[{"3":3,"4":5,"6":9,"7":11,"8":12,"9":13,"12":17,"14":19,"15":20,"16":21,"18":23,"20":25,"21":26,"22":27,"23":28,"25":30,"26":31,"28":33,"32":37,"33":38,"34":39,"35":40,"37":42,"38":43,"39":44,"40":45,"43":48,"45":50,"46":53,"47":54,"48":55,"49":56,"50":57,"52":59,"54":61,"55":63,"56":64,"57":65,"58":66,"59":67,"60":68,"61":72,"62":73,"63":74,"64":76,"67":81,"68":82,"69":83,"70":84,"71":86,"72":87,"74":89,"75":90,"76":91,"77":92,"78":94,"79":95,"80":96,"81":98,"82":99,"83":100,"84":101,"85":102,"86":103,"93":112,"94":113,"95":114,"96":115,"97":116,"98":117,"101":120,"102":121,"103":122,"104":123,"105":124,"106":125,"108":127,"109":128,"110":129,"111":130,"112":132,"113":133,"114":134,"115":135,"116":136,"117":137,"118":139,"119":140,"120":141,"121":142,"122":143,"123":144,"125":146,"126":147,"127":148,"128":149,"129":150,"130":152,"131":154,"133":157,"134":158,"135":160,"136":162,"137":163,"138":164,"141":168,"142":169,"143":170,"144":171,"146":173,"147":174,"148":176,"149":177,"150":178,"152":180,"153":181,"154":183,"156":185,"158":187,"160":189,"162":195,"163":196,"164":197,"165":198,"166":199,"167":201,"168":202,"173":207,"174":208,"175":209,"177":212,"178":213,"181":217,"183":219,"184":220,"185":222,"186":223,"187":224,"189":226,"190":228,"191":229,"193":231,"194":232,"196":234,"199":238,"200":239,"202":242,"204":244,"205":245,"207":247,"208":248,"209":249,"212":253,"214":256,"215":257,"219":261,"220":262,"221":263,"222":265,"223":266,"224":267,"225":269,"226":270,"227":271,"228":272,"229":274,"230":275,"231":276,"232":277,"235":280,"236":281,"238":284,"239":285,"241":287,"243":290,"246":293,"247":295,"248":296,"249":297,"250":298,"251":300,"252":302,"253":303,"256":306,"258":308,"259":309,"260":310,"261":312,"262":314,"265":318,"266":319,"268":321,"269":322,"271":324,"272":325,"274":330,"275":333,"276":334,"278":337,"279":338,"280":339,"281":340,"282":341,"283":342,"284":343,"285":345,"286":346,"287":347,"288":348,"289":350,"290":353,"292":355,"293":357,"295":359,"297":361,"298":362,"299":363,"300":364,"301":365,"302":366,"303":367,"304":370,"305":372,"307":374,"308":376,"309":377,"310":378,"311":379,"312":381,"313":382,"314":383,"316":386,"318":390,"319":391,"321":394,"322":395,"324":398,"325":403,"326":404,"327":405,"328":406,"330":410,"331":411,"332":412,"333":413,"334":414,"335":416,"336":417,"338":419,"340":421,"341":422,"342":423,"343":424,"344":425,"346":427,"347":429,"348":430,"349":431,"350":432,"351":433,"352":434,"355":438,"357":440,"358":443,"359":444,"360":445,"361":446,"362":448,"364":450,"365":451,"366":454,"367":455,"368":458,"369":459,"370":460,"372":462,"373":463,"374":464,"375":465,"376":466,"377":467,"378":470,"379":472,"380":474,"381":477,"382":478,"383":479,"384":480,"385":481,"386":482,"387":483,"388":485,"389":486,"390":489,"391":490,"392":491,"393":492,"394":493,"395":494,"396":495,"397":496,"398":498,"399":499,"400":500,"401":503,"402":504,"403":505,"404":507,"405":509,"406":510,"407":511,"408":512,"409":513,"411":515,"414":518,"415":519,"417":521,"418":524,"419":525,"420":526