bin1 := (1,2,5,10,18,30,47,54,35,21,12,6,3)(4,7,13,22,36,55,77,70,48,31,19,11,8)
     (9,15,25,39,59,83,112,115,86,62,41,26,16)(14,23,37,57,80,107,140,145,111,
     82,58,38,24)(17,27,42,63,87,116,149,151,119,89,64,43,28)(20,32,49,56,78,
     103,134,159,126,96,71,50,33)(29,44,65,90,120,152,186,189,154,121,91,66,
     45)(34,51,72,97,128,161,195,196,162,129,98,73,52)(40,60,84,113,146,180,
     219,224,184,148,114,85,61)(46,67,92,122,155,190,229,231,191,156,123,93,
     68)(53,74,99,130,163,198,236,237,199,164,131,100,75)(69,94,124,157,192,
     232,267,268,233,193,158,125,95)(76,101,132,165,200,238,273,274,239,201,
     166,133,102)(79,104,135,167,202,209,173,141,109,81,108,136,105)(88,117,
     127,160,194,234,270,298,263,226,185,150,118)(106,137,168,203,240,254,220,
     182,147,181,204,169,138)(110,142,174,210,217,179,216,250,279,245,211,175,
     143)(139,170,205,241,275,294,261,225,260,276,242,206,171)(144,176,212,
     246,280,305,269,304,312,281,247,213,177)(153,187,227,197,235,271,307,336,
     330,300,264,228,188)(172,207,243,277,310,328,299,327,337,311,278,244,208)
     (178,214,248,282,313,338,357,335,339,314,283,249,215)(183,221,255,288,
     285,252,218,251,284,315,289,256,222)(223,257,290,318,342,356,334,306,333,
     343,319,291,258)(230,265,301,309,272,308,303,332,355,354,331,302,266)
     (253,286,316,340,323,296,262,295,322,346,341,317,287)(259,292,320,344,
     352,329,351,363,358,359,345,321,293)(297,324,347,360,353,364,362,350,326,
     349,361,348,325);