[[0,1,3,4,5,6,7,8,9,12,13,14,15,16,17,18,19,21,22,23,24,25,27,28,29,30,31,32,33,34,36,39,40,41,42,257,258,260,261,263,264,265,267,268,269,271,272,274,275,279,280,282,283,284,285,286,287,288,290,292,293,294,296,297,298,299,521,531,535,536,552,560,574,575,596,604,606,610,630,648,651,653,669,677,679,683,689,713,721,734,749,753,755,788,795,796,803,810,817,822,838,840,850,869,871,886,896,916,923,943,952,961,971,975,981,985],[2,10,11,26,37,43,44,45,48,49,50,51,55,56,57,58,61,62,63,66,67,69,70,71,72,73,74,75,78,85,256,259,262,266,270,273,276,277,278,281,289,291,295,300,302,305,306,307,308,309,310,311,312,313,314,317,318,319,320,323,324,326,327,328,331,332,334,339,340,342,543,551,553,576,585,611,623,654,657,663,693,712,724,725,729,739,741,750,765,774,777,783,785,787,791,811,815,821,858,859,865,867,898,904,913,919,921,950,957,965,967,970,979,980,984,1005,1006,1017],{"0":20,"1":35,"2":38,"3":46,"4":47,"5":52,"6":53,"7":59,"8":60,"9":64,"10":65,"11":68,"12":76,"13":77,"14":79,"15":80,"16":82,"17":86,"18":89,"19":90,"20":91,"21":92,"22":93,"23":98,"24":99,"25":100,"26":101,"27":102,"28":106,"29":108,"30":116,"31":117,"32":118,"33":119,"34":120,"35":123,"36":128,"37":129,"38":132,"39":139,"40":303,"41":304,"42":315,"43":316,"44":321,"45":322,"46":325,"47":329,"48":333,"49":346,"50":347,"51":348,"52":350,"53":351,"54":353,"56":355,"57":357,"58":359,"59":361,"60":364,"61":366,"62":367,"63":369,"64":370,"65":375,"66":376,"67":378,"68":379,"69":380,"70":386,"71":387,"72":389,"73":393,"74":517,"75":523,"76":529,"77":533,"78":577,"79":578,"80":579,"81":583,"82":614,"83":617,"84":628,"85":634,"86":639,"87":640,"88":644,"89":661,"90":668,"91":674,"92":676,"93":691,"94":692,"95":697,"96":715,"97":748,"98":758,"99":766,"100":768,"101":782,"102":784,"103":814,"104":819,"105":825,"106":826,"107":827,"108":828,"109":852,"110":860,"111":864,"112":880,"113":887,"114":894,"115":903,"116":908,"117":909,"118":926,"119":936,"120":947,"121":956,"122":963,"123":964,"124":974,"125":1001,"126":1007,"127":1012,"128":1015},[81,83,95,96,97,103,104,109,113,115,126,127,130,137,138,141,146,147,150,152,153,154,161,162,163,166,169,172,173,180,182,188,301,330,335,336,337,338,341,343,358,360,362,372,373,381,383,384,385,388,390,392,394,396,397,398,403,406,409,410,411,413,414,417,418,419,421,424,437,442,522,538,546,554,555,559,565,566,568,569,581,598,601,602,605,619,620,624,632,646,660,662,664,665,666,680,694,702,704,709,722,726,737,745,761,778,786,789,839,854,874,883,910,912,922,935,942,944,958,962,978,983,989,991,992,993,995,999,1021,1022],[54,87,88,94,110,111,121,122,136,140,144,145,155,157,158,159,164,170,179,181,185,187,196,201,207,213,217,218,219,220,235,238,344,349,356,363,365,368,371,377,382,391,401,404,408,420,423,427,428,430,435,436,447,448,449,450,454,455,468,470,472,484,490,515,519,520,526,532,540,542,548,567,571,584,586,589,597,622,626,627,633,638,652,659,678,685,687,706,714,731,740,742,743,744,770,779,800,813,820,835,837,841,844,870,891,897,900,902,917,918,927,931,951,954,960,966,1016],{"0":105,"1":112,"2":114,"3":124,"4":131,"5":142,"6":143,"7":148,"8":156,"9":160,"10":165,"11":174,"12":175,"13":177,"14":178,"15":183,"16":184,"17":189,"18":197,"19":198,"20":199,"21":202,"22":216,"23":221,"24":222,"25":228,"26":232,"27":240,"28":242,"29":243,"30":245,"32":250,"33":253,"34":255,"35":345,"36":352,"37":374,"38":402,"39":407,"40":412,"41":415,"42":416,"43":422,"44":432,"45":433,"46":434,"47":438,"48":440,"49":444,"50":456,"51":465,"52":469,"53":474,"54":479,"55":480,"56":482,"57":483,"58":491,"59":494,"60":499,"61":501,"62":503,"63":504,"64":506,"65":511,"66":525,"67":527,"68":564,"69":570,"70":573,"71":590,"72":595,"73":607,"74":641,"75":642,"76":643,"77":671,"78":688,"79":701,"80":710,"81":717,"82":733,"83":754,"84":767,"85":769,"86":776,"87":793,"88":794,"89":802,"90":805,"91":808,"92":829,"93":833,"94":848,"95":857,"96":863,"97":873,"98":882,"99":893,"100":953,"101":959,"102":998,"103":1014},[84,125,133,134,149,151,171,176,186,190,191,192,194,200,204,205,209,210,211,212,214,215,224,226,229,230,233,234,241,246,251,252,395,399,426,429,439,443,451,452,453,458,459,460,461,464,466,467,471,473,476,478,486,487,488,489,497,498,505,510,530,537,550,580,600,656,675,690,716,719,723,728,746,747,759,763,781,797,804,830,849,853,872,876,877,878,884,888,899,905,906,924,934,937,945,949,955,969,977,1011],[107,135,167,168,193,195,203,206,208,223,225,227,244,247,249,254,400,405,431,441,445,457,463,477,492,493,495,500,502,547,556,563,599,616,686,699,707,752,792,798,799,818,823,842,845,875,907,929,941,1000,1002,1013,1018,1023],[231,236,425,462,475,481,485,509,513,516,518,549,558,561,618,625,637,649,695,705,720,732,735,736,738,751,772,780,806,834,920,930,932,946,968,972,982,986,997,1010,1020],[237,239,446,496,507,508,514,524,539,557,588,594,612,647,650,658,667,670,703,711,730,771,824,832,847,855,856,987,996],[541,562,603,613,629,636,655,790,836,851,862,889,890,911,940,994,1019],[534,545,621,645,672,673,708,727,762,879,885,1003,1009],[512,684,698,773,816,861,915,938,976,990,1008],[572,582,587,696,718,801,881,901,925,928,973],[528,592,615,635,807,846,868,892,933],[757,760,775,809,843,895,939,948,988],[609,700,831,866,914,1004],[591,593,681,756,812],[544,608,682],[764],[631]]