[{"0":0,"1":1,"2":3,"5":7,"6":8,"8":10,"9":11,"10":12,"11":13,"12":14,"13":15,"14":16,"15":17,"17":19,"18":20,"19":21,"20":22,"21":23,"22":24,"23":25,"24":26,"25":27,"26":28,"27":29,"28":30,"29":31,"30":32,"31":33,"32":34,"33":35,"34":36,"35":37,"36":38,"37":39,"38":40,"40":42,"41":43,"42":45,"43":46,"44":48,"45":49,"46":50,"47":51,"48":52,"49":53,"50":54,"51":55,"52":56,"53":57,"54":58,"55":59,"56":60,"57":61,"58":62,"60":64,"61":65,"62":66,"63":67,"64":68,"65":69,"66":70,"67":71,"68":72,"69":73,"71":75,"72":76,"73":77,"74":78,"75":79,"76":80,"77":81,"78":82,"79":83,"80":84,"81":85,"82":86,"83":87,"84":88,"85":89,"86":90,"87":91,"88":92,"89":93,"90":94,"91":95,"92":96,"93":97,"94":98,"95":99,"96":100,"97":101,"98":102,"99":103,"100":104,"101":105,"102":106,"103":107,"104":108,"105":111,"106":112,"107":113,"108":114,"109":115,"110":116,"111":117,"112":118,"113":119,"114":120,"115":121,"117":123,"118":124,"119":125,"120":126,"121":127,"122":128,"123":129,"124":130,"125":131,"126":132,"127":133,"129":135,"130":136,"131":137,"132":138,"133":139,"134":140,"135":141,"136":143,"137":144,"138":145,"139":146,"140":147,"141":148,"142":149,"143":150,"144":151,"145":152,"146":153,"147":155,"148":156,"149":157,"150":158,"151":159,"152":160,"153":161,"154":162,"155":163,"156":164,"157":165,"158":166,"159":167,"160":169,"161":170,"163":172,"164":173,"166":175,"167":176,"168":177,"169":178,"170":181,"171":182,"172":183,"173":184,"174":185,"175":186,"176":187,"177":188,"178":189,"179":190,"180":191,"181":192,"182":193,"183":194,"184":195,"185":196,"186":197,"187":198,"188":199,"189":200,"190":201,"191":202,"192":203,"193":204,"194":205,"195":206,"196":207,"197":208,"198":209,"199":210,"200":211,"201":212,"202":213,"203":214,"204":215,"205":216,"206":217,"207":218,"208":219,"209":220,"210":221,"211":222,"212":223,"213":224,"214":225,"215":226,"216":227,"217":228,"218":229,"219":230,"220":231,"221":232,"222":233,"223":234,"224":235,"225":236,"226":237,"227":238,"228":239,"229":240,"230":241,"231":242,"232":243,"233":244,"234":245,"235":246,"236":247,"237":248,"238":249,"239":250,"240":251,"241":252,"242":253,"244":255,"245":256,"246":257,"247":258,"248":259,"249":260,"250":261,"251":262,"253":264,"254":265,"255":266,"256":268,"257":269,"258":270,"259":271,"260":272,"261":273,"262":274,"264":276,"265":277,"266":278,"267":279,"268":280,"269":281,"270":282,"271":283,"272":284,"273":285,"274":286,"275":287,"276":288,"277":289,"278":290,"279":291,"280":292,"281":293,"282":294,"283":295,"284":296,"285":297,"286":298,"287":299,"288":300,"289":301,"290":302,"291":303,"292":304,"293":305,"294":306,"295":307,"296":309,"297":310,"298":311,"299":312,"300":313,"301":314,"302":315,"303":316,"304":317,"305":318,"306":319,"307":320,"308":321,"309":322,"310":323,"311":324,"312":325,"313":326,"314":327,"315":328,"316":329,"317":330,"318":331,"319":332,"320":333,"321":334,"322":335,"323":336,"324":337,"325":338,"326":339,"328":342,"329":343,"331":345,"332":346,"333":347,"334":348,"335":349