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