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547,340;579,378,573,378,569,376,565,378,560,376,556,376,550,373,541,371,538,372,536,376,533,376,527,374,526,372,523,368,519,369,516,368,515,369,511,371,508,374,503,376,501,380,495,376,490,373,488,372,494,369,497,369,503,365,504,362,503,360,504,360,508,359,509,356,508,351,510,348,513,348,515,343,517,338,517,336,515,334,509,334,506,336,505,337,503,337,498,333,494,333,489,331,483,327,483,324,478,321,476,317,470,315,474,315,476,313,479,317,484,317,487,315,489,315,493,313,498,314,500,317,505,317,511,318,512,317,515,315,519,316,522,313,522,312,517,306,515,302,517,303,520,303,519,300,520,299,525,301,531,301,532,299,539,299,540,296,545,295,548,297,562,302,563,305,564,309,565,313,568,313,573,318,581,319,578,323,577,326,580,327,584,326,596,327,604,324,604,326,606,332,609,339,605,340,603,343,602,346,599,347,597,349,595,349,593,347,590,346,585,349,584,353,591,358,593,360,594,361,593,366,592,369,586,370,584,373,581,377,579,378
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517,253;472,264,469,259,473,256,475,257,473,262,476,262,477,260,478,256,481,255,478,253,479,251,486,248,490,248,492,247,491,244,493,242,491,239,487,239,489,237,488,236,484,235,488,233,487,231,491,229,497,227,503,219,507,217,514,219,520,223,523,227,526,228,527,231,529,237,527,237,531,240,532,244,536,249,544,253,547,251,549,250,554,254,556,255,557,257,556,261,553,264,555,266,553,269,558,276,560,275,564,276,565,277,566,282,566,286,561,285,559,285,555,289,556,292,558,293,554,296,550,297,545,295,542,295,533,292,529,284,527,283,526,280,521,279,519,276,509,269,511,268,505,267,501,269,497,267,493,269,484,267,479,267,472,264
435,560;373,562,381,562,386,563,387,557,393,557,398,559,400,560,405,559,409,561,412,560,416,561,417,560,416,553,412,552,412,542,418,541,437,539,444,539,451,541,465,542,471,545,477,552,483,556,485,556,488,553,490,552,492,552,494,554,499,556,505,555,511,553,512,554,514,558,512,566,517,567,514,569,510,574,498,575,501,570,499,569,497,568,495,569,497,570,492,571,488,575,474,574,469,575,465,574,462,575,456,575,450,578,447,580,443,580,441,582,439,581,438,579,435,581,431,584,432,585,434,583,437,586,442,586,438,591,437,596,436,597,432,598,423,599,421,601,416,604,413,602,411,603,407,603,406,599,396,598,394,593,392,591,391,590,384,586,383,582,381,578,378,577,378,574,374,572,367,573,367,571,371,566,371,564,373,562
306,262;313,237,312,236#335,288,339,290,342,290,344,294,331,294,333,292#313,289,312,286,313,280,305,277,301,278,296,282,295,284,290,286,285,287,278,286,278,283,275,279,268,280,266,278,260,278,259,277,259,276,260,274,264,271,266,268,270,265,270,263,267,260,256,257,254,258,249,260,247,259,243,255,245,252,249,247,252,239,269,238,275,241,281,242,290,240,294,241,301,240,304,241,306,246,309,247,313,250,317,250,321,250,317,247,313,243,310,243,310,239,316,239,320,238,326,239,320,235,314,235,314,232,320,234,322,232,312,229,305,230,302,229,302,227,304,225,308,224,312,221,315,220,319,219,326,215,327,209,327,208,329,208,330,212,338,209,335,213,335,217,337,216,342,217,341,221,337,226,338,233,341,233,343,238,343,241,333,241,331,242,329,245,333,245,336,244,343,244,344,244,344,245,343,251,344,252,346,253,351,259,355,258,358,258,363,263,366,265,362,269,359,269,356,273,352,274,351,276,348,277,347,280,346,282,339,281,337,285,335,287,327,286,328,288,327,290,328,292,328,293,324,293,321,293,321,290,319,289,314,289
