PermutationGroup<1600|
\[2,1,4,3,6,5,9,10,7,8,14,15,17,11,12,21,13,23,24,26,
16,29,18,19,33,20,35,36,22,39,40,42,25,44,27,28,47,48,30,
31,52,32,54,34,57,58,37,38,62,63,65,41,68,43,71,72,45,46,
76,77,79,49,50,83,51,85,86,53,89,90,55,56,94,95,97,59,60,
101,61,102,103,105,64,108,66,67,112,113,69,70,117,118,120,
73,74,124,75,126,110,128,78,80,81,133,82,135,136,84,139,99,
141,87,88,145,146,148,91,92,152,93,154,155,157,96,160,98,
163,100,165,166,167,169,104,172,106,107,176,177,109,180,111,
182,183,185,114,115,189,116,159,174,192,119,195,121,122,199,
123,201,149,125,204,205,127,208,129,130,131,213,132,215,216,
134,219,150,221,137,138,225,226,140,229,142,143,233,144,235,
236,238,147,240,242,151,244,245,153,248,249,251,156,253,158,
256,257,161,162,261,262,164,265,255,267,269,168,272,170,171,
276,277,173,280,175,282,283,285,178,179,289,290,181,293,274,
295,184,298,186,187,301,188,302,190,305,191,307,193,194,247,
246,196,197,313,198,315,200,318,210,202,203,322,323,325,206,
207,328,329,209,332,211,334,212,336,337,214,340,231,342,217,
218,346,347,220,350,222,223,354,224,356,357,358,227,228,362,
363,230,366,232,368,369,234,372,373,237,239,377,378,241,381,
243,384,385,387,388,390,250,393,252,396,397,254,400,401,403,
258,259,407,260,409,410,263,264,413,414,266,417,268,420,270,
271,424,425,273,344,275,429,341,431,278,279,435,436,281,439,
422,441,284,444,286,287,288,449,450,451,291,292,455,456,294,
458,296,297,371,370,299,300,464,465,466,303,304,391,470,306,
473,474,308,309,478,310,311,480,312,379,482,314,485,486,316,
317,490,491,319,320,469,321,495,496,498,324,500,326,327,504,
505,330,331,509,510,333,513,502,335,516,352,518,338,339,522,
523,525,343,527,345,529,530,532,348,349,483,536,351,508,353,
540,541,355,544,545,547,549,359,360,361,554,555,557,364,365,
501,367,551,563,565,566,568,374,375,376,572,573,402,380,576,
577,382,383,581,582,493,386,585,389,588,392,437,590,394,395,
593,594,596,398,399,600,477,602,404,405,605,406,607,408,457,
419,586,411,412,613,614,440,415,416,619,620,418,623,624,421,
627,423,616,629,631,426,427,635,428,622,430,639,432,433,643,
434,644,618,646,438,649,650,651,442,443,543,542,445,446,628,
447,658,448,660,459,662,664,452,453,668,454,670,671,673,675,
659,460,678,461,462,681,463,683,684,686,467,468,584,690,471,
472,694,695,697,475,476,701,574,479,503,704,481,707,484,709,
710,487,488,713,489,715,716,718,492,721,494,723,724,497,726,
499,729,621,731,728,733,506,507,737,519,687,534,511,512,609,
526,514,515,744,745,517,546,520,750,521,752,753,755,524,757,
759,760,528,763,764,766,531,533,769,535,771,772,537,538,539,
777,768,779,781,774,783,548,562,550,787,552,789,553,791,785,
793,556,795,558,559,798,560,800,561,801,802,564,805,806,567,
782,569,570,812,571,617,810,815,575,818,819,821,578,579,825,
580,827,828,830,583,833,834,587,837,838,589,840,591,592,844,
