PermutationGroup<720|
\[1,7,3,4,16,6,2,23,19,20,22,12,30,14,32,5,35,36,9,10,
33,11,8,47,48,50,41,43,53,13,56,15,21,61,17,18,68,64,65,
67,27,54,28,57,60,76,24,25,85,26,81,83,29,42,91,31,44,94,
95,45,34,99,100,38,39,109,40,37,112,113,115,105,107,87,90,
46,123,119,120,122,51,130,52,132,49,118,74,135,136,75,55,
140,141,58,59,146,147,150,62,63,157,153,154,156,72,164,73,
166,66,169,170,69,70,179,71,175,177,86,78,79,187,80,77,190,
191,192,183,185,195,82,182,84,198,199,88,89,204,205,208,92,
93,212,214,215,218,96,97,223,222,98,152,151,102,103,232,104,
101,235,236,238,228,230,241,106,244,108,247,168,110,111,216,
252,253,255,116,262,117,264,114,267,268,131,127,271,128,273,
121,276,277,124,125,126,281,282,129,284,285,133,134,290,292,
293,296,137,138,301,300,139,227,304,306,142,309,143,144,171,
313,145,317,220,320,149,148,322,323,324,209,161,327,162,329,
155,332,333,158,159,278,160,337,338,163,343,243,165,347,246,
167,352,351,250,354,172,173,254,174,294,305,314,359,361,366,
176,330,178,370,326,180,181,374,376,184,349,186,380,341,188,
189,237,383,384,193,194,387,196,197,392,394,395,397,200,400,
201,202,256,403,203,407,298,390,207,206,410,411,210,257,211,
307,416,213,417,325,420,217,258,315,424,219,426,319,221,388,
224,225,226,311,266,229,369,231,263,434,233,234,437,438,440,
239,240,385,386,275,342,242,445,379,346,245,448,272,450,249,
248,454,251,458,455,453,457,259,360,260,362,363,396,404,261,
467,468,328,265,473,472,399,269,476,270,478,479,345,274,482,
481,279,280,339,340,283,321,484,299,485,286,444,287,288,364,
289,398,373,291,419,491,295,365,405,495,297,497,409,302,303,
499,413,501,502,308,310,505,401,312,509,510,423,316,513,318,
515,447,516,517,518,519,520,331,523,524,334,335,533,336,529,
531,535,393,344,536,428,348,538,350,503,539,357,353,356,492,
358,355,544,545,547,507,541,464,465,512,367,368,551,552,496,
372,371,480,557,375,558,377,378,474,382,381,559,389,391,560,
542,488,554,562,402,456,563,494,406,471,408,565,412,546,414,
415,451,568,418,571,462,572,421,422,575,466,425,576,427,429,
430,431,432,433,586,589,435,436,525,592,593,595,441,602,442,
604,439,607,443,446,608,449,452,610,463,487,611,459,460,500,
461,616,618,619,469,470,623,489,624,626,475,477,483,486,617,
490,493,628,498,631,609,504,634,637,506,508,622,639,511,514,
641,642,644,645,647,648,649,650,652,521,627,653,522,591,590,
526,527,594,528,596,597,598,658,660,665,530,668,532,605,632,
534,537,567,540,543,625,643,672,635,548,561,549,550,676,657,
573,553,555,612,556,587,564,680,681,566,606,683,569,615,667,
570,685,574,677,577,578,613,579,580,675,581,582,583,584,673,
585,588,679,690,691,621,599,659,600,661,662,663,664,601,666,
636,603,669,698,671,614,651,682,646,620,640,699,654,629,630,
674,633,701,638,702,703,704,705,655,656,708,693,694,695,709,
697,670,678,712,684,686,687,688,689,710,714,692,696,706,713,
700,711,707,717,719,715,720,716,718],
\[2,8,9,10,1,11,18,5,24,25,26,27,3,28,4,33,6,37,38,39,
7,40,46,13,15,17,51,52,12,54,14,57,59,16,60,63,21,69,70,
71,72,19,73,20,22,77,78,79,23,80,29,31,87,89,30,90,93,32,
34,96,97,35,101,102,103,36,104,111,42,44,45,116,117,41,43,
118,49,124,125,126,127,47,128,48,133,50,134,53,55,137,138,
56,58,142,144,62,148,61,149,152,66,158,159,160,161,64,162,
65,167,67,171,172,173,68,174,74,75,181,182,85,76,132,189,82,
84,86,193,194,81,196,83,197,186,88,200,202,92,206,91,207,
210,213,94,216,95,217,220,98,224,225,99,226,227,150,100,214,
234,106,108,110,239,240,105,242,107,245,248,109,249,251,114,
256,257,258,259,112,260,113,265,115,121,269,130,119,195,120,
274,122,123,278,279,280,129,131,283,270,188,286,288,291,135,
294,136,295,298,139,302,303,140,305,141,307,143,310,311,145,
314,315,146,318,147,319,237,151,231,155,325,208,153,292,154,
330,156,223,334,335,157,336,163,165,341,344,164,345,348,166,
349,168,353,169,355,356,357,170,358,176,178,180,364,365,175,
367,177,368,371,179,372,373,184,183,377,185,378,381,187,382,
235,190,191,192,385,386,272,388,390,393,198,396,199,398,201,
401,324,203,404,405,204,408,205,409,277,209,326,411,211,413,
415,212,339,233,418,215,419,219,422,218,423,221,427,428,222,
340,429,430,229,228,267,230,262,433,232,366,436,301,309,322,
441,442,236,238,443,241,276,243,446,244,271,246,449,247,376,
452,250,454,254,459,460,461,462,252,463,253,255,261,263,466,
432,469,264,470,266,431,474,416,268,477,447,480,273,478,275,
444,337,338,281,282,320,450,284,482,285,300,287,484,323,289,
488,490,290,383,328,293,417,297,493,296,494,299,486,384,498,
304,500,306,308,503,504,312,506,507,313,316,511,512,317,513,
321,483,487,402,327,329,331,521,332,525,526,527,333,528,400,
410,342,343,508,346,347,537,350,389,351,491,352,540,536,354,
448,543,360,362,363,548,549,359,361,435,514,550,369,497,370,
553,555,375,374,557,451,380,558,379,538,391,387,394,559,392,
395,561,397,399,453,403,406,564,468,407,471,412,541,414,520,
424,475,492,569,421,445,420,455,547,425,567,467,426,501,578,
580,582,584,577,587,434,588,591,439,596,597,598,599,437,600,
438,605,440,566,573,542,481,609,456,535,457,612,613,614,458,
615,464,465,562,620,622,560,472,625,473,476,479,485,554,489,
495,618,496,629,499,502,632,635,505,636,619,509,510,545,610,
515,643,516,646,517,639,518,651,519,648,522,654,655,523,656,
657,589,524,652,530,532,534,663,664,529,666,531,669,670,533,
671,641,539,576,630,546,673,640,574,674,544,675,572,677,551,
552,631,650,556,678,563,616,611,565,623,682,568,665,570,672,
647,571,583,575,608,607,579,681,604,581,637,586,688,624,585,
689,676,590,661,594,692,649,592,626,593,595,601,603,695,696,
602,697,687,606,686,638,617,679,627,653,621,694,628,668,644,
633,685,634,683,642,645,693,662,706,707,659,658,660,684,667,
700,705,711,680,708,690,691,716,717,714,715,718,699,698,719,
704,701,702,703,720,710,713,709,712]
/*order=120960=2^7*3^3*5*7*/>
