bin1 := (1,3,6,10,17)(2,4,8,13,21)(5,9,15,24,34)(7,11,18,28,39)(12,19,30,41,57)
     (14,22,32,45,61)(16,25,35,50,44)(20,31,43,60,76)(23,33,47,63,78)(26,36,
     51,66,82)(27,37,52,67,84)(29,40,55,71,75)(38,53,69,87,102)(42,58,73,92,
     107)(46,62,49,65,81)(48,64,79,96,112)(54,70,88,83,98)(56,72,90,105,121)
     (59,74,93,109,123)(68,85,100,117,111)(77,95,91,106,122)(80,97,114,108,
     103)(86,101,99,116,127)(89,104,120,129,133)(110,124,119,128,132)(113,115,
     125,130,134)(118,126,131,135,136);