PermutationGroup<1440|
\[1,8,3,4,20,6,7,2,30,25,26,28,29,14,15,44,17,46,19,5,
50,51,23,53,10,11,65,12,13,9,70,71,73,74,59,60,62,64,68,
40,83,42,85,16,88,18,91,92,96,21,22,99,24,106,101,102,104,
105,35,36,94,37,120,38,27,86,123,39,125,31,32,137,33,34,
131,132,134,136,140,116,117,143,41,145,43,66,150,45,152,155,
47,48,159,61,158,49,165,166,52,168,55,56,180,57,58,54,185,
186,188,189,174,175,177,179,183,80,81,154,162,63,146,197,67,
149,69,205,200,201,203,204,75,76,219,77,221,78,72,225,226,
79,215,217,82,229,84,121,232,233,124,87,237,89,239,118,90,
243,244,95,93,248,249,119,251,255,97,98,258,100,265,260,261,
263,264,111,112,279,113,281,114,103,285,286,115,288,107,108,
299,109,110,294,296,298,302,275,277,303,122,306,307,127,128,
319,129,130,126,324,325,326,327,313,314,316,318,322,141,310,
142,336,133,311,135,340,341,333,138,139,309,345,144,348,349,
147,148,354,355,358,151,360,153,363,364,367,156,157,371,372,
376,160,161,379,163,384,382,383,164,389,259,167,257,170,171,
400,172,173,169,405,406,408,409,394,395,397,399,403,194,418,
195,420,176,423,178,426,427,431,181,182,434,184,373,436,437,
439,440,190,450,191,452,192,187,456,457,193,196,461,464,198,
199,467,227,216,220,335,210,211,474,212,476,213,202,480,481,
214,483,206,207,208,209,488,489,490,491,492,224,339,312,218,
495,496,334,222,223,503,501,502,228,506,509,230,231,513,515,
516,519,234,235,524,523,236,392,238,529,532,240,241,537,536,
242,540,541,544,245,246,289,548,549,247,555,556,250,558,562,
253,254,252,568,569,565,571,256,393,573,359,390,270,271,581,
272,583,273,262,587,588,274,590,266,267,486,268,269,596,597,
598,600,603,577,579,606,276,608,278,611,432,280,615,618,282,
283,624,622,623,284,422,629,287,631,290,291,438,292,293,517,
530,550,551,637,639,641,644,649,295,652,297,655,656,580,300,
301,585,660,662,304,542,665,305,669,670,308,672,673,675,676,
677,678,315,681,317,684,685,609,320,321,620,323,566,689,407,
690,328,329,330,331,332,696,697,337,338,703,702,704,708,343,
344,342,713,715,346,591,717,347,576,720,722,350,725,351,352,
441,728,353,732,560,735,357,356,737,738,739,741,361,442,744,
362,748,749,752,366,365,756,757,368,369,462,761,370,765,575,
769,374,375,443,444,772,553,777,377,378,780,380,783,521,782,
381,700,698,387,484,789,385,386,791,388,742,391,663,546,510,
415,796,416,455,396,654,398,764,458,801,401,402,804,404,507,
806,807,809,810,410,411,412,694,413,691,695,414,817,818,417,
822,419,479,619,421,826,683,630,424,830,829,425,610,482,834,
429,430,428,839,840,712,842,433,614,435,850,845,846,848,849,
445,638,446,640,447,642,643,448,721,729,745,773,449,865,795,
451,868,582,453,454,875,873,874,459,740,460,574,881,463,762,
667,885,465,466,724,468,469,893,470,471,472,473,899,821,475,
902,613,477,478,907,905,906,485,487,601,754,788,599,602,493,
494,564,911,563,913,498,497,499,825,917,753,500,919,920,921,
627,504,811,505,912,508,812,925,511,645,512,751,671,514,880,
930,518,646,730,934,520,936,786,522,890,525,526,527,661,528,
572,944,531,647,746,948,533,534,951,723,535,707,692,954,538,
539,768,956,760,543,666,960,584,545,963,794,758,547,969,970,
552,648,972,775,776,554,978,979,557,981,561,559,985,986,734,
