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