[{"0":0,"1":1,"2":2,"5":8,"6":9,"7":10,"9":12,"10":13,"11":14,"12":15,"13":16,"14":17,"15":19,"16":21,"17":22,"18":24,"19":25,"20":26,"21":27,"22":28,"23":29,"26":32,"27":33,"30":36,"31":37,"32":40,"33":41,"34":42,"35":43,"36":44,"37":47,"38":49,"39":50,"40":51,"41":52,"42":53,"44":56,"45":57,"46":58,"47":59,"48":60,"49":61,"50":62,"51":63,"53":65,"54":66,"55":67,"56":68,"57":70,"58":71,"59":72,"60":73,"61":74,"62":75,"63":76,"64":77,"65":78,"66":79,"67":80,"68":81,"69":82,"70":83,"72":85,"73":88,"74":89,"75":91,"76":92,"77":93,"78":94,"79":95,"80":96,"81":98,"82":99,"83":100,"84":102,"85":104,"86":105,"87":106,"88":108,"89":110,"90":111,"91":112,"92":113,"93":114,"94":115,"95":116,"96":117,"97":118,"98":119,"100":121,"101":122,"102":123,"103":124,"104":125,"105":126,"106":127,"109":131,"110":132,"112":134,"113":135,"114":136,"115":137,"116":138,"117":139,"118":140,"119":141,"120":142,"121":143,"122":144,"123":146,"125":150,"126":151,"127":152,"128":153,"129":154,"131":156,"132":157,"133":158,"135":160,"136":161,"138":163,"139":164,"140":165,"142":167,"143":168,"144":169,"145":170,"146":171,"147":172,"148":173,"149":175,"150":176,"151":177,"152":179,"153":180,"154":181,"155":182,"156":183,"158":185,"159":186,"160":187,"162":189,"163":190,"165":192,"166":193,"167":194,"168":195,"169":196,"170":197,"171":198,"172":199,"173":200,"174":201,"175":202,"176":204,"177":205,"178":206,"179":209,"180":210,"181":212,"182":213,"183":214,"184":215,"185":219,"186":220,"187":221,"188":222,"189":223,"190":224,"191":225,"192":226,"193":228,"194":229,"195":230,"196":231,"197":233,"198":234,"199":235,"200":236,"201":237,"202":238,"203":240,"204":241,"205":242,"206":243,"207":244,"208":245,"209":246,"210":248,"211":249,"212":250,"213":251,"214":252,"215":255,"216":256,"218":258,"219":259,"220":260,"222":262,"223":263,"224":264,"225":265,"226":266,"228":268,"229":269,"230":270,"232":272,"233":274,"234":275,"235":276,"236":277,"237":278,"238":279,"239":280,"240":281,"241":282,"242":285,"243":286,"244":287,"245":288,"246":289,"247":290,"248":291,"249":294,"250":295,"251":296,"252":297,"253":298,"254":300,"255":301,"256":303,"257":304,"258":305,"259":306,"260":308,"261":309,"262":310,"264":312,"266":314,"267":315,"268":316,"269":317,"270":318,"271":319,"272":320,"273":322,"274":324,"275":325,"276":326,"278":329,"279":330,"280":331,"281":332,"282":333,"284":337,"285":338,"286":339,"287":340,"288":341,"289":342,"290":345,"291":346,"292":347,"293":351,"294":352,"295":353,"296":355,"297":356,"298":357,"299":360,"300":361,"301":362,"302":363,"303":364,"304":366,"305":367,"306":368,"307":369,"308":370,"309":371,"311":373,"312":374,"313":375,"314":376,"315":377,"316":379,"317":380,"318":381,"319":382,"320":383,"322":385,"323":386,"324":387,"325":390,"327":392,"328":393,"329":394,"330":395,"331":396,"332":397,"333":399,"335":404,"337":406,"338":407,"339":408,"340":409,"341":410,"342":411,"343":412,"344":414,"345":415,"346":416,"347":417,"349":