900,693,567,989,570,990,991,767,651,578,864,993,994,995,586,
998,999,589,1001,592,593,1012,594,595,714,718,1007,1009,1011,
1015,604,605,908,887,680,607,898,1017,705,612,1020,1021,617,
616,1025,1026,1027,621,1028,1029,1030,940,625,626,1032,628,844,
843,633,634,971,635,636,632,1040,1041,1043,1044,967,1035,1019,
1038,859,860,861,862,976,797,650,1052,1051,653,1055,1054,1056,
980,658,659,657,1061,877,1063,1064,726,664,1036,1066,884,668,
983,820,922,923,736,1068,1069,674,1070,1071,1072,1073,823,679,
787,1075,682,918,1076,687,688,686,819,1077,1016,699,716,701,
1078,1079,1080,706,903,709,710,711,888,889,966,719,1082,927,
1084,1085,727,1086,1087,933,731,1091,733,1092,1022,1093,838,
941,1089,1095,743,1037,1042,947,747,1058,977,750,1090,1074,755,
1102,759,1103,1024,959,763,1107,1106,766,1110,1111,924,855,
1113,770,771,847,774,1116,1117,975,863,950,778,779,872,781,
1098,886,1120,784,785,1122,1125,790,792,793,1131,798,799,800,
1136,1140,802,803,1143,805,1002,1145,1146,1148,1149,813,1159,
814,1161,815,808,1165,1166,816,910,824,1169,857,827,828,938,
1171,958,831,832,833,835,836,837,1174,841,1175,1176,856,882,
945,858,1177,851,852,946,853,854,1183,1185,1186,1188,1189,1190,
867,866,1194,870,869,871,1198,949,1199,1201,876,1202,878,879,
1205,883,1208,891,892,894,895,896,897,953,901,904,909,914,915,
916,1210,926,1184,928,929,931,932,1212,942,952,935,937,939,
1216,943,1219,1187,982,1220,1221,1223,955,957,1206,1227,962,
961,1230,1234,964,965,1237,968,1197,1238,973,974,1241,1173,984,
1242,987,1123,1245,988,1249,1250,1252,1253,1255,992,1258,1259,
1260,1262,996,1239,1263,1264,997,1269,1144,1000,1142,1003,1004,
1244,1005,1006,1150,1151,1152,1153,1274,1276,1278,1281,1286,
1008,1289,1010,1292,1247,1296,1013,1014,1299,1300,1018,1302,
1023,1304,1119,1031,1033,1034,1039,1200,1251,1305,1306,1231,
1045,1083,1046,1047,1097,1048,1049,1050,1303,1315,1317,1053,
1318,1272,1114,1057,1059,1178,1060,1062,1322,1325,1065,1104,
1265,1067,1329,1081,1332,1088,1301,1334,1336,1094,1338,1339,
1096,1099,1100,1222,1101,1248,1344,1335,1105,1345,1347,1108,
1182,1291,1288,1109,1350,1351,1112,1115,1137,1319,1118,1121,
1314,1147,1124,1246,1163,1224,1126,1127,1179,1128,1129,1310,
1130,1360,1340,1132,1133,1134,1308,1135,1138,1139,1207,1353,
1363,1365,1141,1273,1367,1196,1270,1154,1279,1155,1341,1156,
1275,1355,1157,1282,1283,1284,1285,1158,1294,1233,1160,1342,
1232,1162,1379,1287,1357,1164,1324,1330,1167,1168,1213,1170,
1191,1172,1180,1181,1316,1261,1343,1254,1383,1349,1384,1243,
1192,1307,1193,1195,1240,1387,1346,1203,1327,1297,1204,1390,
1323,1364,1209,1298,1391,1211,1385,1214,1226,1215,1389,1217,
1218,1257,1277,1290,1309,1225,1228,1321,1229,1396,1312,1235,
1236,1397,1266,1398,1280,1399,1295,1400,1401,1256,1402,1403,
1267,1328,1268,1406,1271,1408,1410,1372,1373,1370,1371,1378,
1411,1382,1409,1374,1293,1413,1405,1376,1311,1313,1333,1414,
1320,1416,1337,1326,1331,1417,1418,1419,1420,1348,1352,1354,
1356,1358,1359,1361,1362,1412,1381,1366,1428,1368,1377,1369,
1375,1404,1380,1386,1421,1388,1392,1393,1394,1395,1415,1424,
1439,1422,1435,1433,1430,1407,1434,1427,1438,1437,1426,1429,
1425,1440,1432,1431,1423,1436],
