(9, 5299)(10, 1203)(11, 4766)(12, 5445)(13, 6126)(14, 402)(15, 2104)(16, 5062)(17, 5907)(18, 179)(19, 4875)(20, 2462)(21, 3013)(22, 4542)(23, 4068)(24, 4021)(25, 680)(26, 2896)(27, 4505)(28, 600)(29, 5525)(30, 5234)(31, 4878)(32, 1885)(33, 527)(34, 5318)(35, 2701)(36, 4037)(37, 3991)(38, 4692)(39, 4325)(41, 1008)(42, 5014)(43, 4303)(44, 1512)(45, 1253)(46, 5607)(47, 3784)(48, 4293)(49, 5187)(51, 2426)(52, 2850)(53, 5562)(54, 332)(55, 3616)(56, 5848)(57, 4770)(58, 1018)(59, 2904)(60, 312)(61, 5495)(62, 5947)(63, 1725)(64, 3144)(65, 2040)(66, 2101)(67, 5144)(68, 5263)(69, 546)(70, 3000)(71, 3614)(72, 5350)(73, 3382)(74, 3421)(75, 4676)(76, 4594)(77, 895)(78, 1044)(79, 5966)(80, 1071)(81, 1413)(82, 2466)(83, 2691)(84, 4729)(85, 4761)(86, 2476)(87, 4503)(88, 3961)(89, 4126)(90, 5129)(91, 5280)(92, 4859)(93, 4556)(94, 4464)(95, 399)(96, 2162)(97, 5604)(98, 3700)(99, 5374)(100, 4749)(101, 2264)(102, 1187)(103, 3721)(104, 3832)(105, 2778)(106, 2839)(107, 1958)(108, 1838)(109, 1552)(110, 3881)(111, 1064)(112, 2555)(113, 5344)(114, 4984)(115, 515)(116, 4252)(117, 4458)(118, 3796)(119, 231)(120, 4623)(121, 5203)(122, 4569)(123, 5631)(124, 5682)(125, 4738)(126, 864)(127, 2304)(128, 4408)(129, 1650)(130, 1560)(131, 3497)(132, 4360)(133, 3123)(134, 3036)(135, 3828)(136, 4720)(137, 2556)(138, 1216)(139, 5568)(140, 4526)(141, 3801)(142, 4545)(143, 4802)(144, 3824)(145, 5504)(146, 4804)(147, 3327)(148, 5338)(149, 2143)(150, 5636)(151, 2322)(152, 4311)(153, 4799)(154, 3481)(155, 2222)(156, 5410)(157, 5206)(158, 1843)(159, 260)(160, 2447)(161, 963)(162, 367)(163, 4241)(164, 326)(165, 1053)(166, 3116)(167, 5650)(168, 4626)(169, 5653)(170, 1884)(171, 496)(172, 5957)(173, 1398)(174, 4058)(175, 5587)(176, 4995)(177, 5526)(178, 5634)(180, 4027)(181, 6148)(182, 3760)(183, 1904)(184, 5153)(185, 4165)(186, 3807)(187, 5648)(188, 4377)(189, 3365)(190, 5456)(191, 4449)(192, 5122)(193, 835)(194, 5640)(195, 5572)(196, 6132)(197, 5138)(198, 3253)(199, 430)(200, 2551)(201, 1608)(202, 4253)(203, 1259)(204, 3691)(205, 3032)(206, 2644)(207, 1702)(208, 1197)(209, 1482)(210, 630)(211, 5765)(212, 1175)(213, 2193)(214, 1531)(215, 3335)(216, 3822)(217, 1509)(218, 1519)(219, 1548)(220, 253)(221, 6134)(222, 6039)(223, 4471)(224, 387)(225, 2726)(226, 1242)(227, 3979)(228, 2230)(229, 756)(230, 4602)(232, 5852)(233, 2129)(234, 1209)(235, 2834)(236, 5200)(237, 3165)(238, 494)(239, 3371)(240, 884)(241, 4288)(242, 5037)(243, 2764)(244, 3495)(245, 1146)(246, 5970)(247, 2804)(248, 1678)(249, 5099)(250, 6155)(251, 1890)(252, 3813)(254, 611)(255, 4499)(256, 2377)(257, 3508)(258, 2470)(259, 3531)(261, 5759)(262, 1392)(263, 6097)(264, 3836)(265, 491)(266, 1639)(267, 3330)(268, 4152)(269, 2370)(270, 5805)(271, 968)(272, 3229)(273, 5775)(274, 451)(275, 826)(276, 1535)(277, 2845)(278, 5694)(279, 1672)(280, 1572)(281, 293)(282, 1215)(283, 4264)(284, 3294)(285, 5115)(286, 1231)(287, 3451)(288, 1066)(289, 1998)(290, 2513)(291, 4976)(292, 1598)(294, 2897)(295, 2725)(296, 2185)(297, 5395)(298, 4124)(299, 4077)(300, 6105)(301, 2431)(302, 3422)(303, 3267)(304, 815)(305, 4142)(306, 5248)(307, 607)(308, 814)(309, 2557)(310, 4414)(311, 2683)(313, 465)(314, 4217)(315, 1621)(316, 385)(317, 3646)(318, 4045)(319, 1849)(320, 1726)(321, 2119)(322, 4612)(323, 1458)(324, 4656)(325, 5524)(327, 1226)(328, 1148)(329, 2266)(330, 5004)(331, 4447)(333, 4317)(334, 2288)(335, 2467)(336, 854)(337, 1618)(338, 4030)(339, 1534)(340, 1070)(341, 5615)(342, 4670)(343, 5360)(344, 373)(345, 1882)(346, 2606)(347, 4240)(348, 890)(349, 1137)(350, 1239)(351, 2480)(352, 2890)(353, 4128)(354, 3519)(355, 522)(356, 5581)(357, 4348)(358, 4117)(359, 2564)(360, 420)(361, 2643)(362, 1915)(363, 710)(364, 2188)(365, 570)(366, 2152)(368, 1707)(369, 4768)(370, 5208)(371, 3685)(372, 5613)(374, 5632)(375, 478)(376, 2603)(377, 5101)(378, 1344)(379, 4461)(380, 438)(381, 3577)(382, 1191)(383, 2387)(384, 1290)(386, 1337)(388, 510)(389, 