PermutationGroup<1464 |  
\[1046,1204,1215,1451,731,291,179,1377,1048,1284,514,137,169,
639,1402,1102,61,412,1260,671,199,1304,185,1150,464,635,508,
281,1126,1315,428,890,848,437,617,1209,119,610,1339,946,709,
459,1186,435,1074,928,997,323,967,331,1439,343,1056,909,346,
877,495,1073,410,576,17,141,1187,231,232,717,1403,1365,1027,
420,753,1404,1171,1424,816,1039,1077,215,1320,269,432,329,1103,
278,770,125,585,926,607,257,957,1301,894,208,695,771,1101,763,
1406,108,998,203,640,1076,787,654,1401,100,779,802,518,262,
659,1100,1119,1218,805,251,37,1002,557,532,1096,934,86,1398,
1123,297,990,389,165,965,716,189,592,455,12,1371,820,515,62,
1061,402,898,487,1275,970,394,1277,290,595,1245,1037,1078,1429,
611,375,449,662,775,1411,332,1003,559,131,192,1153,622,13,320,
987,1273,1425,1346,676,423,961,980,7,345,1384,1179,577,999,23,
643,979,1007,134,700,453,166,897,913,1144,1016,1170,535,21,
994,1438,742,102,813,921,768,1137,94,566,457,543,268,966,1281,
78,390,757,540,1396,1019,288,884,258,1121,1085,971,475,1011,
439,562,64,65,864,843,1142,1069,1238,1352,746,1060,372,902,
363,465,712,1460,319,485,727,842,118,1312,1361,962,1356,602,
90,223,705,1333,963,112,1394,1271,651,1223,1324,212,80,303,
1032,468,1184,1241,937,369,922,84,460,1134,28,945,1192,588,
1015,667,714,221,630,150,6,427,426,355,837,1287,128,1105,752,
302,380,300,270,1066,327,406,534,812,1349,1423,844,951,1163,
1444,896,1332,599,760,247,170,385,537,48,614,761,822,305,1025,
82,398,50,162,1228,1337,477,1418,1319,674,1206,396,1455,956,
52,1325,180,55,601,524,1250,977,367,1298,1000,419,294,865,754,
798,493,929,713,1373,243,1231,554,387,351,1334,276,555,409,
241,489,738,157,570,1190,1052,624,301,1405,804,447,647,321,
1448,366,1261,130,216,1399,959,1010,148,1022,340,436,330,1110,
1185,725,143,939,701,1188,306,686,536,371,59,764,18,925,609,
1158,854,914,1111,354,70,765,948,176,985,1044,293,292,31,694,
1166,629,81,1242,1274,44,397,34,889,229,847,1047,481,1318,
1080,669,476,383,1219,158,782,992,878,191,1234,136,1118,210,
1443,42,279,815,801,519,25,244,1342,841,272,1422,528,1374,883,
747,1050,227,446,335,650,982,766,442,616,807,1345,248,1125,
145,1049,373,1456,615,718,359,1380,57,901,621,1006,1194,1391,
591,578,880,603,1155,758,789,27,849,636,1045,942,1415,11,140,
958,1389,111,463,1278,1224,687,1214,348,561,881,767,470,944,
682,1030,122,1183,307,198,408,322,1199,1020,218,983,1107,211,
824,628,821,665,569,885,1147,1082,1217,1262,365,370,1065,121,
1191,164,600,525,230,1075,852,1279,209,868,1034,548,376,653,
670,1205,1240,783,60,183,502,1313,707,1251,684,680,1383,87,
986,626,284,1302,1297,501,135,1212,1300,151,1135,808,1054,317,
560,347,256,504,811,806,969,89,1059,414,38,156,917,906,324,
491,482,35,1236,1427,1295,497,168,1381,379,1193,587,1348,545,
431,289,740,666,916,1057,26,510,836,1370,14,103,879,1253,186,
975,996,704,384,1130,1360,478,265,1247,571,106,1084,1343,1071,
1357,113,845,835,159,733,681,547,632,286,810,445,572,20,875,
1182,338,799,175,1311,1172,1149,583,664,530,1328,582,1157,407,
522,1437,1445,1450,1464,1452,1408,429,95,1369,1410,1407,1462,
190,404,1079,1207,646,259,1098,580,870,41,911,1252,245,361,
287,1165,133,66,492,1043,795,1151,1024,756,1086,401,1292,249,
