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