\[2,9,10,11,1,12,13,24,5,31,32,33,34,35,36,3,37,4,38,48,
6,7,39,54,55,56,8,57,58,69,16,18,21,22,75,76,77,78,79,80,
14,81,15,86,17,89,19,93,20,94,95,23,100,27,107,108,109,110,
111,112,25,113,26,114,122,28,29,115,126,127,128,30,129,130,
41,43,45,47,52,141,142,40,65,42,146,148,44,149,153,46,154,
59,49,160,161,163,50,51,162,169,170,171,53,172,173,184,61,
63,66,67,157,190,191,192,193,194,195,60,62,196,64,144,198,
68,199,72,206,207,208,209,210,211,70,212,71,213,223,73,74,
214,82,84,120,83,123,231,85,87,234,235,88,116,90,240,241,91,
92,117,246,97,98,250,252,96,253,254,99,259,103,266,267,268,
269,270,271,101,272,102,273,283,104,105,274,289,290,291,106,
292,293,118,119,121,124,238,245,228,304,230,308,309,310,125,
311,312,323,133,135,138,139,328,329,330,331,332,333,131,334,
132,337,134,338,136,342,137,343,344,140,143,346,145,147,350,
352,151,356,150,357,152,361,156,365,155,366,369,158,373,159,
374,375,167,380,164,385,386,388,165,166,387,391,392,255,168,
393,367,404,176,178,181,182,410,411,412,413,414,415,174,416,
175,421,177,424,179,428,180,429,430,183,435,187,441,442,443,
444,445,185,446,186,447,454,188,189,448,459,462,197,463,217,
202,468,469,470,471,226,225,200,340,201,219,478,203,204,336,
205,484,485,486,487,216,218,220,222,227,493,466,215,494,477,
497,221,498,499,224,473,472,504,507,229,508,511,514,232,517,
233,518,521,236,525,526,237,527,530,239,531,534,242,538,539,
243,542,244,543,546,247,550,551,553,248,249,552,559,251,560,
561,566,256,257,570,398,572,258,262,574,575,576,358,260,515,
261,389,585,263,264,540,591,592,593,265,594,595,276,278,280,
282,287,604,605,275,607,277,609,612,279,613,616,281,617,620,
284,625,626,418,285,286,627,632,633,634,288,635,636,295,297,
300,301,645,646,647,648,294,650,296,653,298,657,299,658,659,
302,661,303,663,305,666,667,306,307,671,315,317,320,321,313,
314,679,316,682,318,686,319,687,688,322,405,324,325,326,327,
691,692,693,694,695,335,482,698,700,339,475,705,341,706,707,
711,714,345,558,347,718,719,348,721,349,723,351,726,573,353,
729,730,354,733,355,734,601,359,580,740,360,742,362,745,746,
363,750,364,751,754,368,402,758,759,370,762,763,371,766,372,
767,768,377,378,773,774,376,775,776,379,781,381,784,785,787,
382,383,786,596,384,483,788,390,792,584,793,396,401,794,509,
394,715,395,457,397,456,399,800,400,765,655,403,805,407,568,
811,524,812,567,813,814,406,815,408,409,816,417,419,821,628,
823,824,420,481,422,827,423,480,425,831,606,426,833,427,703,
684,837,432,433,841,431,608,434,844,438,851,852,853,854,855,
436,856,437,857,439,440,858,449,451,453,458,863,866,450,867,
869,452,870,871,455,799,798,738,460,877,879,461,880,465,883,
464,884,887,888,889,890,467,752,735,896,897,900,474,901,903,
476,904,905,479,828,825,597,598,488,489,490,491,492,908,562,
910,495,907,496,912,915,565,500,834,918,919,501,502,922,503,
749,505,924,506,782,510,795,571,512,927,929,513,819,582,516,
757,520,932,519,933,522,937,938,523,820,939,940,528,942,943,
529,925,533,946,532,947,950,535,952,953,536,817,537,689,955,
589,957,541,958,545,961,544,962,547,964,965,967,548,549,966,
557,554,973,974,976,555,556,975,716,982,983,563,564,916,909,