834,736,732,5,730,663,735,734,729,1094,374,1164,631,1288,202,
856,978,905,239,473,1458,1285,984,1036,299,71,357,892,723,217,
506,1232,318,325,831,98,411,421,480,527,206,1417,85,96,1317,
1143,1058,160,1092,817,1379,109,1156,1225,450,575,1330,1237,
1141,105,1294,507,1291,1208,1087,1388,1359,720,1139,1430,358,
675,1289,462,110,1128,382,117,605,483,597,1116,668,604,308,
204,1463,461,75,777,1376,1222,139,546,326,1112,544,1009,1335,
952,1419,910,1067,762,1453,920,728,661,637,295,1201,964,1314,
467,250,234,311,660,1161,440,33,509,1378,1264,564,940,416,
1368,743,1176,918,1306,915,1213,1293,1113,233,356,1104,1175,
567,1181,708,1265,1344,895,1267,672,1269,56,452,641,503,526,
1124,472,222,549,991,973,1351,438,32,1216,755,1257,93,873,315,
193,144,1413,1220,496,242,1235,1211,745,613,1146,1366,54,829,
710,1033,194,417,860,633,612,858,927,833,205,277,974,1355,413,
88,919,46,360,1308,1038,1354,1028,124,1167,1145,275,1454,403,
853,1461,512,1106,529,282,40,1127,422,1421,1336,312,827,1023,
1309,1014,342,91,516,392,1114,177,254,261,839,132,213,49,1042,
606,147,226,1263,887,923,644,1233,350,744,187,178,1203,479,
541,750,424,586,171,1353,1120,129,886,451,1395,200,1140,645,
47,101,184,353,1436,120,163,1243,1122,498,188,1268,825,393,
228,1446,1400,955,285,196,1168,1081,220,539,1290,395,953,722,
328,1117,69,933,1148,531,1202,271,912,568,1280,751,153,931,76,
1347,1375,968,719,425,511,1,441,9,488,474,1299,378,1276,598,
1364,53,634,774,608,240,142,1414,1390,1132,556,304,830,1367,
236,1327,657,1259,58,45,563,104,77,154,702,444,1018,551,1435,
655,225,724,792,1162,1286,1428,1159,776,1095,737,1093,123,1138,
706,1397,114,97,16,83,866,298,943,542,1447,1420,399,418,823,
863,960,1244,809,1026,456,115,989,224,1005,127,882,486,29,947,
803,1426,648,1310,1064,1307,280,596,1200,207,1097,796,995,786,
235,773,195,936,907,550,1029,679,24,721,1416,167,1326,505,780,
685,415,1091,1196,846,1088,313,739,715,430,935,1017,1174,197,
73,678,1303,1169,867,857,1246,1316,182,1338,869,673,533,273,
400,43,63,405,1272,377,558,283,625,499,1221,1160,1382,1412,
538,1136,838,1031,981,2,573,339,703,791,36,1385,904,593,861,
523,3,891,552,116,448,900,1195,819,266,521,781,1409,1230,333,
1258,1227,364,759,976,454,903,618,785,237,1387,574,274,433,
1004,1115,152,1177,652,1270,1358,349,581,711,642,1305,1282,
1434,893,1229,1072,19,388,553,972,851,871,1433,874,1008,876,
1248,264,1189,172,434,146,1053,149,520,565,1035,214,1255,1393,
10,749,1089,296,741,800,1021,790,726,862,788,620,1386,590,352,
1051,594,92,589,1173,22,1254,859,1133,930,954,1131,677,252,
579,840,30,1178,772,443,337,79,1441,1341,1350,267,344,1154,
1070,683,1392,784,1442,316,260,368,826,950,334,1180,39,1432,
1322,466,656,872,484,174,1040,627,309,1323,888,238,988,932,
924,255,658,1249,794,649,253,1449,1431,1055,68,908,1068,855,
696,638,138,1457,362,471,1041,818,8,850,778,494,623,1197,584,
181,1210,1296,1239,793,517,1063,500,1329,1283,263,993,219,1099,
126,391,1013,107,15,67,72,381,99,698,693,1226,697,161,1198,
899,1062,513,1152,769,336,828,1109,949,469,310,74,173,1129,
619,1090,155,797,1363,1340,1266,1256,1083,1001,688,201,51,1459,
1321,1331,458,314,689,1012,1108,386,1362,690,4,692,832,938,
341,490,1372,748,1440,246,941,699,814,691],
