bin1 := (1,2,5,3)(4,7,13,8)(6,10,17,11)(9,14,22,15)(12,19,30,20)(16,24,38,25)
     (18,27,43,28)(21,32,49,33)(23,35,54,36)(26,40,62,41)(29,44)(31,46,70,47)
     (34,51,78,52)(37,56,86,57)(39,59,91,60)(42,63,97,64)(45,67,104,68)(48,72,
     111,73)(50,75,116,76)(53,80,98,81)(55,83,126,84)(58,88,132,89)(61,93,138,
     94)(65,99,146,100)(66,101,129,102)(69,85,128,106)(71,108,157,109)(74,113,
     163,114)(77,118,168,119)(79,121,170,122)(82,115,165,124)(87,130,137,92)
     (90,134,185,135)(95,140,189,141)(96,142,192,143)(103,150,205,151)(105,
     120,169,153)(107,155,210,156)(110,159,215,160)(112,123,172,161)(117,139,
     188,166)(125,174,231,175)(127,148,201,177)(131,179,238,180)(133,182,217,
     183)(144,194,258,195)(145,196,260,197)(147,199,265,200)(149,202,267,203)
     (152,206,271,207)(154,209,247,186)(158,212,278,213)(162,218)(164,220,288,
     221)(167,224,293,225)(171,176,233,227)(173,228,297,229)(178,235,304,236)
     (181,240,310,241)(184,244,313,245)(187,248,301,249)(190,250,319,251)(191,
     252,322,253)(193,255,327,256)(198,262,335,263)(204,269,311,242)(208,273,
     346,274)(211,276,348,277)(214,230,298,280)(216,282,303,283)(219,285,345,
     286)(222,289,294,266)(223,290,356,291)(226,295,360,296)(232,243,312,300)
     (234,302)(237,306,367,307)(239,308,369,309)(246,314,279,315)(254,324,337,
     325)(257,328,358,292)(259,330,372,331)(261,332,341,333)(264,275,347,336)
     (268,339,388,340)(270,342,387,338)(272,343,370,344)(281,349,334,350)(284,
     351,393,352)(287,354,368,321)(299,363,379,323)(305,365,391,366)(316,374,
     376,318)(317,375)(320,377,362,355)(326,381,396,382)(329,357,397,383)(353,
     394,384,395)(359,380,408,398)(361,399,412,400)(364,401,414,402)(371,404,
     413,405)(373,378)(385,390,410,406)(389,407,416,409)(403,415);