419,"350":420,"351":421,"352":422,"353":423,"354":424,"355":425,"357":427,"360":431,"362":433,"363":434,"364":435,"365":437,"366":438,"367":439,"368":440,"369":441,"370":442,"371":443,"372":444,"373":445,"374":446,"375":447,"376":448,"377":449,"378":450,"380":452,"381":453,"382":455,"383":456,"384":458,"385":461,"386":462,"387":463,"388":465,"389":466,"390":467,"391":468,"392":469,"393":470,"394":471,"395":472,"396":473,"397":476,"398":477,"399":478,"400":481,"401":482,"402":483,"403":484,"404":485,"405":486,"406":487,"407":489,"408":490,"409":491,"410":492,"411":493,"412":494,"413":495,"414":496,"415":497,"416":498,"417":500,"418":501,"419":502,"420":503,"421":504,"422":505,"423":506,"424":507,"425":508,"426":510,"428":521,"429":524,"430":527,"431":529,"432":535,"433":539,"434":542,"435":544,"436":545,"437":546,"438":551,"440":561,"442":563,"443":564,"444":566,"445":569,"446":572,"447":574,"448":577,"449":580,"450":584,"451":586,"452":588,"453":591,"454":594,"455":606,"456":609,"457":612,"458":620,"459":624,"460":626,"461":628,"462":630,"463":634,"464":639,"465":642,"466":645,"467":652,"468":654,"469":656,"470":659,"471":662,"473":664,"474":669,"475":670,"476":671,"477":672,"478":679,"479":683,"480":684,"481":691,"482":695,"483":700,"484":704,"485":705,"486":706,"487":707,"488":709,"489":710,"490":712,"491":719,"492":720,"493":723,"494":724,"495":726,"496":731,"497":732,"498":733,"499":735,"500":739,"501":740,"502":742,"503":743,"504":744,"505":745,"506":749,"507":755,"508":758,"509":759,"510":765,"512":768,"514":775,"516":778,"517":780,"518":782,"519":785,"520":788,"521":789,"522":793,"523":794,"524":797,"525":798,"526":801,"527":804,"528":807,"529":809,"530":811,"531":812,"532":814,"533":817,"534":818,"536":825,"537":826,"538":827,"539":830,"540":831,"541":836,"542":844,"543":845,"544":851,"545":852,"546":856,"547":862,"548":866,"549":869,"550":872,"551":873,"552":880,"553":881,"554":890,"555":893,"556":896,"557":897,"558":898,"559":900,"560":901,"561":903,"562":908,"563":909,"564":911,"565":913,"566":918,"567":921,"568":922,"569":927,"570":931,"571":932,"572":942,"573":946,"574":948,"575":952,"576":957,"577":962,"578":964,"579":967,"580":974,"581":979,"582":983,"583":985,"584":986,"585":987,"586":990,"587":996,"588":997,"589":1000,"590":1003,"591":1005,"592":1006,"593":1007,"594":1008,"595":1011,"596":1014,"597":1019,"598":1021,"599":1022},{"0":4,"1":5,"2":7,"3":18,"4":20,"5":23,"6":38,"7":45,"8":46,"9":48,"10":55,"11":69,"12":86,"13":87,"14":90,"15":97,"16":101,"17":103,"18":107,"19":109,"20":130,"21":145,"22":148,"23":149,"24":174,"25":178,"26":203,"27":207,"28":208,"29":211,"30":216,"31":217,"32":227,"33":232,"34":247,"35":253,"36":254,"37":283,"38":284,"40":293,"41":302,"42":307,"43":323,"45":334,"46":343,"47":344,"48":348,"49":349,"50":354,"51":358,"52":359,"53":365,"54":378,"55":388,"56":389,"57":398,"58":402,"59":403,"60":413,"61":428,"62":436,"63":454,"64":457,"65":459,"66":460,"67":464,"68":474,"69