PermutationGroup<800|
\[2,1,5,7,3,10,4,13,15,6,18,20,8,23,9,26,28,11,31,12,
33,35,14,38,39,16,42,17,45,47,19,50,21,53,22,56,58,24,25,
62,64,27,67,68,29,70,30,72,74,32,77,78,34,81,82,36,85,37,
88,90,92,40,95,41,98,99,43,44,89,46,104,48,107,49,110,112,
51,52,116,118,54,55,122,123,57,124,125,59,69,60,129,61,132,
134,63,137,138,65,66,142,144,146,148,71,151,106,73,155,156,
75,159,76,162,163,164,79,167,80,170,172,174,83,84,86,87,180,
182,183,91,186,187,93,190,94,193,195,96,97,198,200,202,100,
178,101,207,102,150,103,211,147,105,215,217,219,108,109,222,
223,111,161,160,113,114,115,230,232,117,234,220,119,237,120,
240,121,243,245,247,143,250,126,252,127,128,256,185,130,131,
260,262,133,263,264,135,267,136,269,271,139,272,140,275,141,
203,239,280,281,145,284,286,288,149,291,293,295,152,298,153,
300,154,169,255,157,158,307,225,310,312,314,282,165,318,166,
283,168,323,325,171,327,204,173,330,331,175,334,176,336,177,
339,341,179,344,181,346,347,221,184,351,353,355,188,358,189,
191,192,363,365,194,366,196,368,197,199,372,360,201,374,362,
377,379,205,206,229,233,208,385,209,386,210,389,391,212,394,
213,352,214,397,399,216,401,218,403,404,406,408,305,409,224,
410,412,226,414,227,417,228,315,419,421,231,424,416,426,427,
235,430,236,381,238,434,436,241,242,332,440,244,433,246,443,
398,248,340,249,448,449,251,452,253,254,455,457,459,257,294,
258,462,259,464,466,261,469,274,471,277,265,475,266,268,478,
270,481,382,482,273,432,276,485,486,278,473,279,490,326,370,
492,493,285,287,494,495,289,498,290,501,496,292,503,439,296,
338,297,507,299,499,301,302,509,303,488,304,306,308,460,309,
420,311,516,320,313,519,316,413,317,467,522,319,524,321,322,
526,429,324,530,373,335,328,533,329,536,537,396,333,538,539,
337,461,445,505,542,342,343,544,546,345,548,517,348,528,349,
551,350,411,444,354,518,356,554,357,422,556,359,532,361,558,
378,474,364,562,563,367,565,566,369,371,569,571,375,376,574,
407,576,380,578,383,384,387,388,393,584,390,402,587,392,534,
395,591,446,581,400,594,405,596,598,513,512,514,600,415,454,
463,418,553,602,423,605,425,577,428,609,456,611,431,614,470,
435,502,616,437,438,441,442,622,624,447,625,450,583,451,628,
453,629,630,458,633,520,465,613,468,637,472,639,579,640,476,
477,642,479,480,567,636,483,573,484,648,570,487,632,489,525,
491,560,652,506,597,545,497,656,658,500,660,662,655,504,665,
666,508,668,510,582,511,671,515,673,521,653,672,523,677,679,
680,527,682,529,681,555,531,684,535,686,688,690,692,694,540,
647,541,543,654,698,547,549,550,701,575,552,703,705,568,557,
708,559,561,710,564,713,715,717,697,623,572,719,720,702,580,
603,626,590,585,723,586,725,588,728,589,730,683,592,593,732,
595,691,735,599,604,601,737,704,709,606,707,607,608,612,610,
664,615,741,617,744,618,743,619,669,620,750,621,740,699,646,
627,696,700,631,651,634,675,635,751,678,638,676,641,756,758,
643,761,644,760,645,764,649,650,766,727,657,733,659,768,722,
661,772,663,771,667,724,765,670,757,674,745,776,695,685,778,
689,687,738,780,767,782,773,693,706,786,769,781,789,711,736,
712,790,716,714,775,770,718,734,721,747,726,753,763,731,729,
749,785,762,739,777,742,796,746,754,748,792,794,774,752,793,
788,755,759,795,783,787,784,791,779,799,800,797,798],
