bin1 := (1,2,5,8,13,21,16,10,6,4,3)(7,11,18,29,46,68,70,47,30,19,12)(9,14,22,34,
     52,77,85,58,38,24,15)(17,26,41,62,92,129,130,93,63,42,27)(20,31,48,72,
     105,88,60,40,25,39,32)(23,35,53,78,109,148,155,113,80,54,36)(28,43,64,95,
     133,180,164,121,86,59,44)(33,50,74,107,76,108,102,69,101,75,51)(37,55,49,
     73,106,145,199,158,115,81,56)(45,65,96,135,183,248,249,184,136,97,66)(57,
     82,116,146,200,265,285,218,160,117,83)(61,89,123,168,230,293,296,233,171,
     125,90)(67,98,119,84,118,161,197,144,185,137,99)(71,103,142,194,260,288,
     226,166,122,87,104)(79,110,150,205,269,334,338,273,207,151,111)(91,126,
     172,235,298,365,366,299,236,173,127)(94,131,177,241,305,297,234,225,244,
     179,132)(100,138,187,253,224,165,223,264,198,188,139)(112,152,208,263,
     328,394,402,339,274,209,153)(114,156,214,259,193,258,322,347,281,215,157)
     (120,162,219,222,257,192,141,191,256,221,163)(124,169,231,294,363,412,
     357,289,295,232,170)(128,174,237,300,367,326,392,329,301,238,175)(134,
     181,217,159,216,283,350,375,312,247,182)(140,189,254,319,382,433,435,384,
     320,255,190)(143,195,261,325,391,441,443,393,327,262,196)(147,201,252,
     317,381,432,445,395,331,266,202)(149,203,267,332,335,398,448,397,333,268,
     204)(154,210,275,340,321,385,324,389,341,276,211)(167,227,271,206,270,
     336,399,414,358,290,228)(176,239,303,355,287,220,286,354,369,304,240)
     (178,242,306,370,424,465,467,425,371,307,243)(186,250,315,344,278,212,
     277,342,379,316,251)(213,279,345,390,440,477,485,452,404,346,280)(229,
     291,359,330,352,284,351,407,416,360,292)(245,308,314,378,318,272,337,400,
     427,372,309)(246,310,373,428,454,487,492,460,420,374,311)(282,348,405,
     447,481,497,468,426,453,406,349)(302,343,403,411,356,410,439,388,323,387,
     368)(313,376,429,380,431,383,434,409,353,408,377)(361,417,458,490,472,
     500,484,451,401,450,418)(362,419,449,482,508,511,488,455,413,446,396)
     (364,421,461,438,386,437,475,503,493,462,422)(415,456,489,469,498,515,
     522,517,509,483,457)(423,463,444,480,507,504,476,466,496,495,464)(430,
     470,459,491,512,519,518,510,486,499,471)(436,473,501,506,479,442,478,505,
     516,502,474)(494,513,520,523,525,527,528,526,524,521,514);