bin1 := (1,3,5,8,2)(4,6,10,15,22)(7,11,17,25,38)(9,13,19,29,44)(12,18,27,41,60)
     (14,20,31,47,67)(16,23,35,51,74)(21,32,49,70,97)(24,36,53,77,106)(26,39,
     57,82,33)(28,42,62,87,66)(30,45,65,92,124)(34,50,72,100,133)(37,54,69,95,
     46)(40,58,83,105,139)(43,63,89,120,157)(48,68,94,126,166)(52,75,91,122,
     117)(55,79,108,144,189)(56,80,110,147,194)(59,84,61,86,116)(64,90,121,
     159,212)(71,98,130,171,228)(73,101,134,177,236)(76,104,138,181,242)(78,
     107,142,186,247)(81,111,128,168,223)(85,115,152,202,237)(88,118,154,205,
     201)(93,125,164,219,287)(96,127,103,136,179)(99,131,173,231,301)(102,135,
     178,238,309)(109,145,191,252,328)(112,149,197,261,339)(113,150,199,264,
     344)(114,151,162,216,282)(119,155,207,193,255)(123,161,215,281,363)(129,
     169,225,294,378)(132,174,153,203,267)(137,180,240,227,296)(140,183,244,
     316,402)(141,184,245,318,368)(143,187,249,324,411)(146,192,254,330,418)
     (148,195,258,334,397)(156,208,273,353,442)(158,210,275,355,444)(160,213,
     279,360,447)(163,217,284,366,454)(165,220,288,370,459)(167,222,290,373,
     463)(170,226,295,253,329)(172,229,298,383,474)(175,233,303,390,404)(176,
     234,305,392,272)(182,243,314,400,190)(185,246,320,406,501)(188,214,280,
     362,450)(196,259,336,422,221)(198,262,341,429,380)(200,250,325,412,209)
     (204,268,260,337,424)(206,270,351,439,523)(211,276,357,224,292)(218,285,
     367,456,558)(230,299,385,477,585)(232,302,389,482,286)(235,306,394,486,
     596)(239,310,398,491,603)(241,311,361,448,549)(248,322,409,504,327)(251,
     326,414,511,497)(256,313,399,493,605)(257,332,419,514,568)(263,342,431,
     528,638)(265,345,434,531,277)(266,346,417,512,621)(269,349,323,410,506)
     (271,352,441,541,652)(274,354,443,542,467)(278,358,446,547,433)(283,365,
     453,555,666)(289,371,460,564,312)(291,374,465,570,684)(293,376,468,572,
     688)(297,381,472,577,693)(300,386,479,587,559)(304,343,432,530,639)(307,
     395,487,598,716)(308,396,489,600,364)(315,401,496,609,726)(317,403,499,
     611,359)(319,405,500,612,727)(321,407,413,509,618)(331,388,481,590,708)
     (333,420,516,625,738)(335,421,518,628,741)(338,425,522,632,744)(340,427,
     524,633,745)(347,435,533,642,753)(348,436,535,644,503)(350,437,536,646,
     757)(356,445,545,656,764)(369,457,560,672,680)(372,461,566,679,784)(375,
     466,571,686,790)(377,469,573,449,550)(379,440,539,650,602)(382,473,579,
     696,800)(384,475,582,698,802)(387,480,588,705,810)(391,484,593,713,818)
     (393,485,498,610,647)(408,502,613,728,529)(415,464,569,683,551)(416,494,
     606,723,828)(423,519,543,653,762)(426,490,601,719,687)(428,525,635,747,
     844)(430,526,527,636,748)(438,537,648,620,733)(451,552,661,562,675)(452,
     553,663,770,866)(455,556,668,495,607)(458,561,674,780,876)(462,567,681,
     785,881)(470,574,689,793,889)(471,575,690,794,890)(476,583,699,803,902)
     (478,586,703,807,907)(483,591,710,815,792)(488,599,718,629,742)(492,604,
     721,825,861)(505,615,730,832,925)(507,617,616,614,508)(510,619,732,835,
     930)(513,622,735,837,932)(515,624,594,709,814)(517,626,739,839,849)(520,
     630,743,841,935)(521,631,634,746,843)(532,641,752,848,580)(534,643,754,
     722,826)(538,649,667,645,755)(540,651,761,858,945)(544,654,763,658,766)
     (546,657,637,749,827)(548,659,767,863,662)(554,664,772,868,952)(557,669,
     776,823,921)(563,676,781,831,924)(565,677,782,878,960)(576,691,796,893,
     967)(578,694,798,850,940)(581,697,801,899,973)(584,700,804,903,655)(589,
     706,812,724,829)(592,711,816,915,988)(595,714,820,918,989)(597,715,799,
     896,970)(608,725,775,871,692)(623,736,838,769,865)(627,740,840,934,976)
     (640,750,846,937,765)(660,768,864,673,779)(665,773,869,953,929)(670,777,
     872,957,695)(671,778,873,819,900)(678,783,880,729,830)(682,786,875,789,
     885)(685,788,884,958,916)(701,805,904,977,1022)(702,806,874,959,737)(704,
     808,909,981,751)(707,813,914,987,1013)(712,817,917,791,887)(717,822,920,
     908,980)(720,824,923,939,998)(731,833,927,994,877)(734,836,756,852,857)
     (758,854,942,851,821)(759,855,853,842,936)(760,856,906,978,787)(771,867,
     951,992,888)(774,870,954,879,941)(795,891,966,1012,1044)(797,894,968,
     1014,913)(809,910,982,1025,1055)(811,912,985,1028,1061)(834,928,905,955,
     1004)(845,862,947,1001,860)(847,938,997,1003,1029)(859,946,990,943,961)
     (882,919,883,963,1009)(886,965,950,964,1010)(892,901,974,1020,1051)(895,
     969,1015,999,1034)(897,971,933,996,1036)(898,972,1017,1048,1075)(911,983,
     1026,1057,1080)(922,991,1008,1019,1050)(926,993,1032,1063,1087)(931,995,
     1035,1030,1002)(944,1000,986,948,949)(956,1005,1037,1065,1088)(962,1007,
     1041,1068,1092)(975,1021,1052,1006,1040)(979,1024,1054,1047,1074)(984,
     1027,1059,1018,1049)(1011,1042,1069,1093,1109)(1016,1046,1073,1095,1111)
     (1023,1053,1076,1096,1112)(1031,1062,1085,1101,1113)(1033,1064,1056,1078,
     1098)(1038,1066,1090,1106,1071)(1039,1067,1091,1108,1117)(1043,1070,1094,
     1107,1116)(1045,1072,1077,1097,1083)(1058,1081,1079,1086,1102)(1060,1082,
     1099,1105,1115)(1084,1100,1110,1118,1120)(1089,1104,1114,1119,1103);