\[910,1238,414,408,1223,22,444,427,437,458,1231,24,518,890,
475,481,712,400,739,1032,488,451,170,436,538,26,1448,1398,
1418,469,498,1150,486,1118,271,270,1137,574,347,1376,380,616,
235,1431,994,1308,779,820,1298,107,1239,648,826,715,2,677,888,
1036,244,531,20,1145,1215,32,1117,645,720,1148,480,1212,1149,
1437,207,1146,275,1444,435,579,1327,593,1147,62,829,14,628,
877,795,891,86,368,714,727,93,607,431,619,889,856,627,623,
1236,1279,859,1037,987,54,1450,1463,1026,684,717,5,278,41,
1440,356,816,17,966,1068,892,958,644,1309,92,213,1358,500,602,
421,221,758,182,1288,1249,1289,11,1464,921,344,650,223,979,
428,1218,318,1058,763,839,718,491,791,1034,1033,685,1237,415,
1175,965,330,711,29,102,1188,930,78,680,1337,649,1396,142,
1008,1131,424,840,911,1171,923,434,8,985,1372,298,520,174,
1246,263,197,745,895,131,1295,568,789,1092,821,630,283,771,
1439,871,63,1355,381,253,1003,588,503,764,1325,220,100,1106,
255,736,694,1004,620,1323,960,191,732,171,957,382,1331,173,
618,1098,1138,1186,759,933,1435,1019,346,1285,53,222,527,1320,
264,68,280,1199,558,81,316,1136,953,1055,978,1066,1095,606,
241,783,58,670,1103,99,1456,562,673,135,1234,1070,822,269,
1370,1242,883,186,861,1073,982,928,793,1056,59,476,1307,1115,
564,629,101,313,277,51,604,119,1050,339,1167,1375,675,746,
1155,659,1104,743,76,1040,850,203,722,281,666,1124,897,361,
322,1457,1368,1322,1206,1384,1041,638,686,1339,1184,1232,1052,
79,1446,105,1021,788,1395,946,128,708,1152,1245,1451,998,1311,
1202,855,942,1195,1367,1332,1091,865,761,47,200,340,295,1200,
342,512,521,590,688,232,1169,814,1216,1094,98,373,1192,194,85,
1025,768,217,1018,172,1259,967,230,1319,744,1108,996,114,753,
1210,1272,569,18,778,441,401,1290,28,885,267,457,525,463,887,
519,1122,3,385,453,461,834,450,704,104,438,439,755,398,397,
19,529,399,937,405,749,384,16,464,963,478,510,185,493,27,180,
1460,454,391,1287,511,479,1348,508,12,506,539,4,1299,701,460,
1121,489,465,1014,710,404,1197,448,6,665,388,499,882,1182,501,
514,809,470,492,103,1016,737,482,145,425,31,1404,442,1114,770,
1454,21,709,307,161,502,726,1211,419,445,210,484,25,707,983,
474,7,997,919,402,467,1142,396,413,836,468,429,332,393,422,
1185,1459,127,9,432,77,38,721,507,1230,528,10,1110,810,1452,
547,411,1183,1012,653,297,71,719,513,981,526,496,674,1294,
1044,652,624,818,1424,1116,485,407,1353,784,1458,319,1102,566,
584,13,637,1374,123,949,691,323,976,1128,1262,1357,683,1132,
995,973,187,1035,1275,294,1112,1196,880,418,828,893,52,631,
509,515,668,1029,226,166,1247,1049,608,206,1160,731,1313,634,
73,806,116,1371,585,1201,452,334,1031,751,598,141,306,823,
1011,863,1173,440,214,1402,1252,693,577,660,1343,249,108,706,
1315,1436,1179,1282,938,1277,164,212,944,1441,1176,261,367,657,
188,1130,301,1361,1324,549,1264,1403,543,121,980,343,775,1270,
550,815,1227,83,572,1330,599,48,970,765,597,1005,1340,285,559,
876,999,854,1253,993,150,594,695,852,1312,321,1024,156,947,
242,873,1364,1415,1362,443,1177,916,449,195,246,1442,1061,868,
1046,787,796,702,922,87,748,769,308,733,955,874,72,687,387,
797,1306,416,111,1161,33,1425,15,741,477,118,1,929,106,951,
705,664,394,1377,423,600,1261,625,866,433,125,360,881,1387,
592,239,927,1153,234,1051,420,154,412,1165,447,542,632,1007,
