[{"0":0,"1":1,"2":2,"3":3,"4":5,"5":6,"6":7,"7":8,"8":9,"9":10,"10":11,"11":12,"12":13,"13":15,"14":17,"15":18,"16":20,"17":21,"18":22,"19":24,"20":25,"21":26,"22":28,"23":29,"24":31,"25":32,"26":33,"27":34,"29":36,"30":37,"31":38,"32":39,"33":40,"34":41,"35":42,"36":43,"37":44,"38":45,"39":46,"40":47,"41":48,"42":49,"43":50,"44":51,"45":52,"46":53,"47":54,"48":55,"49":56,"50":57,"51":58,"52":59,"53":60,"54":61,"55":62,"56":63,"57":65,"58":66,"59":69,"60":70,"61":71,"62":72,"63":74,"64":75,"65":76,"66":78,"67":79,"68":80,"69":81,"70":82,"72":85,"73":86,"74":87,"75":88,"76":90,"77":91,"78":92,"80":94,"81":95,"82":96,"83":97,"84":98,"85":100,"86":102,"87":103,"88":104,"89":105,"90":107,"91":108,"92":109,"93":110,"94":111,"95":112,"96":113,"97":115,"98":116,"99":117,"100":119,"101":120,"102":122,"103":124,"104":125,"105":126,"106":127,"108":130,"109":131,"110":132,"111":136,"112":138,"113":139,"114":140,"115":142,"116":143,"117":144,"118":146,"119":147,"120":148,"121":149,"122":150,"123":151,"124":152,"125":153,"126":154,"127":155,"128":156,"129":157,"130":158,"131":159,"132":160,"133":162,"134":163,"135":164,"136":165,"137":166,"138":167,"139":168,"140":169,"141":170,"142":171,"143":172,"144":173,"145":174,"146":175,"147":178,"148":179,"149":180,"150":181,"151":183,"152":185,"153":186,"154":187,"155":188,"156":190,"157":191,"158":192,"159":193,"160":194,"161":195,"162":196,"163":198,"164":199,"165":200,"166":202,"167":204,"168":205,"169":206,"170":207,"171":208,"173":212,"174":213,"175":215,"177":218,"178":219,"179":220,"180":221,"181":222,"182":223,"183":224,"184":225,"185":227,"186":228,"187":229,"188":231,"189":232,"190":233,"191":234,"192":236,"193":237,"194":238,"195":239,"196":242,"197":243,"198":244,"199":245,"200":246,"201":247,"202":248,"203":256,"204":257,"205":258,"207":260,"208":261,"209":263,"210":264,"211":266,"212":267,"213":268,"214":269,"215":270,"216":272,"217":274,"218":276,"219":277,"220":279,"221":280,"222":282,"223":283,"224":285,"225":286,"226":287,"227":288,"228":289,"229":290,"232":294,"233":295,"234":296,"235":297,"236":298,"237":299,"238":301,"239":302,"240":303,"241":304,"242":305,"243":306,"244":307,"245":308,"246":309,"247":310,"248":311,"249":312,"250":313,"251":314,"253":317,"254":318,"255":320,"256":321,"257":322,"258":324,"259":325,"260":326,"261":328,"262":329,"263":331,"264":332,"265":334,"266":336,"267":337,"268":338,"269":339,"270":340,"271":341,"272":342,"273":344,"274":345,"275":346,"276":347,"277":348,"280":352,"281":353,"282":354,"283":355,"284":356,"285":358,"286":359,"287":360,"288":361,"289":362,"290":363,"291":366,"292":367,"293":368,"294":369,"295":370,"296":371,"297":373,"298":375,"299":376,"300":378,"301":379,"302":381,"303":382,"304":383,"307":387,"308":388,"309":389,"310":390,"311":392,"312":394,"313":395,"314":396,"315":397,"316":398,"317":399,"318":400,"319":401,"320":403,"321":405,"322":406,"323":407,"324":408,"325":409,"326":412,"327":413,"328":414,"329":415,"330":417,"331":418,"332":419,"333":420,"334":421,"335":422,"336":423,"337":425,"338":427,"339":428,"341":430,"342":431,"343":432,"344":434,"345":436,"346":438,"347":439,"348":440,"349":441,"350":442,"351":443,"352":445,"353":446,"354":447,"355":448,"356":449,"357":450,"358":451,"359":453,"360":454,"361":456,"362":458,"363":459,"364":461,"365":462,"366":463,"367":464,"368":466,"369":468,"370":469,"371":470,"372":471,"373":473,"374":475,"375":476,"376":479,"377":481,"378":482,"379":483,"380":484,"381":485,"382":486,"383":487,"384":488,"386":492,"387":493,"388":494,"389":495,"390":497,"391":498,"392":499,"393":500,"394":501,"395":502,"396":503,"397":504,"398":505,"399":513,"400":514,"401":517,"402":524,"403":525,"404":528,"405":531,"406":533,"407":535,"408":538,"409":545,"410":547,"411":550,"412":556,"413":565,"414":566,"415":568,"416":575,"417":577,"418":579,"419":581,"420":583,"421":584,"422":588,"423":591,"424":601,"425":611,"426":613,"427":615,"428":616,"429":622,"430":625,"431":632,"432":633,"433":636,"434":640,"435":646,"436":649,"437":650,"438":657,"439":671,"440":674,"441":687,"442":696,"443":698,"444":706,"445":711,"446":714,"447":717,"448":718,"449":720,"450":728