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