bin1 := (2,4)(3,6)(5,10)(7,13)(8,14)(9,16)(11,18)(12,20)(15,26)(19,31)(22,34)
     (23,25)(24,37)(28,43)(29,45)(32,50)(33,52)(35,56)(36,57)(38,60)(39,61)
     (40,62)(41,64)(42,66)(44,69)(46,72)(48,73)(49,75)(51,79)(53,82)(55,78)
     (58,89)(59,91)(63,99)(65,102)(70,109)(71,111)(74,117)(77,120)(81,126)(83,
     130)(84,131)(85,132)(87,135)(88,137)(90,141)(92,144)(93,145)(94,147)(95,
     149)(96,151)(100,142)(101,158)(103,162)(104,164)(105,166)(108,168)(110,
     172)(112,175)(113,176)(114,178)(115,180)(118,173)(119,186)(121,190)(122,
     191)(123,192)(124,194)(125,196)(127,199)(128,200)(129,202)(134,210)(136,
     213)(138,216)(139,217)(140,219)(143,224)(148,231)(150,234)(153,237)(154,
     238)(157,241)(159,244)(160,245)(163,250)(165,252)(167,255)(169,258)(171,
     259)(174,263)(177,269)(179,272)(181,275)(182,276)(183,277)(184,279)(185,
     281)(187,284)(189,286)(197,298)(201,304)(203,307)(204,308)(205,310)(206,
     312)(207,314)(208,316)(209,318)(212,233)(214,326)(215,328)(218,334)(220,
     336)(221,337)(222,339)(223,341)(225,343)(226,344)(227,346)(228,348)(229,
     350)(230,352)(232,355)(235,360)(236,362)(240,368)(242,297)(243,372)(246,
     378)(247,379)(248,380)(249,382)(253,388)(254,390)(256,394)(257,396)(262,
     402)(264,404)(265,405)(267,408)(270,400)(271,411)(273,415)(274,417)(278,
     423)(280,426)(283,430)(285,434)(287,437)(290,440)(292,443)(293,445)(294,
     435)(295,448)(296,450)(299,455)(300,456)(302,457)(303,454)(305,462)(309,
     438)(311,471)(313,474)(315,477)(317,478)(320,480)(321,482)(322,484)(323,
     485)(327,449)(329,491)(330,492)(333,496)(335,500)(338,506)(342,510)(345,
     514)(349,519)(351,521)(353,524)(354,526)(356,529)(357,389)(358,490)(359,
     531)(361,534)(364,537)(365,539)(366,541)(367,543)(369,547)(370,549)(373,
     551)(374,552)(375,554)(376,556)(377,452)(381,565)(383,566)(384,567)(385,
     569)(386,571)(387,572)(391,577)(392,578)(393,580)(395,582)(397,585)(398,
     586)(399,587)(401,589)(403,592)(406,596)(407,597)(409,600)(410,601)(412,
     604)(413,605)(414,607)(416,611)(418,613)(419,614)(420,615)(421,617)(424,
     546)(425,623)(427,627)(428,629)(431,633)(432,634)(433,636)(439,644)(441,
     646)(442,647)(444,650)(446,652)(447,653)(453,658)(458,665)(461,667)(463,
     643)(464,670)(468,673)(470,675)(473,645)(475,683)(476,685)(479,690)(483,
     694)(486,699)(487,700)(488,701)(489,702)(493,709)(494,710)(495,711)(497,
     714)(501,719)(502,720)(504,723)(505,725)(507,712)(509,730)(511,732)(513,
     733)(515,736)(516,738)(517,740)(520,745)(522,749)(523,751)(527,718)(528,
     757)(530,761)(532,763)(533,764)(536,768)(540,774)(542,777)(544,779)(545,
     780)(550,782)(555,788)(557,621)(558,791)(559,792)(560,794)(561,795)(562,
     797)(563,799)(564,801)(574,814)(581,661)(583,822)(584,824)(588,831)(591,
     671)(593,837)(594,838)(598,843)(599,844)(602,849)(609,858)(610,860)(612,
     863)(618,872)(619,705)(620,873)(624,878)(625,879)(626,881)(628,885)(630,
     888)(631,889)(635,895)(637,898)(638,899)(639,641)(648,909)(655,919)(656,
     921)(657,923)(659,927)(660,928)(662,926)(663,930)(664,932)(666,935)(668,
     938)(672,886)(674,781)(676,786)(677,944)(678,924)(679,945)(680,946)(681,
     947)(684,951)(687,954)(688,956)(689,958)(691,962)(692,918)(695,965)(696,
     967)(697,968)(698,970)(703,977)(706,979)(708,976)(713,990)(715,994)(717,
     995)(721,1002)(722,1003)(724,1006)(726,1008)(727,1009)(728,1011)(731,
     1014)(734,1018)(735,1020)(737,1022)(739,957)(741,1026)(742,1027)(743,