3293)(390, 4384)(391, 1251)(392, 671)(393, 3889)(394, 5812)(396, 1282)(397, 679)(398, 5791)(400, 6138)(401, 1474)(404, 4633)(405, 2632)(406, 2442)(407, 3415)(408, 2413)(409, 2077)(410, 4823)(411, 5186)(412, 6080)(413, 4869)(414, 2226)(415, 3320)(416, 1817)(417, 785)(418, 4035)(419, 5288)(421, 3649)(422, 5667)(423, 1483)(424, 1722)(425, 437)(426, 5467)(427, 4708)(428, 2471)(429, 3636)(431, 4159)(432, 3161)(433, 3702)(434, 2944)(435, 761)(436, 1746)(439, 5974)(440, 4735)(441, 2407)(442, 780)(443, 3544)(444, 1824)(445, 579)(446, 5415)(447, 5533)(448, 1538)(449, 5253)(450, 5937)(452, 5558)(453, 5411)(454, 6071)(455, 5718)(456, 4256)(457, 4722)(458, 2849)(459, 3860)(460, 689)(461, 3605)(462, 4991)(463, 3672)(464, 2951)(466, 3196)(467, 5175)(468, 6067)(469, 5357)(470, 3902)(471, 2033)(472, 2669)(473, 2190)(474, 3600)(475, 1003)(476, 2349)(477, 4243)(479, 2967)(480, 5700)(481, 760)(482, 5315)(483, 4155)(484, 4172)(485, 6042)(486, 4933)(487, 6113)(488, 5971)(489, 1709)(490, 1076)(492, 5209)(493, 3655)(495, 5407)(497, 871)(498, 2932)(499, 4988)(500, 3871)(501, 3115)(502, 4523)(503, 3526)(504, 4274)(505, 6107)(506, 5281)(507, 1262)(508, 3029)(509, 5089)(511, 1653)(512, 4100)(513, 1862)(514, 1279)(516, 1720)(517, 2436)(518, 1433)(519, 4901)(520, 3419)(521, 2287)(523, 5625)(524, 4561)(525, 4412)(526, 6018)(528, 4974)(529, 4139)(530, 4104)(531, 2245)(532, 651)(533, 2883)(534, 4539)(535, 4850)(536, 2073)(537, 3011)(538, 4516)(539, 2107)(540, 4819)(541, 2712)(542, 3970)(543, 2142)(544, 5491)(545, 3427)(547, 2767)(548, 906)(549, 2903)(550, 2836)(551, 4838)(552, 1751)(553, 4186)(554, 1612)(555, 2658)(556, 5880)(557, 5419)(558, 590)(559, 801)(560, 1339)(561, 646)(562, 2622)(563, 3506)(564, 3758)(565, 5264)(566, 640)(567, 6009)(568, 5657)(569, 3402)(571, 5476)(572, 3538)(573, 4570)(574, 4044)(575, 3181)(576, 4033)(577, 5659)(578, 2954)(580, 720)(581, 676)(582, 5933)(583, 5387)(584, 5698)(585, 2545)(586, 5498)(587, 4667)(588, 3145)(589, 1797)(591, 1424)(592, 2711)(593, 1124)(594, 1554)(595, 1147)(596, 1104)(597, 1814)(598, 2225)(599, 5838)(601, 2342)(602, 5670)(603, 2905)(604, 775)(605, 3799)(606, 3126)(608, 5614)(609, 2974)(610, 3305)(612, 2646)(613, 3190)(614, 2693)(615, 4477)(616, 1544)(617, 1140)(618, 4487)(619, 2710)(620, 1420)(622, 3746)(623, 3341)(624, 4684)(625, 3669)(626, 4685)(627, 3792)(628, 749)(629, 5171)(631, 4369)(632, 655)(633, 1576)(635, 4694)(636, 5479)(637, 2857)(638, 2687)(639, 1093)(641, 735)(642, 2065)(643, 2343)(644, 1969)(645, 2698)(647, 6109)(648, 3174)(649, 4798)(650, 2986)(652, 672)(653, 2018)(654, 1973)(656, 2678)(657, 3863)(659, 913)(660, 4111)(661, 5554)(662, 2223)(663, 5995)(664, 2862)(665, 3362)(666, 2082)(667, 960)(668, 3545)(669, 4896)(670, 5512)(673, 2423)(674, 5116)(675, 4990)(677, 4465)(678, 3457)(681, 799)(682, 1386)(683, 1241)(684, 3950)(685, 1451)(686, 2174)(687, 6033)(688, 1985)(690, 1026)(691, 1374)(692, 4620)(693, 3705)(694, 4848)(695, 2824)(696, 5797)(697, 4250)(698, 5217)(699, 2817)(700, 4985)(701, 4968)(702, 2947)(703, 4347)(704, 2705)(705, 4532)(706, 5574)(707, 4218)(709, 6088)(711, 2278)(712, 3003)(713, 2719)(714, 5511)(715, 4125)(716, 2537)(717, 2875)(718, 5737)(719, 4918)(721, 1319)(722, 1444)(723, 4791)(724, 3853)(725, 5923)(726, 4880)(729, 3983)(730, 5610)(731, 3757)(732, 5347)(733, 2302)(734, 1606)(736, 2501)(737, 2543)(738, 1311)(739, 4764)(740, 4640)(741, 5675)(742, 4140)(743, 1438)(744, 1405)(745, 3060)(746, 5159)(747, 1318)(748, 5989)(750, 4581)(751, 3861)(752, 5840)(753, 4793)(754, 1020)(757, 3711)(758, 3884)(759, 4129)(762, 2373)(763, 5082)(764, 5029)(765, 3195)(766, 1353)(767, 2168)(768, 2251)(769, 3984)(770, 4996)(771, 5119)(772, 5485)(773, 4296)(774, 4103)(776, 5290)(777, 3565)(778, 1480)(779, 885)(781, 3808)(782, 1056)(783, 1792)(784, 5644)(786, 4744)(787, 4828)(788, 2356)(789, 1975)(790, 936)(791, 4048)(792, 1456)(793, 4177)(794, 4209)(795, 2672)(796, 4588)(797, 5952)(798, 