[{"0":0,"2":2,"3":3,"4":4,"7":7,"8":8,"10":12,"11":13,"12":14,"13":16,"14":18,"15":19,"16":20,"17":22,"18":24,"19":25,"20":27,"21":28,"22":29,"23":30,"24":31,"25":32,"26":33,"27":34,"28":35,"29":36,"30":37,"32":41,"33":42,"34":44,"35":45,"36":48,"37":49,"38":50,"39":51,"42":54,"43":56,"44":57,"45":58,"46":59,"47":61,"48":62,"49":63,"51":66,"52":67,"53":69,"54":71,"56":73,"57":74,"59":76,"60":77,"61":78,"62":80,"63":81,"64":82,"65":83,"67":85,"68":86,"70":89,"71":91,"72":92,"73":94,"74":95,"75":96,"76":97,"77":98,"78":101,"79":103,"80":104,"81":106,"82":107,"83":109,"84":110,"85":111,"86":112,"87":113,"88":115,"89":116,"90":117,"91":118,"92":119,"93":120,"94":121,"95":122,"96":123,"97":124,"98":126,"99":128,"100":130,"101":131,"103":133,"104":134,"105":135,"106":137,"107":138,"108":139,"109":140,"110":142,"111":143,"112":144,"114":146,"115":148,"116":149,"117":150,"118":151,"119":153,"120":154,"121":155,"123":157,"124":158,"125":159,"126":160,"127":161,"128":162,"129":163,"131":166,"132":167,"133":168,"134":169,"135":170,"136":172,"137":173,"138":174,"139":175,"140":177,"141":179,"142":181,"143":182,"145":184,"146":185,"147":186,"149":189,"150":190,"151":191,"152":192,"153":193,"154":194,"155":195,"156":196,"157":197,"158":200,"159":201,"160":202,"161":204,"162":207,"164":209,"165":210,"166":211,"167":212,"169":214,"170":215,"171":216,"172":217,"173":218,"174":219,"175":220,"176":221,"177":222,"178":223,"179":224,"180":225,"181":226,"182":228,"184":231,"185":232,"186":233,"187":234,"189":236,"190":237,"192":239,"193":240,"194":241,"195":243,"196":245,"197":246,"198":247,"199":248,"200":250,"201":251,"202":252,"203":253,"204":254,"205":255,"206":256,"208":258,"209":259,"210":260,"212":262,"213":263,"214":264,"215":266,"216":267,"217":268,"218":272,"219":273,"220":274,"221":275,"222":276,"223":277,"224":279,"225":280,"226":281,"227":282,"228":283,"229":284,"230":286,"231":287,"232":288,"233":290,"234":291,"235":292,"236":293,"237":294,"238":295,"239":297,"240":298,"241":299,"242":301,"243":302,"244":306,"245":307,"246":309,"247":310,"248":311,"249":312,"250":313,"251":314,"252":315,"253":316,"254":317,"255":318,"256":319,"257":320,"258":321,"259":322,"260":323,"261":325,"262":327,"263":328,"264":329,"265":330,"266":331,"267":332,"268":333,"269":334,"270":336,"271":337,"272":338,"273":513,"275":515,"276":516,"278":518,"279":520,"280":521,"281":524,"282":525,"284":527,"285":528,"286":529,"287":530,"288":531,"289":532,"290":533,"291":534,"292":535,"294":537,"295":538,"296":539,"298":541,"299":542,"301":544,"302":545,"304":547,"305":549,"306":550,"307":551,"308":552,"309":553,"310":555,"311":556,"312":557,"313":558,"314":559,"315":560,"316":561,"317":562,"318":563,"320":566,"321":567,"322":569,"323":571,"324":572,"325":574,"326":575,"327":576,"329":578,"330":579,"331":580,"332":581,"333":582,"334":583,"335":584,"337":586,"338":587,"339":588,"340":590,"341":591,"342":592,"344":594,"345":596,"347":598,"348":599,"349":600,"350":601,"