[{"0":0,"1":1,"2":2,"3":5,"4":6,"5":7,"6":8,"7":9,"8":10,"9":11,"10":12,"11":13,"12":14,"13":16,"14":17,"15":18,"16":19,"17":20,"18":21,"19":22,"20":23,"21":24,"22":25,"23":26,"24":27,"25":28,"26":29,"27":30,"28":31,"29":32,"30":34,"31":35,"32":36,"33":37,"34":40,"35":41,"36":42,"37":43,"38":44,"39":46,"40":47,"41":48,"42":49,"43":50,"44":51,"45":52,"46":53,"47":55,"48":57,"49":58,"50":59,"51":60,"52":61,"53":62,"54":63,"55":65,"56":66,"57":67,"58":68,"59":69,"60":71,"61":74,"62":75,"63":77,"64":79,"65":80,"66":81,"67":82,"68":83,"69":84,"70":85,"71":86,"72":88,"73":89,"74":91,"75":92,"76":93,"77":96,"78":98,"79":99,"80":101,"81":102,"82":103,"83":104,"84":105,"85":106,"86":107,"87":108,"88":109,"89":110,"90":111,"91":112,"92":113,"94":115,"95":116,"96":117,"97":118,"98":119,"99":120,"100":121,"101":122,"102":123,"103":124,"104":125,"105":126,"106":128,"107":129,"108":130,"109":134,"110":135,"111":137,"112":138,"113":139,"114":140,"115":141,"116":142,"117":143,"118":144,"119":145,"120":146,"121":148,"122":149,"123":150,"124":151,"125":152,"126":154,"127":155,"128":156,"129":157,"130":160,"131":162,"132":163,"133":164,"134":165,"135":168,"136":170,"137":173,"138":174,"139":176,"140":179,"141":180,"142":181,"143":182,"144":184,"145":185,"146":188,"147":189,"148":191,"149":192,"150":193,"151":194,"152":195,"153":197,"154":198,"155":199,"156":200,"157":201,"158":202,"159":203,"160":204,"161":205,"162":207,"163":208,"164":209,"165":210,"166":211,"167":212,"168":213,"169":214,"170":215,"171":216,"172":288,"173":289,"174":290,"175":291,"176":292,"177":293,"178":294,"179":295,"180":296,"181":298,"182":299,"183":300,"184":301,"185":302,"186":304,"187":305,"188":306,"189":309,"190":310,"193":314,"194":316,"195":317,"196":318,"197":319,"198":320,"199":321,"200":322,"201":323,"202":325,"203":326,"204":329,"205":330,"206":331,"207":334,"208":335,"209":336,"210":338,"211":339,"212":340,"213":341,"214":342,"215":343,"216":344,"217":345,"218":346,"219":347,"220":348,"221":349,"222":350,"223":351,"224":354,"225":355,"226":356,"227":358,"228":359,"229":360,"230":363,"231":365,"232":367,"233":368,"234":369,"235":372,"236":373,"237":374,"238":375,"239":376,"240":377,"241":378,"242":379,"243":380,"244":382,"245":383,"246":384,"247":385,"248":386,"249":387,"250":388,"251":389,"252":390,"253":391,"254":392,"255":393,"256":394,"257":395,"258":397,"259":398,"260":399,"261":400,"262":401,"263":403,"264":404,"265":405,"266":406,"267":407,"268":408,"270":410,"271":412,"272":413,"273":415,"274":416,"275":417,"276":418,"277":419,"278":420,"279":421,"280":422,"281":423,"282":424,"283":427,"284":428,"285":429,"286":430,"287":431,"288":432,"289":433,"290":435,"291":436,"292":437,"293":438,"294":439,"295":440,"296":442,"297":443,"298":444,"299":445,"300":446,"301":447,"302":449,"303":451,"304":452,"305":453,"306":455,"307":456,"308":457,"309":459,"310":461,"311":463,"312":464,"313":465,"314":466,"315":467,"316":469,"317":470,"318":471,"319":473,"320":475,"321":477,"322":478,"323":479,"324":480,"325":482,"326":483,"327":484,"328":485,"329":486,"330":487,"331":488,"332":489,"333":490,"334":491,"335":492,"336":494,"337":495,"338":496,"339":499,"340":500,"341":501,"342":502,"343":503,"344":504,"345":595,"346":596,"347