[{"0":0,"1":1,"2":2,"3":3,"4":4,"5":6,"6":7,"7":8,"8":9,"9":10,"10":11,"11":12,"12":13,"13":14,"14":15,"15":16,"16":17,"17":18,"18":19,"19":22,"20":23,"21":24,"22":25,"23":26,"24":27,"25":28,"26":29,"27":30,"28":31,"29":32,"30":34,"31":35,"32":37,"33":38,"34":39,"35":40,"36":41,"37":42,"38":43,"39":44,"40":45,"41":46,"42":47,"43":48,"44":49,"45":50,"47":52,"48":53,"49":54,"50":55,"51":56,"52":57,"53":58,"54":60,"55":62,"56":63,"57":64,"58":65,"59":66,"60":67,"61":68,"62":69,"63":70,"64":71,"65":72,"66":73,"67":74,"68":75,"69":76,"70":77,"71":78,"72":79,"73":80,"74":81,"75":82,"76":83,"77":84,"78":85,"79":86,"80":87,"81":88,"82":91,"83":92,"84":93,"85":95,"86":96,"87":97,"88":98,"89":99,"90":100,"91":101,"92":102,"93":103,"94":104,"95":105,"96":106,"97":107,"98":108,"99":109,"100":110,"101":111,"102":112,"103":113,"104":115,"105":116,"106":117,"107":119,"108":121,"109":123,"110":124,"111":125,"112":127,"113":129,"114":131,"115":132,"116":133,"117":134,"118":135,"119":136,"120":137,"121":138,"122":139,"124":142,"125":145,"126":146,"127":148,"128":149,"129":150,"130":152,"131":153,"132":154,"133":155,"134":156,"135":157,"136":158,"137":159,"138":161,"139":162,"140":163,"141":164,"142":165,"143":166,"144":168,"145":169,"146":170,"147":171,"148":174,"149":175,"150":177,"151":178,"152":179,"153":180,"154":181,"155":182,"156":183,"157":184,"158":185,"159":186,"160":188,"161":189,"162":190,"163":191,"164":193,"165":194,"166":195,"167":196,"168":197,"169":199,"170":200,"171":203,"172":204,"173":205,"174":206,"175":207,"176":208,"177":212,"178":213,"179":214,"180":216,"181":217,"182":219,"183":220,"184":221,"185":222,"186":223,"187":224,"188":225,"189":227,"190":229,"191":230,"192":231,"193":232,"194":233,"195":234,"196":235,"197":236,"198":237,"199":238,"200":239,"201":240,"202":241,"203":242,"204":244,"205":245,"206":246,"207":247,"208":248,"209":249,"210":250,"211":251,"212":252,"213":253,"214":255,"215":256,"216":257,"217":258,"218":259,"219":260,"220":261,"221":262,"222":263,"223":264,"224":265,"225":267,"226":268,"227":269,"228":270,"229":271,"231":273,"232":274,"233":275,"234":278,"235":280,"236":281,"237":282,"238":283,"239":284,"240":285,"241":286,"242":289,"243":290,"244":291,"245":292,"246":293,"247":294,"249":297,"250":299,"251":300,"252":301,"253":302,"254":303,"255":304,"256":305,"257":306,"258":307,"259":309,"260":311,"261":312,"262":313,"263":314,"264":315,"265":316,"266":317,"267":318,"268":320,"269":321,"270":322,"271":323,"272":324,"273":326,"274":327,"275":328,"276":329,"277":330,"278":331,"279":332,"280":334,"281":336,"282":339,"283":340,"284":342,"285":345,"286":347,"287":348,"288":349,"289":350,"290":351,"291":353,"292":354,"293":355,"294":356,"295":360,"296":362,"297":364,"298":365,"299":366,"300":367,"301":368,"302":370,"304":372,"305":373,"306":374,"307":375,"308":376,"309":377,"310":378,"311":380,"312":381,"313":383,"314":385,"315":386,"316":387,"317":389,"318":390,"319":391,"321":394,"322":396,"323":397,"324":398,"325":399,"326":400,"327":401,"328":402,"329":403,"330":404,"331":405,"332":406,"333":407,"334":408,"335":409,"336":410,"337":411,"338":413,"339":415,"340":416,"341":418,"342":419,"343":420,"344":421,"345":422,"346":423,"347":424,"348":425,"349":427,"350":428,"351":429,"352":430,"353":431,"354":433,"355":434,"356":435,"357":436,"358":438,"359":439,"360":440,"361":441,"362":442,"363":443,"364":444,"365":445,"366":446,"367":447,"368":448,"369":449,"370":450,"371":451,"372":452,"373":453,"374":454,"375":455,"376":456,"377":457,"378":459,"379":462,"380":463,"381":465,"382":466,"383":468,"384":469,"385":470,"386":471,"387":472,"388":473,"389":476,"390":477,"391":478,"392":480,"393":483,"394":484,"395":485,"396":487,"397":488,"398":489