,"421":527,"425":532,"427":535,"430":540,"431":541,"433":543,"434":544,"436":546,"440":550,"442":553,"443":554,"445":556,"446":557,"447":558,"450":561,"452":564,"453":565,"455":567,"457":569,"458":570,"459":572,"460":573,"461":574,"462":575,"464":577,"465":580,"466":581,"467":583,"469":586,"470":587,"471":588,"472":590,"473":591,"474":592,"476":594,"477":595,"479":597,"480":598,"482":601,"484":603,"486":605,"487":606,"488":607,"489":608,"490":609,"492":614,"493":616,"496":620,"498":623,"501":627,"503":629,"508":634,"510":638,"512":640,"513":642,"514":643,"515":644,"517":646,"518":647,"520":649,"524":653,"525":654,"526":655,"527":656,"528":657,"529":658,"530":659,"531":660,"534":666,"535":667,"536":669,"537":670,"538":671,"539":672,"540":673,"541":674,"544":677,"545":679,"546":680,"547":681,"548":682,"550":685,"551":687,"552":688,"553":689,"554":690,"555":692,"556":693,"557":694,"558":695,"559":696,"560":697,"561":699,"562":700,"563":701,"564":702,"565":703,"567":705,"568":706,"569":707,"570":708,"571":709,"572":710,"573":711,"574":712,"576":714,"580":718,"585":724,"586":725,"588":727,"589":728,"590":729,"591":730,"592":731,"594":733,"597":736,"600":739,"601":740,"602":742,"604":746,"605":747,"606":748,"607":749,"608":750,"609":751,"610":753,"613":758,"614":759,"615":760,"617":762,"618":763,"619":764,"621":766,"623":768,"624":769,"625":770,"626":771,"628":773,"629":774,"630":776,"631":777,"633":779,"634":782,"635":783,"637":787,"638":788,"639":789,"641":791,"643":793,"647":799,"648":801,"649":802,"650":803,"655":808,"657":810,"658":811,"659":812,"660":813,"661":814,"662":815,"666":821,"667":822,"668":823,"670":825,"671":826,"675":830,"679":834,"680":835,"681":836,"682":837,"683":838,"684":839,"686":841,"687":843,"688":844,"689":847,"690":848,"691":849,"692":851,"695":855,"696":856,"697":857,"698":858,"699":859,"700":860,"701":861,"703":864,"705":866,"706":867,"707":868,"708":869,"710":871,"712":873,"713":874,"715":879,"716":881,"717":884,"718":886,"719":887,"720":888,"721":890,"723":892,"724":893,"726":896,"727":897,"728":899,"729":900,"730":901,"731":902,"732":903,"733":905,"734":906,"735":908,"736":909,"737":910,"738":912,"739":913,"740":915,"741":916,"742":918,"744":920,"746":924,"748":926,"749":927,"750":928,"751":929,"754":935,"755":936,"756":939,"757":943,"758":944,"759":945,"761":947,"762":948,"763":949,"764":951,"765":952,"766":953,"767":956,"768":957,"769":958,"770":959,"771":960,"772":961,"773":962,"774":963,"775":965,"776":966,"778":970,"779":971,"780":973,"782":975,"783":976,"785":978,"787":980,"788":981,"789":982,"790":983,"791":984,"792":985,"793":986,"794":987,"795":989,"796":990,"797":991,"798":992,"799":993,"800":994,"801":995,"803":997,"804":998,"805":999,"806":1000,"807":1002,"808":1003,"809":1004,"810":1007,"811":1008,"812":1009,"813":1010,"814":1011,"815":1012,"816":1014,"817":1015,"818":1018,"819":1019,"820":1020,"822":1023,"823":1028,"824":1029,"826":1034,"827":1035,"828":1037,"829":1042,"830":1046,"831":1049,"832":1051,"833":1052,"834":1056,"835":1070,"836":1072,"837":1073,"838":1076