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