[{"0":0,"1":1,"2":2,"3":4,"4":5,"5":6,"6":7,"7":8,"8":9,"9":10,"10":16,"11":20,"12":22,"13":23,"14":24,"15":25,"16":26,"17":28,"18":29,"19":30,"20":32,"21":33,"22":34,"23":36,"24":37,"25":41,"26":43,"27":44,"28":52,"29":54,"30":55,"31":56,"32":58,"33":62,"34":63,"35":64,"36":66,"37":67,"38":68,"39":69,"40":70,"41":73,"43":90,"44":91,"45":92,"46":93,"47":94,"48":95,"49":96,"50":97,"51":98,"52":99,"53":100,"54":101,"55":110,"56":111,"57":112,"58":113,"59":114,"60":115,"61":120,"62":123,"63":124,"64":125,"65":126,"66":127,"67":128,"68":129,"69":131,"70":132,"71":133,"72":134,"73":135,"74":142,"75":146,"76":147,"77":148,"78":152,"79":155,"80":158,"81":159,"82":160,"83":161,"84":162,"85":163,"86":164,"87":165,"88":166,"89":167,"90":172,"91":173,"92":174,"93":176,"94":177,"95":178,"96":180,"97":182,"98":183,"99":186,"100":187,"101":188,"102":189,"103":199,"104":200,"105":202,"106":203,"107":205,"108":209,"109":210,"110":211,"111":213,"112":214,"113":215,"114":216,"115":217,"116":218,"117":219,"118":220,"119":224,"120":226,"121":227,"122":229,"123":230,"124":231,"125":232,"126":233,"127":234,"128":235,"129":236,"130":239,"131":240,"132":242,"133":246,"134":247,"135":248,"136":249,"137":252,"138":253,"139":260,"140":265,"141":266,"142":272,"143":273,"144":277,"145":280,"146":282,"147":283,"148":285,"149":286,"150":287,"151":288,"152":289,"153":291,"154":303,"155":305,"156":306,"157":307,"158":310,"159":313,"160":340,"161":341,"162":345,"163":346,"164":347,"165":348,"166":351,"167":355,"168":358,"169":361,"170":363,"171":364,"172":366,"173":367,"174":368,"175":370,"176":371,"177":372,"178":374,"179":375,"180":376,"181":377,"182":378,"183":379,"184":381,"185":382,"186":383,"187":384,"188":391,"189":395,"190":396,"191":398,"192":399,"193":400,"194":403,"195":404,"196":408,"197":409,"198":410,"199":412,"200":413,"201":414,"202":417,"203":419,"204":420,"205":421,"206":422,"207":423,"208":424,"209":427,"210":434,"211":435,"212":439,"213":441,"214":443,"215":444,"216":446,"217":447,"218":448,"219":449,"220":450,"221":451,"222":452,"223":453,"224":454,"225":455,"226":456,"227":461,"228":462,"229":474,"230":478,"231":479,"232":482,"233":483,"234":488,"235":495,"236":497,"237":549,"238":550,"239":575,"240":588,"241":592,"242":593,"243":594,"244":595,"245":596,"246":597,"247":599,"248":601,"249":605,"250":606,"251":607,"252":608,"253":610,"254":612,"255":613,"256":614,"257":615,"258":616,"259":617,"260":618,"261":619,"262":620,"263":621,"264":638,"265":639,"266":640,"267":641,"268":642,"269":643,"270":644,"271":645,"272":646,"273":649,"274":658,"275":662,"276":665,"277":671,"278":672,"279":673,"280":688,"281":690,"282":691,"283":692,"284":694,"285":695,"286":696,"287":697,"288":698,"289":699,"290":701,"291":702,"292":703,"293":705,"294":707,"295":708,"296":709,"297":710,"298":711,"299":712,"300":713,"301":714,"302":715,"303":717,"304":718,"305":719,"306":720,"307":724,"308":725,"309":726,"310":727,"311":729,"312":734,"313":742,"314":743,"315":745,"316":747,"317":748,"318":750,"319":751,"320":752,"321":754,"322":757,"323":758,"324":759,"325":760,"326":762,"327":763,"328":765,"329":766,"330":767,"331":768,"332":769,"333":776,"334":778,"335":779