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