bin1 := (1,2,3,4,6)(5,7,9,12,16)(8,10,14,19,11)(13,17,23,31,43)(15,20,27,37,51)
     (18,24,33,45,64)(21,28,39,54,55)(22,29,40,56,76)(25,34,47,67,90)(26,35,
     48,68,91)(30,41,58,78,104)(32,44,62,83,112)(36,49,70,94,125)(38,52,73,99,
     133)(42,59,80,106,144)(46,65,87,117,157)(50,71,96,128,173)(53,74,100,135,
     183)(57,75,101,137,185)(60,81,108,147,199)(61,82,110,149,79)(63,84,114,
     152,206)(66,88,119,159,214)(69,92,123,165,223)(72,97,130,176,177)(77,102,
     139,188,249)(85,115,153,154,208)(86,116,155,210,274)(89,120,161,217,283)
     (93,124,167,226,292)(95,126,170,230,298)(98,131,178,237,201)(103,140,190,
     252,328)(105,142,193,256,334)(107,145,196,261,340)(109,148,200,218,284)
     (111,141,191,254,331)(113,151,204,268,349)(118,158,213,278,362)(121,162,
     219,220,286)(122,163,221,288,371)(127,171,232,300,387)(129,174,235,305,
     394)(132,179,239,310,275)(134,181,242,314,317)(136,175,236,307,396)(138,
     186,246,320,408)(143,194,258,337,430)(146,197,263,343,437)(150,202,265,
     203,266)(156,211,276,359,456)(160,215,280,365,346)(164,222,290,166,224)
     (168,227,294,379,380)(169,228,295,273,357)(172,233,302,389,490)(180,240,
     311,241,312)(182,243,316,404,503)(184,244,318,333,424)(187,247,322,411,
     511)(189,250,325,415,517)(192,255,279,363,461)(195,259,338,432,433)(198,
     264,345,440,550)(205,269,351,446,558)(207,271,354,451,287)(209,272,356,
     453,568)(212,277,360,458,364)(216,281,366,463,575)(225,291,375,474,587)
     (229,296,382,481,595)(231,299,386,486,604)(234,303,391,304,392)(238,309,
     398,497,618)(245,319,406,506,407)(248,323,412,513,635)(251,326,417,520,
     642)(253,329,421,526,650)(257,335,427,480,593)(260,339,419,523,441)(262,
     341,435,542,664)(267,347,442,552,673)(270,352,448,561,460)(282,367,465,
     576,701)(285,369,467,579,355)(289,372,471,583,708)(293,377,476,589,714)
     (297,383,482,597,722)(301,388,489,607,732)(306,395,493,614,736)(308,397,
     495,616,529)(313,401,500,535,656)(315,403,502,358,454)(321,409,508,630,
     749)(324,413,426,533,636)(327,418,522,645,763)(330,422,528,644,762)(332,
     423,530,546,361)(336,428,536,402,501)(342,436,544,666,784)(344,438,547,
     669,788)(348,443,554,676,794)(350,445,556,679,464)(353,449,563,688,543)
     (368,466,577,470,496)(370,468,581,704,681)(373,447,559,683,799)(374,472,
     584,709,821)(376,475,567,694,588)(378,477,590,716,829)(381,479,592,657,
     771)(384,483,599,725,837)(385,484,601,727,838)(390,491,610,505,628)(393,
     492,612,735,613)(399,498,619,739,573)(400,499,621,741,611)(405,504,627,
     746,806)(410,509,507,629,748)(414,515,637,756,608)(416,518,640,487,605)
     (420,524,647,766,514)(425,532,654,772,845)(429,537,658,774,881)(431,539,
     661,778,651)(434,540,662,780,527)(439,548,670,790,892)(444,555,678,796,
     578)(450,564,690,553,674)(452,566,693,810,911)(455,570,478,591,718)(457,
     572,698,814,913)(459,545,667,786,803)(462,574,700,816,916)(469,582,706,
     715,617)(473,585,711,824,842)(485,602,728,580,596)(488,606,731,841,941)
     (510,631,750,854,950)(512,633,753,859,955)(516,632,751,856,953)(519,641,
     760,868,962)(521,643,646,764,872)(525,648,755,862,958)(531,652,769,849,
     946)(534,655,773,879,969)(538,659,775,660,776)(541,663,768,876,870)(549,
     671,792,880,707)(551,649,767,875,966)(557,680,797,901,994)(560,684,801,
     813,717)(562,686,804,620,695)(565,691,807,907,935)(569,685,802,747,852)
     (571,696,811,624,743)(586,712,826,905,930)(594,719,830,932,675)(598,723,
     835,938,1018)(600,726,713,827,928)(603,720,831,934,858)(609,733,615,625,
     744)(622,742,848,945,626)(623,697,812,878,967)(634,754,861,957,1029)(638,
     757,863,864,960)(639,758,865,745,850)(653,770,687,805,906)(665,782,765,
     873,965)(668,787,889,968,1035)(672,793,896,987,1057)(677,785,888,979,
     1046)(682,703,818,919,1006)(689,781,885,975,933)(692,808,909,998,923)
     (699,815,914,761,869)(702,817,917,1004,1005)(705,819,921,1008,1076)(710,
     822,925,1012,1078)(721,832,936,1016,1082)(724,836,939,912,1001)(729,839,
     940,730,840)(734,843,942,1021,949)(737,844,943,1023,964)(738,828,929,853,
     877)(740,846,809,910,1000)(752,857,954,1020,1084)(759,866,961,1024,834)
     (777,883,972,1037,931)(779,882,971,976,1041)(783,886,970,1036,1092)(789,
     891,981,1048,1102)(791,893,984,1052,1105)(795,898,990,1060,1114)(798,902,
     996,1066,1121)(800,903,820,922,1009)(823,926,989,1059,1113)(825,927,1013,
     855,951)(833,937,908,918,867)(847,944,1025,1087,952)(851,948,871,963,
     1033)(860,956,904,993,1064)(874,959,1030,1089,1136)(884,973,1038,1094,
     1032)(887,977,1043,1098,1099)(890,980,1047,1071,1095)(894,985,1054,1107,
     1147)(895,915,1002,1072,1126)(897,988,983,1050,1031)(899,991,1061,1116,
     1153)(900,992,1063,1118,1154)(920,1007,1075,1068,1123)(924,1010,1017,
     1070,1125)(947,1026,1085,1028,1022)(974,1039,1003,1073,1128)(978,1044,
     1100,1142,1058)(982,1049,1062,1103,1144)(986,1055,1109,1150,1170)(995,
     1065,997,1067,1122)(999,1069,1124,1156,1155)(1011,1077,1130,1158,1115)
     (1014,1079,1131,1160,1045)(1015,1080,1133,1161,1117)(1019,1083,1134,1162,
     1168)(1027,1088,1135,1097,1086)(1034,1090,1138,1141,1127)(1040,1096,1140,
     1165,1173)(1042,1093,1108,1148,1169)(1051,1104,1145,1167,1174)(1053,1106,
     1056,1110,1151)(1074,1129,1157,1081,1120)(1091,1139,1163,1172,1176)(1101,
     1143,1166,1171,1175)(1111,1146,1132,1137,1164)(1112,1152,1159,1149,1119);