,"336":780,"337":781,"338":783,"339":784,"340":785,"341":790,"342":791,"343":792,"344":793,"345":794,"346":795,"347":797,"348":798,"349":803,"350":805,"351":807,"352":808,"353":809,"354":810,"355":811,"356":812,"357":813,"358":814,"359":816,"360":817,"361":818,"362":835,"363":890,"364":891,"365":892,"366":893,"367":894,"368":895,"369":896,"370":907,"371":918,"372":919,"373":920,"374":921,"375":922,"376":923,"377":925,"378":927,"379":928,"380":929,"381":930,"382":937,"383":938,"384":939,"385":940,"386":942,"387":944,"388":945,"389":946,"390":947,"391":948,"392":949,"393":950,"394":952,"395":954,"396":957,"397":963,"398":984,"399":1053,"400":1054,"401":1056,"402":1057,"403":1058,"404":1059,"405":1061,"406":1062,"407":1064,"408":1077,"409":1080,"410":1081,"411":1087,"412":1090,"413":1092,"414":1093,"415":1096,"416":1098,"417":1100,"418":1101,"419":1102,"420":1103,"421":1111,"422":1112,"423":1113,"424":1115,"425":1116,"426":1119,"427":1121,"428":1122,"429":1123,"430":1128,"431":1129,"432":1131,"433":1133,"434":1134,"435":1135,"436":1146,"437":1150,"438":1152,"439":1156,"440":1157,"441":1158,"442":1159,"443":1161,"444":1162,"445":1163,"446":1164,"447":1165,"448":1173,"449":1174,"450":1175,"451":1176,"452":1177,"453":1179,"454":1181,"455":1186,"456":1188,"457":1189,"458":1190,"459":1191,"460":1197,"461":1198,"462":1200,"463":1205,"464":1208,"465":1211,"466":1215,"467":1216,"468":1219,"469":1220,"470":1221,"471":1222,"472":1223,"473":1224,"474":1226,"475":1252,"476":1253,"477":1264,"478":1265,"479":1266,"480":1272,"481":1273,"482":1274,"483":1275,"484":1276,"485":1277,"486":1278,"487":1279,"488":1280,"489":1281,"490":1283,"491":1291,"492":1296,"493":1297,"494":1298,"495":1304,"496":1305,"497":1306,"498":1307,"499":1308,"500":1310,"501":1311,"502":1313,"503":1321,"504":1324,"505":1333,"506":1334,"507":1335,"508":1336,"509":1337,"510":1338,"511":1339,"512":1340,"513":1341,"514":1344,"515":1345,"516":1353,"517":1354,"518":1357,"519":1358,"520":1359,"521":1360,"522":1361,"523":1362,"524":1365,"525":1366,"526":1367,"527":1368,"528":1371,"529":1372,"530":1373,"531":1375,"532":1376,"533":1378,"534":1379,"535":1385,"536":1387,"537":1388,"538":1390,"539":1393,"540":1394,"541":1395,"542":1398,"543":1399,"544":1404,"545":1407,"546":1414,"547":1423,"548":1424,"549":1430,"550":1431,"551":1432,"552":1433,"553":1435,"554":1437,"555":1438,"556":1445,"557":1447,"558":1448,"559":1449,"560":1450,"561":1451,"562":1456,"563":1457,"564":1458,"565":1459,"566":1460,"567":1461,"568":1462,"569":1463,"570":1464,"571":1465,"572":1466,"573":1467,"574":1468,"575":1470,"576":1472,"577":1480,"578":1481,"579":1483,"580":1484,"581":1485,"582":1487,"583":1488,"584":1489,"585":1492,"586":1493,"587":1496,"588":1497,"589":1499,"590":1500,"591":1501,"592":1502,"593":1505,"594":1517,"595":1518,"596":1524,"597":1525,"598":1530,"599":1532,"600":1533,"601":1534,"602":1535,"603":1537,"604":1539,"605":1540,"606":1547,"607":1548,"608":1554,"609":1557,"610":1558,"611":1562,"612":1563,"613":1565,"614":1566,"615":1568,"616":1570,"617":1571,"618":1572,"619":1573,"620":1584,"621":1586,"622":1587,"623":1589,"624":1590,"625":1592,"626":1593,"627":1594,"628":1597,"629":1599,"630":