[[0,1,2,4,5,13,14,19,22,24,25,26,27,28,29,30,31,33,34,35,36,44,46,47,48,49,50,51,52,55,56,59,61,62,63,64,67,77,80,81,85,86,88,89,91,92,93,106,108,109,110,112,114,115,116,118,119,120,121,122,123,124,125,140,144,145,159,161,190,191,192,193,194,210,213,214,216,221,224,225,226,227,228,229,242,247,249,250,253,255,258,260,280,288,289,299,302,303,316,331,339,340,344,345,358,366,390,391,392,393,394,395,396,397,398,399,400,401,402,404,405,408,410,412,413,416,417,418,444,445,446,447,448,449,450,451,452,453,467,469,470,473,474,476,477,478,480,482,496,497,500,507,512,514,515,516,517,518,519,522,523,536,538,539,540,541,549,551,552,553,555,557,558,559,562,564,565,586,588,589,590,591,594,600,601,602,604,605,607,622,623,625,630,633,647,652,656,662,664,665,666,669,670,671,684,691,695,696,697,698,699,701,702,703,704,705,706,708,709,713,714,718,719,720,730,733,734,735,736,737,739,740,742,743,744,745,747,758,759,762,763,765,766,822,830,831,832,833,835,836,837,838,845,846,847,848,849,852,853,854,855,856,857,858,859,862,866,867,868,869,871,872,873,880,882,884,886,888,889,890,891,892,893,894,895,897,898,899,900,901,904,911,912,913,915,916,920,922,923,924,925,926,928,929,930,931,932,934,935,936,937,945,948,949,950,951,952,953,954,955,956,962,964,965,966,967,968,970,971,973,974,975,976,990,992,995,1001,1003,1006,1008,1010,1012,1017,1029,1036,1039,1062,1064,1066,1069,1070,1080,1081,1084,1093,1097,1098,1100,1102,1103,1104,1105,1117,1119,1122,1126,1131,1133,1134,1136,1137,1142,1143,1151,1155,1161,1164,1165,1166,1168,1169,1171,1184,1185,1190,1193,1195,1205,1209,1210,1211,1212,1230,1235,1236,1239,1248,1249,1250,1251,1254,1255,1259,1269,1270,1273,1286,1287,1290,1291,1293,1295,1296,1297,1309,1313,1314,1318,1322,1324,1325,1326,1327,1329,1330,1331,1345,1346,1352,1356,1358,1367,1368,1378,1379,1381,1382,1383,1394,1396,1398,1399,1402,1405,1406,1407,1414,1422,1423,1434,1460,1461,1462,1463,1465,1466,1468,1473,1481,1482,1483,1484,1485,1513,1516,1517,1519,1520,1521,1522,1523,1528,1529,1530,1531,1532,1534,1536,1537,1567,1594,1617,1619,1624,1646,1650,1651,1656,1657,1658,1659,1660,1661,1662,1663,1664,1665,1667,1675,1678,1679,1681,1682,1683,1684,1687,1688,1689,1690,1691,1692,1693,1697,1698,1699,1700,1702,1707,1712,1715,1717,1720,1747,1749,1750,1751,1752,1764,1765,1769,1770,1772,1773,1774,1775,1778,1779,1786,1788,1789,1793,1794,1797,1798,1799,1800,1804,1821,1839,1864,1865,1866,1867,1869,1870,1871,1877,1881,1884,1885,1886,1892,1893,1894,1895,1896,1897,1904,1907,1908,1909,1914,1915,1917,1918,1919,1920,1921,1923,1931,1932,1933,1934,1935,1938,1940,1942,1943,1944,1945,1947,1948,1951,1963,1969,1970,1971,1972,1974,1982,1983,1986,1987,1990,1992,1993,2028,2029,2030,2036,2037,2040,2046],[6,7,8,12,15,16,17,20,21,32,38,39,42,43,53,54,57,60,66,69,71,74,75,76,78,79,84,94,95,96,97,98,99,102,103,105,107,111,117,133,135,138,139,141,142,143,146,148,150,151,153,154,157,158,160,163,165,166,167,168,169,170,175,177,185,186,187,188,189,195,198,199,202,203,204,205,206,231,232,234,241,244,245,246,248,251,252,254,256,261,262,263,264,265,268,269,270,271,272,277,278,279