bin1 := (1,2,3,4,5)(6,7,9,11,8)(10,12,15,19,25)(13,16,21,28,37)(14,17,22,29,38)
     (18,23,31,41,55)(20,26,34,46,62)(24,32,43,57,79)(27,35,48,65,86)(30,39,
     52,71,94)(33,44,59,45,60)(36,49,67,89,119)(40,53,73,97,128)(42,56,77,102,
     135)(47,63,84,111,149)(50,68,90,91,121)(51,69,92,123,163)(54,74,88,117,
     158)(58,80,105,140,186)(61,82,108,144,192)(64,85,113,152,198)(66,87,116,
     156,204)(70,93,125,72,95)(75,99,131,174,175)(76,100,132,176,145)(78,103,
     137,181,235)(81,106,142,189,122)(83,109,146,110,147)(96,126,167,219,277)
     (98,129,171,224,284)(101,133,177,228,291)(104,138,183,139,184)(107,120,
     161,211,268)(112,150,196,249,321)(114,153,200,255,256)(115,154,201,238,
     305)(118,159,208,265,343)(124,164,215,272,350)(127,168,195,247,319)(130,
     172,225,286,367)(134,178,230,294,378)(136,180,233,299,385)(141,187,239,
     306,392)(143,190,243,241,309)(148,194,246,317,406)(151,197,251,324,414)
     (155,202,257,330,422)(157,205,261,336,431)(160,209,266,214,210)(162,212,
     270,347,442)(165,216,273,352,449)(166,217,274,353,450)(169,221,280,359,
     360)(170,222,281,361,460)(173,226,288,370,472)(179,231,296,380,381)(182,
     236,264,341,439)(185,237,304,390,329)(188,240,308,393,500)(191,244,313,
     400,510)(193,245,315,403,303)(199,253,327,419,295)(203,258,332,424,532)
     (206,262,338,434,466)(207,263,340,437,544)(213,271,349,445,267)(218,275,
     355,453,560)(220,278,269,345,248)(223,282,363,462,571)(227,289,372,314,
     401)(229,292,375,477,587)(232,297,382,484,597)(234,300,386,490,605)(242,
     310,396,504,555)(250,322,411,517,637)(252,325,416,522,523)(254,328,421,
     528,651)(259,333,426,427,534)(260,334,428,536,307)(276,356,455,563,636)
     (279,358,458,568,689)(283,364,464,572,549)(285,366,467,574,485)(287,368,
     470,578,699)(290,373,474,583,688)(293,376,479,590,714)(298,383,486,599,
     725)(301,387,492,493,607)(302,388,494,608,738)(311,397,506,620,476)(312,
     398,508,623,759)(316,404,512,628,766)(318,407,335,429,538)(320,374,475,
     585,707)(323,412,519,640,780)(326,417,524,646,694)(331,423,530,653,792)
     (337,432,540,659,799)(339,435,365,465,573)(342,440,454,561,683)(344,441,
     548,670,737)(346,357,456,565,647)(348,443,550,672,810)(351,447,554,556,
     463)(354,451,557,677,812)(362,461,570,693,830)(369,471,580,702,836)(371,
     433,541,661,527)(377,480,592,430,529)(379,482,595,721,859)(384,487,601,
     728,864)(389,495,610,741,877)(391,497,612,745,883)(394,501,616,697,832)
     (395,502,617,752,843)(399,509,625,762,897)(402,488,602,730,866)(405,513,
     630,767,902)(408,515,633,720,858)(409,491,606,736,875)(410,516,635,774,
     822)(413,520,642,783,916)(415,496,611,743,880)(418,525,648,787,920)(420,
     481,593,718,855)(425,533,457,566,645)(436,543,664,802,929)(438,545,667,
     806,934)(444,551,674,811,941)(446,552,448,553,675)(452,558,679,815,945)
