bin1 := (1,2,5,7,3)(4,8,15,17,9)(6,11,19,21,12)(13,22,35,36,23)(14,24,38,39,25)
     (16,27,42,44,28)(18,29,46,47,30)(20,32,51,53,33)(26,40,63,65,41)(31,48,
     74,76,49)(34,54,83,84,55)(37,58,90,92,59)(43,67,105,106,68)(45,70,110,
     112,71)(50,77,121,122,78)(52,80,125,127,81)(56,85,133,134,86)(57,87,136,
     138,88)(60,93,146,148,94)(61,95,150,152,96)(62,97,153,154,98)(64,100,157,
     159,101)(66,103,163,165,104)(69,107,167,169,108)(72,113,177,179,114)(73,
     115,181,182,116)(75,118,185,187,119)(79,123,193,195,124)(82,128,201,203,
     129)(89,139,218,220,140)(91,142,223,225,143)(99,155,239,240,156)(102,160,
     246,247,161)(109,170,230,147,171)(111,173,262,264,174)(117,183,278,280,
     184)(120,188,285,287,189)(126,197,299,300,198)(130,204,309,311,205)(131,
     206,313,315,207)(132,208,317,319,209)(135,211,322,323,212)(137,214,327,
     329,215)(141,221,338,340,222)(144,226,345,347,227)(145,228,349,351,229)
     (149,232,356,357,233)(151,235,361,363,236)(158,242,371,373,243)(162,248,
     381,383,249)(164,251,386,342,224)(166,253,389,391,254)(168,256,395,397,
     257)(172,260,316,401,261)(175,265,406,407,266)(176,267,199,301,268)(178,
     270,372,412,271)(180,273,416,418,274)(186,282,429,431,283)(190,288,438,
     439,289)(191,290,441,442,291)(192,292,444,446,293)(194,294,447,449,295)
     (196,296,451,452,297)(200,302,458,459,303)(202,305,463,464,306)(210,320,
     481,483,321)(213,324,486,487,325)(216,330,493,494,331)(217,332,495,497,
     333)(219,259,400,501,335)(231,353,525,527,354)(234,358,530,532,359)(237,
     364,538,540,365)(238,366,542,544,367)(241,369,548,550,370)(244,374,553,
     555,375)(245,376,557,558,377)(250,384,568,570,385)(252,344,513,573,387)
     (255,392,579,581,393)(258,398,549,588,399)(263,390,576,593,403)(269,409,
     419,275,410)(272,413,606,608,414)(276,339,507,616,420)(277,421,618,619,
     422)(279,424,622,624,425)(281,427,628,630,428)(284,432,635,637,433)(286,
     435,640,641,436)(298,453,659,660,454)(304,460,666,668,461)(307,465,671,
     672,466)(308,467,404,594,468)(310,469,674,676,470)(312,472,679,680,473)
     (314,475,684,686,476)(318,326,488,691,479)(328,489,703,704,490)(334,498,
     715,716,499)(336,502,721,722,503)(337,504,724,726,505)(341,508,729,731,
     509)(343,511,382,394,512)(346,515,737,739,516)(348,517,741,742,518)(350,
     360,533,746,520)(352,522,750,752,523)(355,528,758,645,440)(362,535,767,
     769,536)(368,545,612,417,546)(378,559,793,700,560)(379,561,796,798,562)
     (380,563,800,802,564)(388,574,510,482,575)(396,583,823,825,584)(402,590,
     833,834,591)(405,595,839,815,577)(408,598,597,842,599)(411,602,850,851,
     603)(415,609,859,861,610)(423,620,874,875,621)(426,625,880,882,626)(430,
     631,890,891,632)(434,638,900,901,639)(437,642,902,903,643)(443,648,777,
     910,649)(445,462,669,913,651)(448,654,918,920,655)(450,656,922,924,657)
     (456,661,929,863,662)(457,663,931,933,664)(471,677,778,543,678)(474,681,