881)(800, 2360)(802, 4820)(803, 2176)(804, 2357)(805, 1813)(806, 4310)(807, 5480)(808, 3543)(809, 3314)(810, 1869)(811, 2070)(812, 3121)(813, 2971)(816, 3030)(817, 3400)(818, 1730)(819, 989)(820, 1505)(821, 2171)(822, 3086)(823, 3976)(824, 5793)(825, 5768)(827, 6111)(828, 955)(829, 4132)(830, 1907)(832, 4510)(833, 2970)(834, 1206)(836, 1761)(837, 2403)(838, 845)(839, 2179)(840, 5809)(841, 5166)(842, 4660)(843, 984)(844, 2714)(846, 5397)(848, 3336)(849, 1138)(850, 2277)(851, 4674)(852, 1826)(853, 5595)(855, 4498)(856, 2025)(857, 1780)(858, 3890)(859, 2122)(860, 4967)(861, 979)(862, 3243)(863, 4222)(865, 1144)(866, 4763)(867, 3664)(868, 2595)(869, 5507)(870, 3222)(872, 3348)(873, 3502)(874, 4220)(875, 3447)(876, 1801)(877, 2400)(878, 4287)(879, 4562)(880, 3033)(882, 5446)(883, 5465)(886, 3704)(887, 1009)(888, 4648)(891, 2892)(892, 1731)(893, 5331)(894, 3515)(896, 1055)(897, 3947)(898, 5813)(899, 1478)(900, 3609)(901, 1561)(902, 4586)(903, 1375)(904, 2660)(905, 5158)(907, 5955)(908, 1217)(909, 6046)(910, 2000)(911, 4235)(912, 4631)(914, 3474)(915, 1542)(916, 2620)(917, 3272)(918, 3718)(919, 4517)(920, 4297)(922, 3284)(923, 995)(924, 3334)(925, 3251)(926, 5921)(927, 3926)(928, 3332)(929, 1245)(930, 4634)(931, 3159)(932, 4745)(933, 3406)(934, 5319)(935, 1897)(937, 4691)(938, 5778)(939, 3276)(940, 3555)(941, 5802)(942, 6052)(943, 3281)(944, 5958)(945, 3989)(946, 5651)(947, 4893)(948, 5543)(950, 4583)(951, 2634)(952, 3941)(953, 1600)(954, 1119)(956, 5460)(957, 2737)(958, 3817)(959, 2591)(961, 1749)(962, 5307)(964, 2976)(965, 1229)(966, 2449)(967, 1986)(969, 4580)(970, 3218)(971, 5633)(972, 2301)(973, 4230)(974, 2415)(975, 1153)(976, 2975)(977, 4089)(978, 3852)(980, 1735)(981, 4388)(982, 1317)(983, 5306)(985, 5335)(986, 2960)(987, 4563)(988, 4703)(990, 4530)(991, 5827)(992, 3570)(993, 3727)(994, 4329)(996, 5376)(997, 1893)(998, 1860)(999, 2469)(1000, 5333)(1001, 5822)(1002, 2518)(1004, 2319)(1005, 3177)(1006, 5583)(1007, 1423)(1010, 4590)(1011, 3062)(1012, 3602)(1013, 1543)(1014, 5671)(1015, 2098)(1016, 3031)(1017, 2515)(1019, 1811)(1021, 2275)(1022, 2618)(1023, 3917)(1024, 2456)(1025, 2087)(1027, 4693)(1028, 2114)(1029, 2629)(1030, 4065)(1031, 4658)(1032, 3433)(1033, 1640)(1034, 1888)(1035, 5019)(1036, 5976)(1037, 5394)(1038, 4899)(1039, 4067)(1040, 3017)(1041, 3920)(1042, 3453)(1043, 5609)(1045, 5945)(1046, 3795)(1047, 5799)(1048, 1515)(1049, 5015)(1050, 5372)(1051, 6147)(1052, 4440)(1054, 5317)(1057, 5658)(1058, 3193)(1059, 5761)(1060, 3464)(1061, 3604)(1062, 2984)(1063, 2014)(1065, 4874)(1067, 1476)(1068, 5429)(1069, 5309)(1072, 2639)(1073, 5145)(1075, 1305)(1077, 6051)(1078, 2840)(1079, 4242)(1080, 4275)(1081, 5373)(1082, 5006)(1083, 1679)(1084, 3916)(1085, 5753)(1086, 4375)(1087, 4324)(1088, 3945)(1089, 5857)(1090, 2874)(1091, 5943)(1092, 3652)(1094, 5936)(1095, 1341)(1096, 2793)(1097, 3566)(1098, 5260)(1099, 4452)(1100, 5763)(1101, 2306)(1102, 5819)(1103, 4192)(1105, 1771)(1106, 5484)(1107, 2161)(1108, 5503)(1109, 5239)(1110, 2977)(1111, 1683)(1112, 1812)(1113, 3829)(1114, 2036)(1115, 4578)(1116, 5073)(1117, 4540)(1118, 4211)(1120, 3736)(1121, 3960)(1122, 5900)(1123, 2861)(1125, 5693)(1126, 5199)(1127, 2085)(1128, 6089)(1129, 1866)(1130, 5748)(1131, 2438)(1132, 5941)(1133, 2848)(1134, 4900)(1135, 5932)(1136, 5227)(1139, 2443)(1141, 1559)(1142, 5131)(1143, 4987)(1145, 2091)(1149, 2936)(1150, 1360)(1151, 5620)(1152, 2109)(1154, 1427)(1155, 2539)(1156, 3066)(1157, 3037)(1158, 4792)(1159, 3156)(1160, 5883)(1161, 2130)(1162, 5816)(1163, 1276)(1164, 3426)(1165, 4930)(1166, 5172)(1167, 2029)(1168, 1896)(1169, 5626)(1170, 6093)(1171, 4315)(1172, 4657)(1173, 3882)(1174, 1738)(1176, 4136)(1178, 5345)(1179, 1714)(1180, 3105)(1181, 4080)(1182, 2432)(1183, 1914)(1184, 4705)(1185, 3986)(1186, 2294)(1188, 2460)(1189, 3136)(1190, 5404)(1192, 3923)(1193, 3903)(1194, 2320)(1195, 4247)(1196, 5770)(1198, 3868)(1199, 1446)(1200, 4952)(1201, 