[{"0":0,"1":1,"2":3,"3":4,"4":5,"5":7,"6":8,"7":9,"8":10,"9":11,"10":12,"11":13,"12":14,"13":15,"14":17,"15":18,"16":19,"18":21,"19":22,"20":23,"22":28,"23":29,"24":30,"25":31,"26":32,"27":33,"28":34,"29":35,"31":37,"32":38,"33":42,"34":43,"35":45,"36":46,"37":47,"38":48,"39":49,"40":50,"41":51,"44":54,"45":55,"46":56,"47":57,"48":58,"49":59,"50":60,"51":61,"52":62,"53":63,"54":66,"55":67,"56":68,"57":70,"59":72,"60":73,"62":75,"63":77,"64":79,"65":80,"66":81,"67":82,"68":83,"69":84,"70":85,"71":86,"72":87,"73":88,"74":89,"75":90,"76":91,"77":92,"78":95,"79":96,"80":97,"81":98,"82":100,"83":101,"84":102,"85":103,"86":104,"87":105,"88":106,"89":107,"90":108,"91":110,"92":111,"94":113,"95":114,"96":115,"97":116,"98":117,"99":118,"100":119,"101":120,"102":121,"103":122,"104":123,"105":124,"106":125,"107":126,"108":127,"109":128,"110":129,"111":130,"114":133,"115":134,"116":135,"117":136,"118":139,"119":140,"120":141,"121":143,"122":144,"124":147,"125":148,"126":149,"127":150,"128":151,"129":152,"130":153,"131":154,"132":155,"133":156,"134":157,"135":158,"136":160,"137":161,"138":162,"139":163,"140":164,"141":165,"143":167,"144":168,"146":170,"147":171,"148":172,"149":173,"150":175,"151":176,"152":177,"153":178,"154":179,"155":181,"156":182,"158":185,"159":187,"160":188,"161":189,"162":190,"163":191,"164":192,"165":193,"166":194,"167":195,"168":196,"169":197,"170":199,"171":200,"172":202,"173":203,"174":204,"175":205,"176":207,"177":208,"178":210,"179":211,"180":213,"181":214,"182":215,"183":217,"184":218,"185":219,"186":221,"187":222,"188":223,"189":224,"190":225,"191":226,"192":227,"193":228,"194":229,"195":230,"196":231,"197":232,"198":234,"199":235,"200":236,"201":237,"202":239,"203":240,"204":241,"206":243,"207":244,"208":245,"209":246,"210":248,"211":250,"212":251,"213":252,"214":254,"215":255,"216":256,"217":257,"220":261,"221":262,"222":264,"224":266,"225":267,"226":268,"227":269,"228":270,"229":271,"230":272,"231":275,"233":278,"234":279,"235":280,"237":282,"238":283,"239":284,"240":285,"241":286,"242":287,"244":289,"245":290,"246":291,"247":292,"248":293,"249":295,"250":296,"251":297,"252":298,"253":299,"254":300,"255":303,"256":304,"258":306,"259":307,"260":308,"261":309,"262":311,"263":312,"264":313,"265":314,"266":315,"267":316,"268":318,"269":320,"270":321,"271":323,"272":324,"273":325,"275":327,"276":328,"277":329,"278":330,"280":333,"281":334,"282":335,"283":336,"284":337,"285":338,"286":339,"287":340,"288":341,"289":342,"290":343,"291":344,"292":346,"293":347,"294":348,"295":349,"296":350,"297":351,"298":352,"299":353,"300":355,"301":356,"302":357,"303":358,"304":359,"305":360,"306":361,"307":362,"308":363,"309":364,"310":367,"311":368,"312":369,"313":370,"314":371,"315":373,"316":374,"317":375,"318":376,"320":378,"322":380,"323":381,"324":382,"325":383,"326":384,"327":385,"328":387,"329":388,"330":389,"331":390,"332":391,"333":392,"334":393,"335":394,"336":395,"337":396,"338":397,"340":399,"341":400,"342":401,"343":402,"344":403,"345":404,"346":405,"347":406,"348":407,"349":408,"350":409