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