,282,291,292,293,294,295,297,298,300,301,304,317,318,319,320,324,334,336,342,346,351,353,357,360,361,363,365,368,369,370,372,374,375,377,381,385,388,389,403,406,419,420,421,422,425,428,429,430,431,432,434,435,436,437,438,440,441,442,443,454,456,457,458,459,460,461,472,479,483,485,487,488,491,494,498,499,501,504,506,508,510,513,521,526,528,529,531,532,533,535,537,543,545,546,547,548,556,560,561,563,567,573,574,579,580,584,585,592,593,595,596,597,599,603,612,615,618,619,626,627,629,631,632,634,635,636,643,646,667,668,672,673,674,675,679,692,693,694,700,710,721,722,725,726,732,741,746,748,749,752,753,754,755,757,767,768,770,771,773,774,775,777,788,791,792,796,799,801,802,803,806,807,809,811,817,820,824,829,839,840,841,843,844,860,861,870,874,876,883,887,902,903,905,907,908,910,917,918,921,933,938,939,940,941,942,943,947,957,958,959,960,961,963,969,972,978,980,981,982,983,984,985,986,987,988,991,993,996,997,1002,1009,1011,1013,1014,1015,1016,1018,1019,1020,1021,1023,1026,1028,1030,1031,1032,1035,1038,1044,1045,1046,1048,1063,1065,1068,1072,1074,1076,1082,1085,1086,1087,1088,1090,1092,1094,1095,1099,1101,1106,1107,1108,1113,1115,1123,1125,1128,1129,1130,1132,1139,1140,1141,1144,1148,1153,1158,1160,1163,1170,1172,1175,1176,1178,1179,1181,1182,1183,1187,1188,1191,1192,1196,1197,1198,1200,1203,1204,1206,1207,1208,1214,1216,1219,1222,1226,1229,1231,1232,1234,1241,1242,1244,1245,1252,1253,1256,1258,1260,1262,1263,1264,1265,1267,1275,1276,1277,1279,1281,1282,1283,1288,1300,1301,1302,1303,1305,1306,1308,1312,1315,1328,1332,1334,1336,1337,1338,1341,1343,1347,1351,1353,1359,1360,1366,1370,1372,1373,1374,1375,1380,1384,1386,1392,1395,1400,1401,1403,1404,1408,1409,1410,1411,1412,1413,1415,1417,1419,1420,1421,1424,1425,1426,1427,1428,1431,1438,1439,1441,1447,1448,1450,1452,1456,1464,1467,1469,1470,1471,1474,1477,1480,1486,1487,1488,1489,1490,1491,1493,1495,1497,1498,1499,1501,1503,1506,1508,1509,1510,1524,1525,1527,1533,1539,1540,1541,1544,1547,1549,1556,1563,1565,1566,1568,1569,1601,1605,1608,1610,1613,1616,1621,1622,1623,1626,1627,1628,1630,1632,1634,1637,1638,1639,1641,1642,1643,1645,1647,1653,1655,1666,1668,1669,1670,1672,1673,1674,1676,1680,1685,1686,1694,1695,1696,1701,1703,1704,1705,1709,1710,1711,1713,1718,1719,1721,1722,1723,1727,1730,1731,1732,1733,1734,1736,1737,1739,1741,1743,1744,1746,1748,1755,1761,1763,1767,1776,1780,1782,1785,1790,1792,1796,1802,1806,1807,1808,1809,1811,1814,1815,1819,1820,1822,1826,1827,1828,1833,1834,1837,1838,1840,1847,1850,1852,1855,1856,1862,1868,1872,1873,1874,1875,1876,1879,1887,1888,1889,1890,1891,1898,1899,1900,1901,1903,1905,1910,1912,1913,1922,1924,1926,1927,1929,1936,1937,1939,1941,1950,1954,1956,1964,1967,1968,1973,1975,1976,1978,1984,1985,1988,1995,1998,2001,2013,2015,2019,2025,2026,2027,2031,2032,2033,2034,2035,2038,2039,2043],[3,10,11,18,23,37,40,45,58,65,68,73,101,113,126,127,128,130,131,136,137,147,149,152,155,156,162,164,171,172,174,176,178,182,184,207,208,209,211,212,215,217,218,219,220,223,230,233,235,236,237,239,240,257,259,266,267,283,284,285,287,290,296,305