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