351":603,"352":604,"353":606,"354":607,"355":609,"356":610,"357":611,"358":612,"359":613,"360":614,"361":615,"362":617,"363":618,"364":619,"366":621,"368":623,"369":624,"370":625,"371":626,"372":627,"373":628,"374":629,"375":631,"376":632,"377":633,"378":635,"379":636,"380":637,"381":638,"382":639,"383":640,"384":641,"385":642,"386":643,"387":644,"388":647,"389":649,"390":650,"391":652,"392":653,"394":655,"395":656,"396":657,"397":658,"398":659,"399":660,"401":662,"402":663,"403":667,"404":668,"405":669,"406":670,"407":671,"408":672,"410":674,"411":675,"413":677,"414":678,"415":679,"416":680,"417":681,"418":682,"419":685,"420":686,"421":692,"422":693,"423":695,"425":698,"426":699,"427":700,"428":701,"429":702,"430":703,"432":705,"433":706,"435":710,"436":711,"437":712,"438":713,"439":714,"440":716,"441":717,"442":718,"443":719,"445":721,"446":722,"447":723,"448":724,"450":726,"451":727,"452":728,"453":729,"454":730,"455":731,"456":732,"457":733,"458":734,"459":735,"461":739,"462":740,"463":741,"464":742,"465":743,"466":744,"467":745,"468":749,"470":751,"471":753,"473":757,"474":758,"475":759,"476":760,"477":762,"478":763,"479":764,"481":766,"482":767,"483":768,"484":769,"485":770,"486":771,"487":772,"488":776,"489":777,"490":778,"491":779,"492":780,"493":781,"494":782,"495":783,"496":784,"497":785,"498":786,"499":787,"500":788,"501":789,"502":791,"504":793,"505":794,"506":795,"507":796,"508":797,"509":798,"510":799,"511":800,"512":801,"513":802,"514":803,"515":804,"516":806,"517":807,"518":808,"519":809,"520":810,"522":812,"523":813,"524":814,"525":815,"526":816,"527":817,"528":819,"529":820,"530":821,"531":822,"532":824,"533":825,"534":827,"536":829,"537":830,"538":832,"539":833,"540":834,"541":835,"542":836,"543":837,"544":838,"545":839,"546":840,"547":841,"548":842,"549":843,"550":844,"551":845,"552":846,"553":847,"554":848,"555":849,"556":850,"557":1031,"558":1037,"559":1039,"561":1043,"562":1055,"563":1095,"564":1110,"565":1111,"566":1128,"567":1130,"568":1138,"569":1140,"570":1146,"571":1149,"572":1151,"573":1152,"574":1153,"575":1157,"576":1174,"577":1177,"578":1214,"579":1229,"580":1232,"581":1233,"582":1240,"584":1251,"585":1255,"586":1260,"587":1274,"588":1282,"589":1287,"591":1299,"592":1309,"593":1312,"594":1315,"595":1339,"596":1342,"597":1346,"599":1362,"600":1365,"601":1366,"602":1398,"603":1399,"604":1400,"605":1410,"606":1413,"607":1414,"608":1422,"609":1426,"610":1428,"611":1437,"612":1444,"613":1455,"614":1458,"615":1461,"616":1480,"617":1485,"618":1492,"619":1496,"620":1497,"621":1498,"622":1502,"624":1512,"625":1526,"626":1550,"627":1552,"628":1556,"629":1564,"630":1567,"631":1570,"632":1599,"633":1606,"634":1607,"635":1611,"636":1613,"637":1627,"638":1633,"639":1634,"640":1636,"641":1637,"642":1649,"643":1658,"644":1662,"645":1670,"646":1672,"647":1674,"648":1675,"650":1699,"651":1703,"652":1705,"653":1715,"654":1726,"655":1745,"656":1748,"657":1755,"658":1761,"659":1783,"660":1798,"662":1814,"663":1817