394,500;361,426,368,416,375,413,376,412,377,414,381,415,394,420,395,421,396,425,395,429,391,433,393,439,391,440,386,441,390,446,386,450,381,449,382,455,384,457,389,462,392,460,391,456,392,455,395,457,396,457,397,455,400,453,404,451,405,448,403,447,404,447,410,442,412,442,420,445,428,450,424,454,422,456,423,460,421,461,426,467,427,473,429,477,432,480,441,484,444,489,447,494,452,499,452,502,454,510,454,514,457,514,458,518,454,520,453,521,456,523,463,528,463,530,462,536,465,542,451,541,444,539,437,539,418,541,413,541,412,552,416,553,417,560,416,561,412,560,409,561,405,559,402,559,398,559,393,557,387,557,387,562,381,562,373,562,374,560,369,559,366,558,365,555,365,552,362,551,365,550,366,547,363,544,364,542,365,538,359,537,356,531,351,532,346,527,340,526,338,527,337,523,338,519,341,516,344,516,344,521,347,520,347,516,352,515,357,514,357,512,358,507,360,502,359,498,361,495,362,491,354,491,352,488,349,487,340,489,336,488,332,489,330,488,327,479,329,476,332,473,332,470,331,467,334,461,337,458,338,456,349,455,346,452,351,450,349,448,352,446,352,444,350,441,351,439,354,436,355,432,366,428,361,426
302,379;107,343,103,342,103,340,104,340,104,341,106,340,108,341,110,339,112,340,112,341#119,342,120,341#98,345,97,344,101,345#116,357,113,357,114,356,116,356#146,380,146,376,149,377#173,393,171,391,172,391,178,391,180,392#156,394,154,394,152,391,156,393#177,404,172,403,171,399,176,394,180,399,179,400,179,403#169,403,167,402,169,400,170,403#379,396,379,397,389,403,386,409,379,410,375,413,368,416,361,426,359,426,355,428,351,427,349,431,350,434,346,436,345,438,342,439,342,441,335,441,328,442,325,442,321,437,318,436,313,433,308,434,303,434,296,435,293,439,290,441,283,443,279,444,275,443,274,439,276,436,274,433,275,431,260,424,258,422,258,419,260,417,260,416,259,415,255,413,255,412,259,413,263,411,264,412,263,413,268,416,266,411,269,407,273,404,271,404,267,406,261,405,256,405,255,405,255,404,265,402,261,401,263,399,266,399,268,398,265,397,262,397,256,396,239,400,225,400,205,402,198,404,192,403,190,398,192,395,191,393,188,399,187,401,182,400,184,396,183,389,185,387,188,388,190,384,186,384,191,380,183,379,184,383,184,385,182,387,178,386,181,381,180,379,178,378,173,382,171,386,168,390,162,392,155,389,153,388,149,390,147,389,149,385,149,384,158,380,162,378,162,376,158,376,161,374,159,373,155,375,155,377,150,376,154,373,154,372,149,373,148,372,146,373,145,379,140,380,132,379,131,378,130,375,126,374,120,376,118,374,113,375,114,371,117,369,120,368,122,370,126,370,129,367,126,366,125,364,132,365,134,364,125,362,121,362,119,360,120,358,118,357,117,355,114,354,110,354,112,352,122,353,122,352,125,350,132,350,135,354,136,354,137,352,134,350,131,348,131,344,133,345,136,344,144,346,150,343,152,342,162,345,172,345,173,344,178,343,180,344,188,344,192,343,192,346,197,348,200,349,209,350,217,352,217,353,221,352,224,353,225,357,221,357,213,357,208,359,213,360,213,361,208,361,206,360,203,359,203,361,197,362,193,360,195,362,199,364,213,364,216,366,220,368,222,371,227,372,230,372,231,373,232,374,242,375,244,376,244,378,242,379,245,383,242,384,245,390,249,392,246,389,246,388,251,389,252,388,252,384,249,383,251,380,253,374,248,374,244,372,241,372,234,368,235,364,238,364,244,363,248,361,251,356,257,353,257,352,255,350,256,348,262,343,264,338,265,336,269,336,273,337,280,336,284,335,288,335,301,333,304,332,311,328,314,326,318,327,327,327,329,328,330,331,338,335,341,337,335,339,338,341,342,345,344,347,350,349,351,356,350,358,351,361,356,369,354,370,354,373,357,374,355,380,356,382,362,385,362,390,366,394,368,395,379,396
412,403;501,380,501,381,506,383,508,385,513,390,511,391,511,393,509,399,503,403,505,404,509,405,508,409,507,410,492,409,499,412,496,415,487,414,480,418,477,417,474,418,472,415,471,412,467,406,459,407,458,410,453,409,451,409,432,413,431,414,432,418,436,423,435,427,431,430,429,433,425,435,423,442,420,445,415,444,410,442,407,445,403,447,405,448,405,449,400,453,399,454,396,457,395,457,392,455,391,456,392,458,391,462,387,459,382,455,382,452,386,450,389,447,386,442,388,440,392,440,390,436,395,432,396,425,395,421,394,420,381,415,377,414,376,412,386,409,389,404,379,397,379,396,382,393,382,391,383,388,388,385,391,384,394,382,399,382,404,385,405,384,408,383,412,384,416,384,422,382,424,381,424,379,431,374,435,374,437,376,439,377,441,382,445,387,448,384,449,385,453,386,456,388,462,386,466,385,478,376,484,375,488,372,490,373,494,375,501,380