":600,"348":610,"349":626,"350":627,"351":628,"352":632,"353":635,"354":637,"355":639,"356":640,"357":645,"358":652,"359":655,"360":660,"361":667,"362":679,"363":684,"364":686,"365":701,"366":712,"367":713,"368":723,"369":732,"370":741,"371":746,"372":748,"373":756,"374":757,"375":759,"376":763,"377":765,"378":770,"379":773,"380":774,"381":777,"382":786,"383":792,"384":796,"385":800,"386":802,"387":804,"388":807,"389":810,"390":819,"391":822,"392":824,"393":825,"394":828,"395":829,"396":831,"397":835,"398":838,"399":840,"400":845,"401":847,"402":851,"403":854,"404":855,"405":861,"406":862,"407":865,"408":866,"409":869,"410":870,"411":871,"412":872,"413":876,"414":882,"415":885,"416":889,"417":897,"418":900,"419":903,"420":904,"421":906,"422":908,"423":911,"424":912,"425":919,"426":930,"427":932,"428":936,"429":939,"430":942,"431":943,"432":948,"433":956,"434":958,"435":962,"436":963,"437":965,"438":968,"439":975,"440":980,"441":982,"442":985,"443":990,"444":993,"445":999,"446":1000,"447":1002,"448":1005,"449":1011,"450":1018,"451":1023,"452":1026,"453":1027,"454":1029,"455":1030,"456":1034,"457":1037,"458":1038,"459":1041,"460":1046,"461":1048,"462":1052,"463":1057,"464":1061,"465":1065,"466":1071,"467":1075,"468":1076,"469":1081,"470":1086,"471":1088,"472":1089,"473":1090,"474":1091,"475":1094,"476":1095,"477":1108,"478":1109,"479":1111,"480":1113,"481":1114,"482":1118,"483":1121,"484":1124,"485":1125,"486":1131,"487":1143,"488":1144,"489":1151},{"0":3,"1":4,"2":15,"3":33,"4":38,"5":39,"6":45,"7":54,"8":56,"9":64,"10":70,"11":72,"12":73,"13":76,"14":78,"15":87,"16":90,"17":94,"18":95,"19":97,"20":100,"21":127,"22":131,"23":133,"24":136,"25":147,"26":153,"27":158,"28":159,"29":161,"30":166,"31":167,"32":171,"33":172,"34":175,"35":177,"36":178,"37":183,"38":186,"39":187,"40":190,"41":196,"42":206,"43":217,"44":218,"45":219,"46":222,"47":223,"48":224,"49":226,"50":227,"51":229,"52":230,"53":231,"54":232,"55":233,"56":235,"57":236,"58":237,"59":238,"60":239,"61":240,"62":241,"63":242,"64":243,"65":244,"66":245,"68":247,"69":252,"70":253,"71":255,"72":256,"73":257,"74":259,"75":260,"76":261,"77":263,"78":264,"79":266,"80":267,"81":268,"82":269,"83":270,"84":272,"85":273,"86":274,"87":278,"88":279,"89":280,"90":281,"91":283,"92":286,"93":287,"94":297,"95":303,"96":307,"97":308,"98":313,"99":315,"100":324,"101":327,"102":328,"103":332,"104":337,"105":352,"106":357,"107":361,"108":362,"109":364,"110":366,"111":370,"112":371,"113":381,"114":396,"115":402,"116":411,"117":414,"118":425,"119":434,"120":441,"121":448,"122":450,"123":454,"124":458,"125":460,"126":462,"127":468,"128":472,"129":474,"130":476,"131":481,"132":493,"133":497,"134":498,"135":505,"136":506,"137":507,"138":508,"139":510,"140":511,"141":512,"142":514,"143":515,"144":516,"145":519,"146":521,"147":524,"148":526,"149":527,"150":531,"151":532,"152":533,"153":542,"154":543,"155":545,"156":547,"157":548,"158":552,"159":553,"160":554,"161":555,"162":556,"163":557,"164":558,"165":559,"166":561,"167":563,"168":564,"169":565,"170":566,"171":567,"172":568,"173":569,"174":570,"175":571,"176":572,"177":573,"178":574,"179":575,"180":576,"181":581,"182":583,"183":586,"184":589,"185":591,"186":592,"187":598,"188":599,"189":601,"190":605