     948,949,682)(477,687,955,894,634)(478,688,957,959,689)(480,692,963,964,
     693)(484,695,966,873,696)(485,697,969,971,698)(491,705,978,980,706)(492,
     707,981,982,708)(496,712,989,991,713)(500,717,996,997,718)(506,727,1010,
     1012,728)(514,734,1019,1021,735)(519,743,1029,1031,744)(521,747,1034,
     1036,748)(524,753,1044,1045,754)(526,755,1046,1048,756)(529,759,1051,
     1053,760)(531,646,906,1056,762)(534,765,1061,1063,766)(537,770,1068,1069,
     771)(539,772,1070,1071,773)(541,775,1075,898,776)(547,694,732,1015,781)
     (551,783,1082,1084,784)(552,572,813,1085,785)(554,786,1086,1087,787)(556,
     789,945,1055,790)(565,803,1108,1110,804)(566,805,1112,1113,806)(567,807,
     1115,1117,808)(569,809,1118,1120,810)(571,811,1122,1124,812)(578,816,
     1129,1131,817)(580,818,1132,1133,819)(582,820,1099,795,821)(585,826,1141,
     862,611)(586,827,1143,1144,828)(587,829,1146,1147,830)(589,832,1007,725,
     736)(592,835,1153,1155,836)(596,840,1008,1160,841)(600,845,1165,1167,846)
     (601,847,1168,1170,848)(604,852,1174,1175,853)(605,854,1176,1177,855)
     (607,856,1126,814,857)(613,864,1187,1189,865)(614,866,1190,1152,867)(615,
     868,1192,1193,869)(617,870,1194,1195,871)(623,876,1199,1200,877)(627,883,
     1207,1209,884)(629,886,934,665,887)(633,892,1217,1219,893)(636,896,994,
     1218,897)(644,904,1228,1230,905)(647,907,1232,1233,908)(650,911,1238,
     1240,912)(652,914,1081,782,915)(653,916,1140,1243,917)(658,925,1249,1250,
     926)(667,936,1262,1264,937)(670,939,1266,1267,940)(673,683,950,1269,941)
     (675,942,1271,1273,943)(685,952,1281,1283,953)(690,960,1291,1293,961)
     (699,738,1023,1307,972)(701,973,1309,1311,974)(702,975,1312,1313,976)
     (709,983,1320,1321,984)(710,985,1251,927,986)(711,987,1324,1003,988)(714,
     992,1329,1330,993)(719,998,1334,1335,999)(720,1000,1337,1338,1001)(723,
     1004,1342,1344,1005)(730,831,1148,1351,1013)(733,1016,1057,763,1017)(740,
     1024,1364,1366,1025)(745,1032,1376,1049,757)(749,1037,1383,1062,1038)
     (751,1040,1060,1386,1041)(761,1054,1399,1196,872)(764,1058,1400,1401,
     1059)(768,1064,1404,1406,1065)(774,1072,1412,1414,1073)(779,1077,838,
     1158,1078)(780,1079,1208,1222,1080)(788,1088,1422,1424,1089)(791,1092,
     1429,1430,1093)(792,1094,938,1265,1095)(794,1097,1433,1434,1098)(797,
     1101,1257,932,1102)(799,1047,1333,1437,1103)(801,1105,1440,1441,1106)
     (822,1135,1470,1471,1136)(824,1137,1473,1475,1138)(837,1156,1215,889,
     1157)(843,1162,1498,1229,923)(844,1163,1499,1500,1164)(849,1171,1505,
     1506,1172)(858,1180,1515,1517,1181)(860,1183,1520,1522,1184)(878,946,
     1276,951,1201)(879,1202,1380,1035,1203)(881,1204,1537,1538,1205)(885,
     1210,1319,1541,1211)(888,1213,1545,1546,1214)(895,1220,1450,1114,1221)
     (899,1223,1551,1359,1224)(909,1234,1563,1565,1235)(919,1244,1574,1576,
     1245)(921,1246,1413,1578,1247)(928,1252,1583,1585,1253)(930,1254,1435,
