bin1 := (2,3,6,4)(5,8,14,9)(7,11,19,12)(10,16,27,17)(13,21,35,22)(15,24,40,25)
     (18,29,48,30)(20,32,53,33)(23,37,61,38)(26,42,68,43)(28,45,73,46)(31,50,
     81,51)(34,55,89,56)(36,58,94,59)(39,63,102,64)(41,66)(44,70,113,71)(47,
     75,121,76)(49,78,126,79)(52,83,134,84)(54,86,138,87)(57,91,146,92)(60,96,
     153,97)(62,99,158,100)(65,104,165,105)(67,107,170,108)(69,110,174,111)
     (72,115,181,116)(74,118,185,119)(77,123,193,124)(80,128,199,129)(82,131,
     204,132)(85,135,210,136)(88,140,218,141)(90,143,223,144)(93,148,231,149)
     (95,150,233,151)(98,155,241,156)(101,160,248,161)(103,125,195,163)(106,
     167,259,168)(109,172,267,173)(112,176,273,177)(114,178,276,179)(117,182,
     280,183)(120,187,288,188)(122,190,293,191)(127,197,304,198)(130,201,310,
     202)(133,206,316,207)(137,212,325,213)(139,215,328,216)(142,220,334,221)
     (145,225,340,226)(147,228,345,229)(152,235,203,236)(154,238,358,239)(157,
     243,366,244)(159,245,369,246)(162,250,377,251)(164,253,382,254)(166,256,
     387,257)(169,261,394,262)(171,264,399,265)(175,270,407,271)(180,277)(184,
     282,425,283)(186,285,430,286)(189,290,214,291)(192,295,442,296)(194,298,
     224,299)(196,301,451,302)(200,307,461,308)(205,313,471,314)(208,269,405,
     318)(209,319,479,320)(211,322,483,323)(217,329,493,330)(219,332,409,272)
     (222,336,504,337)(227,342,514,343)(230,347,521,348)(232,258,389,350)(234,
     352,529,353)(237,355,534,356)(240,360,541,361)(242,363,545,364)(247,371,
     557,372)(249,374,562,375)(252,379,570,380)(255,384,578,385)(260,391,588,
     392)(263,396,595,397)(266,401,481,321)(268,403,604,404)(274,411,615,412)
     (275,413,618,414)(278,417,623,418)(279,419,626,420)(281,422,631,423)(284,
     427,639,428)(287,432,646,433)(289,435)(292,437,653,438)(294,317,476,440)
     (297,444,635,445)(300,448,669,449)(303,453,676,454)(305,456,681,457)(306,
     458,683,459)(309,463,691,464)(311,466,695,467)(312,468,698,469)(315,473,
     705,474)(324,485,717,486)(326,488,721,489)(327,490,724,491)(331,495,731,
     496)(333,498,733,499)(335,501,737,502)(338,506,744,507)(339,508,747,509)
     (341,511,751,512)(344,516,757,517)(346,518,760,519)(349,523,768,524)(351,
     526,770,527)(354,531,777,532)(357,535,782,536)(359,538,787,539)(362,542,
     792,543)(365,547,497,548)(367,550,802,551)(368,552,803,553)(370,555,648,
     434)(373,559,810,560)(376,564,816,565)(378,567,820,568)(381,572,826,573)
     (383,575,830,576)(386,580,835,581)(388,484,715,583)(390,585,840,586)(393,
     590,844,591)(395,593,675,594)(398,597,850,598)(400,600,854,601)(402,602,
     856,603)(406,606,860,607)(408,609,748,610)(410,612,864,613)(415,620,716,
     621)(416,622,812,561)(421,628,882,629)(424,633,888,634)(426,636,657,637)
     (429,641,896,642)(431,643,899,644)(436,650,905,651)(439,655,910,656)(441,
     658,913,659)(443,660,916,661)(446,664,923,665)(447,666,925,667)(450,671,
     930,672)(452,673,932,674)(455,678,937,679)(460,685,947,686)(462,688,951,
     689)(465,693,821,627)(470,700,966,701)(472,702,969,703)(475,706,975,707)
     (477,577,749,510)(478,709,979,710)(480,711,982,712)(482,713,985,714)(487,
     718,989,719)(492,725,584,726)(494,728,997,729)(500,735,911,736)(503,739,
     1007,740)(505,742,723,743)(513,752,1019,753)(515,754,1022,755)(520,762,
     1032,763)(522,765,525,766)(528,771,1044,772)(530,774,1048,775)(533,779,
     1055,780)(537,784,1060,785)(540,789,1063,790)(544,794,857,795)(546,796,
     1069,797)(549,800,1074,801)(554,804,1078,805)(556,647,902,807)(558,617)
     (563,813,592,814)(566,818,649,819)(569,798,1071,822)(571,824,886,825)
     (574,828,1096,829)(579,832,1102,833)(582,837,1106,838)(587,841,1058,783)
     (589,616,869,843)(596,847,1115,848)(599,852,1120,853)(605,859,861,608)
     (611,727,995,732)(614,866,1132,867)(619,871,1047,872)(624,876,1142,877)
     (625,878,781,879)(630,884,1151,885)(632,887,1121,855)(638,891,1145,892)
     (640,893,1160,894)(645,900,1166,901)(652,811,1020,907)(654,776,1050,909)