818,987,569,690,926,727,578,577,652,579,581,583,586,996,587,
588,741,1002,1003,1004,590,1005,1006,599,602,756,791,725,737,
755,790,600,603,832,681,843,610,611,1018,614,615,677,1023,619,
618,621,709,622,623,930,624,968,1031,630,1033,629,1034,1032,
842,631,1020,1026,1039,638,640,642,643,1045,1046,1047,1048,637,
639,641,644,1049,649,1050,651,992,1053,654,803,936,656,984,
1057,1059,660,1062,662,664,1065,1019,665,668,1067,1054,669,670,
674,1029,1028,672,673,1070,675,676,1022,1074,678,685,680,1016,
1076,683,836,1072,1027,701,696,697,699,708,1021,1078,702,835,
704,717,710,1069,1068,1073,712,713,797,1081,720,1083,722,724,
838,728,731,1088,1089,732,872,736,895,876,1094,739,1000,743,
1035,744,747,1097,1051,748,923,885,753,894,1100,931,840,760,
1104,761,1105,764,802,1108,770,771,1112,839,769,846,845,772,
1044,778,779,1118,1119,777,868,865,780,979,917,873,783,1091,
1063,1123,789,1124,1127,1129,796,1132,1134,1121,1137,801,1138,
1139,804,1144,808,1150,1151,1152,1153,1154,806,1155,807,1156,
1163,809,810,1157,822,1168,881,826,1170,914,829,1082,830,1096,
1172,1079,892,891,1173,1086,1114,969,847,1025,848,849,1017,
1178,1179,1180,850,1181,1182,859,860,861,862,864,981,1191,1192,
1085,1099,1195,1197,1092,874,1200,875,1038,878,995,1203,882,
1206,886,893,911,920,1077,899,902,898,906,921,913,1071,1075,
1084,945,1024,928,1106,978,956,1185,935,1213,934,960,1058,1214,
941,1217,944,949,948,951,1222,954,1224,1226,959,985,1209,1228,
1231,963,1232,1233,971,1194,970,972,1188,1041,980,977,1176,986,
1243,988,1246,1247,989,1251,990,1254,991,1256,1238,993,1261,
994,1263,997,1265,1266,1268,998,999,1267,1271,1272,1140,1001,
1273,1262,1008,1010,1013,1014,1282,1283,1284,1285,1007,1287,
1009,1290,1011,1293,1012,1294,1295,1015,1061,1301,1036,1303,
1037,1030,1190,1220,1120,1218,1042,1307,1240,1308,1115,1309,
1040,1310,1311,1043,1312,1313,1174,1098,1316,1052,1113,1319,
1055,1056,1219,1260,1060,1320,1103,1323,1064,1324,1327,1066,
1216,1080,1330,1087,1183,1090,1335,1093,1337,1177,1095,1198,
1175,1340,1101,1342,1343,1102,1321,1302,1346,1107,1286,1109,
1349,1305,1350,1110,1111,1296,1133,1116,1117,1186,1304,1354,
1122,1317,1126,1356,1125,1357,1249,1128,1339,1223,1130,1234,
1332,1131,1136,1361,1345,1135,1362,1360,1363,1141,1142,1364,
1277,1366,1143,1147,1368,1369,1259,1145,1201,1146,1269,1148,
1149,1347,1158,1160,1162,1167,1374,1375,1159,1376,1377,1161,
1378,1164,1380,1381,1383,1165,1166,1382,1329,1169,1227,1171,
1242,1236,1331,1184,1187,1333,1211,1353,1239,1385,1189,1199,
1193,1386,1264,1196,1371,1202,1292,1204,1389,1255,1205,1207,
1208,1300,1306,1210,1257,1212,1299,1215,1252,1328,1289,1391,
1394,1221,1359,1225,1351,1315,1229,1395,1230,1235,1325,1397,
1237,1241,1244,1245,1248,1358,1250,1253,1258,1370,1280,1384,
1270,1404,1372,1407,1275,1279,1274,1276,1278,1281,1348,1288,
1393,1291,1388,1403,1297,1298,1392,1352,1318,1314,1355,1415,
1322,1326,1344,1336,1334,1338,1341,1373,1408,1390,1422,1414,
1419,1398,1426,1427,1428,1365,1429,1430,1431,1367,1432,1387,
1379,1420,1435,1433,1410,1406,1402,1439,1440,1396,1425,1399,
1400,1401,1438,1412,1405,1437,1409,1421,1436,1411,1413,1423,
1416,1417,1418,1424,1434]
/*order=241920=2^8*3^3*5*7*/>
