[[0,2,3,4,6,7,8,9,10,11,12,13,14,15,16,17,18,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,42,43,44,45,46,47,48,49,50,51,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,83,84,85,86,87,88,89,90,92,93,94,95,96,98,99,100,101,102,103,104,105,106,107,108,110,111,113,114,115,116,117,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,156,157,158,161,162,163,165,166,167,168,169,170,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,205,206,208,209,210,211,212,213,214,216,219,220,221,222,223,224,226,228,229,230,231,233,234,235,236,237,238,239,240,241,242,244,245,246,247,248,249,250,251,253,254,255,256,257,258,260,261,262,263,264,265,267,268,269,272,273,274,275,276,277,278,279,280,281,282,283,285,286,287,288,289,291,292,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,311,312,313,314,315,316,317,318,319,320,321,324,325,326,327,328,329,331,332,333,334,335,336,338,340,342,343,344,346,347,348,349,350,351,352,353,354,355,356,357,359,360,361,362,363,364,365,366,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,407,408,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,469,471,472,473,474,475,476,477,480,481,482,483,485,486,487,488,489,490,491,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,530,531,532,533,534,535,536,537,538,539,543,544,548,561,563,570,572,574,576,583,590,595,596,600,606,613,618,621,631,640,650,654,657,659,660,662,669,671,674,680,681,684,687,688,696,700,703,704,722,726,727,730,734,753,756,760,761,766,778,782,793,796,798,800,801,802,814,816,817,819,821,823,829,835,844,845,854,857,858,861,867,871,872,878,881,888,889,891,893,903,912,917,918,920,926,927,928,933,934,936,941,943,944,948,949,950,963,968,971,976,979,982,985,986,988,1001,1003,1004,1005,1009,1011,1022,1026,1036,1040,1041,1042,1044,1049,1059,1060,1061,1065,1068,1070,1073],[1,5,41,52,82,91,97,109,112,118,154,155,159,160,164,171,172,188,204,207,215,217,218,225,227,232,243,252,259,266,270,271,284,290,293,310,322,323,330,337,339,341,345,358,367,406,409,425,451,468,470,478,479,484,492,513,529,541,547,551,552,554,555,568,571,581,582,585,587,592,604,609,610,616,617,620,623,629,632,633,634,637,639,641,645,648,668,676,677,678,683,686,695,697,706,713,714,718,729,731,735,736,745,751,754,758,763,771,784,790,795,804,811,815,820,825,827,828,830,833,840,848,852,855,859,862,868,869,873,879,898,899,904,906,909,913,914,916,921,922,929,932,939,945,946,947,951,952,959,962,989,995,997,1010,1013,1016,1019,1028,1033,1039,1048,1052,1056,1057,1062,1072,1075],[19,405,557,566,567,575,598,601,615,624,625,635,665,672,675,701,705,711,719,740,742,759,762,772,775,780,786,791,803,831,832,838,853,863,865,877,880,886,894,897,900,902,907,915,942,969,972,975,992,1014,1018,1020,1045,1050,1053,1054],[559,564,578,580,584,586,597,605,628,690,692,707,724,737,752,757,768,783,813,923,931,938,955,961,999,1000,1012,1015,1024,1025,1047,1063,1064,1069],[569,611,643,653,666,689,708,712,747,750,765,785,794,797,799,841,849,887,892,905,910,911,924,925,937,983,991,1023,1032,1034,1038,1051,1074,1078],[540,545,579,589,591,602,607,612,638,646,649,656,698,717,732,787,807,809,846,864,874,876,957,1027,1037,1055,1066,1071],[608,655,670,679,702,723,743,789,792,836,856,866,883,901,919,977,981,990,994,998,1006,1008,1031,1058],[550,553,565,573,619,642,647,673,691,739,767,812,824,843,930,958,964,987,993,1043,1079],[549,556,560,603,614,644,738,746,781,806,895,940,973,980,1007,1017,1030,1035,1076],[630,658,699,716,720,721,728,748,755,769,773,777,779,834,837,839,851,935,974],[588,594,710,733,741,744,770,774,822,850,860,885,908,953,960,970],[562,627,682,749,870,875,896,1029],[599,626,636,694,715,776,788,810,818,890,954,967,984,1046],[546,558,622,661,664,826,847,978,996,1021],[663,725,966,1077],[593,652,808],[651,764,1002],[667,709,882,956,1067],[805,842,884],[685,693,965],[542,577]]