bin1 := (2,4,8)(3,6,12)(5,10,19)(7,14,26)(9,17,32)(11,21,31)(13,24,44)(15,28,51)
     (16,30,55)(18,34,61)(20,37,56)(22,40,72)(23,42,76)(25,46,81)(27,49,86)
     (29,53,93)(33,59,102)(35,63,106)(36,65,110)(38,68,116)(39,70,54)(41,74,
     125)(43,78,45)(47,82,136)(48,84,140)(50,88,147)(52,91,153)(57,98,163)(58,
     100,167)(62,105,176)(64,108,181)(66,112,187)(67,114,115)(69,118,195)(71,
     121,199)(73,124,204)(75,127,209)(77,129,212)(79,132,216)(80,133,192)(83,
     138,224)(85,142,230)(87,145,235)(89,149,239)(90,151,225)(92,155,245)(94,
     158,249)(95,160,210)(96,161,120)(97,135,221)(99,165,255)(101,169,164)
     (103,172,262)(104,174,190)(107,179,171)(109,183,273)(111,134,219)(113,
     189,159)(117,194,286)(119,197,180)(122,201,264)(123,203,260)(126,207,301)
     (128,211,305)(130,213,307)(131,214,148)(137,222,154)(139,226,304)(141,
     228,309)(143,232,324)(144,234,244)(146,236,184)(150,240,331)(152,241,333)
     (156,237,296)(157,247,339)(162,251,300)(166,257,349)(168,258,351)(170,
     259,352)(173,248,340)(175,223,196)(177,266,359)(178,267,360)(182,272,278)
     (185,276,366)(186,277,274)(188,279,368)(191,282,371)(193,284,316)(198,
     290,376)(200,293,269)(202,295,281)(205,297,323)(206,299,367)(208,303,369)
     (215,275,320)(217,310,337)(218,312,347)(220,313,377)(227,319,311)(229,
     321,387)(231,322,388)(233,326,393)(238,325,391)(242,334,354)(243,315,256)
     (246,338,287)(250,341,263)(252,343,384)(253,345,401)(254,346,398)(261,
     355,406)(265,358,283)(268,362,285)(270,328,291)(271,364,332)(280,370,308)
     (288,374,394)(289,375,409)(294,379,302)(298,380,395)(306,327,357)(314,
     385,363)(317,386,335)(318,383,361)(329,365,372)(330,336,396)(342,390,413)
     (344,400,403)(348,389,411)(350,397,402)(353,392,410)(356,381,404)(373,
     378,407)(399,412,408)(414,415,416);