PermutationGroup<800|
\[2,4,6,8,10,9,13,1,15,14,18,19,16,22,3,25,26,23,24,30,
31,5,34,35,7,33,39,40,42,36,37,46,47,11,12,45,51,53,48,
49,57,50,59,60,20,52,17,64,65,67,21,69,63,71,72,74,66,77,
68,61,80,81,83,27,28,87,29,89,32,91,84,85,95,86,97,98,88,
101,102,44,90,106,38,108,104,110,41,113,43,116,107,119,120,
122,109,124,111,112,128,129,114,115,132,55,134,117,137,54,
140,56,142,143,58,135,146,62,149,150,138,139,154,133,156,141,
159,160,162,144,145,166,167,147,170,148,78,172,70,175,176,73,
179,75,76,183,184,79,187,188,82,174,191,192,194,177,196,178,
199,200,180,181,203,182,205,206,208,185,186,212,213,94,216,
189,219,204,92,93,223,224,96,227,228,230,99,100,234,235,103,
105,239,241,220,221,244,222,246,215,248,249,225,226,253,254,
229,118,231,232,260,233,262,263,265,236,237,269,270,238,273,
274,240,277,278,280,121,123,283,284,125,126,287,127,288,289,
291,130,131,295,296,298,136,301,257,303,305,279,307,281,310,
271,282,314,315,251,285,286,320,321,323,324,326,290,329,292,
293,333,294,335,336,338,297,155,342,343,299,300,347,348,151,
152,352,153,354,355,157,158,358,359,161,163,164,364,165,366,
367,369,168,169,373,171,375,376,173,379,350,382,351,384,353,
386,387,341,390,391,393,356,357,397,398,399,401,360,361,404,
190,362,407,363,409,268,365,410,411,258,368,414,370,371,417,
372,419,420,422,197,374,426,427,429,377,378,302,433,408,193,
436,195,198,440,252,201,202,444,445,332,448,207,418,209,210,
452,211,454,455,328,214,459,217,218,463,464,405,465,466,434,
469,435,471,437,438,474,388,423,424,478,439,480,481,483,441,
396,442,486,443,488,489,446,349,492,447,243,449,450,451,498,
499,453,500,383,456,261,457,458,504,247,505,506,508,460,461,
512,462,513,514,516,242,518,519,245,521,522,524,250,527,528,
530,255,256,533,534,259,535,536,537,264,539,266,267,541,542,
543,272,546,547,549,275,276,491,517,554,555,494,558,520,561,
562,523,564,565,567,507,421,525,526,572,317,574,575,529,577,
531,532,566,578,413,582,416,584,553,586,538,406,540,590,591,
593,544,311,312,598,545,600,601,603,548,550,551,468,552,606,
304,306,610,308,309,389,313,613,614,316,318,617,319,619,620,
322,325,327,330,331,626,334,627,337,339,340,479,605,344,345,
633,346,634,635,636,624,607,608,502,639,609,641,559,611,612,
645,563,596,621,597,647,648,650,652,615,654,573,616,657,618,
380,659,509,661,622,663,623,665,625,667,668,669,557,628,671,
629,576,477,673,595,392,677,630,631,679,632,681,425,381,685,
515,655,385,687,658,394,395,690,691,400,693,402,403,674,695,
697,684,672,412,415,556,702,580,703,705,428,430,431,432,707,
708,501,710,686,712,713,715,475,666,675,676,599,688,592,689,
642,484,470,720,692,473,694,723,588,724,696,727,698,729,699,
581,700,664,701,497,476,490,733,734,683,709,704,735,706,737,
649,496,467,560,472,741,742,482,485,594,487,725,493,745,495,
747,748,749,651,503,510,750,511,718,738,739,660,719,653,711,
740,756,722,758,759,604,761,743,762,763,678,744,579,714,746,
765,732,767,768,646,568,569,751,717,752,753,772,773,570,571,
775,777,583,670,585,587,589,602,781,782,637,783,785,774,787,
766,770,769,640,776,644,754,778,792,779,780,795,736,730,638,
643,726,656,794,662,788,771,797,680,682,789,799,796,784,791,
728,764,757,790,716,755,721,798,793,731,760,800,786],