\[3,4,6,8,9,11,12,14,16,17,19,21,22,24,25,27,29,30,1,32,
34,36,37,2,40,41,43,44,46,48,49,51,52,54,55,57,59,60,61,
63,65,66,5,69,10,45,71,73,75,76,58,79,80,7,83,84,86,87,
89,91,93,94,96,97,42,26,100,101,102,103,105,106,108,109,111,
113,114,115,117,119,120,121,56,35,88,13,20,126,127,128,130,
131,133,135,136,15,139,140,141,143,145,147,149,150,152,153,
154,18,157,158,160,161,77,50,165,166,168,169,171,173,175,176,
177,178,179,181,23,184,185,187,188,189,191,192,194,196,144,
197,199,201,203,204,205,206,208,209,28,210,212,213,214,216,
218,156,220,221,138,224,225,31,226,227,228,229,231,232,233,
33,235,236,238,239,241,242,244,246,248,249,251,217,253,254,
255,257,258,259,38,261,262,82,39,265,266,268,180,270,74,129,
273,274,276,277,278,279,281,282,283,285,287,289,290,292,294,
296,297,47,299,301,302,303,304,305,306,308,309,311,313,315,
316,317,319,320,321,322,324,326,318,53,328,329,331,332,333,
190,335,337,338,340,342,343,271,345,85,348,349,350,352,354,
356,357,359,360,361,362,364,347,358,62,367,369,370,371,64,
373,334,375,376,378,380,381,67,382,383,384,68,122,387,388,
390,392,393,70,395,396,330,398,400,314,402,162,72,405,407,
107,386,215,280,411,275,413,415,416,418,406,377,420,422,423,
78,425,355,428,429,431,272,432,433,435,437,438,81,439,441,
159,442,260,286,444,445,446,447,449,450,451,237,453,454,456,
458,341,460,90,461,198,463,465,467,468,92,470,472,473,474,
476,414,477,479,480,95,125,483,484,346,455,98,487,488,99,489,
385,491,137,284,207,142,417,459,496,497,499,500,502,269,240,
247,104,504,505,506,223,508,195,365,482,510,511,457,182,512,
513,110,256,514,515,112,517,518,300,507,520,426,521,252,523,
116,481,525,527,528,529,118,531,532,485,534,535,495,401,466,
186,464,540,526,293,541,123,412,543,124,545,547,366,200,549,
550,408,155,503,146,552,522,427,167,553,440,174,555,379,557,
132,548,559,409,560,561,134,524,564,291,533,567,568,570,572,
573,263,575,163,267,577,579,580,581,582,394,583,585,586,148,
588,589,590,183,592,151,593,494,295,595,597,594,264,344,599,
569,601,490,222,578,164,603,604,606,607,608,363,598,610,612,
613,170,615,574,172,617,618,619,620,621,623,493,492,626,250,
544,627,410,397,193,631,632,634,243,635,336,636,638,323,486,
443,591,602,641,643,644,645,646,647,403,325,530,649,628,650,
202,327,312,651,307,653,339,654,655,566,657,659,537,661,663,
211,664,471,667,298,669,670,219,234,665,672,674,675,230,640,
676,678,452,681,430,558,671,683,596,469,576,685,687,689,691,
693,656,695,245,696,399,697,699,700,424,519,702,546,600,704,
706,611,707,709,475,353,711,712,714,716,718,421,658,692,684,
368,721,563,682,419,288,722,724,404,726,727,729,633,731,639,
310,624,625,733,734,571,732,736,562,694,738,739,740,629,516,
666,462,542,609,372,742,743,745,746,747,565,748,749,686,679,
751,720,698,448,551,434,728,374,752,351,753,713,754,755,614,
719,757,759,760,735,762,763,536,765,660,680,630,767,768,389,
769,758,770,771,391,773,741,556,774,775,478,662,705,673,777,
616,501,677,538,779,436,781,717,587,783,784,785,764,787,788,
642,789,652,498,708,554,791,776,690,782,584,723,539,792,688,
710,793,794,715,744,509,730,795,648,668,703,725,780,778,797,
798,772,790,796,750,737,786,799,800,761,605,637,756,622,766,
701]
/*order=276595200=2^9*3^2*5^2*7^4*/>