845,595,848,597,598,852,599,854,855,601,858,603,604,862,606,
864,611,608,867,610,869,612,796,870,872,615,875,876,878,880,
881,883,625,626,886,887,888,889,630,892,632,633,896,634,898,
636,901,637,638,762,761,640,641,907,642,909,653,645,912,647,
648,915,656,917,919,652,922,654,924,655,682,657,926,666,927,
661,930,663,925,665,934,667,936,669,734,895,672,921,674,676,
677,945,942,679,680,949,950,931,688,953,685,956,958,689,960,
961,691,692,965,693,967,963,969,696,971,698,699,975,700,976,
977,702,703,979,902,705,706,983,708,985,986,988,711,712,974,
992,714,995,996,998,717,1000,719,720,1003,1004,722,964,1002,
1007,725,1010,727,1012,1013,730,1015,732,735,1017,736,1019,940,
738,739,1022,740,903,741,742,1025,743,1027,944,746,747,748,
749,1032,1033,751,1036,1037,797,754,1041,756,1024,1044,758,836,
879,1047,1048,1050,765,1052,767,1055,1056,770,1046,1054,773,
1059,775,1061,776,1062,799,778,1065,780,790,784,786,1070,1071,
788,809,1075,1076,792,1079,794,938,937,1014,874,1084,804,1086,
885,803,1089,1090,1091,807,808,1094,1095,811,1097,1093,813,
1099,814,1101,816,817,1103,823,859,820,1106,822,1109,824,1110,
826,1113,1114,846,829,831,832,1119,835,1121,1122,1124,839,1058,
841,842,1130,843,1131,1132,1134,847,994,993,849,850,1136,851,
1138,853,1139,860,856,857,1143,1144,861,1146,1030,863,1148,865,
866,939,868,1151,871,1153,873,1155,1157,877,1159,899,882,1162,
884,1042,1081,1009,1168,890,891,1035,1034,893,894,1172,1173,
1174,897,1028,1177,900,1179,913,904,905,1182,906,1125,908,1185,
914,910,911,1189,984,916,1191,918,920,1194,1195,923,1197,1192,
1085,1198,928,929,1201,1202,1150,932,933,1167,1205,935,1208,
1029,1210,1211,941,1068,943,1212,1213,946,947,948,1218,955,951,
952,1222,954,1224,957,1225,959,1226,962,1126,1229,966,1232,
1233,968,970,1112,1111,972,973,1238,1239,1240,1242,978,1244,
980,981,1246,982,1051,1104,1249,1250,1251,987,989,990,1253,991,
1254,997,1248,999,1001,1236,1258,1260,1005,1006,1264,1008,1266,
1011,1268,1074,1016,1271,1018,1273,1020,1275,1021,1276,1023,
1277,1278,1026,1281,1282,1284,1214,1077,1031,1285,1286,1288,
1038,1039,1040,1291,1292,1043,1294,1045,1296,1297,1049,1299,
1300,1053,1265,1270,1302,1057,1305,1060,1067,1308,1063,1064,
1312,1066,1069,1314,1315,1072,1073,1319,1321,1078,1323,1324,
1080,1327,1082,1083,1087,1088,1166,1332,1334,1335,1092,1337,
1338,1322,1096,1341,1098,1100,1102,1343,1344,1105,1347,1348,
1107,1108,1342,1351,1140,1352,1115,1116,1117,1355,1118,1356,
1120,1290,1123,1359,1137,1127,1128,1129,1363,1133,1135,1366,
1367,1368,1141,1370,1142,1372,1373,1345,1145,1186,1147,1376,
1149,1378,1187,1152,1380,1154,1382,1156,1158,1160,1161,1280,
1279,1163,1164,1387,1165,1169,1170,1391,1171,1329,1245,1175,
1176,1396,1178,1399,1180,1181,1400,1183,1184,1403,1188,1404,
1405,1190,1407,1408,1193,1411,1397,1413,1196,1415,1199,1200,
1417,1418,1420,1203,1422,1204,1221,1206,1207,1426,1427,1209,
