bin1 := (1,2,3,4,5,6,8,10)(7,9,12,16,21,29,40,58)(11,14,18,25,34,49,70,102)(13,
     17,23,31,44,63,90,133)(15,19,27,36,53,75,110,160)(20,28,38,56,79,117,168,
     234)(22,30,42,61,86,128,182,254)(24,32,46,66,95,140,198,276)(26,35,51,73,
     106,155,217,300)(33,47,67,97,142,201,280,378)(37,54,76,112,162,226,312,
     409)(39,57,81,120,172,239,326,430)(41,59,83,123,176,244,331,437)(43,62,
     88,131,185,259,352,459)(45,64,92,136,192,268,364,472)(48,68,99,145,205,
     285,385,500)(50,71,103,150,211,293,393,287)(52,74,108,158,220,305,213,
     296)(55,77,114,165,230,317,417,532)(60,84,125,179,249,339,447,481)(65,93,
     137,194,271,368,478,591)(69,100,146,207,288,388,503,617)(72,104,152,214)
     (78,115,166,232,319,420,506,621)(80,118,169,236,322,425,327,431)(82,121,
     174,241,329,433,545,664)(85,126,180,250,340,448,544,663)(87,129,183,255,
     346,454,324,428)(89,132,186,261,355,461,573,200)(91,134,189,265,362,469,
     583,698)(94,138,196,273,371,482,595,706)(96,141,199,278,376,356,462,574)
     (98,143,203,282,381,494,606,717)(101,147,208,289,390,505,620,731)(105,
     153,215,297,397,511,628,737)(107,156,218,301,400,515,632,487)(109,159,
     221,307,404,518,402,516)(111,161,224,148,209,290,391,354)(113,163,228,
     314,413,527,483,596)(116,167,233,320,422,536,654,602)(119,170,237,323,
     427,540,659,769)(122,175,243,173,240,328,432,351)(124,177,246,334,441,
     556,475,588)(127,181,252,343,451,493,604,592)(130,184,257,349,457,526,
     643,696)(135,190,266,270,367,476,589,702)(139,197,275,373,486,599,710,
     814)(144,204,284,383,498,610,722,823)(149,210,292,248,337,445,560,374)
     (151,212,295,395,302,401,222,308)(154,216,299,399,514,631,304,403)(157,
     219,303,306)(164,229,316,415,530,646,756,854)(171,238,325,429,345,453,
     566,685)(178,247,336,444,559,679,714,818)(187,262,357,463,576,225,311,
     408)(188,263,359,465,579,695,802,896)(191,267,363,470,584,699,804,898)
     (193,269,366,474,587,701,806,881)(195,272,370,480,594,705,810,904)(202,
     281,380,492)(206,286,387,502,616,728,223,309)(227,313,411,524,641,751,
     850,934)(231,318,419,534,650,759,692,800)(235,321,424,538,436,549,668,
     777)(242,330,435,548,666,775,867,949)(245,332,438,552,672,782,874,955)
     (251,341,449,563,384,499,611,724)(253,344,452,565,684,794,888,920)(256,
     347,455,567,416,531,648,623)(258,350,458,569,688,798,893,940)(260,353,
     460,571,690,578,407,520)(264,360,467,580,697,803,897,970)(274,372,484,
     597,708,813,907,466)(277,375,488,600,711,815,572,691)(279,377,490,601,
     712,816,908,974)(283,382,496,608,719,358,464,577)(291,392,333,439,554,
     405,471,585)(294,394,508,624,733,832,924,985)(298,398,512,489,517,634,
     744,842)(310,406,519,636,746,844,575,693)(315,414,528,644,754,852,936,
     779)(335,442,529,645,755,853,937,992)(338,446,561,680,790,883,964,912)
     (342,450,564,682,792,885,966,960)(348,456,568,686,796,890,968,1012)(361,
     468,582,649,758,707,812,906)(365,473,586,700,677,788,880,962)(369,479,
     593,704,809,902,973,1015)(379,491,603,713,817,687,797,891)(386,501,614,
     726,667,776,434,546)(389,504,618,730,829,742,839,735)(396,510,626,736,
     833,925,986,1022)(410,522,639,749,847,612,725,825)(412,525,642,752,851,
     935,886,967)(418,533,615,727,826,916,979,581)(421,535,652,761,857,941,
     995,1026)(423,537,655,764,827,917,876,957)(426,539,657,767,637,747,845,
     931)(440,555,675,786,878,959,1008,1035)(443,558,678,789,882,963,1010,
     1037)(477,590,703,807,899,720,821,913)(485,598,709,557,676,787,879,961)
     (495,607,718,671,781,872,658,768)(497,609,721,822,914,977,1018,1041)(507,
     622,732,831,923,984,991,1025)(509,625,734,550,669,778,647,757)(513,630,
     740,837,741,838,926,987)(521,638,748,651,760,856,939,928)(523,640,750,
     848,933,683,793,887)(541,660,770,739,835,927,988,994)(542,661,771,863,
     947,1000,570,627)(543,662,772,864,948,635,745,843)(547,665,774,866,795,
     889,773,865)(551,670,780,870,952,1002,1029,619)(553,673,784,877,958,1007,
     1034,1049)(562,681,791,884,965,930,990,1024)(605,715,819,909)(613,629,
     738,834)(633,743,840,929,989,1023,861,945)(653,762,858,943,997,1013,1006,
     1032)(656,765,855,938,993,871,953,766)(674,785,873,954,1005,1031,1046,
     753)(689,799,694,801,862,946,999,903)(716,820,911,976,1017,922,983,1021)
     (723,824,808,900,972,895,846,932)(729,828,919,981,1020,869,951,1003)(763,
     859,915,978,1019,1042,1004,1030)(783,875,956,942,996,1027,1044,1051)(805,
     830,921,982,1009,1036,1050,1048)(811,905,894,969,1014,1039,1053,901)(849,
     860,944,998,1011,1038,1052,892)(868,950,1001,1028)(910,975,1016,1040,
     1054,918,980,971)(1033,1047,1058,1062,1045,1056,1061,1064)(1043,1055,
     1060,1057,1059,1063,1065,1066);