bin1 := (1,3,6)(2,4,8)(5,9,14)(7,11,16)(10,15,20)(12,17,23)(13,18,25)(19,26,34)
     (21,28,37)(22,29,39)(24,31,42)(27,35,46)(30,40,41)(32,43,53)(33,44,55)
     (36,45,56)(38,48,59)(47,57,58)(49,60,70)(50,61,72)(51,62,74)(52,63,76)
     (54,65,79)(64,77,78)(66,80,94)(67,81,96)(68,82,98)(69,83,99)(71,85,102)
     (73,87,105)(75,89,108)(84,100,101)(86,103,121)(88,106,107)(90,109,127)
     (91,110,129)(92,111,131)(93,112,133)(95,114,136)(97,116,139)(104,122,144)
     (113,134,135)(115,137,138)(117,140,161)(118,141,163)(119,142,165)(120,
     143,167)(123,145,170)(124,146,172)(125,147,174)(126,148,176)(128,150,179)
     (130,152,182)(132,154,185)(149,177,178)(151,180,211)(153,183,184)(155,
     186,217)(156,187,219)(157,188,221)(158,189,223)(159,190,225)(160,191,227)
     (162,193,230)(164,195,233)(166,197,236)(168,199,239)(169,200,241)(171,
     202,244)(173,204,247)(175,206,250)(181,212,255)(192,228,229)(194,231,273)
     (196,234,235)(198,237,279)(201,242,243)(203,245,287)(205,248,249)(207,
     251,293)(208,252,295)(209,253,297)(210,254,299)(213,256,302)(214,257,304)
     (215,258,306)(216,259,308)(218,261,311)(220,263,314)(222,265,317)(224,
     267,320)(226,268,321)(232,274,326)(238,280,333)(240,282,336)(246,288,341)
     (260,309,310)(262,312,364)(264,315,316)(266,318,370)(269,322,375)(270,
     323,377)(271,324,379)(272,325,381)(275,327,384)(276,328,386)(277,329,388)
     (278,330,390)(281,334,335)(283,337,396)(284,338,398)(285,339,400)(286,
     340,401)(289,342,402)(290,343,404)(291,344,406)(292,345,408)(294,347,411)
     (296,349,414)(298,351,417)(300,352,418)(301,353,420)(303,355,423)(305,
     357,426)(307,359,383)(313,365,432)(319,371,437)(331,391,332)(346,409,410)
     (348,412,477)(350,415,416)(354,421,422)(356,424,488)(358,427,428)(360,
     429,493)(361,430,494)(362,431,496)(363,407,472)(366,433,498)(367,434,499)
     (368,435,501)(369,436,503)(372,438,505)(373,439,447)(374,440,508)(376,
     442,511)(378,444,514)(380,446,507)(382,448,492)(385,450,520)(387,452,523)
     (389,454,525)(392,457,529)(393,458,531)(394,459,533)(395,460,486)(397,
     462,537)(399,464,540)(403,468,544)(405,470,547)(413,478,551)(419,483,557)
     (425,489,561)(441,509,510)(443,512,581)(445,515,516)(449,518,519)(451,
     521,589)(453,475,524)(455,526,471)(456,527,591)(461,535,536)(463,538,602)
     (465,541,466)(467,542,543)(469,545,609)(473,548,611)(474,549,613)(476,
     550,614)(479,552,617)(480,553,619)(481,554,621)(482,555,556)(484,558,625)
     (485,559,627)(487,560,629)(490,562,632)(491,563,634)(495,566,638)(497,
     567,639)(500,570,642)(502,572,607)(504,574,647)(506,576,648)(513,582,652)
     (517,585,655)(522,590,659)(528,592,662)(530,594,665)(532,596,667)(534,
     598,670)(539,603,674)(546,610,679)(564,635,575)(565,636,700)(569,640,705)
     (571,643,644)(573,645,691)(577,649,711)(578,650,713)(579,631,696)(580,
     651,714)(583,653,717)(584,654,719)(586,656,721)(587,657,723)(588,658,725)
     (593,663,664)(595,666,732)(597,668,669)(599,671,734)(600,672,736)(601,
     673,738)(604,675,740)(605,676,622)(606,677,743)(608,678,745)(612,681,749)
     (615,683,750)(616,684,752)(618,686,620)(623,689,757)(624,690,646)(626,
     692,759)(628,693,760)(630,695,763)(633,698,767)(637,701,768)(641,706,770)
     (660,726,786)(661,727,787)(680,747,748)(682,704,703)(685,753,754)(688,
     755,742)(694,761,812)(697,765,766)(699,709,773)(702,769,820)(707,771,823)
     (708,772,744)(710,774,827)(712,776,830)(715,779,834)(716,780,836)(718,
     782,839)(722,784,842)(728,788,730)(731,789,841)(733,790,848)(735,792,851)
     (737,794,854)(739,796,857)(741,798,814)(746,800,860)(751,804,864)(756,
     762,813)(758,809,869)(764,815,797)(775,828,829)(777,831,816)(778,832,885)
     (781,837,838)(783,840,826)(785,843,892)(791,849,898)(793,852,853)(795,
     855,903)(799,858,907)(801,819,876)(802,861,911)(803,862,863)(805,865,912)
     (806,866,914)(807,867,897)(808,833,868)(810,870,916)(811,871,918)(817,
     874,847)(818,875,921)(821,877,923)(822,878,925)(824,880,900)(825,881,929)
     (835,887,933)(844,893,939)(845,894,940)(846,895,896)(850,899,941)(856,
     904,946)(859,908,950)(872,919,873)(879,926,927)(882,902,943)(883,930,967)
     (884,905,928)(886,931,932)(888,934,971)(889,935,972)(890,936,961)(891,
     909,938)(901,942,975)(906,947,978)(910,945,944)(913,952,983)(915,953,984)
     (917,955,986)(920,958,990)(922,960,977)(924,962,993)(948,979,949)(951,
     981,982)(954,973,985)(956,987,1008)(957,988,968)(959,991,992)(963,994,
     1012)(964,995,974)(965,996,989)(966,997,1006)(969,999,980)(970,1000,1016)
     (976,1003,1020)(998,1015,1005)(1001,1017,1010)(1002,1018,1033)(1004,1021,
     1036)(1007,1022,1035)(1009,1024,1038)(1011,1025,1031)(1013,1027,1041)
     (1014,1028,1042)(1019,1034,1043)(1026,1030,1040)(1032,1037,1044);