1429,1289,1371,1431,1215,1432,1216,1217,1435,1219,1220,1428,
1438,1223,1234,1227,1228,1263,1440,1230,1231,1442,1443,1235,
1237,1421,1445,1241,1243,1433,1449,1247,1450,1446,1452,1252,
1455,1456,1255,1256,1257,1459,1259,1330,1261,1262,1441,1465,
1267,1466,1269,1469,1272,1471,1274,1463,1473,1393,1475,1283,
1476,1477,1478,1287,1394,1385,1392,1474,1293,1310,1430,1295,
1298,1482,1483,1301,1303,1304,1486,1306,1307,1490,1491,1309,
1479,1311,1494,1313,1497,1316,1317,1499,1318,1353,1320,1488,
1501,1503,1325,1326,1339,1328,1398,1331,1333,1357,1453,1336,
1509,1511,1340,1514,1346,1374,1349,1350,1470,1354,1361,1519,
1520,1358,1360,1522,1362,1434,1523,1364,1365,1513,1524,1369,
1518,1526,1527,1383,1515,1375,1377,1528,1529,1379,1444,1381,
1533,1384,1395,1386,1388,1389,1390,1412,1481,1480,1401,1402,
1537,1538,1406,1539,1423,1541,1409,1410,1502,1506,1414,1525,
1545,1416,1547,1419,1549,1424,1492,1425,1551,1552,1493,1512,
1553,1436,1555,1437,1507,1457,1439,1464,1556,1557,1460,1447,
1448,1558,1451,1454,1458,1495,1461,1462,1467,1468,1546,1540,
1563,1472,1565,1566,1567,1484,1485,1487,1531,1489,1560,1568,
1569,1496,1530,1498,1573,1500,1575,1504,1505,1508,1579,1510,
1516,1517,1521,1562,1542,1564,1559,1532,1561,1534,1535,1536,
1543,1544,1587,1588,1589,1548,1590,1550,1592,1593,1591,1554,
1581,1580,1596,1594,1586,1597,1584,1570,1571,1572,1574,1578,
1576,1577,1583,1599,1582,1585,1600,1595,1598],
\[3,1,2,5,7,8,4,11,12,13,6,16,18,19,20,9,22,10,25,27,
28,30,31,32,14,34,15,37,38,17,41,35,43,45,24,46,21,49,50,
51,23,53,55,56,26,59,60,61,29,64,66,67,69,70,33,73,74,75,
36,78,80,81,82,39,84,40,87,88,42,91,92,93,44,96,98,99,100,
47,101,48,104,106,107,109,110,111,52,114,115,116,54,119,121,
122,123,57,125,58,127,129,130,131,132,62,134,63,137,138,65,
140,142,143,144,68,147,149,150,151,71,153,72,156,158,159,161,
162,76,164,77,79,168,170,171,173,174,175,83,178,179,85,181,
86,184,186,187,188,89,190,90,191,193,194,196,197,198,94,200,
95,202,203,97,206,207,209,210,211,212,102,214,103,217,218,
105,220,222,223,224,108,227,228,230,231,232,112,234,113,237,
236,239,241,117,243,118,246,247,120,250,238,252,254,255,124,
258,259,260,126,263,264,128,266,268,270,271,273,274,275,133,
278,279,135,281,136,284,286,287,288,139,291,292,141,294,296,
297,299,300,146,145,155,303,304,148,306,308,301,309,152,310,
311,312,154,314,316,317,157,319,320,321,160,324,326,293,327,
163,330,331,165,333,166,335,167,338,339,169,341,343,344,345,
172,348,349,351,352,353,176,355,177,328,359,360,361,180,364,
365,182,367,183,370,371,185,374,375,376,189,379,380,382,383,
192,386,195,389,391,392,394,395,199,398,399,201,402,404,405,
406,204,408,205,411,225,412,208,415,416,418,419,421,422,423,
213,426,427,215,428,216,430,432,433,434,219,437,438,221,440,
442,443,445,446,447,448,226,388,452,453,454,229,261,457,407,