,"840":1078,"841":1080,"842":1084,"844":1087,"846":1093,"847":1095,"848":1096,"850":1101,"851":1102,"852":1103,"854":1113,"856":1119,"857":1130,"858":1132,"860":1137,"861":1140,"862":1142,"863":1145,"864":1147,"865":1149,"866":1150,"867":1151,"868":1157,"869":1158,"870":1166,"871":1168,"872":1169,"873":1173,"874":1174,"875":1185,"876":1188,"877":1193,"878":1199,"880":1217,"881":1218,"882":1219,"883":1220,"884":1231,"885":1239,"886":1240,"888":1247,"889":1248,"890":1252,"891":1260,"892":1261,"893":1262,"894":1264,"897":1278,"898":1280,"899":1288,"900":1291,"901":1294,"902":1298,"903":1299,"904":1303,"905":1307,"906":1310,"907":1313,"908":1316,"909":1319,"910":1321,"911":1322,"912":1323,"913":1326,"914":1328,"915":1343,"916":1345,"917":1346,"918":1350,"919":1351,"920":1353,"921":1358,"922":1359,"923":1363,"924":1364,"926":1376,"927":1377,"928":1379,"929":1385,"930":1387,"931":1388,"932":1395,"933":1396,"934":1409,"935":1416,"936":1421,"937":1425,"938":1431,"939":1435,"940":1439,"942":1442,"943":1449,"945":1459,"946":1460,"947":1466,"949":1480,"950":1481,"951":1482,"952":1483,"953":1488,"954":1493,"955":1500,"956":1504,"958":1513,"959":1522,"960":1523,"961":1525,"962":1527,"963":1528,"964":1534,"965":1537,"966":1538,"967":1540,"968":1546,"969":1548,"970":1551,"971":1559,"973":1570,"974":1574,"975":1580,"976":1581,"977":1584,"978":1587,"979":1595,"980":1599,"981":1601,"982":1603,"983":1608,"984":1609,"986":1616,"987":1619,"988":1622,"989":1623,"990":1624,"991":1633,"992":1635,"993":1637,"994":1640,"995":1641,"996":1644,"997":1646,"998":1652,"999":1653,"1001":1663,"1002":1665,"1003":1672,"1004":1675,"1005":1676,"1006":1681,"1007":1685,"1008":1686,"1009":1687,"1011":1697,"1012":1701,"1013":1702,"1014":1704,"1015":1705,"1016":1707,"1017":1710,"1018":1715,"1019":1716,"1020":1717,"1021":1718,"1022":1720,"1023":1731,"1024":1732,"1025":1737,"1026":1738,"1027":1739,"1028":1740,"1029":1743,"1030":1744,"1031":1745,"1033":1748,"1034":1750,"1035":1760,"1036":1761,"1038":1769,"1041":1776,"1042":1780,"1043":1781,"1045":1785,"1046":1786,"1047":1787,"1048":1788,"1049":1789,"1050":1791,"1051":1793,"1052":1796,"1053":1797,"1054":1801,"1055":1803,"1057":1814,"1058":1821,"1059":1823,"1060":1827,"1061":1829,"1062":1832,"1063":1837,"1064":1838,"1065":1839,"1066":1841,"1067":1846,"1069":1850,"1070":1852,"1071":1855,"1072":1862,"1073":1863,"1074":1871,"1075":1876,"1076":1885,"1077":1886,"1078":1889,"1079":1895,"1080":1902,"1081":1903,"1082":1907,"1084":1912,"1085":1917,"1086":1918,"1087":1920,"1088":1928,"1089":1930,"1090":1931,"1091":1938,"1092":1940,"1093":1942,"1094":1943,"1095":1945,"1096":1954,"1097":1956,"1098":1961,"1099":1963,"1100":1965,"1101":1967,"1102":1969,"1103":1981,"1104":1986,"1105":1988,"1106":1989,"1107":1990,"1108":1991,"1109":1999,"1110":2013,"1111":2017,"1112":2025,"1113":2033,"1114":2039,"1115":2040,"1116":2042,"1117":2044,"1118":2047},{"0":4,"1":6,"2":8,"3":10,"4":15,"7":69,"8":70,"9":71,"10":75,"12":79,"13":93,"14":97,"15":110,"17":131,"18":151,"19":153,"20":155,"21":159,"23":166,"24":175,"25":182,"26":190,"