[{"0":1,"1":2,"2":4,"3":6,"4":9,"5":10,"6":14,"7":26,"8":27,"9":28,"10":30,"11":32,"12":35,"13":36,"14":37,"15":38,"16":49,"17":52,"18":55,"19":56,"20":59,"21":64,"22":69,"23":82,"24":83,"25":84,"26":86,"27":87,"28":92,"29":93,"30":94,"31":95,"32":96,"33":97,"34":99,"35":100,"36":101,"37":102,"38":104,"39":105,"40":106,"41":108,"42":109,"43":110,"44":111,"45":112,"46":113,"47":117,"48":129,"49":131,"50":133,"51":135,"52":140,"53":141,"54":148,"55":149,"56":152,"57":155,"58":157,"59":158,"60":159,"61":162,"62":163,"63":164,"64":165,"65":166,"66":167,"67":169,"68":170,"69":171,"70":172,"71":173,"72":178,"73":179,"74":180,"75":181,"76":183,"77":184,"78":185,"79":186,"80":187,"81":188,"82":190,"83":191,"84":204,"85":207,"86":209,"87":211,"88":214,"89":216,"90":217,"91":218,"92":221,"93":226,"94":228,"95":229,"96":230,"97":233,"98":234,"99":235,"100":236,"101":239,"102":240,"103":241,"104":243,"105":244,"106":246,"107":249,"108":250,"109":251,"110":252,"111":253,"112":254,"113":255,"114":256,"115":269,"116":270,"117":271,"118":273,"119":274,"120":275,"121":281,"122":282,"123":284,"124":285,"125":286,"126":288,"127":291,"128":292,"129":293,"130":294,"131":296,"132":297,"133":301,"134":302,"135":303,"136":304,"137":305,"138":306,"139":307,"140":310,"141":311,"142":313,"143":314,"144":315,"145":319,"146":320,"147":332,"148":333,"149":338,"150":339,"151":341,"152":342,"153":347,"154":349,"155":353,"156":358,"157":360,"158":361,"159":364,"160":367,"161":368,"162":369,"163":370,"164":371,"165":372,"166":373,"167":374,"168":375,"169":376,"170":377,"171":378,"172":379,"173":381,"174":382,"175":383,"176":389,"177":390,"178":391,"179":408,"180":409,"181":410,"182":411,"183":415,"184":421,"185":423,"186":425,"187":427,"188":429,"189":430,"190":431,"191":432,"192":434,"193":435,"194":436,"195":438,"196":442,"197":446,"198":447,"199":448,"200":450,"201":453,"202":454,"203":456,"204":458,"205":461,"206":462,"207":464,"208":465,"209":468,"210":471,"211":472,"212":473,"213":474,"214":489,"215":496,"216":502,"217":503,"218":504,"219":507,"220":511,"221":512,"222":515,"223":519,"224":523,"225":524,"226":525,"227":531,"228":532,"229":534,"230":536,"231":537,"232":538,"233":540,"234":557,"235":558,"236":568,"237":570,"238":582,"239":583,"240":585,"241":587,"242":590,"243":592,"244":595,"245":597,"246":615,"247":619,"248":620,"249":627,"250":631,"251":636,"252":637,"253":640,"254":641,"255":642,"256":644,"257":646,"258":647,"259":648,"260":660,"261":661,"262":668,"263":671,"264":675,"266":678,"267":679,"268":680,"269":681,"270":682,"271":683,"272":685,"273":687,"274":689,"275":690,"276":691,"277":692,"278":693,"279":694,"280":697,"281":701,"282":702,"283":714,"284":724,"285":727,"286":731,"287":737,"288":741,"289":744,"290":745,"291":746,"292":747,"293":750,"294":751,"295":752,"296":754,"297":755,"298":757,"299":758,"300":761,"301":762,"302":763,"303":764,"304":765,"305":766,"306":767,"307":768,"308":769,"309":770,"310":771,"311":784,"312":786,"313":787,"314":788,"315":790,"316":791,"317":794,"318":795,"319":800,"320":802,"321":803,"322":804,"323":810,"324":812,"325":814,"326":816,"327":817,"328":820,"329":823,"330":824,"331":825,"332":826,"333":827,"334":828,"335":829,"336":830,"337":836,"338":837,"339":838,"340":839,"341":840,"342":841,"343":842,"344":843,"345":855,"346":858,"347":860,"348":861,"349":864,"350":866,"351":881,"352":882,"353":886,"354":887,"355":891,"356":892,"357":895,"358":896,"359":897,"360":898,"361":899,"362":900,"363":902,"364":903,"365":904,"366":906,"367":907,"368":929,"369":939,"370":942,"371":943,"372":944,"373":945,"374":946,"375":948,"376":949,"377":950,"378":952,"379":953,"380":956,"381