1935)(1202, 5747)(1204, 1213)(1205, 4945)(1207, 4472)(1208, 4832)(1210, 5051)(1211, 3875)(1212, 4501)(1214, 2830)(1218, 4339)(1219, 1609)(1220, 2353)(1221, 1380)(1222, 4915)(1223, 5894)(1224, 5579)(1225, 4291)(1227, 4134)(1228, 3283)(1230, 5944)(1232, 2380)(1233, 4372)(1234, 2636)(1235, 3707)(1236, 1364)(1237, 3734)(1238, 3390)(1240, 5483)(1243, 3576)(1244, 2083)(1246, 3475)(1247, 3901)(1248, 4093)(1249, 2649)(1250, 3049)(1252, 2807)(1254, 3676)(1255, 3645)(1256, 4182)(1257, 3023)(1258, 2562)(1260, 3900)(1261, 4113)(1263, 2075)(1264, 5110)(1265, 5081)(1266, 5132)(1267, 2254)(1268, 2441)(1269, 3839)(1270, 2386)(1271, 1442)(1272, 5481)(1273, 4955)(1274, 5962)(1275, 5075)(1277, 1370)(1278, 3710)(1280, 2461)(1281, 3639)(1283, 1945)(1284, 3981)(1285, 1809)(1286, 1334)(1287, 4201)(1288, 2115)(1289, 1908)(1291, 2157)(1292, 2899)(1293, 2777)(1294, 3745)(1295, 4723)(1296, 3256)(1297, 5249)(1298, 2285)(1299, 4005)(1300, 2196)(1301, 3247)(1302, 3466)(1303, 2586)(1304, 3039)(1306, 3529)(1307, 5527)(1308, 5308)(1309, 6056)(1310, 3432)(1312, 2335)(1313, 1796)(1314, 3227)(1315, 3012)(1316, 2650)(1320, 2361)(1321, 2792)(1322, 2821)(1323, 5676)(1324, 3166)(1325, 1536)(1326, 3786)(1327, 3442)(1328, 6123)(1329, 5514)(1330, 4546)(1331, 2054)(1332, 1399)(1333, 2212)(1335, 5706)(1336, 3800)(1338, 4679)(1340, 3275)(1342, 3444)(1343, 1408)(1345, 4474)(1346, 3793)(1347, 4328)(1348, 3307)(1349, 4466)(1350, 5224)(1351, 3939)(1352, 3104)(1354, 1922)(1355, 2350)(1356, 3969)(1357, 2855)(1358, 4202)(1359, 1798)(1361, 6112)(1362, 2503)(1363, 2311)(1365, 5755)(1366, 2617)(1367, 4582)(1368, 4423)(1369, 5086)(1371, 1996)(1372, 2670)(1373, 4493)(1376, 2180)(1377, 2315)(1378, 1418)(1379, 4298)(1381, 4221)(1382, 5118)(1383, 3197)(1385, 4164)(1387, 2983)(1388, 3971)(1389, 1948)(1390, 5386)(1391, 4997)(1393, 4353)(1394, 1711)(1395, 4946)(1396, 3331)(1397, 5320)(1400, 3137)(1401, 2581)(1402, 3787)(1403, 2943)(1404, 4522)(1406, 4697)(1407, 1815)(1409, 6050)(1410, 3242)(1411, 4754)(1412, 4775)(1414, 1790)(1415, 3627)(1416, 2938)(1417, 2934)(1419, 1859)(1421, 6028)(1422, 3377)(1425, 3212)(1426, 4352)(1428, 5866)(1429, 2023)(1430, 2160)(1431, 1947)(1432, 4398)(1434, 4490)(1435, 3458)(1436, 3048)(1437, 2734)(1439, 5436)(1440, 5459)(1441, 3162)(1443, 4055)(1445, 2324)(1447, 5850)(1448, 2482)(1449, 2758)(1450, 5045)(1452, 2478)(1453, 1868)(1454, 1898)(1457, 3513)(1459, 3488)(1460, 2192)(1461, 2907)(1462, 4226)(1463, 4495)(1464, 2201)(1465, 4818)(1466, 4123)(1467, 1943)(1468, 2007)(1469, 2530)(1470, 2064)(1471, 5230)(1472, 5412)(1473, 1913)(1475, 2648)(1477, 4437)(1479, 5201)(1481, 3610)(1484, 4337)(1485, 5292)(1486, 3450)(1487, 2988)(1488, 3660)(1489, 2959)(1490, 4419)(1491, 2906)(1492, 1988)(1493, 2707)(1494, 5561)(1495, 1832)(1496, 5033)(1497, 2982)(1498, 5173)(1499, 2258)(1500, 2706)(1501, 5162)(1502, 3763)(1503, 2281)(1504, 2610)(1506, 5762)(1507, 2435)(1508, 3455)(1510, 3737)(1511, 4090)(1513, 1692)(1514, 3866)(1516, 3573)(1517, 3364)(1518, 2510)(1520, 1982)(1521, 4637)(1522, 5781)(1523, 4101)(1524, 1995)(1525, 4882)(1526, 4379)(1527, 3277)(1528, 5743)(1529, 2238)(1530, 2382)(1532, 1865)(1537, 1870)(1539, 4654)(1540, 3512)(1541, 5160)(1545, 5637)(1547, 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involutions :=

[
[
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        5743)(2348, 4451)(2349, 5443)(2350, 5847)(2351, 3191)(2354, 3678)(2355, 
        5587)(2356, 3180)(2357, 4309)(2358, 4737)(2359, 2746)(2361, 3448)(2362, 
        5559)(2363, 6134)(2365, 3324)(2367, 2446)(2369, 5090)(2375, 2889)(2376, 
        5133)(2379, 4833)(2381, 5976)(2382, 3188)(2383, 5894)(2384, 4020)(2386, 
        5069)(2388, 4527)(2390, 4373)(2391, 2804)(2392, 3511)(2393, 4654)(2394, 
        4327)(2395, 3391)(2396, 3375)(2398, 3841)(2399, 4762)(2400, 4982)(2402, 
        3593)(2406, 3519)(2409, 2626)(2410, 4627)(2413, 5327)(2415, 3086)(2416, 