,"399":491,"400":492,"401":493,"402":495,"403":496,"404":497,"405":498,"406":499,"407":500,"408":501,"409":502,"410":504,"411":505,"412":506,"413":507,"414":508,"415":509,"416":510,"417":511,"418":515,"419":519,"420":524,"421":528,"422":531,"423":544,"424":549,"425":551,"426":559,"427":563,"428":564,"429":567,"430":568,"431":571,"432":573,"433":578,"434":582,"435":589,"436":591,"437":592,"438":594,"439":596,"440":600,"441":602,"442":605,"443":611,"444":612,"445":617,"446":619,"447":622,"448":626,"449":630,"450":631,"451":633,"452":639,"453":641,"454":643,"455":644,"456":647,"457":655,"458":659,"459":669,"460":672,"461":673,"462":679,"463":683,"464":688,"465":698,"466":701,"467":716,"468":719,"469":721,"470":724,"471":725,"472":727,"473":729,"474":731,"475":734,"476":742,"477":751,"478":753,"479":755,"480":757,"481":761,"482":763,"483":773,"484":776,"485":781,"486":782,"487":785,"488":786,"489":787,"490":789,"491":790,"492":791,"493":794,"494":798,"495":800,"496":801,"497":803,"498":807,"499":810,"500":812,"501":818,"502":819,"503":820,"504":826,"505":831,"506":839,"507":840,"508":846,"509":852,"510":855,"511":857,"512":858,"513":860,"514":873,"515":874,"516":875,"517":885,"518":888,"519":889,"520":896,"521":897,"522":900,"523":901,"524":902,"525":904,"526":912,"527":919,"528":920,"529":925,"530":932,"531":934,"532":938,"533":940,"534":950,"535":952,"536":953,"537":962,"538":963,"539":965,"540":969,"541":971,"542":976,"543":987,"544":992,"545":994,"546":995,"547":1003,"548":1006,"549":1007,"550":1008,"551":1010,"552":1011,"553":1013,"554":1020,"555":1021,"556":1023},[5,20,21,33,36,59,61,89,90,94,114,120,122,126,128,130,141,143,144,147,151,160,172,176,187,192,198,201,202,209,210,211,215,226,228,243,254,266,276,277,288,296,298,308,310,325,333,335,337,343,344,352,357,358,361,363,379,382,384,388,393,395,412,414,417,426,432,458,460,461,464,467,474,475,479,481,482,486,490,494,503,513,514,516,520,525,529,532,541,543,545,546,548,552,554,562,569,570,572,574,579,580,581,584,587,588,598,603,604,608,609,610,615,618,627,629,634,636,638,640,642,646,649,650,651,652,654,663,665,667,671,678,682,685,695,696,697,702,703,704,706,712,713,717,722,723,726,728,730,732,733,735,736,737,740,745,747,756,759,760,762,764,768,770,772,778,784,788,793,795,799,804,805,808,811,815,821,823,830,832,834,837,838,841,844,845,848,850,851,856,859,868,872,876,883,891,892,899,907,908,909,910,911,913,914,926,927,931,933,942,945,948,956,957,959,960,964,967,968,970,974,978,980,983,984,985,991,993,1005,1009,1019,1022],[118,167,173,218,279,287,319,338,346,359,369,437,517,518,521,527,530,534,538,553,556,558,560,561,566,575,593,599,601,616,620,625,628,637,645,658,676,677,680,684,690,691,693,699,705,707,708,709,714,718,741,746,774,796,797,802,809,814,816,817,825,829,835,847,862,863,864,886,890,893,894,895,905,906,915,917,921,924,928,936,943,946,954,961,966,972,975,977,990,1012,1015,1016,1018],[341,512,537,539,547,557,565,577,585,586,595,597,606,613,621,653,664,674,681,687,689,692,710,711,720,739,754,758,766,767,777,779,792,806,827,828,833,836,849,853,867,869,871,878,882,884,903,916,930,944,947,951,958,973,982,986,997,1000,1001,1002],{"0":522,"1":523,"2":533,"3":535,"4":536,"5":542,"6":550,"7":555,"8":576,"9":583,"10":590,"11":624,"12":632,"13":635,"14":648,"15":660,"16":662,"17":670,"19":700,"20":738,"21":743,"22":748,"23":749,"24":752,"25":765,"26":775,"27":780,"28":813,"29":822,"30":824,"31":842,"32":843,"33":865,"34":879,"35":880,"36":887,"37":923,"38":941,"40":988,"41":989,"42":996,"44":1004},{"0":526,"1":623,"2":656,"3":661,"4":694,"5":750,"6":783,"8":877,"9":922,"10":929,"11":937,"12":939,"13":949,"14":998},[540,657,666,686,715,861,866,935,981,1014],[668,744,769,771,854,898,918,955,1017],[607,614,881]]