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