,"351":410,"352":411,"353":412,"354":415,"357":421,"358":424,"359":425,"360":427,"361":428,"362":429,"363":430,"364":431,"365":433,"366":434,"367":435,"368":436,"369":437,"370":438,"371":440,"374":445,"375":446,"376":447,"377":448,"378":449,"379":450,"380":454,"381":455,"382":456,"383":458,"384":459,"385":460,"386":461,"387":462,"388":463,"389":464,"390":465,"391":466,"392":467,"393":468,"394":471,"395":472,"396":473,"397":474,"398":475,"399":476,"400":477,"401":478,"402":479,"403":480,"404":481,"405":482,"406":483,"407":484,"408":485,"409":486,"410":487,"411":489,"412":490,"413":491,"414":492,"415":493,"416":495,"417":497,"418":498,"419":500,"420":501,"421":502,"422":503,"423":506,"424":509,"425":510,"426":511,"427":512,"428":516,"429":519,"430":526,"431":527,"432":530,"433":532,"434":533,"435":535,"436":537,"437":538,"438":539,"439":541,"440":543,"441":544,"442":545,"443":546,"444":549,"445":551,"446":552,"447":553,"448":555,"449":558,"450":559,"451":560,"452":561,"453":562,"454":563,"455":564,"456":566,"457":567,"458":568,"459":569,"460":571,"461":572,"462":575,"463":578,"464":579,"465":582,"466":586,"467":588,"468":589,"469":591,"470":595,"471":596,"472":598,"473":599,"474":600,"475":602,"476":603,"477":608,"478":610,"479":612,"480":614,"481":615,"482":616,"483":617,"484":618,"485":620,"486":623,"487":625,"488":627,"489":628,"490":630,"491":632,"492":633,"493":634,"494":642,"495":643,"496":644,"497":645,"498":651,"499":652,"500":656,"501":657,"502":659,"503":663,"504":664,"505":669,"506":674,"507":677,"508":679,"509":684,"510":688,"511":689,"512":690,"513":691,"514":692,"515":694,"516":695,"517":696,"518":700,"519":701,"520":702,"521":708,"522":709,"523":710,"524":711,"525":712,"526":714,"527":719,"528":722,"529":723,"530":725,"531":726,"532":727,"533":728,"534":731,"535":733,"536":735,"537":736,"538":739,"539":741,"540":743,"541":744,"542":745,"543":746,"544":747,"545":749,"546":750,"547":754,"548":759,"549":761,"550":763,"551":768,"552":769,"553":770,"554":771,"555":772,"556":775,"557":777,"558":779,"559":780,"560":781,"561":783,"562":784,"563":786,"564":787,"565":788,"566":790,"567":791,"568":792,"569":793,"570":795,"571":797,"572":802,"573":803,"574":804,"575":806,"576":812,"577":814,"578":815,"579":817,"580":823,"581":824,"582":826,"583":832,"584":841,"585":842,"586":843,"587":844,"588":846,"589":849,"590":851,"591":852,"592":853,"594":858,"595":860,"596":864,"597":866,"598":867,"599":870,"600":871,"601":877,"602":879,"603":880,"604":882,"605":884,"606":885,"607":886,"608":888,"609":891,"610":892,"611":895,"613":905,"614":909,"615":911,"616":912,"617":913,"618":914,"619":919,"620":920,"621":925,"622":926,"623":927,"624":929,"625":930,"626":933,"627":938,"628":939,"629":940,"630":943,"631":946,"632":947,"633":948,"634":949,"635":953,"636":954,"637":957,"638":959,"639":960,"640":962,"641":964,"642":965,"643":966,"644":969,"645":971,"646":974,"647":976,"648":979,"649":983,"650":987,"651":988,"652":990,"653":992,"654":993,"655":994,"656":996,"657":1000,"658":1002,"659":1003,"660":1007,"661":