     1028)(744,1030)(747,1033)(748,1035)(750,1039)(752,1042)(753,1043)(754,
     1038)(756,1047)(759,1050)(760,1052)(762,1055)(765,1060)(766,1062)(767,
     854)(769,1066)(770,1067)(771,922)(775,1074)(778,1076)(783,869)(784,1083)
     (785,853)(789,1090)(790,1091)(793,1096)(796,1100)(800,1104)(802,1107)
     (804,1109)(805,1111)(807,1114)(808,1116)(809,1105)(810,1119)(811,1121)
     (812,1123)(813,1125)(815,1127)(816,1128)(817,1130)(820,1134)(823,1078)
     (825,1139)(826,1140)(827,1142)(828,1136)(829,1145)(832,1149)(833,1150)
     (834,1151)(835,1152)(836,1154)(840,1159)(842,1161)(846,1166)(847,1163)
     (848,1169)(850,1173)(855,1172)(856,1178)(857,1179)(859,1182)(862,1185)
     (864,1186)(865,1188)(866,1183)(868,1191)(871,1093)(875,1197)(876,1198)
     (877,1056)(880,1095)(882,1101)(883,1206)(884,1208)(887,1212)(891,1216)
     (893,1218)(894,1215)(896,1222)(900,1225)(901,1226)(904,1227)(905,1229)
     (906,1231)(907,1108)(908,1012)(910,1236)(911,1237)(912,1239)(913,939)
     (915,1241)(916,1242)(920,1207)(925,1248)(931,1256)(933,1258)(934,1259)
     (936,1102)(937,1263)(940,1224)(941,1268)(942,1270)(943,1272)(948,1279)
     (949,1021)(952,1280)(953,1282)(955,1286)(959,1290)(961,1292)(963,1296)
     (964,1297)(966,1300)(969,1304)(971,1306)(972,983)(973,1308)(974,1310)
     (978,1316)(981,1319)(985,1322)(986,1238)(987,1323)(988,1070)(989,1214)
     (991,1327)(992,1328)(993,1084)(996,1234)(997,1332)(998,1333)(999,1193)
     (1000,1336)(1001,1331)(1004,1341)(1005,1343)(1015,1354)(1016,1355)(1017,
     1356)(1019,1359)(1024,1363)(1025,1365)(1029,1372)(1031,1174)(1032,1375)
     (1034,1379)(1036,1381)(1037,1382)(1044,1391)(1045,1059)(1046,1058)(1048,
     1392)(1049,1393)(1051,1395)(1053,1398)(1061,1402)(1063,1403)(1065,1405)
     (1068,1410)(1069,1411)(1073,1413)(1075,1415)(1077,1190)(1081,1418)(1085,
     1211)(1086,1421)(1089,1423)(1094,1431)(1097,1427)(1103,1436)(1112,1448)
     (1113,1449)(1117,1451)(1118,1452)(1120,1455)(1124,1460)(1126,1394)(1129,
     1464)(1131,1466)(1133,1467)(1135,1469)(1137,1472)(1138,1474)(1143,1479)
     (1144,1480)(1146,1482)(1147,1189)(1153,1488)(1155,1491)(1156,1366)(1157,
     1492)(1158,1493)(1162,1374)(1167,1501)(1168,1324)(1170,1503)(1171,1504)
     (1175,1509)(1176,1510)(1177,1511)(1181,1516)(1184,1521)(1187,1462)(1199,
     1533)(1200,1534)(1201,1351)(1202,1535)(1203,1532)(1204,1536)(1209,1539)
     (1210,1540)(1213,1544)(1217,1283)(1220,1549)(1221,1278)(1223,1550)(1228,
     1558)(1232,1561)(1233,1562)(1235,1564)(1240,1571)(1243,1573)(1244,1317)
     (1245,1575)(1246,1577)(1249,1581)(1250,1526)(1251,1582)(1253,1584)(1254,
     1586)(1255,1587)(1260,1593)(1261,1595)(1264,1599)(1265,1600)(1266,1601)
     (1267,1602)(1269,1311)(1273,1439)(1274,1330)(1275,1606)(1277,1609)(1281,
     1615)(1284,1618)(1285,1614)(1287,1623)(1289,1312)(1291,1605)(1293,1627)
     (1294,1628)(1295,1630)(1299,1635)(1303,1640)(1305,1643)(1307,1645)(1309,
     1647)(1313,1648)(1314,1608)(1318,1632)(1321,1654)(1325,1658)(1329,1663)
     (1334,1665)(1335,1666)(1337,1668)(1338,1669)(1339,1670)(1340,1440)(1345,
     1675)(1346,1676)(1347,1678)(1349,1674)(1350,1560)(1353,1684)(1357,1690)
     (1360,1688)(1362,1679)(1364,1695)(1368,1699)(1369,1701)(1371,1703)(1373,
     1696)(1376,1710)(1378,1709)(1380,1714)(1384,1438)(1385,1719)(1386,1389)
     (1388,1443)(1396,1726)(1397,1730)(1399,1734)(1401,1604)(1404,1574)(1406,
     1740)(1407,1563)(1408,1742)(1412,1747)(1416,1520)(1417,1749)(1420,1657)
