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