bin1 := (1,3,6)(2,4,8)(5,9,13)(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)(60,76,99)(61,77,101)(63,79,104)(66,83,107)
     (73,94,119)(75,97,122)(78,102,128)(80,105,132)(81,106,134)(84,108,137)
     (85,109,139)(87,111,142)(89,113,145)(90,114,147)(92,116,150)(95,120,153)
     (98,123,157)(100,125,160)(103,129,163)(110,140,175)(112,143,179)(115,148,
     185)(117,151,189)(118,152,191)(121,154,194)(124,158,199)(126,161,203)
     (127,162,205)(130,164,183)(131,165,209)(133,167,212)(135,169,215)(136,
     170,217)(138,172,220)(141,176,223)(144,180,228)(146,182,230)(149,186,232)
     (155,195,241)(156,196,242)(159,200,237)(166,210,251)(168,213,255)(171,
     218,261)(173,221,265)(174,222,267)(177,224,269)(178,225,271)(181,229,274)
     (184,231,276)(187,233,206)(188,234,278)(190,236,280)(192,238,281)(193,
     239,282)(197,243,286)(198,227,273)(201,244,288)(202,245,290)(204,246,291)
     (207,247,293)(208,248,268)(211,252,296)(214,256,235)(216,258,303)(219,
     262,306)(226,272,315)(240,283,323)(249,294,334)(250,295,336)(253,297,339)
     (254,298,341)(257,301,345)(259,304,349)(260,305,350)(263,307,352)(264,
     308,354)(266,310,357)(270,313,360)(275,316,363)(277,318,365)(279,300,343)
     (284,324,371)(285,325,372)(287,327,375)(289,329,377)(292,331,380)(299,
     342,392)(302,346,393)(309,355,400)(311,358,404)(312,326,373)(314,361,407)
     (317,364,409)(319,366,412)(320,367,414)(321,368,416)(322,369,418)(328,
     376,421)(330,378,383)(332,381,362)(333,382,428)(335,384,430)(337,386,433)
     (338,387,435)(340,389,438)(344,379,410)(347,394,348)(351,395,444)(353,
     397,446)(356,401,449)(359,405,452)(370,419,461)(374,422,463)(385,431,471)
     (388,436,476)(390,439,480)(391,440,482)(396,427,468)(398,447,489)(399,
     448,491)(402,450,494)(403,451,475)(406,453,498)(408,455,500)(411,456,501)
     (413,457,503)(415,454,499)(417,459,506)(420,462,510)(423,464,472)(424,
     465,513)(425,466,514)(426,467,429)(432,443,485)(434,473,520)(437,477,522)
     (441,483,529)(442,484,530)(445,487,531)(458,504,548)(460,507,528)(469,
     516,560)(470,517,562)(474,521,544)(478,523,565)(479,524,566)(481,526,567)
     (486,518,542)(488,532,570)(490,534,563)(492,536,527)(493,537,575)(495,
     539,577)(496,540,579)(497,541,580)(502,545,582)(505,549,585)(508,552,589)
     (509,553,590)(511,554,592)(512,555,519)(515,558,597)(525,543,581)(533,
     571,606)(535,573,608)(538,576,611)(546,583,615)(547,584,614)(550,586,618)
     (551,587,619)(556,594,578)(557,595,596)(559,598,569)(561,593,564)(568,
     603,624)(572,607,632)(574,602,628)(588,601,627)(591,622,641)(599,626,616)
     (600,623,642)(604,630,646)(605,631,647)(609,633,648)(610,634,613)(612,
     629,644)(617,636,649)(620,638,643)(621,639,651)(625,637,650)(635,640,652)
     (645,653,656)(654,655,657);