,"336":350,"337":351,"338":352,"339":353,"340":354,"341":355,"342":356,"343":357,"344":358,"345":359,"346":360,"347":362,"348":363,"349":364,"350":365,"351":366,"352":367,"353":368,"355":370,"356":371,"357":372,"358":373,"359":374,"361":376,"362":377,"363":378,"364":379,"365":380,"366":381,"367":382,"368":383,"369":384,"370":385,"371":386,"372":388,"373":389,"374":390,"375":391,"376":392,"377":393,"378":394,"379":395,"380":396,"381":397,"382":398,"383":399,"384":400,"385":401,"386":402,"387":403,"388":404,"389":405,"390":407,"391":408,"393":410,"394":411,"395":412,"396":413,"397":414,"398":415,"399":416,"400":417,"401":418,"402":419,"403":420,"404":421,"405":422,"406":423,"407":424,"408":425,"409":426,"410":427,"411":428,"412":429,"413":430,"414":431,"415":432,"416":433,"418":435,"419":436,"420":437,"421":438,"422":439,"423":440,"424":441,"425":442,"426":443,"427":444,"429":446,"430":447,"431":449,"432":450,"434":452,"436":454,"437":455,"438":456,"439":457,"440":458,"441":459,"442":460,"443":461,"444":462,"445":463,"446":464,"447":465,"448":466,"449":467,"450":468,"451":469,"452":470,"453":471,"454":472,"455":473,"456":474,"457":475,"458":476,"459":477,"460":478,"462":480,"463":481,"464":482,"465":484,"467":486,"468":487,"469":488,"470":489,"472":492,"473":493,"474":494,"475":495,"476":496,"477":497,"478":498,"480":500,"481":501,"482":502,"483":504,"484":505,"485":506,"486":507,"487":508,"488":509,"489":510,"490":511,"491":513,"492":515,"493":517,"494":519,"495":530,"496":532,"497":535,"498":536,"499":540,"500":543,"501":546,"502":547,"503":553,"504":557,"505":559,"506":564,"507":568,"508":580,"509":589,"510":592,"511":597,"512":600,"513":604,"514":610,"515":613,"516":615,"517":619,"518":623,"519":629,"520":633,"521":640,"522":645,"523":658,"524":662,"525":669,"526":671,"527":688,"528":695,"529":703,"530":704,"531":705,"532":711,"533":712,"534":714,"535":716,"536":717,"537":735,"538":737,"539":746,"540":755,"541":758,"542":764,"543":765,"544":768,"545":778,"546":779,"547":784,"548":786,"549":792,"550":796,"551":798,"552":804,"553":817,"554":822,"555":827,"556":830,"557":839,"558":850,"559":856,"560":857,"561":864,"562":867,"563":868,"564":869,"565":874,"566":886,"567":889,"568":910,"570":925,"571":926,"572":927,"573":929,"574":930,"575":935,"576":937,"577":943,"578":945,"579":965,"580":966,"581":971,"582":976,"583":979,"584":991,"585":997,"586":1006,"587":1012,"588":1016,"589":1019,"590":1021},{"0":2,"1":6,"2":44,"3":47,"4":109,"5":110,"6":142,"7":154,"8":168,"9":179,"10":180,"11":267,"12":308,"13":340,"14":361,"16":406,"17":448,"18":483,"19":490,"20":503,"21":512,"22":521,"23":538,"24":550,"25":551,"26":552,"27":554,"28":556,"29":560,"30":561,"31":571,"32":572,"33":586,"34":594,"35":598,"36":608,"38":612,"39":617,"40":618,"41":630,"42":637,"43":638,"44":641,"45":642,"46":644,"47":648,"48":665,"49":672,"50":675,"51":676,"52":684,"53":690,"54":696,"55":701,"56":702,"57":706,"58":707,"59":713,"60":718,"61":720,"62":722,"63":723,"64":725,"65":733,"66":736