,306,307,308,309,310,311,312,313,314,315,321,322,323,335,343,354,362,364,367,371,373,380,382,384,387,423,424,426,427,433,439,455,466,481,484,486,492,493,495,502,503,505,509,511,525,527,530,534,550,554,569,571,572,575,578,581,582,583,587,606,610,614,616,617,620,624,628,649,653,655,657,658,659,663,676,677,678,680,681,682,683,686,687,688,689,690,723,724,727,728,729,731,738,750,751,772,776,778,779,783,784,785,787,790,797,800,804,812,814,815,823,825,826,827,834,850,851,863,864,865,875,877,885,896,906,909,914,919,927,944,946,977,979,989,994,998,999,1000,1004,1005,1022,1024,1025,1027,1033,1037,1047,1067,1073,1075,1077,1079,1083,1089,1091,1109,1110,1111,1112,1114,1118,1120,1124,1127,1135,1138,1146,1150,1157,1167,1177,1180,1186,1189,1201,1202,1215,1217,1218,1220,1221,1225,1227,1233,1237,1238,1240,1246,1247,1257,1266,1268,1271,1272,1274,1278,1284,1285,1289,1292,1294,1299,1304,1307,1319,1320,1323,1333,1335,1340,1342,1348,1349,1350,1354,1357,1362,1363,1365,1376,1377,1387,1388,1389,1393,1397,1418,1429,1430,1432,1435,1436,1440,1444,1445,1446,1453,1457,1459,1475,1492,1496,1500,1507,1514,1518,1535,1538,1542,1543,1548,1551,1552,1558,1562,1564,1570,1571,1575,1576,1577,1579,1580,1581,1583,1584,1588,1591,1592,1593,1597,1612,1614,1618,1620,1625,1629,1633,1635,1640,1644,1648,1652,1671,1677,1706,1708,1714,1716,1724,1728,1729,1735,1742,1753,1754,1756,1757,1758,1760,1762,1768,1777,1781,1783,1784,1787,1791,1795,1801,1803,1805,1810,1812,1816,1817,1818,1823,1824,1825,1830,1831,1835,1836,1842,1844,1848,1849,1854,1857,1858,1859,1860,1863,1925,1928,1930,1946,1949,1955,1965,1977,1979,1980,1981,1989,1991,1994,1996,1999,2002,2003,2004,2005,2006,2009,2011,2012,2017,2020,2021,2022,2024,2041,2044,2045,2047],[9,41,70,72,83,90,100,104,129,132,134,179,181,197,200,222,243,274,276,281,286,376,378,383,386,407,489,490,520,524,544,566,568,576,577,598,609,611,613,637,638,639,640,641,642,644,645,650,660,685,781,782,786,789,794,795,805,808,810,813,816,842,879,881,1007,1034,1078,1096,1116,1121,1145,1147,1149,1152,1154,1159,1173,1174,1194,1199,1213,1223,1224,1228,1243,1261,1280,1310,1311,1316,1317,1321,1339,1364,1369,1371,1385,1391,1416,1433,1437,1451,1455,1472,1479,1494,1505,1511,1512,1515,1545,1546,1550,1554,1555,1557,1559,1560,1561,1572,1573,1574,1582,1585,1586,1587,1589,1590,1595,1596,1598,1599,1600,1602,1603,1604,1607,1609,1615,1631,1649,1654,1725,1726,1738,1740,1745,1759,1766,1813,1829,1832,1841,1843,1845,1846,1851,1853,1902,1906,1911,1916,1952,1953,1959,1960,1997,2000,2007,2008,2010,2016,2018,2023,2042],[82,87,173,180,183,196,201,238,273,332,347,379,542,608,621,648,661,793,798,878,1156,1162,1298,1344,1355,1390,1476,1478,1502,1504,1526,1553,1578,1606,1611,1636,1771,1957,1961,1962,1966,2014],[275,414,475,570,651,654,780,818,819,821,828,1040,1041,1043,1049,1050,1052,1054,1056,1061,1071,1361,1861,1958],[325,326,327,329,337,338,341,350,356,409,415,462,463,464,471,707,712,716,717,761,1042,1060,1442,1880,1882,1883],[328,330,333,348,349,352,355,359,411,465,711,715,756,760,769,1878],[468,764,1058,1059,1449,1454],[1053,1057,1443,1458],[1051,1055]]