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