,"664":1818,"665":1822,"666":1825,"667":1826,"668":1827,"670":1844,"671":1855,"672":1856,"674":1869,"675":1871,"676":1880,"677":1882,"678":1891,"679":1898,"680":1901,"681":1910,"682":1917,"683":1922,"684":1933,"685":1937,"686":1938,"687":1940,"688":1949,"689":1950,"690":1951,"691":1954,"692":1955,"693":1958,"694":1966,"695":1977,"696":1978,"697":1988,"698":1996,"699":2011,"700":2014,"702":2024,"703":2026,"704":2034,"705":2043,"706":2047},{"0":10,"1":11,"2":15,"4":21,"7":39,"8":43,"9":46,"10":47,"11":55,"13":65,"14":68,"15":70,"16":79,"17":87,"18":90,"19":93,"20":99,"21":100,"22":102,"23":105,"24":108,"25":114,"26":125,"27":127,"28":129,"29":136,"30":141,"31":147,"33":165,"34":176,"35":178,"36":180,"37":199,"38":203,"39":205,"40":206,"41":227,"42":229,"43":242,"44":249,"45":265,"46":269,"47":270,"48":271,"49":278,"50":285,"51":289,"52":296,"53":300,"54":303,"55":304,"56":305,"57":308,"58":324,"59":326,"60":335,"61":340,"62":342,"63":343,"64":344,"65":346,"66":350,"67":351,"68":352,"69":355,"70":356,"71":357,"72":358,"73":361,"74":362,"75":364,"76":365,"77":366,"78":367,"79":368,"80":369,"82":375,"83":376,"85":379,"87":382,"88":383,"89":384,"90":385,"91":388,"92":389,"94":392,"95":393,"96":394,"97":398,"98":399,"99":400,"102":407,"103":408,"104":409,"105":411,"106":412,"107":413,"108":415,"109":417,"110":418,"111":419,"112":421,"113":422,"114":424,"115":425,"116":428,"117":429,"118":430,"119":431,"120":433,"121":434,"122":435,"123":437,"124":438,"125":439,"126":440,"127":441,"128":443,"129":445,"130":446,"131":447,"132":449,"133":450,"134":451,"135":452,"136":453,"137":454,"138":455,"139":456,"140":458,"141":459,"142":460,"145":463,"148":467,"149":469,"150":470,"151":471,"152":472,"153":473,"154":474,"155":475,"156":477,"157":478,"158":479,"159":480,"160":482,"161":483,"162":484,"163":486,"164":487,"165":489,"166":490,"167":491,"168":493,"169":494,"170":495,"172":498,"173":502,"174":503,"175":504,"176":506,"177":508,"178":509,"179":510,"180":511,"181":512,"182":519,"184":523,"185":548,"186":564,"188":570,"189":573,"190":595,"191":602,"192":605,"193":608,"194":616,"195":630,"196":634,"197":645,"198":646,"200":651,"201":664,"203":666,"204":683,"205":687,"206":689,"207":690,"208":691,"209":697,"210":707,"211":715,"212":736,"213":738,"214":746,"215":747,"216":748,"217":752,"218":756,"219":773,"220":774,"221":775,"222":790,"223":805,"224":818,"225":823,"226":826,"227":831,"228":851,"229":852,"230":853,"231":854,"232":855,"233":856,"234":860,"235":861,"236":865,"238":868,"239":869,"240":871,"241":873,"242":874,"243":876,"244":878,"245":879,"246":880,"247":881,"248":883,"249":885,"250":886,"252":889,"253":890,"254":891,"255":892,"256":893,"257":896,"258":897,"259":899,"260":900,"261":902,"262":903,"263":904,"264":906,"265":907,"266":908,"267":909,"268":910,"269":912,"270":913,"271":915,"273":917,"274":918,"275":920,"276":924,"277":926,"278":929,"279":930,"280":932,"281":933,"282":937,"283":938,"284":939,"285":940,"286":941,"287":943