[{"0":0,"1":1,"2":3,"3":4,"4":5,"5":6,"6":7,"7":8,"8":9,"9":10,"10":11,"11":13,"12":15,"13":16,"14":17,"15":18,"16":19,"17":20,"18":21,"19":22,"20":23,"21":24,"22":25,"23":26,"24":27,"25":28,"26":29,"27":30,"28":31,"29":32,"30":33,"31":34,"32":35,"33":37,"34":38,"35":39,"36":40,"37":43,"38":44,"39":46,"40":47,"41":48,"42":49,"43":50,"44":51,"45":52,"46":53,"47":55,"48":56,"49":57,"50":60,"51":61,"52":62,"53":63,"54":64,"55":66,"56":67,"57":68,"58":69,"59":70,"60":71,"61":72,"62":73,"63":74,"64":76,"65":78,"66":79,"67":80,"68":82,"69":83,"70":84,"71":85,"72":86,"73":87,"74":88,"75":89,"76":90,"77":91,"78":93,"79":94,"80":95,"81":96,"82":97,"83":98,"84":99,"85":100,"86":101,"87":102,"88":104,"89":106,"91":110,"92":111,"93":112,"95":115,"96":116,"97":117,"98":121,"99":122,"100":124,"101":125,"102":126,"103":127,"104":128,"105":129,"106":130,"107":132,"109":134,"110":137,"111":138,"112":140,"113":141,"114":142,"115":143,"116":144,"117":145,"118":146,"119":147,"120":148,"121":149,"122":151,"123":153,"124":154,"125":156,"126":160,"127":161,"128":163,"129":164,"130":167,"131":168,"132":169,"133":170,"134":171,"135":172,"136":173,"137":174,"138":175,"139":176,"140":177,"141":178,"142":179,"143":182,"144":183,"145":185,"146":186,"147":188,"148":191,"149":192,"150":193,"151":194,"152":256,"153":258,"154":260,"155":261,"156":262,"157":263,"158":264,"159":265,"160":266,"161":267,"162":268,"163":269,"164":271,"165":272,"167":274,"168":275,"169":276,"170":277,"171":278,"172":280,"173":282,"174":284,"175":285,"176":286,"177":287,"178":288,"179":289,"180":290,"181":291,"182":292,"183":293,"184":294,"185":295,"186":296,"187":297,"188":298,"189":299,"190":300,"191":301,"192":302,"193":305,"194":306,"195":307,"196":308,"197":309,"198":310,"199":311,"200":312,"201":313,"202":314,"203":315,"204":316,"205":317,"206":318,"207":319,"208":320,"209":322,"210":323,"211":324,"212":327,"213":328,"214":329,"215":330,"216":332,"217":333,"218":334,"219":335,"220":336,"221":337,"222":338,"223":339,"225":344,"226":345,"227":346,"228":347,"229":349,"230":350,"231":353,"232":354,"233":355,"234":356,"235":357,"236":360,"237":363,"238":364,"239":365,"240":366,"241":368,"242":370,"243":371,"244":372,"245":374,"246":375,"247":377,"248":378,"249":379,"251":381,"252":382,"253":383,"254":384,"256":386,"257":387,"258":388,"259":389,"260":390,"261":391,"262":392,"263":393,"264":395,"265":396,"266":399,"267":400,"268":401,"269":402,"270":403,"271":404,"272":405,"273":407,"274":408,"275":409,"276":410,"277":411,"278":413,"279":414,"280":415,"281":416,"282":418,"283":419,"284":420,"285":421,"286":423,"287":425,"288":427,"289":428,"290":431,"291":433,"292":434,"293":435,"294":436,"295":438,"296":439,"297":443,"298":444,"299":445,"300":446,"301":447,"302":448,"303":450,"304":452,"305":514,"306":516,"307":520,"308":523,"309":525,"310":528,"311":542,"312":548,"313":550,"314":557,"315":563,"316":569,"317":571,"318":573,"319":585,"320":590,"321":604,"322":606,"323":620,"324":623,"325":624,"326":626,"327":655,"328":659,"329":669,"330":675,"331":680,"332":681,"333":684,"334":690,"335":