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