,"288":944,"289":945,"290":946,"291":947,"292":948,"293":949,"294":952,"295":953,"296":954,"297":955,"298":956,"299":958,"300":960,"302":962,"304":965,"305":966,"306":967,"307":971,"308":972,"309":977,"310":978,"312":981,"313":983,"314":984,"315":987,"316":988,"317":989,"318":990,"319":991,"320":992,"321":994,"322":995,"323":997,"324":998,"325":999,"326":1000,"328":1002,"329":1004,"331":1010,"332":1014,"333":1015,"334":1016,"335":1017,"336":1018,"337":1019,"338":1021,"339":1030,"340":1034,"341":1046,"342":1050,"343":1060,"344":1072,"345":1074,"346":1077,"347":1081,"348":1083,"349":1089,"350":1096,"351":1097,"352":1104,"353":1107,"354":1117,"355":1124,"356":1125,"357":1139,"358":1154,"359":1155,"360":1167,"361":1172,"362":1180,"363":1182,"364":1199,"365":1213,"366":1219,"367":1220,"368":1235,"369":1236,"370":1237,"371":1239,"372":1248,"373":1249,"374":1250,"375":1261,"376":1262,"377":1263,"378":1266,"379":1273,"380":1278,"381":1290,"382":1292,"383":1302,"384":1303,"385":1310,"386":1317,"387":1321,"388":1328,"389":1333,"390":1335,"391":1336,"392":1344,"393":1349,"394":1350,"395":1364,"396":1375,"397":1386,"398":1389,"399":1392,"400":1394,"401":1404,"402":1409,"403":1411,"404":1434,"405":1438,"406":1439,"407":1441,"408":1474,"410":1478,"411":1483,"412":1489,"413":1494,"414":1517,"415":1535,"416":1537,"417":1538,"418":1548,"419":1553,"420":1573,"421":1578,"422":1580,"423":1581,"424":1583,"425":1588,"426":1589,"427":1598,"429":1622,"430":1630,"431":1632,"432":1643,"433":1648,"434":1655,"435":1666,"436":1667,"437":1691,"438":1693,"439":1708,"440":1709,"441":1712,"442":1721,"443":1725,"444":1737,"445":1753,"446":1758,"447":1765,"448":1776,"449":1779,"450":1784,"451":1786,"452":1799,"453":1802,"454":1806,"455":1809,"456":1810,"457":1811,"458":1812,"459":1819,"460":1823,"461":1829,"462":1834,"463":1840,"464":1842,"465":1847,"466":1852,"467":1870,"468":1893,"469":1895,"470":1897,"471":1902,"472":1905,"473":1908,"474":1911,"475":1919,"476":1921,"477":1923,"478":1929,"479":1939,"480":1948,"481":1959,"482":1962,"483":1972,"484":1973,"485":1974,"486":1976,"487":1987,"488":1990,"489":1991,"490":1992,"491":1995,"492":1998,"493":1999,"494":2007,"495":2029,"496":2031,"497":2038,"498":2044},{"0":40,"1":171,"2":188,"3":198,"4":244,"5":339,"6":341,"7":345,"8":348,"9":349,"10":353,"11":354,"12":359,"13":360,"14":363,"15":370,"16":371,"17":372,"18":374,"19":378,"20":380,"21":386,"22":387,"23":391,"24":396,"25":397,"26":401,"27":403,"28":404,"29":406,"30":410,"31":414,"32":416,"33":420,"34":423,"35":426,"36":427,"37":432,"38":436,"39":442,"40":444,"41":448,"42":457,"43":466,"44":468,"45":476,"46":481,"47":485,"48":488,"49":492,"50":497,"51":499,"52":501,"53":505,"54":507,"55":554,"56":589,"57":684,"58":688,"59":694,"60":709,"61":754,"62":761,"63":857,"64":858,"65":859,"66":862,"67":863,"68":864,"69":867,"70":870,"71":872,"72":875,"73":877,"74":882,"75":884,"76":888,"77":894,"78":895,"79":898,"80":901,"81":911,"82":914,"83":919,"84":921,"85":922,"86