bin1 := (1,3,7,11,15,19,21,16,12,8,4)(2,5,9,13,17,22,24,18,14,10,6)(20,25,30,39,
     52,69,74,56,42,32,26)(23,27,34,45,60,79,84,64,48,36,28)(29,37,50,66,86,
     104,107,89,68,51,38)(31,40,53,71,91,109,111,93,73,55,41)(33,43,58,76,95,
     113,116,98,78,59,44)(35,46,61,81,100,118,120,102,83,63,47)(49,54,72,92,
     110,130,141,122,103,85,65)(57,62,82,101,119,140,150,132,112,94,75)(67,87,
     70,90,108,127,129,121,125,106,88)(77,96,80,99,117,137,139,131,135,115,97)
     (105,123,142,161,192,231,234,194,163,143,124)(114,133,151,176,210,257,
     260,212,178,152,134)(126,145,167,199,241,299,300,242,200,168,146)(128,
     148,171,203,246,305,310,250,206,173,149)(136,154,182,217,267,333,334,268,
     218,183,155)(138,157,186,221,272,339,344,276,224,188,158)(144,164,160,
     191,229,284,353,294,237,196,165)(147,169,201,243,302,360,288,232,193,162,
     170)(153,179,175,209,255,318,389,328,263,214,180)(156,184,219,269,336,
     396,322,258,211,177,185)(159,189,226,279,347,420,424,350,282,228,190)
     (166,197,239,297,371,446,447,372,298,240,198)(172,204,247,306,377,453,
     456,380,309,249,205)(174,207,252,313,383,460,464,386,316,254,208)(181,
     215,265,331,407,486,487,408,332,266,216)(187,222,273,340,413,493,496,416,
     343,275,223)(195,235,291,365,440,523,525,441,366,292,236)(202,244,303,
     375,450,537,539,452,376,304,245)(213,261,325,401,480,570,572,481,402,326,
     262)(220,270,337,411,490,584,586,492,412,338,271)(225,277,345,417,497,
     543,593,500,419,346,278)(227,280,348,422,502,595,531,503,423,349,281)
     (230,285,355,429,511,433,359,287,358,357,286)(233,289,362,352,283,351,
     426,506,438,364,290)(238,295,369,444,529,629,630,530,445,370,296)(248,
     307,378,454,541,642,644,542,455,379,308)(251,311,381,457,544,590,647,547,
     459,382,312)(253,314,384,462,549,649,578,550,463,385,315)(256,319,391,
     469,558,473,395,321,394,393,320)(259,323,398,388,317,387,466,553,478,400,
     324)(264,329,405,484,576,683,684,577,485,406,330)(274,341,414,494,588,
     696,698,589,495,415,342)(293,367,374,301,373,449,535,627,528,443,368)
     (327,403,410,335,409,489,582,681,575,483,404)(354,427,508,601,710,807,
     810,713,603,509,428)(356,430,512,607,717,743,639,538,451,513,431)(361,
     434,516,439,522,621,732,722,612,517,435)(363,436,518,614,724,821,824,727,
     617,520,437)(390,467,555,655,758,852,855,761,657,556,468)(392,470,559,
     661,765,791,693,585,491,560,471)(397,474,563,479,569,675,780,770,666,564,
     475)(399,476,565,668,772,866,869,775,671,567,477)(418,498,421,501,594,
     703,628,643,701,592,499)(425,504,597,638,742,835,892,804,707,598,505)
     (432,514,608,718,815,898,826,730,620,610,515)(442,526,625,636,536,635,
     731,825,728,626,527)(448,533,633,715,812,733,623,524,622,634,534)(458,
     545,461,548,648,751,682,697,749,646,546)(465,551,651,692,790,880,918,849,
     755,652,552)(472,561,662,766,860,924,871,778,674,664,562)(482,573,679,
     690,583,689,779,870,776,680,574)(488,580,687,763,857,781,677,571,676,688,
     581)(507,599,708,805,798,702,746,839,806,709,600)(510,604,714,811,736,
     814,729,619,521,618,605)(519,615,725,822,830,737,704,800,823,726,616)
     (532,631,738,831,907,939,889,801,832,739,632)(540,640,744,837,817,900,
     944,910,838,745,641)(554,653,756,850,843,750,794,884,851,757,654)(557,
     658,762,856,784,859,777,673,568,672,659)(566,669,773,867,875,785,752,845,
     868,774,670)(579,685,786,876,933,951,915,846,877,787,686)(587,694,792,
     882,862,926,956,936,883,793,695)(591,699,795,885,937,962,964,938,886,796,
     700)(596,705,802,829,735,624,734,828,891,803,706)(602,711,606,716,611,
     721,613,723,820,809,712)(609,719,816,899,834,741,637,740,833,818,720)
     (645,747,840,911,949,972,974,950,912,841,748)(650,753,847,874,783,678,
     782,873,917,848,754)(656,759,660,764,665,769,667,771,865,854,760)(663,
     767,861,925,879,789,691,788,878,863,768)(797,799,888,893,940,897,813,896,
     943,904,887)(808,894,941,967,946,903,819,902,945,942,895)(827,905,947,
     970,948,909,836,908,890,901,906)(842,844,914,919,952,923,858,922,955,930,
     913)(853,920,953,977,958,929,864,928,957,954,921)(872,931,959,980,960,
     935,881,934,916,927,932)(961,966,982,989,984,969,963,968,983,981,965)
     (971,976,986,990,988,979,973,978,987,985,975);