\[3,5,7,9,11,12,1,14,16,17,2,20,21,23,24,4,27,28,29,6,
32,33,8,36,37,38,10,41,43,44,45,13,48,49,50,15,52,54,55,
56,18,58,19,51,61,62,63,22,66,68,30,25,70,26,73,75,76,78,
79,72,31,82,84,85,86,34,88,35,90,92,93,94,39,96,40,99,100,
42,103,104,105,46,107,47,109,111,112,114,115,117,118,53,121,
60,123,125,126,127,57,130,116,131,59,133,135,136,138,139,64,
141,65,144,145,67,147,148,69,151,152,153,71,155,157,158,74,
161,163,164,165,77,168,169,80,171,81,173,174,83,177,178,180,
181,182,87,185,186,89,101,189,190,91,193,195,154,197,198,95,
201,159,202,97,204,98,207,209,210,211,102,214,215,217,218,
106,220,221,222,108,225,226,110,229,231,232,233,113,236,237,
238,240,230,242,243,119,245,120,247,122,250,251,252,124,255,
256,257,258,259,128,261,129,264,266,267,268,132,271,272,134,
275,276,137,279,281,223,282,140,285,227,286,142,150,143,290,
292,293,294,146,297,299,300,149,302,304,306,244,308,309,311,
312,313,156,316,317,318,319,160,322,162,325,327,328,330,331,
332,166,334,167,337,339,340,341,170,344,345,346,172,349,350,
351,175,353,176,356,357,315,179,360,361,362,363,183,365,184,
368,370,371,372,187,374,188,377,378,380,381,191,383,192,385,
194,388,389,196,392,394,395,396,199,200,400,402,320,403,203,
405,406,205,408,206,329,260,208,412,413,333,415,335,416,212,
418,213,421,423,424,425,216,428,430,431,432,219,434,435,352,
437,438,439,224,441,442,443,228,446,447,449,338,450,451,324,
234,453,235,456,457,458,460,461,462,239,379,301,241,467,468,
448,470,472,348,473,246,475,476,477,248,479,249,482,284,397,
484,485,253,487,254,490,410,491,367,493,494,495,496,497,262,
263,427,265,501,502,364,398,503,269,474,270,507,509,510,511,
273,499,274,515,386,517,277,278,520,280,523,525,526,283,529,
531,444,532,287,288,305,289,291,538,452,540,454,469,295,296,
544,545,298,548,550,551,552,530,553,303,556,557,559,560,307,
486,563,310,566,568,569,567,570,571,314,573,419,576,387,578,
579,580,321,323,581,583,326,585,404,587,498,588,589,336,592,
594,595,596,597,342,599,343,602,414,512,513,604,347,605,607,
608,609,611,464,612,354,504,355,615,527,616,358,618,359,621,
536,622,623,624,625,366,547,369,628,483,629,373,630,631,632,
375,492,376,555,521,637,638,463,382,455,640,384,642,643,644,
422,564,646,390,393,391,649,651,653,572,542,655,656,399,658,
401,601,660,549,662,407,664,409,666,411,429,670,590,518,417,
672,420,524,674,675,676,636,678,488,426,680,682,683,684,433,
591,686,641,436,617,688,689,440,692,522,465,694,600,445,696,
698,533,699,626,700,701,657,459,704,539,633,634,706,508,466,
709,639,654,711,471,714,693,645,716,603,717,478,708,480,718,
481,558,719,721,543,722,695,489,697,725,726,668,728,702,730,
584,731,500,613,732,729,505,506,677,598,620,679,647,736,514,
516,738,739,519,740,671,712,690,743,528,562,703,744,534,746,
535,537,727,541,586,619,546,751,752,741,753,554,754,610,614,
755,561,757,565,760,759,574,665,575,577,685,667,582,764,627,
720,766,724,769,593,705,770,771,742,737,606,723,774,772,681,
776,659,756,661,778,779,780,750,733,635,650,784,786,783,788,
758,652,648,789,790,791,663,763,673,793,794,669,795,785,707,
796,687,747,691,748,775,777,798,767,782,745,710,735,713,768,
715,800,797,765,792,781,787,734,799,762,749,773,761]
/*order=117600=2^5*3*5^2*7^2*/>
