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