bin1 := (1,3,6,11,19,32,53)(2,4,8,14,24,40,66)(5,9,16,27,45,72,111)(7,12,21,35,
     58,91,141)(10,17,29,48,77,118,179)(13,22,37,61,96,149,218)(15,25,42,69,
     106,165,241)(18,30,50,80,123,186,270)(20,33,55,86,133,200,288)(23,38,63,
     99,154,224,320)(26,43,57,89,138,208,300)(28,46,74,113,175,256,365)(31,51,
     82,126,95,147,216)(34,56,88,136,205,296,415)(36,59,93,144,213,306,425)
     (39,64,76,116,177,242,346)(41,67,103,160,233,334,466)(44,71,109,169,248,
     355,495)(47,75,115,49,78,120,181)(52,83,128,192,279,394,538)(54,85,131,
     197,90,139,153)(60,94,146,70,107,166,243)(62,97,151,220,315,438,577)(65,
     101,157,228,327,455,610)(68,104,162,236,338,471,627)(73,112,173,253,361,
     501,456)(79,121,183,266,379,519,682)(81,124,188,273,388,532,556)(84,129,
     194,281,398,542,702)(87,134,202,291,411,560,114)(92,142,174,254,363,504,
     665)(98,152,222,318,443,595,745)(100,155,226,323,449,310,430)(102,158,
     230,329,459,614,330)(105,163,238,341,476,634,503)(108,167,245,350,489,
     646,414)(110,170,250,150,219,314,436)(117,178,259,369,451,215,309)(119,
     180,262,373,513,676,808)(122,184,268,381,523,190,275)(125,189,143,212,
     304,422,427)(127,191,277,391,536,292,235)(130,195,232,332,463,204,294)
     (132,198,285,403,548,561,716)(135,203,293,413,562,196,283)(137,206,298,
     417,567,176,257)(140,210,255,211,193,280,396)(145,214,308,428,578,655,
     378)(148,217,311,432,480,508,671)(156,227,325,452,608,754,868)(159,231,
     331,461,617,762,680)(161,234,336,468,624,488,645)(164,239,343,479,636,
     698,824)(168,246,352,492,650,435,586)(171,251,357,498,658,520,649)(172,
     252,359,500,660,796,891)(182,264,376,516,679,412,393)(185,269,383,526,
     687,815,901)(187,271,385,528,689,817,588)(199,286,405,551,267,380,521)
     (201,289,408,555,247,353,493)(207,299,305,423,573,395,539)(209,301,420,
     470,626,770,878)(221,316,440,590,740,859,903)(223,319,444,597,747,864,
     563)(225,321,446,600,571,724,715)(229,328,457,611,757,870,742)(237,339,
     473,630,774,881,694)(240,344,481,637,780,884,594)(244,348,486,439,465,
     621,766)(249,356,497,656,782,885,938)(258,367,507,670,803,896,604)(260,
     370,509,672,804,869,749)(261,371,511,673,806,644,784)(263,374,514,677,
     564,718,839)(265,377,518,681,809,897,942)(272,386,530,690,691,522,684)
     (274,364,505,667,801,895,633)(276,389,533,695,821,419,569)(278,392,307,
     426,576,730,846)(282,399,544,467,622,765,874)(284,401,375,345,482,638,
     781)(287,368,437,326,453,609,755)(290,409,557,537,607,462,618)(295,322,
     447,602,750,678,566)(297,416,565,720,842,916,945)(302,421,572,726,631,
     775,620)(303,354,494,652,312,433,583)(313,434,585,737,855,333,464)(317,
     441,592,743,861,926,950)(324,450,606,752,485,642,723)(335,454,342,477,
     387,531,692)(337,469,625,704,760,543,703)(340,474,632,776,882,936,756)
     (347,484,641,763,873,807,475)(349,487,605,751,778,554,712)(351,490,647,
     786,372,512,675)(358,491,648,787,424,574,728)(360,499,659,794,418,568,
     722)(362,502,663,798,382,524,685)(366,458,612,407,553,711,834)(384,527,
     688,816,902,445,598)(390,534,696,822,657,793,889)(397,541,651,789,431,
     581,734)(400,545,705,828,506,668,661)(402,547,559,442,593,744,862)(404,
     549,529,448,603,510,601)(406,552,570,666,800,893,907)(410,558,714,837,
     912,866,894)(429,579,732,849,920,947,653)(460,615,721,731,847,854,771)
     (472,628,635,777,883,858,779)(478,587,738,856,812,546,706)(483,639,582,
     515,669,693,819)(496,654,791,540,700,827,727)(517,662,797,795,890,941,
     955)(525,686,813,900,944,713,836)(535,697,823,841,580,733,850)(550,709,
     810,898,717,838,913)(575,729,845,918,932,826,875)(584,735,852,708,831,
     599,748)(589,739,857,923,832,707,830)(591,741,860,925,949,792,843)(596,
     746,818,674,683,811,805)(613,759,872,919,946,877,931)(616,761,640,725,
     844,917,935)(619,764,820,623,768,643,783)(629,773,880,934,758,871,930)
     (664,799,892,710,833,910,785)(699,825,906,814,848,888,915)(701,769,876,
     909,904,924,767)(719,840,914,851,790,865,802)(736,853,921,948,956,829,
     908)(753,867,929,772,879,933,922)(788,887,939,954,952,958,953)(835,911,
     863,928,951,886,937)(899,943,957,960,959,905,927);