[{"0":0,"1":1,"2":2,"3":3,"4":5,"5":6,"6":8,"7":9,"8":10,"9":11,"11":13,"12":14,"13":15,"14":16,"15":17,"16":18,"17":20,"18":21,"19":23,"20":24,"21":25,"22":27,"23":28,"24":30,"25":31,"26":32,"27":33,"28":34,"29":36,"30":37,"31":38,"32":41,"33":42,"34":43,"35":44,"36":45,"37":46,"38":47,"39":48,"40":49,"41":50,"42":51,"43":52,"44":53,"45":54,"46":55,"47":56,"48":57,"50":59,"51":62,"52":63,"53":64,"54":65,"55":66,"56":67,"57":69,"58":70,"59":71,"60":72,"61":73,"62":74,"63":75,"64":76,"65":77,"66":78,"67":80,"68":81,"69":82,"70":83,"71":84,"72":86,"73":87,"74":88,"75":89,"76":90,"77":91,"78":92,"79":93,"80":95,"81":96,"82":97,"83":98,"84":99,"85":100,"86":101,"87":102,"88":105,"89":106,"90":107,"91":108,"92":109,"93":110,"94":113,"95":114,"96":115,"97":116,"98":117,"99":118,"100":119,"101":120,"102":122,"103":123,"104":124,"105":125,"106":126,"107":127,"108":128,"109":129,"111":131,"114":134,"115":135,"116":136,"117":137,"118":138,"119":139,"120":141,"121":142,"122":143,"123":144,"124":145,"125":146,"126":147,"127":148,"128":149,"129":150,"130":151,"131":152,"132":153,"133":154,"134":155,"135":156,"136":157,"137":158,"138":159,"140":161,"141":162,"142":163,"143":164,"144":166,"145":167,"146":168,"147":169,"148":170,"149":171,"150":172,"151":173,"152":174,"153":175,"154":176,"155":177,"156":178,"157":179,"158":180,"159":181,"160":182,"161":183,"162":184,"164":186,"165":187,"166":188,"167":189,"168":190,"169":191,"170":192,"171":193,"172":194,"173":195,"174":196,"175":197,"176":198,"177":199,"178":200,"179":201,"180":202,"181":203,"182":204,"183":205,"184":206,"185":207,"186":209,"189":213,"190":214,"191":215,"192":216,"193":217,"194":218,"195":219,"196":220,"197":221,"198":222,"199":223,"200":224,"201":225,"202":226,"203":227,"204":228,"205":229,"206":232,"207":233,"208":234,"209":235,"210":236,"211":237,"212":239,"213":240,"214":241,"215":242,"216":244,"217":246,"218":247,"219":248,"220":249,"221":250,"222":252,"223":255,"224":256,"225":257,"227":259,"228":260,"229":261,"230":262,"231":264,"232":265,"233":266,"234":267,"235":268,"236":269,"237":270,"238":271,"239":272,"240":273,"241":274,"242":275,"243":276,"244":277,"245":278,"246":279,"247":280,"248":281,"249":282,"250":283,"251":284,"252":286,"253":287,"254":288,"255":289,"256":290,"257":291,"258":292,"260":294,"261":296,"262":297,"263":298,"264":299,"265":300,"266":301,"267":302,"268":303,"269":304,"270":305,"271":306,"272":308,"274":311,"276":313,"278":315,"279":316,"280":317,"281":318,"282":319,"283":320,"284":321,"285":322,"286":323,"287":324,"288":325,"289":326,"290":327,"291":328,"292":329,"294":331,"295":332,"296":333,"297":334,"298":335,"299":336,"300":337,"301":338,"302":339,"303":340,"304":342,"305":344,"306":345,"307":346,"308":347,"309":348,"310":349,"311":350,"312":351,"313":352,"314":353,"315":354,"316":355,"317":356,"318":357,"319":358,"320":359,"321":360,"322":361,"323":362,"324":363,"325":364,"326":365,"327":366,"328":367,"329":368,"330":369,"331":370,"332":371,"334":374,"335":375,"336":376