     (662,918,1186,919)(663,920,1189,921)(668,926)(670,928,759,929)(677,934,
     944,935)(680,939,1211,940)(682,942,1214,943)(684,945,1215,946)(687,949,
     948,720)(690,953,1159,897)(692,954,868,955)(694,957,1229,958)(696,959,
     1231,960)(697,961,1232,962)(699,963,1234,964)(704,971,1243,972)(708,977,
     1249,978)(722,788,1062,992)(730,999,1270,1000)(734,1002,1272,1003)(738,
     922,1191,987)(741,1008,1276,1009)(745,1011)(746,1012,1281,1013)(750,1015,
     1284,1016)(756,1024,1291,1025)(758,1027,941,1028)(761,1030,1296,1031)
     (764,1034,1240,1035)(767,1037,1301,1038)(769,1040,839,1041)(773,1046,
     1169,903)(778,1052,1312,1053)(786,863,1068,806)(791,1064,1212,1065)(793,
     1066,881,998)(799,1072,1324,1073)(808,1081,1129,1082)(809,1083,1133,889)
     (815,1086,1334,1087)(817,1088,1233,1089)(823,1092,1161,895)(827,1094,
     1130,865)(831,1099,1352,1100)(834,983,1254,1103)(836,1104,1308,1045)(842,
     1108,1356,1109)(845,1110,1358,1111)(846,1112,1057,1113)(849,1116,1209,
     1117)(851,1118,1244,973)(858,1124,1182,1105)(862,1128,1326,1077)(870,
     1134,1376,1135)(873,1137,1250,1138)(874,967,1239,1139)(875,1140,1366,
     1123)(880,1146,1385,1147)(883,1149,1387,1150)(890,1155,906,1156)(898,
     1163,990,1164)(904,1170,1402,1171)(908,1173,914,1174)(912,1177,1407,1178)
     (915,1180,1315,1181)(917,1183,1410,1184)(924,1193,1418,1194)(927,1196,
     1422,1197)(931,1200,1425,1201)(933,1203,1429,1204)(936,1207,1431,1208)
     (938,1210,1001,968)(950,1219,1437,1220)(952,1222,1439,1223)(956,1226,
     1051,1227)(965,1236,1205,1237)(970,1241,1377,1242)(974,1245,1452,1246)
     (976,1179,1408,1247)(980,1061)(981,1251,1454,1252)(984,1255,1459,1256)
     (986,1257,1381,1258)(988,1165,1085,1259)(991,1026,1292,1261)(993,1263,
     1465,1264)(994,1265,1175,1266)(996,1268,1228,1269)(1004,1274,1420,1195)
     (1005,1021,1288,1275)(1006,1141,1383,1192)(1010,1277,1472,1278)(1014,
     1282,1476,1283)(1017,1122,1365,1213)(1018,1285,1355,1286)(1023,1289,1075,
     1290)(1029,1293,1482,1294)(1033,1298,1485,1299)(1036,1300,1167,1230)
     (1039,1303,1487,1304)(1042,1305,1386,1148)(1043,1306,1490,1307)(1049,
     1309,1491,1310)(1054,1313,1495,1314)(1056,1316,1497,1317)(1059,1067,1168,
     1319)(1070,1190,1354,1107)(1076,1325,1409,1320)(1079,1185,1412,1328)
     (1080,1329,1323,1330)(1084,1332,1297,1333)(1090,1338,1504,1336)(1091,
     1339,1221,1340)(1093,1341,1321,1342)(1095,1344,1411,1345)(1097,1347,1318,
     1348)(1098,1349,1510,1350)(1101,1162,1399,1353)(1114,1360,1225,1361)
     (1119,1364,1144,1357)(1125,1322,1494,1367)(1126,1368,1198,1359)(1127,
     1369,1517,1370)(1131,1372,1172,1373)(1136,1378,1522,1379)(1143,1371,1380,
     1331)(1152,1389,1501,1390)(1153,1391,1515,1392)(1154,1248,1453,1393)
     (1157,1395,1531,1396)(1158,1397,1430,1206)(1176,1404,1539,1405)(1187,
     1414,1516,1415)(1188,1416)(1199,1423,1363,1424)(1202,1427,1498,1428)
     (1216,1432,1549,1433)(1217,1434,1551,1435)(1218,1280,1475,1436)(1224,
     1440,1533,1441)(1235,1445,1558,1446)(1238,1447,1520,1448)(1253,1455,1565,
     1456)(1260,1413,1401,1461)(1262,1462,1568,1463)(1267,1337,1505,1467)
     (1271,1438,1553,1468)(1273,1406,1374,1469)(1279,1473,1572,1474)(1287,
     1478,1464,1479)(1295,1346,1509,1483)(1302,1486,1457,1458)(1311,1492,1449,
     1493)(1327,1499,1575,1500)(1335,1503,1537,1403)(1343,1507,1578,1508)
     (1351,1375,1519,1484)(1362,1443,1541,1512)(1382,1523,1488,1524)(1384,
     1511,1496,1444)(1388,1527,1398,1528)(1394,1518,1582,1530)(1400,1534,1560,
     1535)(1417,1489,1480,1502)(1419,1544,1471,1545)(1421,1547,1581,1514)
     (1426,1543,1583,1548)(1442,1555,1593,1556)(1450,1561,1552,1562)(1451,
     1563,1466,1540)(1460,1567,1546,1557)(1470,1570,1525,1559)(1477,1569,1580,
     1513)(1481,1526,1521,1529)(1506,1576,1592,1577)(1532,1564,1594,1585)
     (1536,1587,1542,1588)(1538,1573,1554,1589)(1550,1590,1599,1591)(1566,
     1584,1600,1595)(1571,1596,1586,1597)(1574,1598);