459,460,233,461,462,463,235,244,467,468,469,240,471,472,242,
475,476,477,245,479,289,248,481,249,483,484,251,487,488,489,
253,492,493,494,256,377,257,497,499,295,501,502,503,262,506,
507,508,265,511,512,267,514,515,269,517,519,520,521,272,524,
482,526,276,528,277,531,533,534,535,280,537,538,282,539,283,
542,543,285,546,548,550,551,552,553,290,556,558,559,560,561,
562,532,564,298,567,569,439,570,571,302,403,574,575,305,578,
579,580,307,486,583,584,586,587,589,342,313,591,592,384,315,
595,597,598,599,318,601,603,565,604,322,606,323,608,325,609,
610,611,612,329,615,616,617,618,332,621,622,334,625,626,336,
628,337,630,632,633,634,340,636,637,638,640,641,642,346,368,
347,645,647,648,350,464,652,653,654,354,655,555,656,356,657,
357,659,358,661,663,665,666,667,362,669,363,672,674,366,676,
677,369,679,680,372,682,373,685,687,688,689,378,691,692,693,
381,696,698,699,700,385,702,703,387,705,706,390,708,393,711,
662,712,396,714,397,717,719,720,400,722,401,670,725,727,728,
730,409,410,732,734,735,736,413,414,738,726,739,740,417,741,
742,743,420,746,747,748,749,424,751,425,754,675,756,758,429,
761,762,431,765,767,744,768,435,770,436,773,774,775,776,441,
778,780,444,782,784,785,745,786,449,788,450,790,451,792,544,
794,796,496,797,455,799,456,523,458,803,804,495,807,808,809,
810,811,465,813,466,814,816,817,470,820,822,823,824,473,826,
474,829,831,832,478,835,836,480,839,695,841,842,843,485,846,
847,849,850,851,490,853,491,856,857,859,860,861,863,510,498,
865,866,500,868,504,658,505,871,873,874,509,877,879,513,882,
884,885,549,516,783,518,890,891,893,894,895,522,897,899,900,
525,902,903,527,904,905,906,529,908,530,910,911,913,914,901,
536,916,918,920,921,540,923,541,925,545,627,547,733,928,929,
593,931,932,933,554,935,937,938,557,939,940,941,942,943,944,
563,946,947,948,566,951,568,952,954,955,957,572,959,573,962,
963,964,576,966,577,968,707,970,972,973,974,581,917,582,880,
716,978,585,980,981,982,588,984,590,987,989,990,991,594,993,
994,596,997,833,999,1001,1002,988,600,912,1005,602,1006,1008,
1009,605,1011,607,1014,881,976,1016,924,613,1018,614,919,1020,
1021,619,1023,620,701,1024,623,1026,624,643,1028,1029,1030,
1031,629,1034,1035,631,1038,1039,1040,1042,1043,635,979,1045,
1044,1046,639,1049,1022,1051,1053,1054,644,1057,721,646,1058,
805,649,1060,650,737,651,1063,1064,1066,1067,1068,1069,1007,
660,1072,1073,1074,664,1077,1078,1080,1081,668,1082,671,1083,
673,1085,1032,1087,1088,678,915,1092,1093,815,681,683,1096,684,
1098,1061,686,1100,950,986,1102,690,995,1104,1105,1107,1108,
694,852,1111,1112,697,1115,1116,1117,731,1118,1120,757,704,
1123,1125,1126,1127,1128,1129,709,1065,710,1133,996,1135,713,
1113,818,845,715,1137,969,1109,718,1140,1141,1142,1052,723,
1145,724,1147,985,1019,1149,889,729,1150,1086,1152,1154,864,
1156,1158,764,1160,867,1161,1163,1164,1165,1166,1167,1013,801,