,"451":732,"452":735,"453":741,"454":742,"455":745,"456":746,"457":747,"458":749,"459":756,"460":759,"461":771,"462":773,"463":774,"464":780,"465":787,"466":789,"467":795,"468":797,"469":802,"470":806,"471":807,"472":812,"473":814,"474":816,"475":818,"476":823,"477":840,"478":852,"479":862,"480":864,"481":865,"482":867,"483":868,"484":870,"485":886,"486":887,"487":889,"488":894,"489":895,"490":900,"491":904,"492":908,"493":911,"494":919,"495":920,"496":923,"497":930,"498":938,"499":939,"500":940,"501":946,"502":949,"503":950,"504":953,"505":955,"506":958,"507":959,"508":961,"509":966,"510":973,"511":976,"512":977,"513":991,"514":993,"515":994,"516":995,"517":996,"518":998,"519":999,"520":1002,"521":1005,"522":1007,"523":1013,"524":1014,"525":1015,"526":1019,"527":1023},{"0":4,"1":14,"2":16,"3":19,"4":23,"5":27,"6":30,"7":64,"8":67,"9":68,"10":73,"11":77,"12":84,"13":89,"14":99,"15":101,"16":106,"17":114,"18":121,"19":123,"20":129,"21":133,"22":134,"23":135,"24":137,"25":141,"26":145,"27":161,"28":182,"29":184,"30":189,"31":197,"32":201,"33":209,"34":210,"35":214,"36":226,"37":230,"38":235,"39":240,"40":241,"44":252,"45":254,"46":255,"47":262,"48":265,"49":271,"50":273,"51":275,"52":278,"53":281,"54":284,"55":293,"56":300,"57":315,"58":319,"59":323,"60":327,"61":330,"62":333,"63":335,"64":343,"65":351,"66":365,"67":372,"68":374,"69":377,"70":380,"71":386,"72":402,"73":404,"74":410,"75":411,"76":416,"77":424,"78":426,"79":433,"80":435,"81":437,"82":444,"83":452,"84":455,"85":457,"86":460,"87":465,"88":467,"89":474,"90":477,"91":480,"92":489,"93":496,"97":510,"98":511,"99":512,"100":518,"101":529,"102":532,"103":541,"104":544,"105":548,"106":549,"107":552,"108":559,"109":561,"110":562,"111":564,"112":567,"113":569,"114":573,"115":574,"116":578,"117":586,"118":589,"119":592,"120":596,"121":598,"122":600,"123":602,"124":603,"125":604,"126":608,"127":635,"128":638,"130":648,"131":651,"132":660,"133":661,"134":662,"135":665,"136":668,"137":669,"138":670,"139":672,"140":673,"141":678,"142":681,"143":683,"144":685,"145":686,"146":688,"147":689,"148":690,"149":691,"150":694,"151":703,"152":707,"153":710,"154":713,"156":729,"157":760,"158":772,"159":779,"160":785,"161":796,"162":799,"163":808,"164":813,"165":825,"166":829,"167":832,"168":834,"169":837,"170":838,"171":839,"172":845,"173":848,"174":853,"175":855,"176":859,"177":869,"178":876,"179":878,"180":881,"181":882,"182":883,"183":891,"184":893,"186":905,"187":914,"188":922,"189":929,"190":933,"191":943,"192":954,"194":963,"195":969,"196":980,"197":988,"198":997,"199":1000,"200":1003,"201":1010,"202":1017},{"0":118,"1":176,"2":177,"3":203,"4":217,"5":253,"6":357,"7":364,"8":391,"9":393,"10":472,"11":478,"12":491,"13":509,"14":527,"15":536,"16":537,"17":539,"18":542,"19":546,"21":571,"22":582,"23":590,"24":593,"25":594,"26":610,"27":614,"28":618,"29":620,"30":627,"31":634,"32":654,"34":663,"35":676,"36":702,"37":704,"38":715,"39":722,"40":724,"41":738,"42":751,"43":753,"44":757,"45":768,"46":786,"47":809,"48":810,"49":811,"50":820,"51":842,"52":843,"53":846,"54":850,"55":854,"56":879,"57":884,"58":885,"59":903,"60":910,"61":912,"62":925,"63":928,"64":932,"65":948,"66":952,"67":972,"68":975,"69":987,"70":992,"71":1004,"72":1008,"73":1018},[516,522,543,563,572,595,599,606,609,624,631,659,675,680,695,712,725,737,740,744,750,761,762,767,769,782,790,793,803,805,824,827,828,833,835,844,926,927,931,937,944,956,968,981,989,990,1009,1022],[515,526,540,551,555,576,605,617,621,623,642,647,666,693,697,736,739,754,770,776,777,784,791,794,815,826,830,847,856,858,861,871,898,917,979,984,1006],[585,626,628,629,652,653,677,679,682,700,701,705,721,778,783,817,822,863,873,880,892,901,915,941,947,971,985,1016,1020,1021],[519,534,558,560,580,607,641,667,708,723,731,733,743,758,763,804,841,857,874,877,888,899,913,916,942,960,1011],[520,521,523,587,637,639,664,692,699,727,765,781,788,801,821,831,836,849,851,860,890,906,909,918,934,935,945,951,967,986],[557,658,726,748,752,755,764,766,775,792,798,819,875,897,921,936,964],[612,630,655,684,957,970,974,1001],[553,554,645,709,866,965,978,983],[530,619,644,800,872,982],[734,896,907],[597],[716,924],[730,1012]]