[[0,1,2,4,5,9,10,11,13,17,19,20,21,22,23,27,28,31,32,33,36,45,48,51,53,220,221,223,226,227,230,231,233,234,236,238,239,241,242,243,247,249,252,255,256,260,262,264,267,269,270,272,273,442,449,450,453,454,455,459,462,473,477,479,485,502,508,513,514,523,535,540,558,562,569,575,578,580,587,593,604,610,621,628,630,638,646,648,652,660,667,672,675,677,678,680,693,707,718,725,742,747,757,766,773,779,795,805,808,809,815,822,825,827,842,845,846,849,852,853,859,860,863],{"0":3,"1":7,"2":12,"3":14,"4":15,"5":16,"6":25,"7":40,"8":41,"9":42,"10":43,"11":44,"12":46,"13":50,"14":57,"15":60,"16":61,"17":64,"18":65,"19":67,"20":68,"21":71,"22":75,"23":76,"24":77,"25":79,"26":96,"27":98,"28":109,"29":112,"30":114,"31":115,"32":118,"33":222,"34":232,"35":235,"36":240,"37":250,"38":253,"39":254,"40":257,"41":258,"42":261,"43":263,"44":265,"45":268,"46":271,"47":279,"48":280,"49":282,"50":283,"51":286,"52":287,"53":290,"54":291,"56":294,"57":295,"58":297,"59":298,"60":299,"61":301,"62":310,"63":311,"64":319,"65":323,"66":335,"67":438,"68":440,"69":451,"70":457,"71":463,"72":466,"73":469,"74":489,"75":490,"76":494,"77":496,"78":505,"79":522,"80":528,"81":529,"82":533,"83":536,"84":537,"85":541,"86":543,"87":544,"88":545,"89":551,"90":552,"91":553,"92":556,"93":559,"94":561,"95":566,"96":570,"97":582,"98":586,"99":591,"100":592,"101":599,"102":605,"103":607,"104":611,"105":612,"106":618,"107":625,"108":627,"109":636,"110":643,"111":655,"112":665,"113":669,"114":670,"115":679,"116":682,"117":686,"118":696,"119":705,"120":710,"121":712,"122":716,"123":724,"124":727,"125":730,"126":731,"127":735,"128":740,"129":741,"130":753,"131":756,"132":770,"133":780,"134":784,"135":793,"136":798,"137":799,"138":803,"139":813,"140":824,"141":831,"142":840,"143":855,"144":856,"145":861,"146":865,"147":870},{"0":6,"1":24,"2":26,"3":29,"4":30,"5":34,"6":35,"7":37,"8":39,"9":47,"10":49,"11":52,"12":54,"13":56,"14":58,"15":59,"16":62,"17":69,"18":70,"19":74,"20":85,"21":90,"22":91,"23":92,"24":95,"25":97,"26":99,"27":100,"28":102,"29":104,"30":105,"31":110,"32":122,"33":124,"34":125,"35":131,"36":132,"37":133,"38":134,"39":137,"40":147,"41":149,"43":151,"44":159,"45":161,"46":162,"47":167,"48":168,"49":172,"50":224,"51":225,"52":237,"53":244,"54":245,"55":248,"56":251,"57":266,"58":274,"59":275,"60":276,"61":277,"62":278,"63":281,"64":288,"65":289,"66":292,"67":303,"68":304,"69":307,"70":312,"71":313,"72":315,"73":316,"74":322,"75":325,"76":326,"77":333,"78":348,"79":349,"80":350,"81":352,"82":354,"83":355,"84":356,"85":357,"86":365,"87":366,"88":367,"89":368,"90":369,"91":370,"92":371,"93":378,"94":384,"95":390,"96":394,"97":439,"98":447,"99":456,"100":460,"101":467,"102":472,"103":487,"104":493,"105":497,"106":503,"107":515,"108":516,"109":520,"110":526,"111":542,"112":554,"113":555,"114":564,"115":571,"116":572,"117":581,"118":583,"119":588,"120":615,"121":620,"122":632,"123":641,"124":642,"125":651,"126":661,"127":662,"128":685,"129":689,"130":692,"131":698,"132":700,"133":701,"134":706,"135":709,"136":719,"137":720,"138":722,"139":736,"140":739,"141":743,"142":748,"143":750,"144":758,"145":759,"146":762,"147":763,"148":768,"149":771,"150":777,"151":778,"152":781,"153":785,"154":790,"155":791,"156":796,"157":801,"158":806,"159":811,"160":817,"161":819,"162":823,"163":839,"164":851,"165":858,"166":873},[8,18,38,55,63,72,73,78,81,83,84,86,88,89,93,101,108,111,116,126,127,130,135,139,140,142,146,152,153,156,160,163,165,174,178,183,192,193,194,195,196,206,210,211,212,213,219,229,246,284,296,302,305,321,327,329,330,331,334,336,338,341,342,351,353,360,361,362,364,373,380,383,386,387,397,408,411,412,413,423,429,430,437,445,448,464,468,470,491,492,498,499,501,510,512,519,534,539,549,579,584,602,616,622,629,631,634,635,645,671,673,681,684,691,704,711,717,721,728,737,752,772,788,802,804,810,818,832,834,835,836,844,857,862,867],[80,82,87,94,103,106,107,117,119,120,121,123,129,138,141,143,144,148,155,157,158,169,170,171,187,188,189,191,202,205,215,228,259,300,306,308,309,314,317,320,324,332,337,339,346,358,359,363,374,379,382,385,388,391,392,396,400,401,402,403,404,406,407,410,425,428,435,461,465,475,476,506,511,521,546,547,557,563,601,619,624,656,659,690,694,695,702,703,708,713,715,732,744,749,767,774,775,782,789,794,800,812,816,829,864,868],[66,128,166,173,175,177,179,180,182,184,185,186,197,200,203,216,218,285,318,328,340,344,345,347,376,377,381,389,395,399,405,409,414,417,418,419,420,421,422,424,432,433,434,443,446,471,483,504,565,567,576,585,595,597,598,637,644,647,664,676,683,697,738,746,754,783,797,814,826,828,830,838],[113,136,145,154,164,176,181,190,198,201,208,209,214,217,343,372,393,398,415,416,426,427,444,524,525,550,560,577,589,596,600,633,640,650,657,699,726,729,745,792,820,841,847,850,854,866,872],[199,204,207,375,431,436,441,452,481,486,495,527,531,573,590,623,666,687,714,733,769,837],[458,478,482,530,594,609,639,649,663,668,688,723,734,761,776,821,869],[474,484,517,518,532,538,614,658,764,807,833,871],[488,608,617,626,653,751,843],[500,509,548,674,848],[574,613,786],[480,507,603,760],[568,606,654,765],[755,787]]