     1100,1255)(935,1260,1594,1596,1261)(944,1274,1607,1608,1275)(947,1277,
     1610,1611,1278)(954,1284,1619,1620,1285)(956,1287,1584,1624,1288)(958,
     1022,1362,1625,1289)(962,1294,1629,1631,1295)(965,1298,1634,1636,1299)
     (967,1301,1638,1639,1302)(968,1303,1641,1461,1127)(970,1305,1539,1409,
     1067)(977,1314,1649,1328,1315)(979,1317,1652,1653,1318)(990,1325,1659,
     1660,1326)(995,1074,1116,1125,1331)(1002,1339,1671,1672,1340)(1006,1345,
     1415,1677,1346)(1009,1347,1679,1680,1348)(1011,1349,1681,1682,1350)(1014,
     1352,1683,1685,1353)(1018,1357,1691,1692,1358)(1020,1360,1693,1694,1361)
     (1026,1367,1698,1700,1368)(1027,1369,1702,1511,1370)(1028,1363,1491,1704,
     1371)(1030,1373,1706,1707,1374)(1033,1377,1711,1712,1378)(1039,1384,1718,
     1720,1385)(1042,1387,1721,1722,1388)(1043,1389,1723,1724,1390)(1050,1341,
     1673,1728,1394)(1052,1396,1729,1731,1397)(1066,1407,1741,1743,1408)(1076,
     1416,1748,1654,1417)(1083,1419,1752,1753,1420)(1090,1425,1758,1760,1426)
     (1091,1427,1761,1714,1428)(1096,1290,1534,1765,1432)(1104,1438,1770,1771,
     1439)(1107,1442,1773,1774,1443)(1109,1444,1775,1777,1445)(1111,1446,1779,
     1780,1447)(1119,1453,1587,1786,1454)(1121,1456,1789,1790,1457)(1123,1458,
     1644,1306,1459)(1128,1462,1794,1795,1463)(1130,1145,1481,1798,1465)(1134,
     1468,1802,1527,1188)(1139,1476,1810,1811,1477)(1142,1382,1717,1812,1478)
     (1149,1483,1815,1593,1484)(1150,1485,1558,1782,1449)(1151,1486,1379,1713,
     1487)(1154,1489,1820,1822,1490)(1159,1494,1800,1467,1495)(1161,1496,1678,
     1623,1497)(1166,1178,1512,1392,1272)(1169,1191,1528,1833,1502)(1173,1507,
     1839,1840,1508)(1179,1513,1844,1845,1514)(1182,1518,1686,1354,1519)(1185,
     1523,1755,1482,1524)(1186,1525,1657,1323,1526)(1197,1529,1451,1783,1530)
     (1198,1531,1855,1703,1532)(1206,1480,1813,1841,1509)(1212,1542,1516,1846,
     1543)(1216,1547,1633,1297,1548)(1225,1552,1304,1642,1553)(1226,1554,1763,
     1431,1555)(1227,1556,1874,1875,1557)(1231,1559,1877,1601,1560)(1236,1566,
     1884,1885,1567)(1237,1568,1886,1784,1452)(1239,1569,1687,1355,1570)(1241,
     1455,1787,1888,1572)(1242,1472,1725,1391,1310)(1248,1579,1895,1896,1580)
     (1256,1411,1746,1903,1588)(1258,1589,1904,1906,1590)(1259,1591,1907,1828,
     1592)(1263,1597,1911,1827,1598)(1268,1603,1919,1920,1604)(1270,1605,1921,
     1922,1606)(1279,1612,1925,1927,1613)(1280,1448,1781,1928,1614)(1282,1616,
     1931,1932,1617)(1286,1621,1665,1935,1622)(1292,1562,1879,1938,1626)(1296,
     1632,1943,1719,1479)(1300,1536,1858,1946,1637)(1308,1646,1953,1667,1336)
     (1316,1650,1957,1958,1651)(1322,1655,1533,1648,1656)(1327,1661,1961,1962,
     1662)(1332,1664,1965,1739,1405)(1343,1674,1974,1866,1549)(1356,1688,1980,
     1981,1689)(1365,1696,1734,1987,1697)(1372,1705,1991,1988,1699)(1375,1708,
     1992,1993,1709)(1381,1715,1998,1999,1716)(1393,1726,2005,2006,1727)(1395,
