[[2,3,4,5,6,7,8,9,10,11,12,13,25,26,27,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,45,46,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,74,76,78,79,80,81,83,84,85,86,87,88,91,92,97,98,100,101,102,103,104,105,108,109,110,112,113,114,115,116,118,148,151,152,153,154,155,156,157,158,159,160,161,162,163,165,174,175,176,177,180,181,182,183,184,185,186,187,188,189,190,191,193,194,195,197,199,200,202,204,206,207,209,210,211,212,213,214,215,216,217,218,219,220,221,224,226,227,228,229,230,231,232,233,234,235,236,237,238,240,241,242,243,246,248,250,251,252,253,254,257,259,260,263,264,266,267,300,308,338,339,344,348,356,360,365,373,385,411,415,420,421,425,431,432,442,443,444,446,448,459,465,469,484,489,497,502,503,507,518,521,552,561,583],[0,1,14,15,16,17,18,19,21,22,23,28,44,47,72,73,75,77,82,89,90,93,94,95,96,99,106,107,111,117,121,122,123,130,131,139,142,149,150,164,166,167,168,169,170,171,172,178,192,196,198,201,203,205,208,222,223,225,239,244,245,247,249,256,258,262,265,272,277,278,279,280,291,294,296,297,309,310,317,319,322,324,328,330,345,349,374,375,377,380,388,389,397,404,409,412,426,427,429,445,458,467,471,474,475,486,488,492,493,499,500,501,504,508,511,515,517,531,537,543,544,546,547,554,560,563,567,576,580,581,587],[20,24,120,129,132,133,134,136,138,143,145,146,173,255,261,268,269,270,271,273,281,282,283,286,287,289,290,292,293,302,314,315,320,329,333,337,341,343,347,357,363,364,371,379,390,423,437,452,456,461,472,476,482,494,509,513,527,545,556,562,574,582,589,590],[119,124,125,126,127,128,135,137,140,144,147,179,274,275,276,284,285,301,305,312,313,316,325,331,334,335,372,393,396,398,401,403,410,434,441,463,468,483,491,514,530,551,568,586],[141,288,295,303,304,307,326,332,381,408,413,414,416,417,419,439,447,449,455,505,532,534,541,564,578,579,584],[327,336,350,361,367,400,418,435,440,478,529,533],[306,340,351,359,368,370,395,485,498,555,569,570,588],[353,354,466,585],[342,378,394,433,490,506,559],[318,392,399,428,523],[479,496,536],[473,525],[298,457,549],[321,520,577],[299,539],[346,538],[369,477,571],[366,575,591],[383,402,462,565],[355,487,495,524,526],[311,382,384,387,450,470,516,535],[406,422,430,460,548,550,553,557],[323,386,405,451,480,542,573],[407,424,481,528],[358,453,519,522,566],[362,376,540,558,572],[352,438,454],[464],[391,436,510],[512]]