        2685)(2417, 4967)(2419, 2967)(2421, 3224)(2422, 2709)(2425, 5120)(2426, 
        3919)(2428, 3261)(2432, 3959)(2433, 2579)(2434, 4113)(2436, 3587)(2437, 
        4792)(2438, 5495)(2439, 4121)(2442, 3449)(2444, 2572)(2445, 4423)(2447, 
        5236)(2451, 5033)(2452, 2687)(2453, 2838)(2454, 3586)(2456, 5078)(2459, 
        6043)(2460, 5041)(2461, 3346)(2463, 5044)(2467, 2952)(2469, 6131)(2470, 
        2655)(2474, 6074)(2475, 4336)(2476, 2899)(2477, 2857)(2478, 4203)(2479, 
        4436)(2481, 4139)(2482, 5406)(2485, 3341)(2486, 5467)(2488, 5708)(2489, 
        3190)(2491, 4176)(2492, 4402)(2493, 3536)(2495, 3833)(2496, 4104)(2497, 
        3183)(2499, 2933)(2500, 2942)(2501, 5436)(2502, 3011)(2507, 4127)(2509, 
        3093)(2510, 5323)(2511, 4860)(2512, 3069)(2513, 3517)(2518, 3463)(2522, 
        5755)(2523, 2537)(2527, 4588)(2529, 5837)(2530, 5625)(2531, 3813)(2532, 
        3295)(2533, 2646)(2534, 3618)(2535, 6001)(2536, 5368)(2538, 4006)(2539, 
        3769)(2540, 3820)(2541, 4321)(2542, 3571)(2543, 4845)(2546, 2722)(2547, 
        5387)(2548, 4790)(2550, 2667)(2551, 4080)(2552, 2592)(2553, 3884)(2554, 
        5063)(2556, 2978)(2558, 5537)(2560, 4046)(2561, 4339)(2563, 5316)(2564, 
        5600)(2566, 2849)(2567, 4202)(2569, 2768)(2570, 3653)(2571, 3807)(2574, 
        4869)(2575, 5830)(2577, 6083)(2578, 5551)(2580, 4344)(2581, 4551)(2582, 
        5953)(2584, 5127)(2585, 3970)(2586, 5438)(2588, 4418)(2590, 2896)(2593, 
        5780)(2595, 4376)(2597, 2958)(2598, 3538)(2600, 4228)(2602, 3811)(2603, 
        5141)(2604, 2741)(2606, 5607)(2607, 4582)(2610, 3696)(2611, 5234)(2612, 
        5293)(2614, 4107)(2615, 2925)(2618, 4289)(2619, 5688)(2620, 5016)(2622, 
        3695)(2624, 3017)(2625, 4913)(2629, 4192)(2630, 3094)(2634, 6087)(2638, 
        4911)(2640, 5145)(2641, 4115)(2642, 6073)(2643, 4148)(2644, 5510)(2645, 
        4659)(2649, 5853)(2651, 3731)(2653, 4136)(2654, 3864)(2656, 4787)(2659, 
        5294)(2662, 4716)(2664, 4360)(2665, 4197)(2666, 5506)(2670, 4403)(2671, 
        5876)(2673, 4727)(2675, 4388)(2676, 4425)(2677, 2712)(2678, 4924)(2679, 
        5599)(2680, 4783)(2681, 3140)(2682, 4443)(2683, 5253)(2684, 5550)(2686, 
        4851)(2688, 6033)(2689, 3955)(2690, 3413)(2691, 5695)(2692, 3647)(2694, 
        6048)(2696, 3590)(2697, 2717)(2699, 4942)(2703, 4420)(2704, 5636)(2705, 
        5415)(2706, 5569)(2708, 4957)(2714, 4921)(2716, 5326)(2718, 3669)(2725, 
        3738)(2726, 5671)(2727, 5993)(2728, 4042)(2729, 4051)(2731, 3793)(2732, 
        6088)(2733, 5645)(2734, 4996)(2736, 3088)(2737, 5511)(2738, 3843)(2739, 
        2757)(2740, 3325)(2742, 3774)(2743, 5612)(2744, 2754)(2750, 3606)(2751, 
        4994)(2752, 2910)(2755, 3924)(2756, 5834)(2759, 3619)(2760, 5694)(2761, 
        4600)(2762, 3562)(2765, 4878)(2766, 3201)(2770, 6038)(2773, 5978)(2775, 
        4134)(2778, 6154)(2779, 4206)(2781, 5394)(2782, 3441)(2784, 4067)(2785, 
        5749)(2786, 4454)(2787, 3207)(2788, 4462)(2789, 5168)(2792, 5999)(2794, 
        2995)(2795, 4964)(2796, 5554)(2799, 3545)(2801, 5240)(2802, 4544)(2805, 
        6098)(2807, 3911)(2808, 5512)(2810, 5376)(2812, 3206)(2813, 4319)(2814, 
        4230)(2815, 5502)(2816, 4142)(2817, 6037)(2821, 5054)(2824, 5819)(2825, 
        5556)(2826, 5518)(2828, 2898)(2830, 5979)(2831, 3766)(2832, 5373)(2834, 
        5355)(2837, 5185)(2839, 3347)(2840, 6123)(2842, 6039)(2843, 5970)(2844, 
        4479)(2845, 4850)(2846, 3994)(2848, 4279)(2854, 3416)(2855, 5051)(2861, 
        5720)(2863, 3373)(2864, 3846)(2865, 3457)(2868, 2923)(2869, 6022)(2871, 
        3283)(2872, 4798)(2873, 3717)(2874, 3930)(2875, 4158)(2876, 4456)(2878, 
        4738)(2879, 5075)(2882, 3269)(2883, 4745)(2886, 4909)(2887, 5132)(2888, 
        5158)(2891, 5838)(2892, 4014)(2894, 5856)(2895, 4542)(2897, 4242)(2900, 
        4487)(2902, 3960)(2904, 4106)(2906, 4520)(2907, 5937)(2908, 4070)(2911, 
