#################################################################################### #################################################################################### #################################################################################### ### ### ### ### ### TRIANGULATIONS OF AKBULUT-KIRBY SPHERES ### ### by Frank H. Lutz and Mimi Tsuruga ### ### http://matsguru.com/research/AKspheres.html ### ### ### ### name of example: ### ### ### ### AK_III_009 ### ### ### ### ### ### description: ### ### ### ### Type 3 construction of triangulation of Akbulut-Kirby sphere ### ### ### ### ### ### properties: ### ### ### ### f=(458,6588,21792,26100,10440) ### ### H_*=(Z,0,0,0,Z) ### ### PL 4-sphere ### ### ### ### ### ### references: ### ### ### ### Frank H. Lutz and Mimi Tsuruga. ### ### Constructing complicated spheres. ### ### arXiv:1302.6856[math.CO], 2013. ### ### ### ### ### #################################################################################### #################################################################################### #################################################################################### facets:=[ [0,1,2,5,305],[0,1,2,35,335],[0,1,2,302,305],[0,1,2,302,335], [0,1,4,5,305],[0,1,4,154,304],[0,1,4,304,305],[0,1,34,35,335], [0,1,34,142,292],[0,1,34,142,442],[0,1,34,184,292],[0,1,34,334,335], [0,1,34,334,442],[0,1,141,142,292],[0,1,141,142,442],[0,1,141,291,292], [0,1,141,291,441],[0,1,141,441,442],[0,1,151,154,304],[0,1,151,184,292], [0,1,151,291,292],[0,1,151,291,441],[0,1,301,302,305],[0,1,301,302,335], [0,1,151,301,304],[0,1,301,304,305],[0,1,301,334,335],[0,1,301,334,442], [0,1,151,301,441],[0,1,301,441,442],[0,2,5,26,176],[0,2,5,26,326], [2,5,26,176,326],[0,2,5,155,176],[2,5,155,176,326],[0,2,5,305,326], [2,5,155,305,326],[0,2,26,29,179],[0,2,26,29,329],[2,26,29,179,329], [0,2,26,176,179],[2,26,176,179,329],[0,2,26,326,329],[2,26,176,326,329], [0,2,29,145,295],[0,2,29,145,445],[0,2,29,179,295],[0,2,29,329,445], [0,2,35,145,295],[0,2,35,145,445],[0,2,35,185,295],[0,2,35,335,445], [0,2,152,155,176],[2,152,155,176,326],[2,152,155,305,326],[0,2,152,176,179], [2,152,176,179,329],[2,152,176,326,329],[0,2,152,179,295],[0,2,152,185,295], [0,2,302,305,326],[2,152,302,305,326],[0,2,302,326,329],[2,152,302,326,329], [0,2,302,329,445],[0,2,302,335,445],[0,3,4,5,305],[0,3,4,154,304], [0,3,4,304,305],[0,3,5,26,176],[0,3,5,26,326],[0,3,5,155,176], [0,3,5,305,326],[0,3,24,26,176],[0,3,24,26,326],[0,3,24,174,176], [0,3,24,174,324],[0,3,24,324,326],[0,3,153,154,304],[0,3,153,155,176], [0,3,153,174,176],[0,3,153,174,324],[0,3,153,303,304],[0,3,303,304,305], [0,3,303,305,326],[0,3,153,303,324],[0,3,303,324,326],[0,24,26,29,179], [0,24,26,29,329],[0,24,26,176,179],[0,24,26,326,329],[0,24,27,29,179], [0,24,27,29,329],[0,24,27,177,179],[0,24,27,177,327],[0,24,27,327,329], [0,24,174,176,179],[0,24,174,177,179],[0,24,174,177,327],[0,24,324,326,329], [0,24,174,324,327],[0,24,324,327,329],[0,27,29,145,295],[0,27,29,145,445], [0,27,29,179,295],[0,27,29,329,445],[0,27,138,142,292],[0,27,138,142,442], [0,27,138,145,295],[0,27,138,145,445],[0,27,138,288,292],[0,27,138,288,295], [0,27,138,438,442],[0,27,138,438,445],[0,27,141,142,292],[0,27,141,142,442], [0,27,141,291,292],[0,27,141,291,441],[0,27,141,441,442],[0,27,177,179,295], [0,27,177,288,292],[0,27,177,288,295],[0,27,177,291,292],[0,27,177,291,441], [0,27,327,329,445],[0,27