1602,"631":1603,"632":1604,"633":1607,"634":1608,"635":1609,"636":1618,"637":1620,"638":1621,"639":1622,"640":1627,"641":1629,"642":1630,"643":1633,"644":1634,"645":1636,"646":1638,"647":1640,"648":1641,"649":1642,"650":1643,"651":1647,"652":1649,"653":1653,"654":1659,"655":1678,"656":1680,"657":1691,"658":1693,"659":1696,"660":1702,"661":1703,"662":1704,"663":1705,"664":1707,"665":1708,"666":1710,"667":1711,"668":1712,"669":1716,"670":1717,"671":1718,"672":1719,"673":1720,"674":1722,"675":1725,"676":1726,"677":1727,"678":1728,"679":1729,"680":1730,"681":1731,"682":1732,"683":1733,"684":1734,"685":1735,"686":1737,"687":1738,"688":1739,"689":1743,"690":1744,"691":1745,"692":1748,"693":1752,"694":1755,"695":1756,"696":1757,"697":1758,"698":1759,"699":1760,"700":1761,"701":1769,"702":1773,"703":1774,"704":1775,"705":1777,"706":1778,"707":1779,"708":1781,"709":1782,"710":1783,"711":1784,"712":1785,"713":1786,"714":1787,"715":1788,"716":1789,"717":1793,"718":1795,"719":1796,"720":1799,"721":1801,"722":1803,"723":1805,"724":1807,"725":1810,"726":1811,"727":1812,"728":1813,"729":1816,"730":1820,"731":1822,"732":1828,"733":1834,"734":1836,"735":1837,"736":1838,"737":1842,"738":1843,"739":1844,"740":1846,"741":1850,"742":1853,"743":1854,"744":1856,"745":1857,"746":1858,"747":1860,"748":1861,"749":1862,"750":1863,"751":1866,"752":1867,"753":1868,"754":1869,"755":1870,"756":1871,"757":1872,"758":1874,"759":1875,"760":1879,"761":1880,"762":1881,"763":1884,"764":1886,"765":1887,"766":1888,"767":1891,"768":1894,"769":1895,"770":1900,"771":1905,"772":1908,"773":1909,"774":1910,"775":1912,"776":1913,"777":1914,"778":1916,"779":1917,"780":1918,"781":1919,"782":1920,"783":1922,"784":1923,"785":1925,"786":1926,"787":1930,"788":1931,"789":1932,"790":1933,"791":1935,"792":1937,"793":1938,"794":1939,"795":1940,"796":1944,"797":1945,"798":1946,"799":1947,"800":1948,"801":1952,"802":1953,"803":1958,"804":1963,"805":1964},{"0":3,"1":11,"2":12,"3":13,"4":14,"5":15,"6":18,"7":19,"8":35,"9":38,"10":40,"11":42,"12":45,"13":49,"14":60,"15":65,"16":71,"17":72,"32":102,"33":103,"34":105,"35":107,"36":116,"37":117,"38":118,"39":119,"40":121,"41":122,"42":130,"43":140,"44":141,"45":150,"46":151,"47":153,"48":154,"49":156,"50":168,"51":169,"52":179,"53":185,"54":190,"55":191,"56":193,"57":194,"58":197,"59":204,"60":206,"61":207,"62":208,"63":212,"64":221,"65":222,"66":225,"67":237,"68":238,"69":244,"70":245,"71":250,"72":251,"73":255,"74":261,"75":263,"76":268,"77":269,"78":275,"79":278,"80":279,"81":294,"82":298,"83":299,"84":300,"85":301,"86":302,"87":304,"88":308,"89":309,"90":311,"91":312,"92":315,"93":316,"94":317,"95":318,"96":319,"97":321,"98":327,"99":331,"100":332,"101":333,"102":334,"103":336,"104":342,"105":343,"106":344,"107":349,"108":354,"109":373,"110":385,"111":386,"112":387,"113":389,"114":390,"115":392,"116":393,"117":394,"118":397,"119":402,"120":415,"121":416,"122":425,"123":426,"124":428,"125":430,"126":431,"127":436,"128":437,"129":438,"130":440,"131":442,"132":445,"133":459,"134":460,"135":463,"136":466,"137":469,"138":470,"139":472,"140":473,"141":475,"142":491,"143":494,"144":496,"145":498,"146":501,"147":502,"148":503,"149":504,"150