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