691,"336":698,"337":720,"338":739,"339":746,"340":752,"341":753,"342":754,"343":763,"344":765,"345":774,"346":780,"347":792,"348":793,"349":807,"350":816,"351":820,"352":824,"353":833,"354":837,"355":846,"356":851,"357":853,"358":854,"359":859,"360":874,"361":877,"362":883,"363":886,"364":888,"365":893,"366":895,"367":901,"368":911,"369":925,"370":930,"371":931,"372":949,"373":954,"374":959,"375":967,"376":968,"377":971,"378":972,"379":992,"380":1000,"381":1001,"382":1020},[2,12,14,36,41,42,54,58,59,65,77,81,103,105,107,113,118,119,123,131,135,139,150,152,155,157,158,159,162,165,166,180,181,184,187,189,190,195,196,197,198,200,201,202,203,204,205,207,208,209,213,214,215,216,218,221,222,223,224,225,227,229,230,232,233,234,235,236,238,239,240,241,242,243,244,246,247,251,252,253,254,259,270,279,281,283,304,321,325,326,331,340,342,352,358,359,361,367,369,394,397,398,406,412,417,422,426,429,432,440,441,442,449,451,453,454,455,459,460,461,463,464,465,466,467,468,469,470,471,473,474,475,477,478,479,480,483,484,485,487,488,489,492,493,497,498,500,501,502,503,504,505,506,508,509,510,511,522,534,535,537,539,558,560,566,577,578,589,592,593,608,618,634,635,636,641,643,646,653,656,664,702,709,718,723,726,740,743,775,785,787,788,797,798,810,813,815,817,819,821,832,836,852,867,873,879,880,891,896,900,903,907,909,921,932,934,936,941,942,957,958,969,978,980,981,986,990,1004,1010,1012],[45,75,92,108,120,136,199,206,210,212,217,219,220,226,228,231,237,248,249,250,255,257,303,343,348,351,362,373,376,424,430,437,457,458,462,476,482,486,490,491,494,495,496,499,507,512,513,519,529,532,541,543,546,553,559,562,582,583,597,610,616,661,663,670,676,679,683,694,695,704,712,725,744,750,764,769,771,776,782,783,795,801,808,812,825,826,839,861,871,882,894,899,904,933,952,956,963,964,966,984,1019],[211,245,456,472,481,527,536,544,554,561,565,568,574,581,607,609,614,621,639,645,648,649,650,662,665,687,696,700,719,724,731,734,748,757,762,777,790,802,806,838,840,842,856,857,862,864,881,885,890,912,927,928,937,938,962,991,995,998,1011,1018,1022],[521,538,575,576,591,595,605,611,615,622,628,630,631,660,677,710,711,713,736,749,759,781,848,850,869,870,876,908,917,918,919,922,923,924,926,953,974,1002,1006,1023],[517,547,551,601,612,637,652,671,678,688,689,693,701,717,721,730,738,767,768,786,789,818,843,849,898,935,947,950,951,970,975,979,983,993,997,1003,1008],[515,518,545,552,567,570,584,603,613,651,667,668,673,686,697,706,715,742,758,791,794,800,822,823,830,844,868,910,920,977,985,989,1009,1014,1016],[530,533,540,587,588,627,629,632,644,674,705,707,732,733,735,737,779,784,827,828,835,878,884,889,994],[526,638,756,799,863,902,905,906,913,914,915,939,944,996],[549,594,596,642,685,703,741,747,773,778,814,847,872,945,961,973],[524,555,579,617,633,658,727,729,770,804,858,866,875,929,948,965,1007,1013],[556,580,586,600,640,647,657,722,761,809,831,897,940,946,960,976,987,988,1015],[531,572,598,625,692,716,751,755,760,772,834,841,887,892,916,999,1017],[672,699,714,728,855,860,943,1021],[599,602,666,682,766,865,955],[654,829,982],[619,708,796,1005],[564,745,803,805],[845],[811]]