     (1422,1755)(1424,1620)(1426,1759)(1428,1689)(1429,1570)(1430,1762)(1432,
     1764)(1433,1704)(1434,1766)(1437,1769)(1441,1772)(1444,1767)(1445,1776)
     (1446,1778)(1447,1686)(1454,1785)(1456,1788)(1457,1514)(1459,1791)(1461,
     1680)(1465,1797)(1468,1801)(1471,1805)(1473,1806)(1475,1809)(1476,1720)
     (1477,1567)(1478,1572)(1481,1814)(1483,1752)(1485,1816)(1487,1817)(1489,
     1819)(1490,1821)(1494,1827)(1495,1707)(1498,1828)(1499,1829)(1500,1830)
     (1502,1832)(1505,1838)(1507,1831)(1508,1517)(1518,1847)(1522,1849)(1523,
     1846)(1524,1850)(1525,1851)(1528,1852)(1529,1853)(1530,1854)(1537,1859)
     (1541,1862)(1542,1837)(1545,1659)(1547,1864)(1548,1865)(1551,1869)(1552,
     1870)(1553,1871)(1555,1872)(1556,1873)(1559,1876)(1565,1882)(1566,1883)
     (1568,1624)(1569,1880)(1576,1790)(1579,1894)(1580,1597)(1583,1900)(1588,
     1779)(1590,1905)(1591,1786)(1594,1908)(1596,1629)(1598,1912)(1603,1918)
     (1612,1917)(1613,1926)(1619,1934)(1621,1903)(1622,1833)(1625,1936)(1626,
     1937)(1633,1944)(1634,1945)(1636,1799)(1638,1947)(1639,1700)(1641,1753)
     (1642,1694)(1644,1950)(1646,1952)(1649,1955)(1650,1956)(1653,1959)(1660,
     1951)(1662,1861)(1667,1968)(1671,1928)(1672,1972)(1673,1973)(1677,1977)
     (1681,1813)(1682,1733)(1683,1978)(1692,1984)(1693,1985)(1697,1746)(1702,
     1990)(1708,1960)(1711,1995)(1712,1996)(1715,1997)(1717,1965)(1718,2000)
     (1721,2001)(1722,2002)(1723,2003)(1724,2004)(1725,1736)(1727,1913)(1729,
     2007)(1731,2008)(1732,2009)(1741,1789)(1743,2018)(1744,2019)(1745,2020)
     (1748,2023)(1751,2026)(1754,1961)(1757,2030)(1760,2031)(1761,2032)(1763,
     2034)(1765,2035)(1768,1974)(1770,2039)(1771,1836)(1774,1962)(1777,2042)
     (1780,1971)(1781,2044)(1782,2045)(1783,1975)(1784,1941)(1787,2048)(1792,
     2052)(1793,2053)(1794,1843)(1795,2016)(1796,2054)(1798,2041)(1800,1842)
     (1803,2058)(1804,2051)(1807,2062)(1811,2067)(1812,2068)(1815,2070)(1818,
     2073)(1820,1897)(1822,2075)(1825,2076)(1826,2077)(1834,2081)(1835,1949)
     (1840,2086)(1841,1907)(1844,2089)(1845,2090)(1855,1993)(1856,1946)(1857,
     1957)(1858,1998)(1863,2083)(1866,2109)(1867,2110)(1868,1904)(1875,2119)
     (1885,2124)(1886,2125)(1887,2126)(1888,2128)(1889,2118)(1891,2131)(1893,
     1987)(1896,1916)(1898,1911)(1901,2136)(1902,2137)(1906,2115)(1914,2141)
     (1915,1958)(1919,2025)(1920,2145)(1921,2146)(1922,2140)(1923,1938)(1924,
     2147)(1930,2043)(1931,2151)(1932,2152)(1933,2013)(1939,2156)(1940,2157)
     (1942,2159)(1948,2162)(1963,2024)(1969,2091)(1970,2102)(1976,2161)(1980,
     2121)(1981,2172)(1982,2173)(1983,2036)(1986,2178)(1991,2179)(1992,2180)
     (1994,2181)(1999,2183)(2006,2189)(2011,2047)(2012,2022)(2015,2117)(2027,
     2072)(2033,2143)(2037,2202)(2038,2196)(2040,2203)(2046,2204)(2049,2208)
     (2055,2213)(2059,2209)(2061,2211)(2063,2216)(2064,2217)(2071,2129)(2078,
     2223)(2079,2224)(2080,2085)(2084,2227)(2088,2094)(2100,2160)(2101,2236)
     (2104,2238)(2105,2171)(2111,2212)(2112,2241)(2113,2201)(2114,2222)(2120,
     2170)(2123,2243)(2130,2205)(2132,2176)(2134,2221)(2139,2247)(2142,2182)
     (2148,2251)(2149,2235)(2150,2252)(2153,2169)(2164,2177)(2165,2185)(2166,
     2184)(2168,2215)(2174,2199)(2186,2262)(2188,2265)(2193,2249)(2195,2240)
     (2206,2273)(2207,2272)(2214,2275)(2218,2231)(2220,2234)(2226,2229)(2232,
     2253)(2239,2259)(2245,2276)(2266,2287)(2267,2288)(2274,2279)(2278,2282)
     (2283,2291)(2284,2292)(2285,2290)(2286,2289);