,"191":607,"192":609,"193":618,"194":620,"195":621,"196":623,"197":625,"198":629,"199":630,"200":634,"201":638,"202":641,"203":642,"204":644,"205":646,"206":647,"207":648,"208":649,"209":653,"210":656,"211":665,"212":668,"213":674,"214":677,"215":678,"216":680,"217":687,"218":689,"219":691,"220":692,"221":693,"222":694,"223":695,"224":698,"225":703,"226":704,"227":711,"228":714,"229":718,"230":719,"231":724,"232":728,"233":736,"234":739,"235":751,"236":752,"237":758,"238":760,"239":766,"240":769,"241":771,"242":776,"243":780,"244":783,"245":784,"246":787,"247":795,"248":803,"249":818,"250":821,"251":830,"252":832,"253":836,"254":852,"255":857,"256":864,"257":877,"258":878,"259":879,"260":880,"261":881,"262":886,"263":888,"264":895,"265":899,"266":901,"267":902,"268":914,"269":915,"270":934,"271":952,"272":953,"273":959,"274":960,"275":969,"276":978,"277":986,"278":988,"279":989,"280":995,"281":998,"282":1004,"283":1009,"284":1010,"285":1012,"286":1013,"287":1016,"288":1021,"289":1022,"290":1025,"291":1031,"292":1036,"293":1043,"294":1045,"295":1047,"296":1049,"297":1053,"298":1055,"299":1060,"300":1064,"301":1067,"302":1068,"303":1069,"304":1070,"305":1072,"306":1074,"307":1082,"308":1084,"309":1085,"310":1098,"311":1100,"312":1101,"313":1106,"314":1112,"315":1116,"316":1123,"317":1127,"318":1132,"319":1133,"320":1136,"321":1138,"322":1145,"323":1149},[132,169,220,221,225,228,234,248,249,250,251,254,258,265,271,276,277,282,284,285,333,353,426,509,513,517,518,520,522,523,529,530,534,535,536,537,538,539,540,541,544,546,549,550,551,560,562,577,580,585,587,593,597,614,615,619,622,631,636,661,662,663,669,683,688,697,699,720,725,731,738,742,743,745,749,750,753,762,768,772,778,781,785,793,794,797,799,801,805,809,811,812,815,820,823,827,839,842,850,875,887,890,891,909,916,920,921,922,925,929,931,941,949,950,964,967,981,987,991,992,994,996,1001,1003,1007,1014,1015,1017,1019,1024,1039,1044,1051,1054,1056,1059,1066,1078,1080,1093,1097,1103,1107,1110,1117,1128,1137,1140,1142,1147,1148,1150],[262,275,525,528,578,579,594,603,608,611,672,675,702,707,709,721,727,729,730,737,755,775,788,789,791,808,813,814,834,841,844,853,859,860,863,867,868,907,910,927,928,933,935,940,944,971,973,983,984,997,1028,1035,1040,1042,1073,1077,1079,1083,1134,1139,1146],{"0":582,"1":588,"2":602,"3":604,"4":612,"5":616,"6":617,"7":633,"8":651,"9":657,"10":658,"11":664,"12":666,"13":670,"15":685,"16":690,"17":706,"18":708,"19":715,"20":716,"21":717,"22":726,"23":764,"24":790,"25":798,"26":806,"27":826,"28":837,"29":874,"30":892,"31":894,"32":898,"33":905,"34":913,"35":917,"36":946,"38":951,"39":966,"40":976,"41":1032,"42":1033,"43":1062,"44":1063,"45":1087,"46":1096,"47":1099,"48":1102,"49":1119,"50":1120,"51":1126,"52":1130},{"0":584,"1":606,"2":613,"3":624,"4":654,"5":676,"6":681,"7":682,"9":710,"10":740,"11":761,"12":779,"13":816,"14":817,"15":833,"16":873,"17":883,"18":896,"19":937,"20":954,"21":955,"22":961,"23":970,"24":977,"25":979,"26":1006,"27":1008,"28":1050,"29":1104,"30":1105,"31":1115,"32":1122,"33":1129,"34":1141},[671,722,734,744,747,767,782,846,848,856,858,893,926,972,974,1020],{"0":590,"1":659,"2":696,"3":735,"4":754,"6":938,"7":1058,"8":1092,"9":1135},[650,700,849,918,923,945],[884,924,957],[643,733]]