[{"0":1,"1":2,"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":16,"15":17,"16":18,"17":19,"18":20,"19":21,"20":22,"21":23,"22":24,"23":25,"24":26,"25":27,"26":30,"27":31,"28":32,"29":33,"30":34,"31":35,"32":36,"33":37,"34":38,"35":39,"36":40,"37":41,"38":42,"39":43,"40":44,"41":45,"42":46,"43":47,"44":48,"45":49,"46":50,"47":51,"48":52,"49":53,"50":54,"51":55,"53":57,"55":59,"56":60,"57":62,"58":63,"59":64,"60":65,"61":66,"62":68,"63":69,"64":70,"65":71,"66":72,"67":73,"68":74,"69":75,"70":76,"71":77,"72":78,"73":81,"74":82,"75":83,"76":84,"77":85,"78":86,"79":87,"80":88,"81":89,"82":90,"83":91,"84":93,"85":94,"86":95,"87":96,"88":98,"89":99,"90":100,"91":101,"92":102,"93":104,"94":105,"95":107,"96":108,"97":109,"98":110,"99":111,"100":112,"101":113,"102":114,"103":115,"104":116,"105":118,"106":119,"107":120,"108":121,"109":122,"110":123,"111":124,"112":125,"113":127,"114":128,"115":129,"116":130,"117":131,"118":133,"119":134,"120":135,"121":136,"123":138,"124":139,"125":140,"126":142,"127":143,"128":144,"129":145,"130":146,"131":147,"132":148,"133":149,"134":150,"135":151,"136":153,"137":154,"138":155,"139":156,"140":157,"141":158,"142":159,"143":160,"144":161,"145":163,"146":164,"147":165,"148":166,"149":167,"150":168,"151":169,"152":171,"153":173,"154":174,"155":175,"156":176,"157":177,"158":178,"159":179,"160":180,"161":181,"162":182,"163":183,"164":184,"165":185,"166":186,"167":187,"168":188,"169":189,"170":191,"171":192,"172":193,"173":194,"174":195,"175":196,"176":197,"177":198,"178":199,"179":202,"180":203,"181":204,"182":205,"183":206,"184":207,"185":209,"186":210,"187":211,"188":212,"189":213,"190":214,"191":215,"192":216,"193":217,"194":218,"195":219,"196":220,"197":222,"198":223,"199":224,"200":225,"201":226,"202":227,"203":228,"204":230,"205":232,"206":233,"207":234,"208":236,"209":237,"210":238,"211":240,"212":241,"213":242,"214":243,"215":244,"216":245,"217":246,"218":249,"219":250,"220":251,"221":252,"222":253,"223":254,"224":255,"225":256,"226":257,"227":258,"228":259,"229":260,"230":261,"231":262,"232":263,"233":264,"234":265,"235":266,"236":267,"237":268,"238":269,"239":270,"240":271,"241":272,"242":273,"243":275,"244":276,"245":277,"246":278,"247":279,"248":280,"249":281,"250":282,"251":283,"252":284,"253":285,"254":286,"255":287,"256":288,"257":289,"258":290,"259":291,"260":292,"261":293,"262":294,"263":295,"264":296,"265":297,"266":298,"267":299,"268":301,"269":302,"270":303,"271":304,"272":305,"273":306,"274":307,"275":309,"276":310,"277":311,"278":312,"279":313,"280":314,"281":315,"283":317,"284":318,"285":319,"286":320,"287":321,"288":322,"289":323,"290":324,"291":325,"292":328,"293":329,"294":330,"295":331,"296":332,"297":333,"298":334,"299":335,"300":337,"301":338,"302":340,"303":341,"304":344,"305":345,"306":346,"307":347,"308":348,"309":349,"310":350,"311":352,"312":353,"313":354,"314":355,"315":356,"316":357,"317":358,"318":359,"319":360,"320":361,"321":362,"322":364,"323":365,"324":366,"325":367,"326":368,"327":369,"328":370,"329":371,"330":372,"331":374,"332":375,"333":376,"334":377,"335":378,"336":379,"337":380,"338":382,"339":383,"340":384,"341":385,"342":386,"343":387,"344":389,"345":390,"346":391,"347":392,"348":393,"349":394,"350":396,"351":397,"352":398,"353":399,"354":400,"355":401,"356":402,"357":403,"358":404,"359":406,"360":407,"361":408,"362":410,"363":411,"364":412,"365":413,"366":414,"367":415,"368":416,"369":417,"370":418,"371":419,"372":420,"373":421,"374":423,"375":424,"376":425,"377":427,"378":428,"379":429,"380":430,"381":431,"382":432,"383":433,"384":434,"385":435,"386":436,"387":437,"388":438,"389":439,"390":440,"392":442,"393":443,"394":444,"395":445,"396":446,"397":448,"398":449,"399":450,"400":451,"401":453,"402":454,"403":455,"404":456,"405":457,"406":458,"407":459,"408":460,"409":461,"410":462,"411":464,"412":465,"413":466,"414":467,"415":468,"416":469,"417":470,"418":471,"419":472,"420":473,"421":474,"422":475,"423":476,"424":478,"425":479,"426":481,"427":482,"428":483,"429":484,"430":485,"431":486,"432":487,"433":488,"434":490,"435":491,"436":492,"437":493,"438":495,"439":497,"440":498,"441":499,"442":