,327,438,442],[0,27,327,438,445],[0,27,177,327,441], [0,27,327,441,442],[0,33,34,35,335],[0,33,34,142,292],[0,33,34,142,442], [0,33,34,184,292],[0,33,34,334,335],[0,33,34,334,442],[0,33,35,145,295], [0,33,35,145,445],[0,33,35,185,295],[0,33,35,335,445],[0,33,138,142,292], [0,33,138,142,442],[0,33,138,145,295],[0,33,138,145,445],[0,33,138,288,292], [0,33,138,288,295],[0,33,138,438,442],[0,33,138,438,445],[0,33,183,184,292], [0,33,183,185,295],[0,33,183,288,292],[0,33,183,288,295],[0,33,333,334,335], [0,33,333,334,442],[0,33,333,335,445],[0,33,333,438,442],[0,33,333,438,445], [150,151,152,155,305],[150,151,152,185,335],[150,151,152,302,305],[150,151,152,302,335], [150,151,154,155,305],[0,150,151,154,304],[150,151,154,304,305],[150,151,184,185,335], [0,150,151,184,292],[150,151,184,292,442],[150,151,184,334,335],[150,151,184,334,442], [0,150,151,291,292],[150,151,291,292,442],[0,150,151,291,441],[150,151,291,441,442], [150,151,301,302,305],[150,151,301,302,335],[0,150,151,301,304],[150,151,301,304,305], [150,151,301,334,335],[150,151,301,334,442],[0,150,151,301,441],[150,151,301,441,442], [0,150,152,155,176],[150,152,155,176,326],[150,152,155,305,326],[0,150,152,176,179], [150,152,176,179,329],[150,152,176,326,329],[0,150,152,179,295],[150,152,179,295,445], [150,152,179,329,445],[0,150,152,185,295],[150,152,185,295,445],[150,152,185,335,445], [150,152,302,305,326],[150,152,302,326,329],[150,152,302,329,445],[150,152,302,335,445], [150,153,154,155,305],[0,150,153,154,304],[150,153,154,304,305],[0,150,153,155,176], [150,153,155,176,326],[150,153,155,305,326],[0,150,153,174,176],[150,153,174,176,326], [0,150,153,174,324],[150,153,174,324,326],[0,150,153,303,304],[150,153,303,304,305], [150,153,303,305,326],[0,150,153,303,324],[150,153,303,324,326],[0,150,174,176,179], [150,174,176,179,329],[150,174,176,326,329],[0,150,174,177,179],[150,174,177,179,329], [0,150,174,177,327],[150,174,177,327,329],[150,174,324,326,329],[0,150,174,324,327], [150,174,324,327,329],[0,150,177,179,295],[150,177,179,295,445],[150,177,179,329,445], [0,150,177,288,292],[150,177,288,292,442],[0,150,177,288,295],[150,177,288,295,445], [150,177,288,438,442],[150,177,288,438,445],[0,150,177,291,292],[150,177,291,292,442], [0,150,177,291,441],[150,177,291,441,442],[150,177,327,329,445],[150,177,327,438,442], [150,177,327,438,445],[0,150,177,327,441],[150,177,327,441,442],[150,183,184,185,335], [0,150,183,184,292],[150,183,184,292,442],[150,183,184,334,335],[150,183,184,334,442], [0,150,183,185,295],[150,183,185,295,445],[150,183,185,335,445],[0,150,183,288,292], [150,183,288,292,442],[0,150,183,288,295],[150,183,288,295,445],[150,183,288,438,442], [150,183,288,438,445],[150,183,333,334,335],[150,183,333,334,442],[150,183,333,335,445], [150,183,333,438,442],[150,183,333,438,445],[0,300,301,302,305],[150,300,301,302,305], [0,300,301,302,335],[150,300,301,302,335],[0,150,300,301,304],[0,300,301,304,305], [150,300,301,304,305],[0,300,301,334,335],[150,300,301,334,335],[0,300,301,334,442], [150,300,301,334,442],[0,150,300,301,441],[0,300,301,441,442],[150,300,301,441,442], [0,300,302,305,326],[150,300,302,305,326],[0,300,302,326,329],[150,300,302,326,329], [0,300,302,329,445],[150,300,302,329,445],[0,300,302,335,445],[150,300,302,335,445], [0,150,300,303,304],[0,300,303,304,305],[150,300,303,304,305],[0,300,303,305,326], [150,300,303,305,326],[0,150,300,303,324],[0,300,303,324,326],[150