27":191,"28":192,"29":194,"30":200,"32":221,"33":227,"34":240,"35":251,"36":254,"37":264,"38":268,"39":273,"40":283,"41":288,"42":294,"43":299,"44":301,"45":311,"46":313,"47":315,"48":327,"49":328,"50":329,"51":331,"52":332,"53":336,"54":344,"55":349,"56":351,"57":352,"58":356,"59":368,"60":369,"61":371,"62":380,"63":385,"64":387,"65":389,"66":393,"67":396,"68":399,"69":400,"70":401,"71":402,"72":407,"73":408,"74":415,"75":428,"76":441,"77":442,"78":447,"80":453,"81":456,"82":457,"83":468,"84":469,"85":471,"86":473,"87":475,"88":476,"89":484,"90":487,"91":488,"92":501,"93":502,"94":506,"95":523,"96":528,"97":534,"98":537,"99":538,"100":551,"101":563,"102":571,"103":578,"104":579,"106":589,"107":600,"108":610,"109":611,"110":612,"111":615,"112":619,"113":622,"114":625,"115":635,"116":641,"117":662,"118":664,"119":665,"120":668,"121":678,"122":684,"123":686,"124":691,"125":698,"126":720,"127":741,"128":743,"129":744,"130":752,"131":754,"132":757,"133":775,"134":780,"135":784,"136":785,"138":800,"139":816,"140":817,"141":842,"142":845,"144":854,"145":862,"146":876,"147":877,"148":878,"149":880,"150":882,"151":883,"152":885,"153":889,"154":894,"155":898,"156":904,"157":907,"158":911,"159":914,"160":922,"161":923,"162":930,"163":931,"164":934,"165":937,"166":938,"167":940,"168":942,"169":950,"170":954,"171":955,"172":964,"173":967,"174":968,"175":972,"176":988,"177":1001,"178":1005,"179":1013,"180":1016,"181":1017,"182":1022,"183":1025,"184":1032,"185":1033,"186":1040,"187":1041,"188":1048,"189":1050,"190":1055,"191":1058,"192":1059,"193":1060,"194":1064,"195":1065,"197":1067,"198":1068,"199":1086,"200":1089,"201":1094,"203":1099,"205":1108,"206":1120,"208":1126,"209":1128,"210":1129,"211":1131,"212":1133,"213":1139,"214":1143,"215":1144,"216":1154,"217":1156,"218":1162,"219":1164,"220":1165,"222":1172,"223":1176,"224":1178,"226":1182,"227":1183,"228":1184,"230":1197,"231":1198,"232":1200,"233":1208,"235":1211,"236":1214,"237":1215,"238":1216,"240":1222,"242":1229,"243":1232,"245":1238,"246":1243,"247":1246,"249":1257,"250":1259,"251":1268,"252":1274,"253":1281,"256":1300,"257":1302,"258":1305,"260":1314,"261":1318,"262":1329,"263":1330,"264":1331,"265":1333,"266":1340,"267":1342,"268":1354,"269":1356,"270":1360,"271":1361,"272":1365,"273":1368,"274":1370,"276":1375,"277":1380,"278":1381,"279":1382,"280":1389,"281":1390,"282":1393,"283":1405,"285":1407,"286":1411,"287":1413,"288":1414,"289":1420,"291":1424,"293":1429,"294":1436,"295":1437,"296":1444,"297":1448,"298":1450,"299":1453,"300":1457,"301":1458,"302":1463,"304":1472,"305":1473,"306":1485,"307":1487,"308":1489,"309":1502,"310":1503,"311":1507,"312":1510,"314":1514,"315":1519,"316":1526,"317":1529,"318":1530,"319":1531,"320":1532,"321":1536,"322":1541,"323":1543,"324":1547,"325":1549,"326":1550,"327":1554,"328":1555,"330":1558,"331":1561,"332":1564,"333":1565,"334":1567,"335":1573,"336":1576,"337":1578,"339":1588,"340":1589,"341":1591,"342":1592,"343":1594,"344":1598,"345":1602,"346":1614,"347":1617,"348":1618,"349":1620,"350":1626,"351":1628,"352":1636,