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