bin1 := (2,4,6)(5,10,12)(8,15,17)(9,18,13)(11,22,20)(14,26,27)(16,31,33)(21,30,
     34)(23,42,40)(25,36,45)(28,46,48)(29,50,52)(32,56,54)(39,53,64)(43,70,68)
     (47,75,76)(49,79,80)(51,84,86)(55,83,87)(57,93,91)(59,96,97)(60,99,101)
     (62,103,104)(65,108,109)(67,111,90)(71,117,115)(77,122,125)(78,121,123)
     (81,130,131)(82,132,134)(85,137,135)(94,148,146)(98,152,154)(100,157,159)
     (102,155,160)(105,162,164)(107,151,153)(112,170,171)(124,182,183)(126,
     186,187)(127,189,181)(133,197,199)(136,196,200)(138,205,203)(143,211,212)
     (145,215,202)(149,221,219)(156,226,228)(158,231,229)(161,225,235)(163,
     238,239)(165,242,243)(172,250,251)(174,254,216)(179,259,261)(184,265,268)
     (185,264,266)(188,273,274)(190,246,276)(192,270,279)(195,282,284)(198,
     287,285)(206,297,295)(208,300,301)(209,252,303)(213,307,310)(227,325,327)
     (230,324,328)(232,332,330)(234,335,336)(236,339,340)(240,342,345)(241,
     309,343)(245,311,350)(249,306,308)(255,358,359)(260,365,367)(267,372,373)
     (269,376,377)(275,384,385)(278,389,391)(283,395,397)(286,394,398)(288,
     403,401)(294,410,400)(298,416,414)(302,419,422)(304,356,425)(313,432,433)
     (315,436,411)(320,441,443)(321,423,444)(323,446,448)(326,451,449)(333,
     459,457)(337,461,464)(338,421,462)(341,469,470)(344,473,474)(346,477,478)
     (347,429,472)(351,430,484)(360,492,493)(362,496,437)(364,499,501)(366,
     504,502)(374,510,512)(375,509,511)(378,517,518)(379,520,522)(381,514,525)
     (386,530,531)(390,536,534)(393,524,541)(396,543,542)(404,553,551)(408,
     558,559)(418,507,420)(424,573,574)(427,569,577)(434,582,585)(442,593,595)
     (445,572,597)(447,601,603)(450,600,604)(452,609,607)(456,614,606)(463,
     619,620)(465,623,624)(466,571,535)(475,633,636)(476,632,634)(479,641,642)
     (480,488,579)(482,638,646)(483,647,648)(485,651,652)(486,494,653)(487,
     586,654)(489,657,554)(491,581,583)(495,661,663)(497,664,665)(500,669,671)
     (503,656,672)(506,675,537)(513,680,550)(519,686,687)(521,689,691)(532,
     700,690)(540,706,708)(544,695,710)(556,720,721)(560,725,728)(564,681,716)
     (575,739,742)(576,584,740)(578,729,745)(580,747,655)(587,751,753)(588,
     754,755)(589,757,759)(590,760,733)(592,763,765)(594,768,766)(596,771,772)
     (598,775,776)(599,778,780)(602,783,781)(610,792,790)(621,800,803)(622,
     799,801)(625,808,809)(627,805,813)(635,818,819)(637,822,823)(643,830,831)
     (645,833,835)(649,836,839)(650,727,837)(662,852,848)(666,855,856)(667,
     857,761)(668,859,861)(670,864,862)(676,868,703)(688,877,878)(693,882,884)
     (701,890,879)(707,896,894)(722,909,912)(723,914,746)(724,915,726)(730,
     919,921)(731,922,923)(732,925,927)(734,929,931)(738,913,933)(741,937,938)
     (743,941,942)(744,750,936)(748,916,950)(752,955,849)(756,958,961)(758,
     963,965)(764,969,971)(767,949,972)(769,976,974)(773,977,980)(774,911,978)
     (777,985,986)(779,988,990)(782,987,991)(784,996,994)(789,1000,993)(796,
     1006,1001)(802,1010,1011)(804,1014,1015)(810,1022,1023)(812,1025,895)
     (820,1030,1032)(821,1029,1031)(824,1037,1038)(825,1040,1042)(827,1034,
     966)(834,1050,1048)(838,1054,1055)(840,1058,1059)(841,918,1049)(844,1063,
     1064)(845,1066,1067)(846,948,1069)(847,960,1071)(850,952,944)(851,1073,
     1075)(854,957,959)(858,893,1079)(860,1082,1084)(863,1081,1085)(866,1072,
     1087)(867,1089,1091)(873,1095,1097)(883,1104,1106)(889,1110,1112)(891,
     1115,1113)(892,1116,1105)(902,1123,1125)(903,1126,1127)(904,1129,1131)
     (906,1133,1135)(907,1136,934)(908,1137,910)(920,1147,951)(924,1150,1153)
     (926,1156,1158)(930,1162,1164)(932,1166,1168)(939,1173,1175)(940,1172,
     1165)(943,1179,1180)(945,1181,1182)(946,1142,1184)(947,1152,1187)(953,
     1190,1192)(954,1193,956)(962,1198,1200)(964,1203,1201)(967,1204,1205)
     (968,1206,1208)(970,1211,1209)(979,1220,1221)(981,1224,1225)(982,1140,