":962,"382":963,"383":965,"384":967,"385":968,"386":970,"387":971,"388":972,"389":973,"390":974,"391":978,"392":979,"393":980,"394":981,"395":984,"396":985,"397":986,"398":988,"399":989,"400":991,"401":992,"402":993,"403":996,"404":997,"405":1003,"406":1004,"407":1005,"408":1006,"409":1007,"410":1009,"411":1011,"412":1012,"413":1013,"414":1015,"415":1016,"416":1017,"417":1018,"418":1019,"419":1021,"420":1022},[0,3,5,7,12,13,15,16,18,24,29,31,34,39,41,44,45,65,66,77,85,91,103,107,115,116,121,123,124,125,126,128,130,132,134,138,139,142,144,146,147,150,153,156,161,168,174,175,176,177,182,192,193,195,196,198,200,201,202,203,205,208,210,212,213,215,219,220,223,227,232,238,242,245,247,248,257,258,259,264,267,278,280,283,289,295,298,299,300,308,309,312,317,318,322,323,325,328,329,330,334,335,336,340,345,350,351,352,355,357,359,363,365,380,385,387,388,392,393,394,395,396,397,398,399,400,401,403,406,412,414,416,417,418,419,420,422,424,426,428,433,439,440,441,444,445,451,452,455,457,459,460,467,475,480,481,485,486,488,491,492,495,497,498,499,501,506,509,510,513,518,522,526,528,529,530,535,539,543,554,555,562,573,575,584,588,593,594,598,603,614,616,621,623,624,625,635,639,649,651,655,658,659,662,663,664,665,666,667,669,670,673,676,684,688,700,703,705,707,709,712,717,718,721,723,732,734,743,759,760,772,773,774,776,777,778,779,781,783,785,789,792,793,796,797,798,806,807,808,809,811,813,815,818,819,821,822,832,835,848,850,851,853,856,857,862,863,865,868,869,870,871,872,873,874,875,884,885,888,889,894,901,905,908,910,912,913,914,915,916,920,924,927,931,933,940,947,951,958,966,969,975,976,977,982,983,987,990,994,995,998,1000,1002,1010,1014,1020,1023],{"0":8,"1":11,"2":19,"3":20,"4":21,"5":22,"6":23,"7":33,"8":40,"9":42,"10":47,"11":48,"12":61,"13":78,"14":98,"15":114,"16":118,"17":119,"18":120,"19":122,"20":127,"21":136,"22":137,"23":143,"24":145,"25":154,"26":189,"27":197,"28":199,"29":206,"30":222,"31":225,"32":260,"33":261,"34":262,"35":263,"36":265,"37":266,"38":268,"39":272,"40":276,"41":277,"42":279,"43":290,"44":316,"45":321,"46":326,"47":327,"48":337,"49":343,"50":344,"51":362,"52":366,"53":384,"54":386,"55":404,"56":405,"57":407,"58":413,"59":449,"60":463,"61":469,"62":470,"63":476,"64":478,"65":479,"66":482,"67":483,"68":487,"69":490,"70":493,"71":494,"72":500,"73":505,"74":514,"75":516,"76":517,"77":520,"78":521,"79":527,"80":533,"81":541,"82":547,"83":548,"84":550,"85":551,"86":552,"87":556,"88":559,"89":560,"90":561,"91":564,"92":565,"93":577,"94":578,"95":579,"96":580,"97":581,"98":586,"99":589,"100":591,"101":596,"102":600,"103":602,"104":604,"105":606,"106":607,"107":611,"108":617,"109":618,"110":622,"111":630,"112":638,"113":643,"114":645,"115":650,"116":652,"117":654,"118":656,"119":657,"120":672,"121":674,"122":686,"123":695,"124":696,"125":699,"126":704,"127":708,"128":710,"129":711,"130":720,"132":738,"133":739,"134":753,"135":756,"136":775,"137":780,"138":799,"139":801,"140":805,"141":833,"142":834,"143":849,"144":854,"145":859,"146":867,"147":876,"148":877,"149":878,"150":880,"151":883,"152":890,"153":893,"154":909,"155":911,"156":917,"157":954,"158":955,"159":957,"160":960,"161":961,"162":964,"163":999,"164":1001,"165":1008},[17,25,43,67,70,151,160,194,287,324,331,346,348,354,402,443,466,477,484,508,544,549,569,571,572,574,576,599,601,605,608,612,613,629,633,634,653,698,713,782,831,844,845,846,847,852,879,934,959],[58,74,224,231,237,356,542,545,546,553,563,566,706,722,725,726,735,736,742,748,918,921,922,928,932,935,936,937],[46,72,81,88,567,626,715,716,729,730,925,926,930,938,941],[51,57,60,62,68,71,75,76,89,437,628,919,923],[53,54,63,73,79,80,90,632,728,740,749],[50,609,610],[719]]