":507,"151":512,"152":514,"153":515,"154":516,"155":517,"156":518,"157":519,"158":520,"159":522,"160":524,"161":525,"162":532,"163":533,"164":534,"165":535,"166":536,"167":537,"168":538,"169":551,"170":556,"171":557,"172":563,"173":568,"174":571,"175":578,"176":582,"177":589,"178":590,"179":591,"180":598,"181":602,"182":603,"183":609,"184":611,"185":622,"186":623,"188":626,"189":627,"190":633,"191":637,"192":647,"193":653,"194":654,"195":655,"196":656,"197":659,"198":661,"199":666,"200":668,"201":670,"202":674,"203":676,"204":677,"205":680,"206":681,"207":682,"208":683,"209":684,"210":686,"211":693,"212":700,"213":706,"214":716,"215":722,"216":723,"217":728,"218":731,"219":735,"220":737,"221":739,"222":740,"223":741,"224":744,"225":753,"226":755,"227":764,"228":771,"229":772,"230":773,"231":774,"232":775,"233":777,"234":782,"235":786,"236":787,"237":788,"238":796,"239":799,"240":804,"241":806,"242":815,"243":819,"244":820,"245":821,"246":832,"247":833,"248":836,"249":837,"250":840,"251":841,"252":843,"253":844,"254":845,"255":846,"256":847,"257":848,"258":849,"259":850,"260":851,"261":852,"262":853,"263":861,"264":868,"265":869,"266":870,"267":871,"268":872,"269":873,"270":874,"271":875,"272":879,"273":880,"274":881,"275":882,"276":883,"277":884,"278":889,"279":897,"280":898,"281":899,"282":901,"283":902,"284":903,"285":906,"286":916,"287":917,"288":924,"289":926,"290":933,"291":934,"292":935,"293":936,"294":943,"295":953,"296":955,"297":956,"298":959,"299":961,"300":962,"301":965,"302":966,"303":967,"304":968,"305":969,"306":972,"307":978,"308":980,"309":981,"310":982,"311":986,"312":988,"313":990,"314":991,"315":992,"316":993,"317":994,"318":996,"319":998,"320":999,"321":1000,"322":1001,"323":1002,"324":1003,"325":1005,"326":1006,"327":1007,"328":1008,"329":1009,"330":1011,"331":1012,"332":1013,"333":1014,"334":1015,"335":1016,"336":1017,"337":1018,"338":1022,"339":1024,"340":1027,"341":1030,"342":1031,"343":1033,"344":1034,"345":1035,"346":1036,"347":1037,"348":1039,"349":1041,"350":1049,"351":1055,"352":1060,"353":1063,"354":1068,"355":1069,"356":1070,"357":1072,"358":1073,"359":1074,"360":1075,"361":1084,"362":1085,"363":1088,"364":1091,"365":1094,"366":1095,"367":1099,"368":1104,"369":1105,"370":1107,"371":1108,"372":1109,"373":1114,"374":1117,"375":1118,"376":1120,"377":1124,"378":1125,"379":1126,"380":1130,"381":1132,"382":1136,"383":1141,"384":1143,"385":1144,"386":1147,"387":1148,"388":1151,"389":1160,"390":1166,"391":1168,"392":1169,"393":1170,"394":1171,"395":1172,"396":1180,"397":1183,"398":1184,"399":1201,"400":1202,"401":1203,"402":1206,"403":1209,"404":1225,"405":1227,"406":1228,"407":1230,"408":1231,"409":1232,"410":1233,"411":1240,"412":1241,"413":1242,"414":1243,"415":1246,"416":1248,"417":1250,"418":1255,"419":1256,"420":1258,"421":1259,"422":1260,"423":1261,"424":1262,"425":1267,"426":1268,"427":1269,"428":1270,"429":1271,"430":1282,"431":1284,"432":1285,"433":1286,"434":1287,"435":1290,"436":1292,"437":1294,"438":1309,"439":1312,"440":1314,"441":1315,"442":1316,"443":1317,"444":1318,"445":1323,"446":1327,"447":1328,"448":1330,"449":1332,"450":1342,"451":1343,"452":1346,"453":1347,"454":1351,"455":1355