     (459,569,691,828,961)(468,575,696,757,895)(469,576,579,700,584)(473,542,
     662,546,668)(478,588,711,848,982)(483,596,723,861,935)(489,603,732,869,
     761)(498,613,747,885,537)(499,614,749,641,781)(503,618,754,892,1014)(505,
     619,755,893,819)(507,621,665,803,746)(511,626,763,898,1018)(514,631,769,
     652,790)(518,638,777,910,1029)(521,643,785,918,1035)(526,649,788,805,932)
     (531,654,794,798,927)(535,644,786,919,1037)(539,657,701,658,797)(547,669,
     807,936,1048)(559,680,816,947,1055)(562,684,820,734,872)(564,686,823,955,
     1061)(567,615,750,888,577)(581,703,838,627,764)(582,704,839,972,1076)
     (586,708,844,977,1083)(589,712,850,884,1009)(591,715,852,985,1094)(594,
     719,857,989,692)(598,705,840,974,1078)(600,726,863,991,1099)(604,733,871,
     996,1102)(609,739,634,772,907)(622,758,655,795,925)(624,760,896,724,862)
     (629,731,867,994,791)(632,770,905,1024,782)(639,778,911,1031,1101)(650,
     789,921,1039,1131)(656,796,900,1021,1119)(660,800,924,1041,727)(663,687,
     824,956,1062)(666,804,931,814,673)(671,808,938,1050,1138)(676,682,818,
     951,942)(678,813,943,1052,1141)(681,817,949,744,881)(685,821,954,1060,
     1145)(690,826,959,1064,1066)(695,831,964,768,903)(698,833,966,1042,1134)
     (706,841,975,1080,1153)(709,845,978,1085,1155)(710,846,887,882,1007)(713,
     773,904,1023,1091)(716,853,986,835,968)(717,854,987,971,1075)(722,771,
     906,1025,1122)(729,837,970,1074,1150)(735,873,901,1022,1120)(740,876,
     1001,1107,1002)(742,878,1003,1108,993)(748,886,1011,779,912)(751,889,
     1008,1111,1043)(753,756,894,860,990)(765,899,1020,1118,1179)(775,909,
     1027,1124,981)(776,847,980,1088,1157)(784,917,1034,1127,1185)(793,923,
     1040,969,1072)(801,928,1044,834,967)(809,939,1051,1139,1189)(825,957,915,
     958,1063)(827,960,1065,1142,1192)(829,962,1067,948,1056)(842,976,1081,
     950,1006)(849,983,1090,1159,1164)(851,984,1092,1160,1071)(856,988,913,
     1032,870)(865,879,1004,1109,1171)(868,926,930,1046,1136)(874,999,1105,
     1168,1169)(890,1012,1114,1087,1057)(891,1013,1115,1177,1210)(908,1026,
     1096,1047,940)(914,1033,1036,1129,1174)(922,1005,1110,1173,1184)(933,
     1038,1130,1121,1178)(937,1049,1137,1140,1191)(944,1053,1015,946,1054)
     (952,1058,1097,1019,998)(953,1059,1144,1028,1125)(963,1068,979,1086,1156)
     (965,1070,1016,1116,995)(973,1077,1045,1135,1183)(992,1100,1073,1132,
     1151)(997,1103,1166,1205,1219)(1000,1106,1170,1207,1182)(1010,1112,1175,
     1113,1079)(1017,1117,1069,1148,1197)(1030,1126,1123,1181,1146)(1082,1147,
     1195,1216,1190)(1084,1154,1200,1218,1196)(1089,1158,1201,1194,1214)(1093,
     1161,1202,1128,1186)(1095,1162,1203,1149,1133)(1098,1163,1204,1213,1222)
     (1104,1167,1206,1220,1224)(1143,1193,1180,1211,1215)(1152,1188,1212,1165,
     1199)(1172,1208,1198,1217,1223)(1176,1209,1221,1225,1187);