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