1008,"662":1009,"663":1010,"664":1012,"665":1013,"666":1018,"667":1022},{"0":2,"1":6,"2":16,"3":24,"4":26,"5":27,"6":40,"7":41,"8":44,"9":64,"10":65,"11":69,"12":76,"13":78,"14":93,"15":94,"16":99,"17":138,"18":142,"19":159,"20":174,"21":180,"23":186,"24":198,"25":201,"26":206,"27":209,"28":212,"29":216,"30":220,"31":233,"32":247,"33":253,"34":259,"35":263,"36":273,"37":274,"38":276,"39":294,"40":301,"41":302,"42":317,"43":319,"44":322,"45":345,"46":354,"47":365,"48":366,"49":372,"50":386,"51":413,"52":414,"53":416,"54":417,"55":420,"56":422,"57":423,"58":426,"59":432,"60":439,"61":443,"62":444,"63":451,"64":452,"65":453,"66":457,"67":470,"68":488,"69":494,"70":496,"71":499,"72":504,"73":505,"74":507,"75":513,"76":517,"77":520,"78":523,"79":525,"80":529,"81":531,"82":534,"83":536,"84":540,"85":542,"86":547,"87":548,"88":550,"89":554,"90":557,"91":565,"92":570,"93":580,"95":593,"96":594,"97":605,"98":607,"99":609,"100":611,"101":613,"102":622,"104":629,"105":631,"106":635,"107":636,"108":638,"109":641,"110":647,"111":655,"112":660,"113":666,"114":670,"115":671,"116":673,"117":678,"118":680,"119":681,"120":682,"121":683,"122":685,"123":687,"124":697,"125":698,"126":706,"127":713,"128":715,"129":716,"130":718,"131":721,"132":724,"133":730,"134":732,"135":737,"136":738,"137":740,"138":748,"139":751,"140":752,"141":756,"142":758,"143":760,"144":762,"145":765,"146":767,"147":773,"148":774,"149":776,"150":778,"151":782,"152":785,"153":789,"154":794,"155":796,"156":798,"157":799,"158":805,"159":808,"160":809,"161":810,"162":811,"163":813,"164":819,"165":825,"166":831,"167":835,"168":836,"169":837,"170":839,"171":840,"172":845,"173":847,"174":848,"175":850,"176":862,"177":863,"178":865,"179":868,"180":869,"181":872,"182":875,"183":876,"184":878,"185":881,"186":887,"187":889,"188":893,"189":894,"190":900,"191":901,"192":903,"193":904,"194":907,"195":908,"196":916,"197":917,"198":918,"199":923,"200":931,"201":932,"202":935,"203":936,"204":942,"205":945,"206":950,"207":951,"208":952,"209":955,"210":958,"211":963,"212":967,"213":968,"214":972,"215":973,"216":978,"217":982,"218":985,"219":986,"220":989,"221":995,"222":998,"223":1004,"224":1014,"225":1016,"226":1019,"227":1020},{"0":39,"1":109,"2":137,"3":145,"4":238,"5":249,"6":310,"7":331,"8":469,"9":508,"10":515,"11":521,"12":522,"14":528,"15":556,"16":577,"17":597,"18":604,"19":606,"20":621,"21":637,"22":639,"23":640,"24":649,"25":650,"27":661,"28":662,"29":665,"30":686,"31":699,"32":705,"33":720,"34":734,"35":742,"36":753,"37":757,"38":807,"39":822,"40":833,"41":856,"42":874,"43":890,"44":899,"45":902,"46":906,"47":921,"48":934,"49":937,"50":941,"51":944,"52":956,"53":961,"54":975,"55":980,"56":984,"57":997,"58":999,"59":1006,"60":1017,"61":1023},{"0":518,"1":573,"2":585,"3":587,"5":648,"6":654,"7":676,"8":704,"11":755,"12":764,"13":800,"14":873,"15":1001,"16":1005,"17":1011},{"0":619,"1":626,"2":703,"3":801,"4":820,"5":834,"6":854,"7":896,"8":910,"9":915,"11":977},[514,583,693,766,828,838,1015],{"1":592,"3":672,"4":729,"5":859},{"2":827,"3":897},[],[],[],[]]