        4820)(2913, 3775)(2914, 6124)(2916, 3451)(2917, 4114)(2919, 3948)(2920, 
        5093)(2921, 4567)(2922, 3660)(2924, 5527)(2926, 3125)(2927, 5725)(2930, 
        4795)(2931, 3875)(2934, 3629)(2936, 5568)(2937, 6040)(2940, 3857)(2941, 
        4395)(2945, 5920)(2947, 5814)(2948, 5150)(2949, 3012)(2956, 5553)(2957, 
        5270)(2959, 5829)(2960, 5029)(2961, 5746)(2962, 4465)(2963, 5884)(2964, 
        2988)(2969, 4123)(2970, 4019)(2975, 4954)(2976, 3407)(2981, 4562)(2982, 
        5181)(2985, 2986)(2987, 4078)(2989, 4061)(2990, 5547)(2991, 5263)(2993, 
        5700)(2994, 3980)(2996, 4630)(2998, 3944)(2999, 3262)(3000, 3547)(3002, 
        4812)(3003, 5104)(3004, 4408)(3005, 5799)(3007, 3893)(3008, 3527)(3009, 
        4267)(3014, 4246)(3015, 4547)(3016, 4254)(3018, 4649)(3020, 5752)(3021, 
        4074)(3022, 3041)(3023, 3748)(3028, 4768)(3032, 6042)(3034, 5265)(3035, 
        5037)(3037, 5110)(3038, 3542)(3039, 4694)(3040, 3639)(3042, 4424)(3045, 
        5115)(3048, 3272)(3049, 3355)(3052, 3255)(3054, 4118)(3061, 5563)(3062, 
        5593)(3064, 3524)(3065, 5343)(3066, 4281)(3068, 4001)(3070, 4269)(3072, 
        3861)(3073, 6056)(3074, 4736)(3075, 5297)(3078, 4251)(3080, 5296)(3082, 
        4017)(3084, 3815)(3085, 5748)(3089, 5129)(3091, 4103)(3092, 3662)(3095, 
        4623)(3096, 5475)(3098, 5697)(3099, 3942)(3102, 4144)(3105, 4152)(3106, 
        4521)(3107, 5958)(3108, 6146)(3109, 4715)(3110, 4143)(3111, 3468)(3112, 
        3372)(3118, 4705)(3119, 4453)(3121, 6086)(3123, 5224)(3124, 3360)(3127, 
        3473)(3128, 5851)(3130, 3390)(3131, 3242)(3133, 4594)(3137, 4512)(3138, 
        4352)(3143, 3170)(3148, 4524)(3149, 3195)(3151, 3967)(3152, 5262)(3154, 
        3522)(3155, 3477)(3157, 4874)(3158, 4041)(3160, 4469)(3162, 4675)(3163, 
        5285)(3164, 5483)(3165, 5585)(3167, 5411)(3168, 5973)(3169, 4005)(3172, 
        4166)(3173, 3306)(3174, 5068)(3176, 3610)(3177, 3351)(3178, 4872)(3179, 
        4775)(3181, 3870)(3182, 3338)(3184, 5962)(3189, 4534)(3192, 4149)(3194, 
        3926)(3196, 3205)(3197, 5761)(3199, 4031)(3200, 4857)(3202, 5333)(3203, 
        3887)(3209, 5500)(3210, 5823)(3212, 5352)(3214, 5902)(3215, 4670)(3219, 
        3327)(3220, 4587)(3221, 4827)(3222, 5102)(3227, 4651)(3229, 4407)(3233, 
        4405)(3234, 4290)(3236, 4663)(3237, 5201)(3238, 3810)(3239, 5959)(3241, 
        3408)(3243, 5988)(3244, 5341)(3245, 4411)(3246, 4109)(3247, 3420)(3248, 
        5221)(3251, 3927)(3256, 4010)(3258, 5448)(3259, 4223)(3260, 3796)(3263, 
        4011)(3266, 4609)(3267, 3903)(3270, 5173)(3271, 3564)(3274, 4785)(3275, 
        5652)(3276, 3609)(3279, 5271)(3282, 3686)(3284, 5259)(3286, 5913)(3289, 
        3652)(3291, 5955)(3293, 5946)(3297, 4361)(3299, 4848)(3301, 4116)(3303, 
        4695)(3307, 4048)(3308, 4434)(3312, 5980)(3314, 4245)(3315, 6076)(3316, 
        4653)(3317, 5754)(3318, 4468)(3320, 5548)(3329, 3418)(3331, 3705)(3332, 
        5416)(3334, 4003)(3336, 4515)(3337, 4572)(3342, 5711)(3343, 3991)(3345, 
        4811)(3349, 5862)(3350, 4724)(3352, 4740)(3353, 5534)(3354, 4232)(3356, 
        4886)(3358, 3613)(3359, 6017)(3362, 5672)(3365, 5660)(3367, 6008)(3368, 
        5787)(3369, 3936)(3374, 5300)(3377, 6031)(3379, 5169)(3382, 3642)(3383, 
        4709)(3386, 4974)(3388, 5030)(3396, 3548)(3397, 5529)(3398, 3772)(3399, 
        4619)(3400, 3768)(3402, 4470)(3405, 3410)(3409, 3585)(3411, 4586)(3412, 
        4968)(3414, 3437)(3419, 4853)(3422, 3909)(3425, 5773)(3427, 4752)(3428, 
        4885)(3430, 3663)(3431, 3744)(3432, 4131)(3435, 5421)(3440, 5898)(3442, 
        4170)(3443, 5557)(3444, 3715)(3452, 4990)(3455, 5514)(3456, 5292)(3458, 
        5857)(3460, 4847)(3461, 5831)(3462, 3814)(3470, 6013)(3471, 5064)(3472, 
        4821)(3474, 5821)(3475, 4677)(3476, 3569)(3478, 5482)(3479, 5632)(3486, 
        6029)(3491, 4703)(3492, 4901)(3494, 4182)(3495, 6028)(3496, 4446)(3500, 