1170,523,1240,609,894,1434,654,201,204,554,830,165,40,1154,
358,977,39,44,1336,1393,522,494,1141,1077,216,1410,1090,517,
1213,808,1023,698,383,1305,348,913,716,790,1013,886,950,914,
357,1302,366,1075,1064,703,113,147,692,1433,690,314,633,1269,
1229,459,1063,961,1273,1060,964,1316,802,1401,341,903,813,728,
66,1082,1422,1120,740,651,909,1203,1428,537,1430,238,786,1303,
647,409,245,934,617,1266,663,1144,122,986,864,1067,643,734,37,
362,304,1394,898,49,646,845,1088,1156,233,1002,350,363,591,
544,462,120,1328,655,902,149,236,905,1276,320,869,1382,752,
1233,530,776,1363,299,89,1027,168,193,1057,917,1420,65,430,
541,495,1000,956,84,1423,639,1360,417,1349,1244,1413,1166,303,
1207,1342,603,1017,504,725,780,292,1168,196,713,1333,912,906,
827,1426,167,455,490,151,376,1194,552,1432,1365,785,282,696,
288,91,756,867,379,853,1251,266,1062,157,218,254,1054,1268,
811,473,534,1397,975,1093,878,1427,925,781,586,1053,300,1329,
97,1443,837,662,211,1405,563,130,1293,1256,291,1391,1087,1028,
533,46,1224,1392,1006,331,754,1243,1296,1163,1447,240,1417,
1453,870,1181,1347,327,901,1235,767,345,1178,835,1085,1250,932,
918,1159,611,57,1373,661,583,370,862,1097,377,372,1009,900,
129,355,257,1219,74,395,812,1381,43,945,1135,1189,642,259,90,
1214,948,1263,610,456,1143,61,738,1105,962,258,406,1386,262,
899,146,471,335,1193,1390,700,636,136,1226,907,215,1429,250,
1078,1359,1081,729,794,992,589,155,1406,1310,152,1187,205,175,
860,70,392,1001,924,75,1407,782,896,369,940,1346,747,279,117,
989,972,45,612,1101,1379,846,199,991,682,672,844,939,1399,974,
1283,1408,177,968,858,1217,954,153,126,1274,1113,817,575,679,
545,378,1042,198,824,884,1281,1354,535,678,410,656,1378,336,
773,1065,1356,1445,573,227,658,1286,1369,328,613,843,375,1119,
231,990,766,596,497,82,1015,247,243,524,64,317,595,842,132,
183,667,941,1300,337,546,615,825,143,540,819,847,565,1338,
1341,189,1100,1099,290,1205,1292,1291,1111,1059,228,1209,181,
1030,184,312,208,1140,1127,622,1258,556,1191,1198,532,139,353,
1352,681,365,831,1317,80,293,268,134,1366,248,1010,1304,1301,
225,69,1069,1126,109,202,311,260,466,446,1220,1409,872,112,
1084,1096,581,849,1350,1260,354,137,553,1222,935,1083,286,671,
55,289,1080,124,35,760,1076,1043,273,1383,1129,265,560,832,
582,959,1038,219,159,875,1022,364,801,1284,1190,969,1047,338,
403,621,1157,1278,841,1134,777,1334,1411,284,931,1267,800,163,
750,34,96,229,723,1318,1389,95,1204,1048,1414,626,158,807,60,
1449,252,1045,848,605,1335,1180,329,570,1321,386,792,926,971,
1241,803,1265,576,952,1221,42,774,352,237,920,256,1208,1345,
1255,587,483,730,325,274,697,169,578,140,176,805,1158,148,879,
908,669,1123,359,988,1086,676,315,1351,838,179,190,1380,1079,
567,1164,1139,305,555,1455,505,251,571,799,56,1257,296,1072,
1174,641,798,1271,36,857,133,1071,635,351,757,67,309,851,1228,
371,984,580,1151,1385,1254,1326,1074,1133,1297,374,561,209,
1089,160,23,1020,390,1225,1421,516,94,548,30,804,936,1388,
1172,1314,472,1107,915,310,389,1344,536,276,162,115,272,1461,
1109,88,1416,333,1412,551,601,324,1162,762,178,689,1280,735,
833,699,138,349,1419,724,110,224,302,1248,1462,640,426,192,50,
1125,772,487,943,557,1039,287,742,904,144,1400,326,614,1438]>
