bin1 := (2,4,6)(5,10,12)(7,14,15)(8,17,19)(9,20,13)(11,24,22)(16,27,29)(18,33,
     35)(23,32,36)(25,43,41)(28,47,48)(30,51,52)(31,54,56)(34,60,58)(38,65,66)
     (40,57,69)(44,74,72)(49,78,81)(50,63,79)(53,86,87)(55,91,93)(59,90,94)
     (61,100,98)(64,103,105)(67,106,108)(71,113,97)(75,119,117)(80,124,125)
     (82,128,129)(83,111,123)(88,135,136)(89,137,139)(92,142,140)(101,153,151)
     (104,157,159)(107,161,162)(109,165,166)(114,170,171)(126,182,185)(127,
     181,183)(130,190,191)(132,187,195)(138,202,204)(141,201,205)(143,210,208)
     (146,172,213)(148,216,164)(150,218,207)(154,224,222)(156,226,228)(158,
     231,229)(163,235,237)(167,242,243)(174,250,219)(184,258,259)(186,262,263)
     (192,270,271)(194,274,276)(200,281,283)(203,286,284)(211,296,294)(214,
     248,300)(227,313,315)(230,312,265)(232,319,317)(236,322,323)(238,326,327)
     (239,247,303)(251,337,338)(256,343,275)(260,347,350)(261,346,348)(264,
     355,356)(267,352,360)(272,365,366)(278,359,372)(282,377,379)(285,376,380)
     (287,385,383)(293,392,382)(297,398,396)(299,400,401)(301,404,405)(305,
     408,403)(307,410,393)(311,415,417)(314,420,418)(324,427,430)(325,390,428)
     (328,435,436)(330,432,440)(334,339,443)(341,450,411)(344,454,368)(349,
     457,375)(351,460,461)(357,468,469)(371,482,484)(378,490,488)(386,500,498)
     (402,511,513)(416,527,529)(419,526,530)(421,535,533)(425,539,532)(429,
     542,543)(431,546,547)(437,553,554)(439,555,557)(444,448,561)(447,519,515)
     (451,564,565)(453,568,570)(455,572,571)(458,575,489)(459,574,487)(462,
     580,581)(465,577,585)(470,590,591)(472,556,592)(474,584,595)(480,600,483)
     (486,594,606)(491,610,609)(497,576,608)(501,622,620)(507,626,617)(512,
     631,632)(514,635,636)(521,641,642)(523,645,627)(525,648,650)(528,653,651)
     (544,663,666)(545,662,664)(548,671,672)(550,668,676)(559,675,683)(560,
     643,684)(562,566,686)(563,688,687)(567,691,646)(569,694,696)(582,704,705)
     (601,721,602)(605,723,724)(611,717,728)(624,737,634)(633,736,743)(637,
     748,749)(639,745,751)(640,752,685)(644,755,757)(649,762,764)(652,761,765)
     (654,770,768)(658,772,767)(661,775,773)(665,776,760)(667,779,780)(673,
     787,788)(682,794,796)(690,753,754)(692,722,801)(693,802,804)(695,807,805)
     (706,813,759)(715,795,819)(720,822,818)(738,832,834)(740,836,838)(742,
     839,840)(744,843,844)(750,850,851)(756,855,799)(758,857,800)(763,861,859)
     (777,870,860)(778,869,858)(781,875,876)(784,872,879)(789,808,884)(791,
     878,856)(797,833,888)(798,853,889)(803,894,896)(806,893,814)(820,823,903)
     (821,904,905)(828,910,841)(830,912,914)(831,915,917)(835,921,852)(837,
     923,925)(842,911,927)(845,933,934)(847,930,926)(854,924,938)(862,943,942)
     (866,871,941)(868,947,945)(877,951,952)(890,891,939)(892,928,959)(895,
     962,960)(901,966,967)(902,969,922)(906,970,968)(908,961,971)(909,937,972)
     (913,976,956)(916,978,979)(918,965,981)(919,982,920)(929,974,984)(958,
     973,964)(963,997,994)(975,980,977)(983,987,998)(985,1001,995);