461,437;420,445,423,442,425,435,429,433,429,431,435,427,437,424,432,418,431,416,432,413,451,409,453,409,457,410,458,408,465,406,471,412,472,415,474,418,477,417,480,418,487,414,496,415,499,412,502,412,503,414,499,417,501,419,505,425,505,429,501,436,500,438,504,442,509,444,513,443,516,447,519,451,519,457,519,463,519,466,515,469,511,468,505,471,501,466,496,466,494,462,494,459,487,456,483,458,481,461,479,462,474,461,470,463,468,467,467,467,462,470,457,469,455,472,449,470,445,469,442,469,441,467,439,466,433,469,430,472,427,473,427,468,422,464,423,460,422,456,424,454,429,451,422,448
398,282;436,292,435,292,430,292,428,294,425,295,424,298,419,302,414,303,414,308,412,311,407,311,405,308,404,309,403,312,395,311,394,308,392,302,391,302,387,301,388,300,385,294,383,292,382,293,379,296,374,295,374,291,373,287,378,284,375,281,375,279,374,274,377,273,380,273,381,268,384,262,383,260,379,258,373,257,376,263,376,266,373,265,369,264,366,265,363,263,358,258,355,258,351,259,346,255,344,252,343,251,344,245,344,244,343,242,343,238,342,234,338,233,337,227,340,224,342,217,337,216,335,217,333,216,339,212,350,208,351,209,353,209,356,209,362,209,364,209,366,213,369,215,367,215,360,213,356,211,354,212,350,212,350,213,355,213,360,215,370,220,372,218,380,225,385,225,389,232,393,235,389,239,385,243,382,242,379,245,382,249,381,253,386,252,388,254,393,254,398,259,401,262,405,263,405,265,408,267,411,264,418,266,420,269,426,272,431,275,433,278,436,278,438,284,439,287,436,290
288,514;216,506,224,506,241,501,249,499,253,497,256,499,260,499,262,496,266,493,270,492,275,491,283,491,286,493,288,491,293,490,297,491,302,488,304,488,304,489,302,492,303,493,304,495,309,495,312,494,312,490,317,486,320,486,322,484,321,480,326,477,328,486,332,489,336,488,340,489,349,487,352,488,353,491,361,490,361,495,359,498,360,502,356,505,357,512,357,514,355,515,347,516,346,517,346,521,344,516,341,516,338,519,337,523,336,525,340,526,346,527,348,529,356,531,359,537,365,538,364,542,363,544,366,546,365,550,362,551,358,550,351,551,347,545,344,544,342,545,337,550,332,550,324,552,322,552,319,550,316,547,313,548,309,542,306,541,303,539,302,536,295,538,289,536,287,537,285,535,276,541,274,544,263,547,265,550,257,546,244,543,238,547,235,548,233,549,231,546,226,544,222,541,218,540,221,537,223,536,219,532,222,528,219,524,220,521,220,519,222,514,219,512,218,508
554,522;520,522,525,522,528,521,529,517,532,514,532,511,536,507,539,498,540,498,545,495,552,495,555,492,552,488,556,488,560,484,562,485,565,485,570,488,575,486,578,483,581,481,583,478,585,477,585,474,590,472,595,471,597,472,599,473,602,471,606,471,608,474,612,474,617,479,617,482,612,486,609,492,608,496,611,504,610,509,605,516,592,531,591,533,590,538,591,541,588,539,586,540,583,539,578,540,577,536,573,539,576,541,580,545,579,547,583,548,585,550,588,545,588,549,591,555,595,556,596,558,595,561,591,567,586,567,588,563,587,562,583,566,577,565,578,564,574,565,567,566,563,568,556,564,550,562,544,561,536,563,535,562,537,561,538,559,540,557,540,555,539,555,538,557,533,559,531,558,532,560,531,562,534,562,532,565,525,570,521,575,519,576,523,570,521,566,522,563,514,557,514,555,514,552,511,551,511,544,511,540,512,538,517,534,517,531,520,529,520,525,521,524