,"337":377,"338":378,"339":379,"340":380,"341":381,"342":382,"343":383,"344":384,"345":385,"346":386,"347":387,"348":388,"349":389,"350":390,"351":391,"352":392,"353":393,"354":395,"355":397,"356":398,"357":399,"358":400,"359":402,"360":403,"361":404,"363":406,"364":408,"365":409,"366":410,"367":411,"368":412,"369":413,"370":414,"371":415,"372":416,"373":417,"374":418,"375":419,"376":420,"377":421,"378":422,"379":423,"380":424,"381":425,"382":426,"383":427,"384":428,"385":429,"386":430,"387":431,"388":432,"389":433,"390":434,"391":435,"392":437,"393":438,"394":439,"395":440,"396":441,"397":442,"398":443,"400":446,"401":447,"402":448,"403":449,"404":450,"405":451,"406":453,"407":454,"408":455,"409":456,"410":457,"411":458,"412":459,"413":461,"414":462,"415":463,"416":464,"417":465,"418":466,"419":467,"420":468,"421":469,"422":470,"423":471,"424":472,"425":473,"426":474,"427":475,"428":476,"429":477,"430":478,"431":479,"432":480,"433":481,"434":482,"435":483,"436":484,"437":485,"438":486,"439":487,"440":488,"441":489,"442":490,"443":491,"444":492,"445":493,"446":494,"447":495,"448":496,"449":497,"450":498,"451":499,"452":500,"453":501,"454":502,"455":503,"456":504,"457":505,"458":506,"459":507,"460":508,"461":510,"462":512,"464":516,"465":518,"466":520,"467":523,"468":528,"469":535,"470":537,"471":538,"472":542,"473":543,"474":544,"475":545,"476":546,"477":550,"478":551,"479":556,"480":557,"481":559,"482":560,"483":561,"484":564,"485":565,"486":566,"487":569,"488":570,"489":571,"490":573,"491":578,"492":580,"493":581,"494":582,"495":585,"496":587,"497":588,"498":589,"499":596,"500":597,"501":612,"502":614,"503":615,"504":617,"505":624,"506":626,"507":628,"508":633,"509":638,"510":639,"511":640,"512":642,"513":644,"514":645,"515":650,"516":652,"517":656,"518":657,"519":660,"520":662,"521":663,"522":666,"523":670,"524":673,"525":676,"526":678,"527":681,"528":684,"529":685,"530":688,"531":692,"532":693,"533":695,"534":696,"535":697,"536":700,"537":702,"538":704,"539":705,"540":707,"541":711,"543":713,"544":715,"545":718,"546":725,"547":727,"548":730,"549":732,"550":733,"551":736,"552":741,"553":745,"554":752,"555":754,"556":758,"557":759,"558":760,"559":761,"560":762,"561":763,"562":764,"563":765,"564":766,"565":770,"566":774,"567":775,"568":776,"569":777,"570":778,"571":779,"572":782,"573":783,"574":791,"575":796,"576":797,"577":798,"578":800,"579":802,"580":803,"581":808,"582":810,"583":812,"584":813,"585":816,"586":818,"587":820,"588":823,"589":826,"590":828,"591":830,"592":832,"593":835,"594":837,"595":840,"596":842,"597":843,"598":847,"599":851,"600":856,"601":859,"602":864,"603":868,"604":870,"605":874,"606":875,"607":876,"608":879,"609":881,"610":885,"611":887,"612":889,"613":892,"614":893,"615":896,"616":898,"617":906,"618":910,"619":912,"620":914,"621":917,"622":923,"623":926,"624":927,"625":932,"626":933,"627":936,"628":937,"629":939,"630":940,"631":941,"632":946,"633":947,"634":948,"635":950,"636":954,"637":957,"638":958,"639":960,"640":970,"641":972