        6097)(3503, 5653)(3504, 3698)(3507, 3673)(3508, 5047)(3510, 5358)(3512, 
        3950)(3513, 5167)(3514, 5832)(3515, 5701)(3520, 3915)(3523, 4495)(3526, 
        3719)(3529, 3979)(3530, 4908)(3531, 4068)(3533, 4225)(3541, 4081)(3543, 
        4543)(3544, 3704)(3550, 4196)(3553, 5124)(3554, 4953)(3555, 4689)(3557, 
        6110)(3565, 5470)(3568, 4096)(3572, 5588)(3573, 5367)(3579, 4760)(3583, 
        5685)(3584, 4529)(3588, 5096)(3589, 5324)(3596, 4200)(3597, 4904)(3599, 
        5426)(3605, 4262)(3614, 4098)(3615, 5031)(3621, 5346)(3623, 5280)(3624, 
        3832)(3625, 5716)(3626, 5151)(3628, 5123)(3631, 4807)(3633, 4291)(3634, 
        5456)(3635, 4650)(3637, 5140)(3638, 4138)(3641, 3998)(3643, 4222)(3644, 
        4173)(3645, 5952)(3651, 5933)(3654, 5965)(3657, 4914)(3661, 5268)(3664, 
        5594)(3665, 4284)(3667, 5582)(3668, 5567)(3670, 5710)(3674, 4188)(3675, 
        5925)(3676, 4130)(3679, 5772)(3682, 5021)(3689, 5452)(3691, 5359)(3692, 
        3710)(3694, 5526)(3700, 5776)(3701, 5561)(3703, 5642)(3706, 4186)(3708, 
        3826)(3712, 5606)(3720, 4491)(3722, 4342)(3729, 3801)(3730, 4554)(3733, 
        4328)(3734, 5611)(3735, 5603)(3737, 4162)(3739, 5026)(3740, 4147)(3741, 
        3745)(3746, 4338)(3751, 4498)(3752, 5531)(3754, 5013)(3756, 5309)(3757, 
        5036)(3760, 4965)(3761, 5116)(3762, 4796)(3763, 5065)(3764, 5634)(3765, 
        4035)(3767, 4937)(3770, 4550)(3777, 5698)(3778, 4399)(3779, 5663)(3780, 
        4167)(3782, 6065)(3783, 5741)(3784, 4826)(3786, 5860)(3792, 5885)(3799, 
        4629)(3802, 4830)(3803, 5196)(3804, 4391)(3805, 4931)(3816, 6061)(3817, 
        5012)(3819, 4237)(3824, 5126)(3829, 5350)(3834, 4700)(3835, 5289)(3836, 
        5269)(3837, 5775)(3839, 6092)(3840, 3851)(3842, 5310)(3844, 5940)(3847, 
        5209)(3850, 4981)(3854, 4181)(3855, 4918)(3859, 5513)(3865, 5926)(3866, 
        5575)(3867, 3986)(3869, 4718)(3873, 5002)(3877, 4686)(3880, 4433)(3881, 
        4900)(3886, 4494)(3889, 4056)(3890, 4583)(3891, 4428)(3892, 5363)(3895, 
        5159)(3896, 3982)(3902, 4580)(3905, 5122)(3906, 5295)(3907, 4929)(3912, 
        4963)(3913, 5425)(3914, 4861)(3920, 5082)(3928, 5248)(3931, 5875)(3932, 
        4278)(3933, 5802)(3934, 5412)(3935, 4814)(3937, 5945)(3941, 5960)(3943, 
        4358)(3945, 5058)(3946, 4522)(3947, 4047)(3949, 4249)(3954, 5609)(3956, 
        4272)(3957, 5143)(3958, 4030)(3961, 5738)(3962, 4555)(3963, 4445)(3965, 
        4666)(3966, 4747)(3969, 5017)(3972, 6075)(3974, 5091)(3977, 5422)(3978, 
        5083)(3981, 4168)(3983, 4920)(3984, 5165)(3985, 4012)(3987, 5888)(3988, 
        6151)(3989, 6116)(3990, 5085)(3992, 5598)(3995, 5251)(3996, 4899)(3999, 
        4125)(4008, 5154)(4009, 5986)(4015, 4643)(4022, 6036)(4023, 5967)(4025, 
        6137)(4028, 5486)(4029, 4840)(4037, 5497)(4038, 5250)(4039, 4753)(4040, 
        5001)(4044, 4179)(4045, 4215)(4053, 5995)(4058, 4574)(4059, 4280)(4060, 
        5081)(4062, 4910)(4063, 4568)(4064, 4897)(4065, 5389)(4066, 5162)(4069, 
        4119)(4073, 4271)(4077, 5858)(4083, 5385)(4085, 4676)(4086, 6106)(4089, 
        4478)(4091, 5954)(4095, 5194)(4101, 6078)(4122, 4784)(4124, 5413)(4128, 
        4439)(4129, 4440)(4132, 5112)(4137, 5320)(4156, 4684)(4163, 5241)(4164, 
        5461)(4165, 5677)(4171, 5890)(4175, 4755)(4189, 5740)(4194, 4493)(4198, 
        4545)(4199, 5121)(4201, 4838)(4207, 5022)(4209, 5114)(4210, 4430)(4211, 
        5941)(4213, 5794)(4216, 5329)(4218, 5852)(4220, 4414)(4226, 5929)(4227, 
        4672)(4229, 4499)(4235, 4823)(4236, 5605)(4238, 4940)(4239, 4283)(4240, 
        5763)(4247, 4912)(4248, 5782)(4255, 5927)(4256, 5039)(4257, 5084)(4258, 
        5028)(4260, 4905)(4264, 6004)(4265, 5330)(4266, 4480)(4268, 4816)(4273, 
        4483)(4274, 4678)(4282, 5134)(4287, 4397)(4297, 5764)(4300, 4507)(4301, 
        5211)(4306, 5639)(4308, 5365)(4312, 4691)(4315, 5342)(4318, 5420)(4320, 