,"67":739,"68":741,"69":744,"70":749,"71":751,"72":760,"73":762,"74":766,"75":767,"76":777,"77":782,"78":789,"79":799,"80":800,"81":802,"82":805,"83":806,"84":807,"85":816,"86":825,"87":829,"88":832,"89":833,"90":836,"91":837,"92":848,"94":855,"95":859,"96":860,"97":871,"98":873,"99":876,"100":877,"101":880,"102":882,"103":885,"104":890,"105":891,"106":893,"108":896,"109":899,"111":902,"112":904,"114":908,"115":911,"116":924,"117":928,"118":931,"119":938,"120":944,"121":948,"122":955,"123":956,"124":959,"125":964,"126":970,"127":973,"128":975,"129":981,"130":982,"132":986,"133":1008,"136":1011,"137":1013,"138":1014,"139":1015,"140":1018,"141":1023},{"1":524,"3":534,"4":541,"5":544,"6":562,"7":575,"8":576,"9":577,"10":588,"11":590,"12":593,"13":595,"14":606,"15":607,"16":621,"17":624,"18":625,"21":639,"22":652,"23":655,"24":657,"25":659,"27":663,"28":664,"29":667,"30":677,"31":678,"32":679,"33":681,"34":682,"35":689,"36":699,"37":715,"38":719,"39":721,"40":727,"41":734,"42":740,"43":743,"44":747,"45":761,"46":769,"47":773,"48":775,"49":776,"50":783,"51":788,"52":794,"53":803,"54":810,"55":813,"56":818,"57":823,"58":842,"59":844,"60":846,"61":851,"62":853,"63":854,"64":872,"65":879,"66":884,"67":887,"68":897,"69":898,"71":912,"72":918,"73":936,"74":941,"75":942,"76":952,"77":960,"78":969,"79":978,"80":994,"81":995,"82":1000,"83":1001,"84":1004,"85":1007},{"0":514,"1":516,"2":518,"3":520,"4":525,"5":528,"6":529,"7":558,"8":563,"9":565,"10":566,"11":570,"12":573,"13":574,"14":581,"15":584,"16":585,"17":587,"18":599,"19":605,"20":611,"21":626,"22":634,"23":650,"24":656,"25":674,"26":687,"27":691,"28":693,"29":697,"30":698,"31":700,"32":708,"33":710,"34":726,"35":729,"36":732,"37":738,"40":757,"41":759,"42":770,"43":772,"44":774,"45":780,"46":781,"47":785,"49":795,"50":814,"51":820,"52":831,"54":843,"56":852,"57":858,"58":863,"59":881,"60":883,"61":888,"62":892,"63":905,"64":909,"65":914,"66":917,"69":934,"71":950,"72":957,"73":958,"74":962,"75":963,"76":983,"77":987,"78":990,"79":993,"80":1017},{"0":531,"1":539,"2":545,"3":548,"4":555,"5":567,"6":583,"7":591,"8":596,"9":602,"10":614,"11":620,"12":628,"13":631,"14":636,"15":646,"16":649,"17":651,"18":673,"19":680,"20":692,"21":742,"22":750,"23":787,"24":790,"25":812,"26":815,"27":821,"28":824,"29":834,"30":838,"31":840,"32":841,"33":861,"35":875,"36":919,"37":920,"38":922,"39":933,"40":940,"41":967,"42":980,"43":989,"44":999,"45":1002,"46":1020},{"0":527,"1":533,"2":582,"3":603,"4":616,"5":647,"6":666,"8":685,"9":694,"10":724,"11":730,"12":771,"13":793,"14":797,"15":808,"16":811,"17":819,"18":826,"19":870,"20":901,"21":906,"22":949,"23":951,"25":972,"26":977,"27":992,"28":996,"29":1003},{"0":579,"1":622,"2":686,"3":728,"4":753,"5":754,"6":801,"7":866,"8":878,"9":894,"11":932,"12":968,"13":974,"14":985,"15":998},{"0":523,"1":549,"2":569,"3":601,"4":643,"5":661,"6":731,"8":946,"9":954,"10":988},{"0":537,"1":542,"2":627,"3":654,"4":668,"6":745,"7":748,"8":845},{"0":578,"2":809,"3":947,"4":961,"5":1022},[],[]]