":923,"87":925,"88":927,"89":928,"90":931,"91":934,"92":935,"93":936,"94":942,"95":950,"96":951,"97":957,"98":959,"99":964,"100":968,"101":969,"102":970,"103":973,"104":974,"105":975,"106":976,"107":980,"108":982,"109":985,"110":986,"111":993,"112":996,"113":1003,"114":1005,"115":1006,"116":1007,"117":1009,"118":1011,"119":1012,"120":1013,"121":1020,"122":1023,"123":1026,"124":1027,"125":1038,"126":1062,"127":1064,"128":1073,"129":1080,"130":1086,"131":1098,"132":1103,"133":1105,"134":1129,"135":1156,"136":1164,"137":1179,"138":1186,"139":1194,"140":1196,"141":1208,"142":1209,"143":1216,"144":1217,"145":1218,"146":1221,"147":1222,"148":1223,"149":1253,"150":1254,"151":1265,"152":1269,"153":1291,"154":1293,"155":1306,"156":1343,"157":1376,"158":1378,"159":1379,"160":1384,"161":1388,"162":1397,"163":1403,"164":1418,"165":1419,"166":1425,"167":1447,"168":1451,"169":1456,"170":1457,"171":1460,"172":1467,"173":1468,"174":1484,"175":1491,"176":1507,"177":1511,"178":1524,"179":1529,"180":1532,"181":1536,"182":1554,"183":1557,"184":1559,"185":1562,"186":1569,"187":1574,"188":1577,"189":1586,"190":1590,"191":1595,"192":1602,"193":1610,"194":1615,"195":1616,"196":1618,"197":1625,"198":1626,"199":1628,"200":1629,"201":1635,"202":1639,"203":1640,"204":1642,"205":1644,"206":1647,"207":1652,"208":1665,"209":1677,"211":1704,"212":1710,"213":1711,"214":1720,"215":1729,"216":1730,"217":1732,"218":1747,"219":1762,"220":1770,"221":1771,"222":1777,"223":1780,"224":1781,"226":1790,"227":1796,"228":1804,"229":1835,"230":1839,"231":1841,"233":1872,"234":1879,"235":1894,"236":1899,"238":1906,"239":1918,"240":1920,"241":1982,"242":1985,"243":1994,"244":1997,"245":2009,"246":2013,"247":2027,"249":2035,"250":2041},{"0":347,"1":395,"2":500,"3":905,"4":1022,"5":1056,"7":1069,"8":1071,"10":1094,"11":1122,"12":1135,"13":1136,"14":1137,"15":1148,"16":1161,"17":1162,"18":1169,"19":1173,"20":1178,"21":1183,"22":1192,"23":1201,"24":1203,"25":1204,"26":1227,"27":1230,"29":1277,"30":1281,"31":1313,"32":1318,"33":1319,"34":1322,"35":1323,"36":1324,"37":1326,"38":1334,"39":1337,"40":1345,"41":1352,"42":1393,"43":1401,"44":1417,"45":1429,"46":1448,"47":1450,"48":1465,"49":1470,"50":1472,"51":1487,"54":1509,"55":1522,"56":1523,"58":1527,"59":1531,"60":1533,"61":1555,"62":1575,"63":1582,"64":1587,"65":1605,"67":1624,"68":1631,"69":1646,"70":1650,"71":1671,"72":1685,"73":1692,"75":1702,"76":1714,"77":1716,"78":1724,"79":1728,"80":1759,"81":1813,"82":1828,"83":1878,"84":1886,"85":1892,"86":1913,"88":1953,"89":1963,"90":1965,"91":1986,"92":2005,"93":2015,"94":2018,"95":2030,"96":2032,"97":2040,"98":2045},{"0":1041,"1":1047,"2":1058,"3":1066,"4":1068,"5":1078,"6":1084,"7":1091,"8":1106,"9":1120,"10":1127,"11":1159,"12":1176,"16":1252,"17":1280,"18":1295,"19":1301,"20":1347,"21":1360,"23":1373,"24":1380,"25":1385,"27":1427,"29":1459,"30":1482,"32":1528,"34":1541,"35":1591,"36":1593,"37":1596,"38":1608,"39":1619,"40":1621,"41":1654,"42":1656,"43":1657,"44":1719,"45":1722