"353":1639,"355":1648,"356":1649,"357":1659,"358":1661,"359":1666,"360":1669,"361":1670,"362":1677,"363":1679,"364":1680,"365":1683,"366":1688,"367":1689,"368":1691,"369":1694,"371":1706,"372":1708,"373":1709,"374":1712,"375":1714,"377":1726,"378":1727,"379":1736,"380":1753,"381":1755,"382":1756,"383":1765,"384":1767,"385":1770,"386":1772,"387":1777,"388":1798,"389":1802,"390":1805,"391":1809,"393":1816,"394":1824,"395":1828,"396":1836,"397":1840,"398":1844,"400":1847,"401":1854,"402":1856,"403":1858,"404":1860,"405":1866,"406":1867,"407":1872,"408":1875,"409":1877,"410":1888,"411":1891,"412":1896,"413":1897,"414":1904,"415":1906,"416":1909,"417":1915,"418":1924,"419":1925,"420":1926,"421":1929,"422":1935,"423":1937,"424":1939,"426":1944,"427":1948,"428":1950,"429":1951,"430":1953,"431":1957,"432":1966,"433":1968,"435":1974,"436":1975,"437":1977,"438":1978,"439":1983,"440":1985,"441":1987,"443":1993,"444":1994,"445":1995,"446":1998,"447":2000,"448":2005,"450":2014,"451":2015,"452":2016,"453":2018,"454":2023,"455":2024,"456":2026,"457":2029,"458":2030,"459":2031,"460":2032,"461":2035,"462":2045},{"0":52,"1":85,"2":138,"3":210,"4":235,"5":375,"6":436,"7":497,"8":508,"9":522,"10":585,"11":636,"12":781,"13":850,"14":941,"15":1006,"16":1036,"17":1038,"18":1039,"19":1062,"20":1069,"21":1083,"22":1091,"23":1118,"24":1163,"25":1190,"26":1191,"27":1192,"28":1194,"29":1204,"31":1213,"32":1223,"33":1235,"34":1236,"35":1242,"36":1244,"37":1251,"38":1256,"39":1258,"40":1270,"41":1273,"42":1286,"43":1292,"44":1304,"46":1311,"47":1339,"48":1347,"49":1357,"50":1384,"51":1401,"52":1403,"53":1404,"55":1430,"57":1433,"58":1441,"59":1447,"60":1461,"61":1469,"62":1474,"63":1490,"64":1494,"65":1495,"66":1497,"67":1552,"68":1553,"69":1557,"70":1613,"72":1627,"73":1630,"74":1631,"75":1632,"76":1654,"77":1662,"78":1664,"80":1674,"81":1682,"82":1711,"83":1713,"84":1733,"85":1734,"86":1749,"87":1759,"88":1790,"90":1826,"91":1848,"92":1865,"93":1879,"94":1880,"95":1882,"98":1901,"99":1921,"100":1923,"103":1962,"104":1971,"105":1972,"106":1997,"107":2001,"108":2011,"110":2022},{"0":795,"1":917,"2":1081,"3":1090,"4":1125,"5":1153,"6":1155,"7":1287,"8":1295,"9":1296,"11":1362,"12":1398,"13":1399,"14":1402,"15":1478,"16":1520,"17":1535,"18":1568,"19":1660,"21":1723,"22":1757,"23":1800,"26":1857,"29":1869,"30":1874,"32":1936,"33":1952,"34":2002,"35":2020},{"0":1057,"1":1160,"2":1443,"6":1645,"8":1699,"9":1725,"10":1830,"12":1881,"13":1890,"16":1949,"17":2007,"18":2019},{"0":1110,"2":1212,"3":1249,"5":1320,"6":1336,"8":1383,"9":1400,"10":1462,"11":1465,"12":1471,"13":1476,"14":1515,"15":1521,"17":1634,"22":1861},{"0":1024,"1":1043,"5":1367,"6":1475,"7":1477,"9":1491,"11":1566,"12":1605,"13":1729,"17":1868,"18":1873,"20":1960},{"3":1171,"8":1386,"9":1391,"12":1470,"18":1771,"19":1794,"21":1806},{"5":1341,"14":1763,"17":1910,"18":1911,"20":2006},{"9":1446,"13":1629,"16":1807,"17":1813,"19":1922,"20":2009},{"0":1045,"2":1074,"3":1079,"9":1338,"10":1452,"12":1651,"16":1979},{"9":1604},{"4":1344},{"9":1508,"15":1698},[],[],[],[],[],[],[],[],[]]