,"642":974,"643":975,"644":979,"645":981,"646":982,"647":983,"648":985,"649":986,"650":987,"651":990,"652":993,"653":994,"654":996,"655":997,"656":1003,"657":1007,"658":1010,"659":1013,"660":1015,"661":1021},{"0":7,"1":19,"2":22,"3":26,"4":29,"5":35,"6":39,"7":40,"8":60,"9":61,"10":68,"11":79,"12":85,"13":94,"14":103,"15":104,"16":111,"17":112,"18":121,"19":140,"20":165,"21":208,"22":212,"23":230,"24":238,"25":243,"26":245,"27":251,"28":253,"29":254,"30":263,"31":285,"32":295,"33":310,"34":343,"35":372,"36":394,"37":396,"38":401,"39":407,"40":436,"41":445,"42":452,"43":460,"44":509,"45":513,"46":514,"47":517,"48":519,"49":521,"50":526,"51":527,"52":530,"53":531,"54":532,"55":533,"56":534,"57":536,"58":547,"59":548,"60":549,"61":552,"62":553,"63":554,"64":555,"65":558,"66":562,"67":563,"68":567,"70":583,"71":586,"72":591,"73":592,"74":593,"75":594,"76":595,"77":599,"78":600,"79":601,"80":603,"81":606,"82":608,"83":609,"84":610,"85":618,"86":620,"87":621,"88":622,"89":625,"90":627,"91":630,"92":631,"93":632,"94":634,"95":637,"96":641,"97":647,"98":648,"99":649,"100":651,"101":654,"102":655,"103":659,"104":664,"105":667,"106":668,"107":669,"108":671,"109":674,"110":675,"111":680,"112":686,"113":690,"114":691,"115":698,"116":699,"117":703,"118":706,"119":709,"120":710,"121":714,"122":719,"123":721,"124":723,"125":728,"126":729,"127":731,"128":734,"129":737,"130":742,"131":746,"132":749,"133":750,"134":751,"135":753,"136":755,"137":756,"138":757,"139":767,"140":769,"141":772,"142":781,"143":784,"144":785,"145":787,"146":788,"147":789,"148":790,"149":792,"150":793,"151":799,"152":809,"153":811,"154":817,"155":819,"156":822,"157":824,"158":827,"159":829,"160":836,"161":838,"162":845,"163":846,"164":849,"165":850,"166":853,"167":857,"168":861,"169":865,"170":867,"171":869,"172":872,"173":873,"174":878,"175":882,"176":886,"177":888,"178":895,"179":897,"180":903,"181":905,"182":907,"183":908,"184":909,"185":911,"186":913,"187":916,"188":918,"189":924,"190":925,"191":931,"192":935,"193":942,"194":943,"195":949,"196":952,"197":955,"198":961,"199":978,"200":984,"201":988,"202":992,"203":999,"204":1000,"205":1001,"206":1005,"207":1006,"208":1012,"209":1020,"210":1022,"211":1023},[4,231,307,341,511,529,540,541,568,575,579,598,602,604,605,611,613,616,623,629,636,646,661,665,677,679,682,683,687,689,694,717,720,726,738,739,743,747,748,780,795,801,806,821,825,833,834,852,854,858,860,863,877,880,884,891,899,900,901,902,920,921,922,929,934,938,951,953,966,967,976,977,980,989,998,1008,1009,1014,1019],{"0":522,"1":524,"3":539,"4":574,"5":577,"6":584,"8":607,"9":643,"10":653,"11":672,"12":701,"13":716,"14":722,"15":740,"16":744,"17":768,"18":773,"19":794,"20":805,"21":815,"22":831,"23":839,"24":844,"25":848,"26":855,"27":883,"29":915,"30":919,"31":930,"32":944,"33":956,"34":959,"35":963,"36":968,"37":969,"38":971,"39":991,"40":995,"41":1004,"42":1018},[576,708,724,735,807,814,841,862,871,928,945,964,965,973,1011,1016,1017],{"0":771,"1":786,"2":804,"4":962,"5":1002},[619],[890],[]]