":475,"70":479,"71":480,"72":488,"73":499,"74":509,"75":512,"76":513,"77":514,"78":516,"79":518,"80":519,"81":522,"82":523,"83":528,"84":530,"85":534,"86":540,"87":541,"88":543,"89":547,"90":550,"91":553,"92":567,"93":573,"94":579,"95":581,"96":582,"97":585,"98":589,"99":590,"100":593,"101":596,"102":599,"103":601,"104":603,"105":610,"106":611,"107":615,"108":632,"109":633,"110":635,"111":636,"112":637,"113":640,"114":641,"115":643,"116":653,"117":658,"118":661,"119":666,"120":667,"121":675,"122":676,"123":677,"124":678,"125":680,"126":686,"127":688,"128":690,"129":694,"130":696,"132":708,"133":711,"134":715,"135":716,"136":718,"137":729,"138":734,"139":737,"140":746,"141":748,"142":752,"143":753,"144":754,"145":756,"146":757,"147":769,"148":770,"149":771,"150":773,"151":779,"152":783,"153":799,"154":803,"155":808,"156":810,"157":815,"158":819,"159":822,"160":829,"161":834,"162":839,"163":841,"164":846,"165":847,"166":849,"167":850,"168":853,"169":858,"170":859,"171":860,"172":861,"173":864,"174":867,"175":868,"176":876,"178":882,"179":883,"180":886,"181":888,"182":891,"183":895,"184":899,"185":902,"186":904,"187":907,"188":912,"189":914,"190":915,"191":916,"192":923,"193":930,"194":935,"195":938,"196":939,"197":940,"198":941,"199":943,"200":945,"201":947,"202":950,"203":954,"204":959,"205":960,"206":965,"207":970,"208":971,"209":975,"210":980,"211":982,"212":984,"213":988,"214":991,"215":992,"216":993,"218":995,"219":999,"220":1001,"221":1004,"222":1009,"223":1013,"224":1020},{"0":39,"1":218,"2":273,"3":299,"4":321,"5":335,"6":350,"7":400,"8":520,"9":526,"10":532,"11":533,"12":536,"13":537,"14":538,"15":549,"16":552,"17":558,"18":559,"19":568,"20":575,"21":583,"22":602,"23":604,"24":605,"25":607,"26":619,"27":622,"28":623,"29":625,"30":631,"31":646,"32":648,"34":674,"35":689,"36":692,"37":717,"38":725,"39":736,"40":750,"41":761,"42":762,"43":763,"44":767,"45":776,"46":781,"48":795,"49":806,"50":832,"51":835,"52":848,"53":855,"54":857,"55":865,"56":870,"57":889,"58":920,"59":924,"60":925,"61":934,"62":951,"63":956,"64":969,"65":977,"66":978,"67":1002,"68":1023},{"0":239,"1":525,"2":548,"3":555,"4":565,"5":570,"6":595,"7":608,"9":629,"10":647,"11":650,"12":651,"13":660,"14":693,"15":701,"16":727,"17":747,"18":786,"19":790,"21":805,"22":863,"23":871,"24":884,"25":894,"26":906,"27":910,"28":928,"29":944,"30":953,"31":955},{"0":517,"1":587,"3":598,"4":600,"5":614,"6":649,"7":673,"8":741,"9":751,"10":772,"12":802,"13":820,"14":824,"15":877,"16":905,"17":936,"18":949,"19":961,"20":966,"21":972,"22":976,"23":1016},{"0":515,"1":531,"2":560,"3":571,"4":597,"6":713,"7":730,"8":760,"9":837,"10":840,"11":842,"12":917,"13":929,"14":998},{"0":613,"1":617,"3":682,"4":697,"5":702,"6":792,"7":813,"8":816,"9":833,"10":887,"11":968,"12":973,"13":989,"15":1017},{"0":576,"1":616,"2":618,"3":685,"6":728,"7":784,"9":919},{"0":621,"1":657,"2":699,"3":721,"5":787,"6":843,"7":854,"8":926,"9":1018},{"2":874,"5":963,"6":981},[],[],[],[]]