,"456":1356,"457":1363,"458":1364,"459":1369,"460":1370,"461":1374,"462":1377,"463":1380,"464":1381,"465":1382,"466":1383,"467":1384,"468":1386,"469":1389,"470":1392,"471":1396,"472":1397,"473":1412,"474":1416,"475":1418,"476":1419,"477":1420,"478":1421,"479":1422,"480":1425,"481":1429,"482":1434,"483":1436,"484":1444,"485":1446,"486":1454,"487":1455,"488":1469,"489":1471,"490":1478,"491":1482,"492":1486,"493":1490,"494":1491,"495":1494,"496":1495,"497":1503,"498":1504,"499":1506,"500":1507,"501":1516,"502":1522,"503":1526,"504":1536,"505":1538,"506":1542,"507":1543,"508":1544,"509":1545,"510":1546,"511":1549,"512":1551,"513":1553,"514":1564,"515":1567,"516":1569,"517":1575,"518":1576,"519":1578,"520":1579,"521":1580,"522":1581,"523":1583,"524":1585,"525":1588,"526":1591,"527":1595,"528":1596,"529":1598,"530":1600,"531":1601,"532":1605,"533":1606,"534":1610,"535":1611,"536":1614,"537":1615,"538":1616,"539":1617,"540":1619,"541":1624,"542":1628,"543":1631,"544":1632,"545":1635,"546":1639,"547":1644,"548":1646,"549":1650,"550":1651,"551":1654,"552":1656,"553":1657,"554":1660,"555":1661,"556":1664,"557":1666,"558":1668,"559":1669,"560":1673,"561":1674,"562":1679,"563":1683,"564":1686,"565":1688,"566":1689,"567":1692,"568":1698,"569":1700,"570":1701,"571":1706,"572":1709,"573":1713,"574":1715,"575":1721,"576":1723,"577":1736,"578":1741,"579":1742,"580":1749,"581":1750,"582":1751,"583":1753,"584":1762,"585":1763,"586":1764,"587":1767,"588":1768,"589":1770,"590":1771,"591":1772,"592":1780,"593":1790,"594":1791,"595":1792,"596":1794,"597":1798,"598":1800,"599":1802,"600":1806,"601":1808,"602":1809,"603":1814,"604":1815,"605":1824,"606":1826,"607":1833,"608":1835,"609":1839,"610":1841,"611":1847,"612":1849,"613":1851,"614":1852,"615":1859,"616":1865,"617":1873,"618":1876,"619":1877,"620":1882,"621":1883,"622":1885,"623":1889,"624":1890,"625":1892,"626":1893,"627":1896,"628":1897,"629":1898,"630":1899,"631":1906,"632":1907,"633":1921,"634":1924,"635":1927,"636":1928,"637":1929,"638":1936,"639":1941,"640":1942,"641":1943,"642":1950,"643":1951,"644":1954,"645":1955,"646":1956,"647":1957,"648":1962,"649":1965,"650":1969},{"0":17,"1":31,"2":39,"3":50,"4":57,"5":61,"7":104,"8":106,"9":108,"10":109,"11":157,"12":170,"13":171,"14":175,"15":181,"16":184,"17":192,"18":198,"19":201,"20":223,"21":228,"22":241,"23":243,"24":254,"25":256,"26":258,"27":259,"28":264,"29":270,"30":271,"31":276,"32":281,"33":284,"34":290,"35":293,"36":295,"37":296,"38":297,"39":314,"40":320,"41":323,"42":324,"43":326,"44":328,"45":329,"46":330,"47":335,"48":338,"49":339,"50":350,"51":352,"52":353,"53":356,"54":357,"55":359,"56":360,"57":362,"58":365,"59":369,"60":380,"61":388,"62":418,"63":429,"64":432,"65":433,"66":457,"67":458,"68":464,"69":465,"70":467,"71":471,"72":476,"73":477,"74":481,"75":484,"76":486,"77":487,"78":489,"79":490,"80":499,"81":500,"82":505,"83":506,"84":508,"85":509,"86":510,"87":511,"88":513,"89":521,"90":523,"91":526,"92":527,"93":528,"94":529,"95":530,"96":531,"97":539,"98":543,"99":545,"100":553,"101":559,"102":561,"103":562,"104":569,"105":572,"106":574,"107":576,"108":579,"109":583,"110":587,"111":600,"112":604,"114":629,"116":648,"117