p1 := (1,2,4)(3,5,8)(6,9,13)(7,10,15)(11,16,22)(12,17,24)(14,19,27)(18,25,34)
     (20,28,38)(21,29,40)(23,31,43)(26,35,46)(30,41,53)(32,44,57)(33,45,59)
     (36,47,62)(37,48,64)(39,50,67)(42,54,70)(49,65,82)(51,68,86)(52,69,88)
     (55,71,91)(56,72,93)(58,74,96)(60,76,98)(61,77,100)(63,79,102)(66,83,105)
     (73,94,116)(75,97,120)(78,92,113)(80,103,126)(81,104,128)(84,106,130)(85,
     107,132)(87,108,112)(89,110,136)(90,111,138)(95,117,141)(99,122,147)(101,
     124,133)(109,134,158)(114,139,164)(115,140,166)(118,142,169)(119,143,171)
     (121,145,174)(123,148,178)(125,149,180)(127,151,183)(129,153,186)(131,
     155,189)(135,159,194)(137,161,196)(144,172,173)(146,175,208)(150,181,215)
     (152,184,185)(154,187,221)(156,190,225)(157,191,227)(160,195,231)(162,
     197,234)(163,198,236)(165,200,239)(167,202,242)(168,203,244)(170,205,247)
     (176,209,252)(177,210,254)(179,212,256)(182,216,259)(188,222,264)(192,
     228,269)(193,229,270)(199,237,276)(201,240,280)(204,245,286)(206,248,290)
     (207,249,292)(211,255,235)(213,257,300)(214,258,302)(217,260,305)(218,
     261,307)(219,262,309)(220,263,311)(223,230,271)(224,265,313)(226,266,314)
     (232,272,319)(233,273,299)(238,277,323)(241,281,328)(243,283,331)(246,
     287,334)(250,293,339)(251,253,295)(267,315,357)(268,316,359)(274,321,365)
     (275,322,367)(278,324,370)(279,325,372)(282,329,375)(284,332,377)(285,
     333,379)(288,335,381)(289,336,383)(291,338,384)(294,340,387)(296,342,390)
     (297,343,392)(298,344,394)(301,346,308)(303,348,398)(304,349,400)(306,
     351,347)(310,352,404)(312,354,382)(317,360,411)(318,361,412)(320,363,356)
     (326,373,424)(327,374,403)(330,376,337)(341,388,368)(345,395,435)(350,
     401,442)(353,405,432)(355,407,434)(358,369,419)(362,413,448)(364,415,451)
     (366,417,453)(371,421,457)(378,426,460)(380,428,393)(385,431,389)(386,
     418,454)(391,410,447)(396,436,465)(397,437,466)(399,439,462)(402,443,471)
     (406,444,472)(408,445,420)(409,446,474)(414,449,429)(416,452,478)(422,
     455,479)(423,458,480)(425,459,482)(427,461,484)(430,463,485)(433,464,487)
     (438,467,489)(440,469,491)(441,470,493)(450,476,496)(456,473,494)(468,
     490,499)(475,477,497)(481,488,502)(483,498,506)(486,500,503)(492,504,509)
     (495,501,510)(505,507,508)(511,512,513);