502,"443":503,"444":504,"445":505,"446":506,"447":507,"448":508,"449":510,"450":511,"451":512,"452":513,"453":516,"454":518,"455":519,"456":520,"457":521,"458":525,"459":526,"460":527,"461":528,"462":529,"463":530,"464":533,"465":539,"466":542,"467":543,"468":544,"469":546,"470":547,"471":551,"472":555,"473":557,"474":558,"475":560,"476":561,"477":562,"478":565,"479":566,"480":567,"481":568,"482":569,"483":571,"484":572,"485":573,"486":575,"487":576,"488":577,"489":579,"490":580,"491":581,"492":588,"493":589,"494":590,"495":591,"496":593,"497":594,"498":595,"499":597,"500":598,"501":600,"502":603,"503":605,"504":606,"505":609,"506":611,"507":612,"508":615,"509":616,"510":617,"511":620,"512":622,"513":624,"514":630,"515":632,"516":633,"517":634,"518":636,"519":637,"520":638,"521":640,"522":641,"523":643,"524":645,"525":648,"526":649,"527":650,"528":651,"529":654,"530":655,"531":656,"532":658,"533":659,"534":661,"535":662,"536":664,"537":669,"538":670,"539":673,"540":674,"541":676,"542":681,"543":683,"544":684,"545":686,"546":688,"547":691,"548":692,"549":693,"550":694,"551":695,"552":696,"553":697,"554":702,"555":703,"556":704,"557":705,"558":706,"559":707,"560":708,"561":713,"562":714,"563":717,"564":719,"565":721,"566":722,"567":723,"568":725,"569":727,"570":728,"571":729,"572":730,"573":732,"574":733,"575":735,"576":736,"577":738,"578":740,"579":744,"580":746,"581":747,"582":748,"583":749,"584":751,"585":753,"586":757,"587":758,"588":759,"589":760,"590":762,"591":767,"592":769,"593":770,"594":772,"595":773,"596":774,"597":775,"598":777,"599":778,"600":780,"601":783,"602":785,"603":786,"604":787,"605":789,"606":790,"607":792,"608":794,"609":795,"610":798,"611":804,"612":806,"613":808,"614":809,"615":810,"617":816,"618":817,"619":820,"620":822,"621":824,"622":825,"623":827,"624":831,"625":832,"626":833,"627":834,"628":835,"629":836,"630":837,"631":838,"632":839,"633":840,"634":841,"635":842,"636":845,"637":848,"638":850,"639":851,"640":852,"641":854,"642":855,"643":856,"644":858,"645":859,"646":860,"647":863,"648":864,"649":865,"650":866,"651":868,"652":871,"653":874,"654":875,"655":877,"656":878,"657":879,"658":882,"659":883,"660":884,"661":885,"662":889,"663":892,"664":893,"665":894,"666":895,"667":896,"668":898,"669":901,"670":903,"671":904,"672":910,"673":912,"674":913,"675":914,"676":916,"677":917,"678":918,"679":920,"680":923,"681":924,"682":925,"683":926,"684":933,"685":934,"686":935,"687":936,"688":938,"689":940,"690":945,"691":950,"692":951,"693":952,"694":953,"695":954,"696":955,"697":956,"698":960,"699":961,"700":962,"701":963,"702":964,"703":965,"704":966,"705":967,"706":970,"707":974,"708":975,"709":976,"710":977,"711":978,"712":979,"713":980,"714":983,"715":993,"716":994,"717":995,"718":996,"719":999,"720":1000,"721":1006,"722":1007,"723":1008,"724":1009,"725":1012,"726":1014,"727":1016,"728":1017,"729":1020,"730":1021,"731":1022},[0,6,28,29,61,67,79,80,92,97,103,106,117,126,132,141,152,162,170,172,200,201,208,221,229,231,235,247,300,308,326,327,336,339,342,343,351,363,373,381,388,395,405,409,422,426,447,452,463,477,480,489,494,496,501,509,514,515,517,523,524,531,535,536,538,541,545,549,550,552,554,556,559,574,582,584,585,592,599,604,608,610,613,614,618,619,623,625,626,627,628,629,639,642,647,653,657,663,665,666,667,668,671,675,678,679,682,685,689,690,698,699,701,709,710,711,712,716,718,720,726,734,739,741,743,745,750,755,756,761,763,764,765,771,776,781,782,784,793,796,799,800,803,805,811,812,819,821,828,829,830,844,846,847,853,857,862,867,869,870,872,873,876,880,886,887,888,902,905,907,911,915,919,922,928,929,931,937,941,942,943,946,947,957,958,968,969,971,972,973,981,985,987,989,990,992,997,1001,1002,1003,1004,1005,1010,1011,1013,1015,1018,1019,1023],[190,239,248,500,522,532,534,540,548,553,563,564,570,578,583,586,587,596,601,602,607,621,635,646,652,677,680,700,731,752,768,779,788,791,801,807,814,818,826,843,849,861,881,890,891,899,900,909,927,930,932,939,944,982,984,988,991],{"0":274,"2":660,"3":672,"5":715,"6":737,"7":766,"8":802,"9":813,"10":897,"11":906,"12":908,"13":921,"14":948,"15":949,"16":986},{"0":644,"3":823,"4":998},{"1":724,"2":959},[]]