":650,"118":651,"119":652,"120":657,"121":660,"122":669,"123":675,"124":687,"125":689,"126":733,"127":736,"128":738,"129":746,"130":749,"131":761,"132":789,"133":800,"134":801,"135":802,"136":827,"137":828,"138":829,"139":831,"140":834,"141":838,"142":839,"143":842,"144":860,"145":867,"146":876,"147":877,"148":885,"149":886,"150":887,"151":888,"152":900,"153":908,"154":912,"155":931,"156":932,"157":941,"158":951,"159":958,"160":960,"161":971,"162":973,"163":974,"164":977,"165":985,"166":987,"167":989,"168":995,"169":997,"170":1004,"171":1010,"172":1019,"173":1020,"174":1023,"175":1025,"176":1026,"177":1028,"178":1029,"179":1032,"180":1038,"181":1042,"182":1043,"183":1045,"184":1050,"185":1065,"186":1066,"187":1067,"188":1071,"189":1076,"190":1078,"191":1083,"192":1086,"193":1097,"194":1106,"195":1110,"196":1127,"197":1137,"198":1139,"199":1140,"200":1142,"201":1145,"202":1149,"203":1153,"204":1154,"205":1155,"206":1182,"207":1187,"208":1192,"209":1193,"210":1194,"211":1195,"212":1196,"213":1204,"214":1207,"215":1210,"216":1212,"217":1213,"218":1214,"219":1217,"220":1229,"221":1234,"222":1235,"223":1236,"224":1237,"225":1238,"226":1244,"227":1245,"228":1247,"229":1249,"230":1251,"231":1254,"232":1257,"233":1263,"234":1293,"235":1299,"236":1300,"237":1302,"238":1303,"239":1320,"240":1322,"241":1325,"242":1326,"243":1329,"244":1331,"245":1349,"246":1350,"247":1352,"248":1391,"249":1400,"250":1401,"251":1402,"252":1403,"253":1405,"254":1406,"255":1411,"256":1413,"257":1415,"258":1426,"259":1428,"260":1452,"261":1453,"262":1473,"263":1474,"264":1475,"265":1476,"266":1498,"267":1508,"268":1509,"269":1510,"270":1511,"271":1514,"272":1519,"273":1521,"274":1523,"275":1527,"276":1529,"277":1556,"278":1561,"279":1574,"280":1577,"281":1582,"282":1612,"283":1613,"284":1623,"285":1625,"286":1626,"287":1637,"288":1648,"289":1652,"290":1655,"291":1658,"292":1662,"293":1663,"294":1665,"295":1667,"296":1670,"297":1671,"298":1675,"299":1676,"300":1677,"301":1681,"302":1682,"303":1684,"304":1690,"305":1694,"306":1695,"307":1697,"308":1724,"309":1740,"310":1746,"311":1754,"312":1766,"313":1776,"314":1797,"315":1804,"316":1817,"317":1818,"318":1819,"319":1821,"320":1823,"321":1825,"322":1827,"323":1829,"324":1830,"325":1831,"326":1832,"327":1840,"328":1845,"329":1848,"330":1855,"331":1864,"332":1878,"333":1901,"334":1902,"335":1903,"336":1911,"337":1915,"338":1934,"339":1959,"340":1961,"341":1966,"342":1967},[21,46,48,51,53,59,136,137,138,139,144,196,262,267,274,292,325,337,468,480,485,493,548,552,554,565,570,584,628,663,664,685,721,730,732,756,770,823,824,825,830,878,911,964,975,976,979,983,1040,1046,1052,1079,1089,1138,1178,1185,1199,1218,1239,1288,1289,1295,1301,1319,1348,1408,1409,1410,1417,1427,1441,1442,1443,1477,1479,1513,1515,1520,1528,1531,1541,1552,1559,1560,1645,1672,1685,1687,1699,1714,1747,1904,1949,1960,1968],[27,47,143,145,195,257,322,492,547,580,585,667,678,679,704,822,826,970,1021,1047,1051,1082,1167,1439,1440,1512,1555,1765],[149,405,406,558,914,915,1044,1048,1550],[401,407,542,564,566,567,573,581,636,855,857,858,859,863,866,904,905,910,913],[411,541,544,555,560,854,862,909],[540,577,586,856,864],[546,865],[630,631,635],[632]]