,"47":1743,"48":1751,"49":1768,"51":1794,"52":1795,"53":1800,"54":1803,"55":1807,"56":1848,"57":1857,"58":1885,"59":1914,"60":1926,"61":1927,"62":1930,"63":1941,"65":1957,"66":1961,"67":1980,"68":2004,"70":2036},{"0":1032,"1":1033,"2":1042,"3":1048,"5":1087,"6":1109,"9":1185,"11":1264,"12":1268,"13":1276,"14":1338,"15":1353,"16":1354,"17":1356,"19":1367,"21":1391,"22":1402,"23":1421,"25":1443,"26":1469,"28":1477,"29":1505,"30":1506,"31":1518,"32":1521,"33":1540,"34":1547,"36":1566,"37":1612,"38":1638,"39":1651,"40":1660,"41":1663,"42":1664,"43":1680,"44":1681,"45":1683,"46":1688,"47":1698,"48":1701,"49":1718,"51":1740,"52":1778,"53":1789,"54":1797,"55":1816,"57":1837,"59":1874,"60":1900,"61":1928,"63":1934,"65":1956,"66":1960,"67":1970,"68":1989,"69":2002,"70":2039},{"0":1028,"1":1052,"3":1076,"4":1090,"5":1092,"6":1100,"7":1131,"8":1165,"9":1184,"10":1190,"12":1207,"13":1212,"14":1224,"15":1246,"17":1259,"18":1272,"19":1289,"20":1314,"21":1320,"22":1331,"23":1340,"24":1371,"26":1381,"27":1382,"28":1406,"29":1416,"30":1420,"31":1432,"32":1433,"33":1442,"34":1446,"35":1466,"36":1479,"37":1499,"38":1508,"39":1516,"40":1519,"41":1597,"42":1603,"43":1604,"44":1645,"45":1659,"46":1661,"48":1707,"49":1749,"50":1752,"52":1821,"53":1833,"54":1845,"55":1858,"56":1860,"57":1862,"59":1884,"60":1887,"61":1896,"62":1924,"63":1936,"64":1943,"65":1946,"66":1964,"67":2012,"68":2023},{"0":1061,"1":1075,"2":1079,"3":1101,"4":1113,"5":1126,"6":1170,"8":1198,"9":1210,"10":1211,"11":1279,"12":1284,"13":1286,"15":1307,"16":1308,"17":1329,"19":1408,"22":1486,"23":1488,"24":1520,"25":1544,"26":1546,"28":1558,"29":1560,"31":1584,"32":1600,"33":1614,"34":1669,"35":1673,"36":1682,"41":1757,"42":1767,"43":1772,"44":1793,"46":1831,"47":1873,"48":1875,"49":1904,"50":1952,"51":1967,"52":1969,"53":1981,"54":1984,"55":2006},{"0":1025,"2":1045,"3":1057,"4":1067,"6":1093,"7":1108,"8":1115,"9":1116,"10":1121,"12":1145,"13":1166,"14":1191,"17":1271,"18":1288,"19":1316,"20":1341,"23":1383,"26":1563,"27":1585,"29":1641,"30":1668,"32":1686,"35":1738,"36":1739,"37":1744,"38":1754,"39":1766,"40":1815,"42":1832,"46":1865,"48":1877,"49":1993,"50":2016,"51":2021},{"2":1114,"3":1118,"9":1258,"10":1283,"11":1305,"14":1363,"15":1407,"17":1449,"18":1452,"20":1471,"21":1476,"22":1495,"24":1504,"26":1543,"27":1561,"28":1568,"33":1756,"35":1846,"36":1853,"38":1916,"39":1944,"40":1983,"41":2000,"44":2046},{"0":1024,"1":1053,"2":1099,"4":1123,"7":1143,"10":1168,"12":1195,"13":1215,"15":1243,"16":1256,"20":1332,"24":1445,"28":1549,"30":1617,"31":1676,"32":1678,"33":1727,"34":1736,"35":1769,"36":1801,"38":1876,"39":1971,"40":1975,"41":2001},{"0":1036,"1":1132,"5":1304,"7":1359,"10":1501,"12":1594,"15":1888,"17":1909,"18":1979},{"5":1694,"8":1773,"9":1881,"11":1945,"12":2042},{"0":1044,"2":1405,"3":1430,"7":1782,"10":1942},{"2":1225,"3":1298,"5":1679,"7":1763,"8":1836,"9":1890,"10":1925,"11":2003},{"5":1785,"6":2008},{"0":1070,"6":1838,"7":1915},{"1":1285,"2":1571},{"1":1361},[]]