        6044)(4323, 5361)(4324, 5868)(4325, 4756)(4329, 6082)(4332, 5353)(4335, 
        5841)(4337, 4767)(4340, 5964)(4347, 5291)(4348, 4973)(4350, 4503)(4353, 
        6016)(4355, 5581)(4356, 6119)(4362, 5745)(4363, 4903)(4366, 4980)(4367, 
        4906)(4368, 5006)(4370, 6125)(4372, 5273)(4374, 5399)(4377, 5261)(4380, 
        4633)(4381, 6150)(4384, 5468)(4389, 4652)(4393, 5272)(4394, 4822)(4396, 
        6014)(4400, 5459)(4404, 5139)(4406, 4461)(4410, 4599)(4413, 5623)(4416, 
        6130)(4422, 5994)(4429, 5177)(4442, 4777)(4444, 5442)(4447, 4485)(4449, 
        5589)(4452, 4704)(4458, 6059)(4460, 4829)(4463, 4766)(4464, 5824)(4466, 
        5214)(4467, 5088)(4475, 4803)(4481, 5379)(4484, 5492)(4489, 5220)(4490, 
        4611)(4492, 5463)(4496, 4802)(4497, 6118)(4504, 4585)(4505, 5170)(4506, 
        4595)(4510, 5187)(4511, 5118)(4513, 5714)(4518, 4950)(4519, 4698)(4523, 
        5246)(4530, 4612)(4531, 5596)(4533, 4674)(4535, 6148)(4536, 6050)(4538, 
        5923)(4540, 5274)(4549, 4564)(4552, 5757)(4553, 5801)(4557, 5871)(4560, 
        4693)(4561, 4579)(4566, 5530)(4575, 4721)(4590, 5555)(4593, 4805)(4596, 
        5507)(4603, 4719)(4606, 5574)(4608, 5245)(4610, 4656)(4614, 4749)(4628, 
        5679)(4631, 5774)(4632, 4986)(4635, 5886)(4640, 6023)(4646, 5768)(4655, 
        5189)(4660, 5771)(4661, 5828)(4665, 6141)(4667, 5414)(4673, 5004)(4681, 
        5686)(4688, 5239)(4690, 5520)(4701, 5721)(4706, 5718)(4710, 5444)(4711, 
        5629)(4712, 5626)(4714, 4943)(4723, 5893)(4726, 6139)(4731, 5179)(4742, 
        6144)(4748, 6080)(4754, 6145)(4765, 6136)(4769, 4923)(4771, 5212)(4778, 
        5267)(4779, 5779)(4781, 6121)(4782, 5736)(4786, 4804)(4788, 6096)(4799, 
        5418)(4800, 4915)(4806, 5395)(4813, 4975)(4815, 5810)(4818, 4880)(4825, 
        5410)(4828, 5919)(4832, 5985)(4834, 5430)(4837, 5895)(4844, 5951)(4856, 
        5338)(4862, 5319)(4864, 5947)(4866, 5489)(4871, 5312)(4873, 5351)(4884, 
        5807)(4887, 5508)(4889, 5462)(4890, 5570)(4894, 5377)(4895, 5540)(4916, 
        5912)(4917, 5522)(4928, 5675)(4934, 5366)(4935, 5356)(4938, 5586)(4941, 
        5877)(4945, 5696)(4947, 6138)(4951, 5307)(4958, 5904)(4970, 5549)(4971, 
        6035)(4978, 5583)(4984, 5176)(4987, 5128)(4989, 6133)(4991, 5620)(4992, 
        5266)(4997, 5097)(5011, 5874)(5018, 5564)(5023, 5918)(5042, 5809)(5045, 
        5488)(5048, 5345)(5053, 5595)(5055, 5405)(5056, 5690)(5062, 6034)(5066, 
        5206)(5070, 5733)(5073, 6129)(5076, 5543)(5079, 5905)(5080, 6126)(5086, 
        5372)(5094, 5659)(5095, 5423)(5106, 5742)(5108, 5869)(5111, 5487)(5135, 
        5164)(5136, 5437)(5138, 5678)(5146, 6077)(5155, 5213)(5157, 5702)(5160, 
        5371)(5172, 5948)(5174, 5276)(5178, 5434)(5184, 5881)(5186, 5375)(5188, 
        5845)(5190, 5602)(5191, 5362)(5199, 5840)(5200, 6108)(5203, 5896)(5208, 
        5661)(5210, 5501)(5222, 5454)(5232, 5521)(5233, 5464)(5243, 5432)(5247, 
        5445)(5249, 5649)(5252, 5825)(5254, 5566)(5258, 5519)(5260, 5854)(5282, 
        5963)(5288, 5381)(5299, 5431)(5302, 5901)(5305, 5728)(5311, 5777)(5321, 
        6068)(5347, 5910)(5364, 5684)(5382, 5658)(5386, 6122)(5392, 5610)(5393, 
        5706)(5398, 5957)(5401, 6079)(5417, 5930)(5424, 5704)(5440, 6095)(5446, 
        5572)(5465, 5703)(5466, 6114)(5481, 5613)(5504, 5914)(5505, 5730)(5528, 
        5618)(5532, 5656)(5533, 5693)(5565, 5640)(5597, 6085)(5604, 5909)(5622, 
        6047)(5627, 6140)(5644, 5796)(5650, 5833)(5654, 5727)(5665, 5924)(5681, 
        6115)(5719, 6090)(5729, 6002)(5734, 5866)(5753, 6041)(5765, 6000)(5789, 
        5848)(5808, 6052)(5816, 5903)(5908, 5950)(5931, 6054)(5938, 6094)(5968, 
        5972)
]

];

geometries := [* *];


for i in [1..#involutions] do
	G1 := sub<G|involutions[i][2],involutions[i][3]>;
	G2 := sub<G|involutions[i][1],involutions[i][3]>;
	G3 := sub<G|involutions[i][1],involutions[i][2]>;
	Append(~geometries,CosetGeometry(G,{G1,G2,G3}));
end for;