572,294;602,266,606,270,611,273,616,277,620,277,623,283,621,285,617,286,599,281,593,280,591,280,593,282,590,285,588,290,588,296,591,299,594,302,605,304,604,309,608,315,606,316,604,324,596,327,584,326,580,327,577,326,578,323,580,320,573,318,569,316,565,313,564,309,563,307,562,302,550,297,554,296,558,294,556,292,555,289,559,285,561,285,565,287,567,284,567,280,564,276,560,275,565,274,570,273,573,273,578,270,580,271,580,273,589,272,590,265,592,264,596,267,601,265
229,295;241,250,236,248,241,249#120,251,119,250,120,249#110,263,110,260,112,262#105,266,106,264,109,263#112,272#140,301,136,300,132,296,128,296,127,293,129,290,126,287,121,289,119,288,113,288,112,289,106,287,102,287,108,285,111,283,115,281,122,283,124,280,128,279,132,280,136,280,143,283,141,285,140,290,145,290,143,292,144,294,142,297#147,284,148,283#151,287,152,284,153,286#177,308#181,309,180,308,182,309#129,316,136,310,140,312,140,314,138,315#131,328,132,327#119,331,120,328,124,328,123,330#217,352,224,348,223,347,224,345,222,343,225,341,225,338,225,336,223,335,224,333,223,332,219,332,215,338,211,343,207,345,201,346,209,347,209,350,203,351,197,348,193,347,192,343,190,343,180,344,178,343,173,344,160,344,146,337,146,334,145,330,148,323,147,320,154,318,158,318,162,316,164,317,175,316,184,317,187,316,189,314,187,313,183,311,185,309,183,308,188,306,190,304,187,303,189,302,188,300,182,299,174,298,170,298,167,299,158,302,146,304,142,302,144,301,144,297,147,294,146,290,148,289,152,289,159,291,159,293,161,296,161,290,159,288,158,290,155,288,154,283,150,282,149,280,147,279,148,273,152,272,150,271,153,269,154,268,156,265,153,264,151,265,149,269,143,272,137,267,146,264,140,260,144,259,138,255,142,255,143,252,139,252,135,248,132,250,134,253,129,253,127,257,126,262,126,265,121,268,119,266,119,264,123,256,124,255,124,251,126,248,123,248,124,245,125,242,127,240,132,238,134,235,137,238,142,240,145,240,147,241,149,241,147,245,141,248,139,245,140,249,149,249,149,247,151,242,154,240,158,240,163,242,164,242,160,239,164,238,162,236,158,237,155,234,155,231,160,230,166,231,174,234,179,233,195,234,198,233,202,235,207,235,210,235,212,237,217,234,218,232,227,235,228,237,234,239,233,244,236,245,235,246,233,249,238,251,242,255,243,260,244,257,249,260,253,260,256,257,265,259,268,262,270,265,267,266,264,269,261,273,259,276,259,277,260,278,266,278,268,280,275,279,276,282,278,286,285,287,290,286,292,283,296,282,301,280,305,277,313,280,312,286,313,289,310,290,302,287,300,289,300,293,306,298,305,303,301,302,299,302,298,305,296,309,294,311,299,314,302,317,299,322,298,325,295,328,291,329,286,330,283,334,273,337,269,336,265,336,264,338,262,343,259,345,255,349,257,352,257,353,251,356,248,361,245,362,238,364,235,364,234,360,232,361,232,360,225,357,224,353,221,352,219,354,217,352
355,312;313,289,319,289,321,290,321,293,324,294,328,295,333,295,330,295,344,294,342,292,339,290,335,288,336,287,335,287,337,286,338,284,344,282,347,280,348,277,351,276,352,274,357,276,359,272,362,269,365,268,369,264,373,265,376,266,375,269,376,270,377,273,374,274,374,277,375,281,378,284,373,287,372,290,374,295,376,295,382,293,383,292,384,293,388,298,387,301,389,305,394,308,395,309,395,313,396,314,400,315,399,318,395,321,391,326,388,329,385,334,383,334,380,338,378,339,380,345,379,346,381,350,385,351,386,353,386,357,386,361,388,363,387,366,389,368,390,371,394,375,395,379,394,382,391,384,388,385,383,388,382,391,382,393,379,396,368,395,366,394,363,392,362,385,356,382,355,380,358,376,354,373,354,372,356,369,351,364,350,358,351,356,348,351,346,348,343,346,338,344,335,340,341,338,338,335,330,332,330,328,327,327,318,327,314,326,311,328,306,329,301,333,291,335,284,335,283,334,286,330,291,329,295,328,298,325,299,322,302,318,299,314,294,311,296,309,296,307,299,302,301,302,305,303,307,300,302,296,301,290,300,288,310,290,312,289
-1,-1;0;0