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