1157,750,1169,1170,1171,752,753,1175,1176,755,1178,759,772,760,
1180,1181,763,1183,1184,858,766,1186,1187,1188,769,771,1190,
830,1192,1193,777,1196,855,779,870,781,1199,1148,1200,787,1099,
789,1203,1204,791,1206,1207,793,1209,795,798,1041,800,869,802,
1214,1215,1216,1217,806,1219,1220,1221,1185,1223,812,930,1198,
1213,1227,1228,819,1230,1231,821,1234,1235,1136,825,1236,848,
1237,827,828,1241,1121,1243,834,977,1245,837,1247,838,1248,840,
1010,960,1252,1239,1229,844,1197,1255,1240,1256,1257,1238,854,
1259,1261,1262,1263,927,1265,862,1267,1269,1225,1270,1233,1272,
872,1274,875,1250,876,1050,878,1279,1280,883,1283,886,887,888,
1284,892,1287,1289,1290,1047,1244,896,1084,1293,898,1295,1173,
1281,1298,1159,907,953,909,1301,1303,1304,1306,1307,956,1309,
1310,1311,922,1313,958,926,1316,1317,1318,1320,1322,1195,934,
1325,1326,936,1328,1329,1330,1331,945,1333,1275,1336,1218,949,
1266,1339,1340,1342,1212,1015,1226,961,1345,1346,965,1349,1350,
1017,967,1000,971,1353,1354,1341,1110,975,1334,1357,1358,1264,
1179,1360,983,1361,1033,1362,1364,1365,1351,992,998,1343,1369,
1003,1371,1004,1374,1375,1122,1297,1094,1070,1377,1012,1379,
1355,1381,1208,1314,1090,1383,1384,1385,1025,1386,1048,1277,
1027,1388,1389,1390,1036,1392,1037,1393,1394,1395,1397,1398,
1246,1285,1146,1401,1400,1402,1055,1370,1056,1348,1406,1059,
1409,1410,1062,1412,1205,1414,1134,1155,1416,1071,1419,1421,
1210,1075,1423,1076,1424,1425,1079,1273,1428,1319,1430,1224,
1101,1286,1089,1433,1434,1091,1436,1437,1095,1439,1131,1097,
1138,1438,1103,1132,1441,1189,1106,1444,1445,1446,1114,1139,
1447,1448,1119,1174,1399,1124,1451,1453,1454,1130,1457,1408,
1300,1458,1460,1461,1462,1463,1464,1143,1144,1429,1467,1468,
1151,1470,1153,1472,1440,1282,1474,1162,1356,1168,1296,1332,
1299,1479,1172,1475,1473,1480,1177,1481,1477,1391,1182,1367,
1484,1418,1485,1487,1488,1489,1191,1492,1324,1194,1493,1495,
1496,1491,1476,1498,1201,1363,1202,1403,1500,1502,1411,1415,
1504,1505,1506,1211,1435,1469,1242,1507,1508,1510,1512,1513,
1222,1276,1515,1516,1517,1232,1254,1518,1271,1387,1432,1521,
1249,1452,1251,1420,1499,1442,1253,1465,1525,1258,1302,1260,
1478,1482,1368,1509,1268,1530,1449,1531,1532,1534,1292,1278,
1291,1529,1359,1372,1288,1535,1294,1373,1536,1422,1528,1471,
1305,1540,1366,1542,1315,1308,1543,1544,1312,1426,1546,1404,
1548,1321,1550,1323,1497,1537,1327,1376,1335,1431,1554,1337,
1547,1338,1344,1556,1347,1456,1541,1352,1501,1483,1539,1559,
1560,1524,1561,1514,1562,1405,1417,1378,1380,1486,1564,1382,
1396,1520,1427,1553,1450,1407,1443,1555,1413,1570,1571,1503,
1572,1455,1574,1519,1576,1577,1578,1466,1490,1526,1527,1580,
1581,1582,1459,1557,1551,1583,1584,1585,1586,1587,1565,1494,
1575,1511,1579,1591,1545,1563,1594,1538,1588,1595,1522,1523,
1533,1569,1598,1599,1592,1573,1590,1593,1549,1568,1589,1552,
1558,1596,1597,1566,1567,1600]
/*order=17971200=2^11*3^3*5^2*13*/>