     1602,1917,1976,1676)(1398,1732,2010,2011,1733)(1402,1735,2012,2013,1736)
     (1403,1737,1488,1818,1738)(1410,1744,1945,2021,1745)(1418,1750,2025,2027,
     1751)(1421,1754,2028,1831,1501)(1423,1756,2029,1764,1757)(1436,1767,2037,
     1805,1768)(1460,1792,1618,1933,1793)(1464,1521,1848,1956,1796)(1466,1647,
     1954,2056,1799)(1469,1803,2042,2059,1804)(1474,1807,2063,2064,1808)(1492,
     1823,2033,1762,1824)(1493,1825,2070,1872,1826)(1503,1834,1891,1575,1835)
     (1504,1836,2082,2083,1837)(1510,1842,2087,2088,1843)(1535,1856,1959,2100,
     1857)(1540,1860,1749,2024,1861)(1544,1710,1994,2104,1863)(1550,1867,2111,
     2112,1868)(1561,1628,1941,2120,1878)(1564,1880,2067,2121,1881)(1571,1887,
     2127,1951,1645)(1573,1889,2129,2130,1890)(1577,1892,2132,2133,1893)(1581,
     1829,2078,2135,1897)(1582,1898,1675,1975,1899)(1586,1901,1747,2022,1902)
     (1595,1909,2041,1776,1910)(1599,1913,2140,2142,1914)(1600,1915,2143,2126,
     1916)(1609,1923,2138,1908,1924)(1615,1929,2150,2128,1930)(1627,1939,1947,
     2158,1940)(1630,1668,1969,1876,1942)(1635,1643,1949,1670,1849)(1640,1948,
     2163,1989,1701)(1658,1960,1869,2113,1955)(1663,1963,2166,2086,1964)(1666,
     1966,2167,2168,1967)(1669,1970,2169,2137,1971)(1684,1979,2159,2057,1801)
     (1690,1982,2174,2175,1983)(1695,1819,2074,1973,1986)(1740,2014,2058,2194,
     2015)(1742,2016,2195,2196,2017)(1759,1853,2097,2172,1997)(1766,2036,2201,
     2182,1996)(1769,2038,2151,2043,1778)(1772,2040,2188,2004,1968)(1785,2046,
     2157,2205,2047)(1788,2049,1817,2026,2050)(1791,2051,2076,2162,2020)(1797,
     1952,2165,2039,2055)(1806,2060,2214,2215,2061)(1809,2065,2131,2218,2066)
     (1814,2069,2045,2153,1934)(1816,2071,2146,2181,2072)(1821,2032,2183,2119,
     1995)(1830,2079,2001,2000,2062)(1832,2080,2213,2209,2052)(1838,2084,2228,
     2229,2085)(1847,2091,2035,2200,2092)(1850,2093,1883,1900,2094)(1851,1936,
     2154,2212,2054)(1852,2095,2232,2233,2096)(1854,2098,2234,2235,2099)(1859,
     2101,2237,2199,2031)(1862,2102,2044,2023,2103)(1864,2105,1950,2164,2106)
     (1865,2107,2239,2110,2108)(1870,1990,1912,2139,2114)(1871,2115,2156,2242,
     2116)(1873,2117,2018,2197,2118)(1882,2122,2090,2231,2123)(1894,2089,2230,
     2245,2134)(1905,2019,2198,2155,1937)(1918,2144,2249,2222,2077)(1926,2148,
     2145,2250,2149)(1944,2160,2241,2254,2161)(1972,2170,1978,2034,2030)(1977,
     2171,2255,2240,2109)(1984,2124,1985,2177,2176)(2002,2184,2260,2261,2185)
     (2003,2186,2263,2264,2187)(2007,2190,2173,2256,2191)(2008,2009,2193,2267,
     2192)(2048,2206,2274,2216,2207)(2053,2210,2136,2246,2211)(2068,2152,2253,
     2275,2219)(2073,2220,2277,2257,2178)(2075,2141,2248,2278,2221)(2081,2225,
     2279,2223,2226)(2125,2147,2251,2238,2244)(2179,2252,2285,2276,2217)(2180,
     2258,2236,2283,2259)(2189,2247,2284,2288,2266)(2202,2268,2243,2208,2269)
     (2203,2262,2286,2273,2270)(2204,2271,2227,2282,2272)(2224,2280,2289,2290,
     2281)(2287,2293,2295,2291,2294);