     1219)(989,1233,1232)(1012,1250,1253)(1013,1249,1251)(1016,1258,1259)
     (1017,1227,1261)(1019,1255,1264)(1027,1263,1271)(1033,1274,1239)(1039,
     1280,1281)(1041,1189,1282)(1051,1287,1103)(1056,1289,1292)(1057,1288,
     1290)(1060,1297,1298)(1062,1294,1302)(1065,1246,1304)(1068,1306,1308)
     (1070,1197,1312)(1074,1313,1315)(1076,1270,1316)(1080,1252,1320)(1083,
     1323,1321)(1090,1328,1329)(1092,1213,1138)(1096,1334,1336)(1102,1341,
     1335)(1107,1117,1344)(1108,1345,1346)(1109,1347,1348)(1111,1351,1352)
     (1114,1350,1333)(1119,1356,1358)(1120,1359,1361)(1121,1362,1364)(1122,
     1365,1366)(1124,1370,1144)(1128,1373,1376)(1130,1379,1381)(1134,1386,
     1388)(1141,1375,1395)(1143,1392,1330)(1145,1397,1399)(1146,1400,1148)
     (1149,1404,1151)(1154,1408,1410)(1155,1411,1159)(1157,1414,1412)(1160,
     1416,1417)(1161,1418,1420)(1163,1423,1421)(1167,1426,1428)(1169,1429,
     1430)(1170,1391,1432)(1174,1436,1437)(1176,1440,1441)(1183,1446,1448)
     (1185,1451,1452)(1186,1407,1422)(1191,1454,1456)(1194,1453,1457)(1195,
     1405,1461)(1199,1464,1466)(1202,1301,1467)(1207,1471,1472)(1210,1470,
     1473)(1216,1460,1475)(1222,1481,1484)(1223,1480,1482)(1226,1489,1490)
     (1229,1486,1494)(1244,1275,1502)(1247,1506,1504)(1254,1511,1512)(1260,
     1519,1520)(1291,1536,1537)(1293,1540,1541)(1299,1548,1549)(1303,1550,
     1551)(1305,1524,1553)(1307,1555,1556)(1309,1559,1560)(1311,1317,1462)
     (1314,1355,1564)(1318,1468,1469)(1319,1510,1567)(1322,1509,1568)(1326,
     1572,1570)(1327,1573,1575)(1337,1342,1579)(1338,1580,1581)(1339,1583,
     1584)(1340,1585,1463)(1349,1588,1590)(1354,1593,1595)(1357,1598,1600)
     (1360,1603,1604)(1363,1608,1393)(1367,1611,1614)(1368,1615,1617)(1369,
     1618,1371)(1372,1622,1374)(1377,1626,1628)(1378,1629,1382)(1380,1633,
     1631)(1383,1635,1636)(1384,1455,1638)(1385,1639,1389)(1387,1641,1640)
     (1390,1613,1644)(1394,1625,1648)(1398,1651,1653)(1402,1650,1654)(1403,
     1656,1658)(1409,1661,1663)(1413,1660,1664)(1415,1439,1667)(1419,1670,
     1671)(1425,1672,1674)(1427,1677,1675)(1431,1678,1680)(1433,1683,1684)
     (1438,1685,1686)(1442,1690,1691)(1447,1692,1693)(1449,1696,1697)(1459,
     1503,1704)(1465,1706,1602)(1483,1716,1717)(1485,1720,1721)(1491,1728,
     1729)(1493,1730,1566)(1513,1742,1533)(1516,1740,1554)(1522,1731,1605)
     (1529,1751,1753)(1538,1757,1759)(1539,1756,1758)(1542,1764,1765)(1543,
     1647,1766)(1545,1761,1705)(1552,1733,1772)(1557,1775,1778)(1558,1774,
     1776)(1561,1782,1783)(1562,1780,1666)(1574,1789,1790)(1576,1788,1791)
     (1577,1792,1793)(1582,1587,1796)(1586,1798,1800)(1589,1802,1803)(1591,
     1801,1804)(1592,1806,1805)(1594,1808,1746)(1596,1795,1809)(1597,1810,
     1601)(1599,1794,1811)(1606,1676,1815)(1607,1816,1609)(1610,1818,1612)
     (1616,1821,1823)(1620,1820,1824)(1621,1826,1829)(1623,1748,1711)(1627,
     1831,1833)(1632,1830,1834)(1634,1836,1838)(1637,1784,1842)(1643,1819,
     1845)(1652,1847,1849)(1657,1736,1852)(1659,1817,1855)(1662,1856,1857)
     (1668,1860,1669)(1673,1863,1864)(1679,1866,1867)(1681,1870,1871)(1687,
     1877,1712)(1694,1882,1885)(1695,1881,1883)(1698,1890,1891)(1699,1887,
     1893)(1702,1892,1895)(1703,1896,1837)(1707,1861,1898)(1713,1878,1900)
     (1718,1902,1904)(1719,1901,1903)(1722,1907,1754)(1723,1844,1813)(1725,
     1905,1773)(1747,1916,1917)(1752,1862,1812)(1755,1797,1919)(1760,1922,
     1923)(1771,1927,1839)(1777,1930,1931)(1779,1934,1935)(1799,1940,1915)
     (1807,1884,1942)(1822,1944,1945)(1828,1912,1949)(1832,1952,1953)(1840,
     1958,1841)(1850,1962,1954)(1851,1964,1963)(1853,1937,1966)(1858,1961,
     1960)(1868,1974,1976)(1869,1973,1975)(1872,1979,1918)(1873,1972,1928)
     (1886,1983,1984)(1897,1986,1956)(1932,1947,1996)(1933,1995,1967)(1936,
     1982,1990)(1943,1969,1955)(1946,1970,1959)(1950,1994,1998)(1965,2001,
     2000)(1991,1997,1999);