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