,300,303,324,326], [0,300,324,326,329],[150,300,324,326,329],[0,150,300,324,327],[0,300,324,327,329], [150,300,324,327,329],[0,300,327,329,445],[150,300,327,329,445],[0,300,327,438,442], [150,300,327,438,442],[0,300,327,438,445],[150,300,327,438,445],[0,150,300,327,441], [0,300,327,441,442],[150,300,327,441,442],[0,300,333,334,335],[150,300,333,334,335], [0,300,333,334,442],[150,300,333,334,442],[0,300,333,335,445],[150,300,333,335,445], [0,300,333,438,442],[150,300,333,438,442],[0,300,333,438,445],[150,300,333,438,445], [1,2,5,41,191],[1,2,5,41,341],[2,5,41,191,341],[1,2,5,155,191], [2,5,155,191,341],[1,2,5,305,341],[2,5,155,305,341],[1,2,35,145,295], [1,2,35,145,445],[1,2,35,185,295],[1,2,35,335,445],[1,2,38,41,191], [1,2,38,41,341],[2,38,41,191,341],[1,2,38,148,298],[1,2,38,148,448], [1,2,38,188,191],[2,38,188,191,341],[1,2,38,188,298],[1,2,38,338,341], [2,38,188,338,341],[1,2,38,338,448],[1,2,144,145,295],[1,2,144,145,445], [1,2,144,148,298],[1,2,144,148,448],[1,2,144,294,295],[1,2,144,294,298], [1,2,144,444,445],[1,2,144,444,448],[1,2,152,155,191],[2,152,155,191,341], [2,152,155,305,341],[1,2,152,185,295],[1,2,152,188,191],[2,152,188,191,341], [1,2,152,188,298],[2,152,188,338,341],[1,2,152,294,295],[1,2,152,294,298], [1,2,302,305,341],[2,152,302,305,341],[1,2,302,335,445],[1,2,302,338,341], [2,152,302,338,341],[1,2,302,338,448],[1,2,302,444,445],[1,2,302,444,448], [1,4,5,41,191],[1,4,5,41,341],[1,4,5,155,191],[1,4,5,305,341], [1,4,39,41,191],[1,4,39,41,341],[1,4,39,189,191],[1,4,39,189,339], [1,4,39,339,341],[1,4,154,155,191],[1,4,154,189,191],[1,4,154,189,339], [1,4,304,305,341],[1,4,154,304,339],[1,4,304,339,341],[1,34,35,145,295], [1,34,35,145,445],[1,34,35,185,295],[1,34,35,335,445],[1,34,139,142,292], [1,34,139,142,442],[1,34,139,145,295],[1,34,139,145,445],[1,34,139,289,292], [1,34,139,289,295],[1,34,139,439,442],[1,34,139,439,445],[1,34,184,185,295], [1,34,184,289,292],[1,34,184,289,295],[1,34,334,335,445],[1,34,334,439,442], [1,34,334,439,445],[1,36,38,41,191],[1,36,38,41,341],[1,36,38,148,298], [1,36,38,148,448],[1,36,38,188,191],[1,36,38,188,298],[1,36,38,338,341], [1,36,38,338,448],[1,36,39,41,191],[1,36,39,41,341],[1,36,39,189,191], [1,36,39,189,339],[1,36,39,339,341],[1,36,139,142,292],[1,36,139,142,442], [1,36,139,145,295],[1,36,139,145,445],[1,36,139,289,292],[1,36,139,289,295], [1,36,139,439,442],[1,36,139,439,445],[1,36,141,142,292],[1,36,141,142,442], [1,36,141,291,292],[1,36,141,291,441],[1,36,141,441,442],[1,36,144,145,295], [1,36,144,145,445],[1,36,144,148,298],[1,36,144,148,448],[1,36,144,294,295], [1,36,144,294,298],[1,36,144,444,445],[1,36,144,444,448],[1,36,186,188,191], [1,36,186,188,298],[1,36,186,189,191],[1,36,186,189,339],[1,36,186,289,292], [1,36,186,289,295],[1,36,186,291,292],[1,36,186,291,441],[1,36,186,294,295], [1,36,186,294,298],[1,36,336,338,341],[1,36,336,338,448],[1,36,186,336,339], [1,36,336,339,341],[1,36,336,439,442],[1,36,336,439,445],[1,36,186,336,441], [1,36,336,441,442],[1,36,336,444,445],[1,36,336,444,448],[1,151,152,155,191], [151,152,155,191,341],[151,152,155,305,341],[1,151,152,185,295],[151,152,185,295,445], [151,152,185,335,445],[1,151,152,188,191],[151,152,188,191,341],[1,151,152,188,298], [151,152,188,298,448],[151,152,188,338,341],[151,152,188,338,448],[1,151,152,294,295], [151,152,294,295,445],[1,151,152,294,298],[151,152,294,298,448],[151,152,294,444,445], [151,152,294,444,448],[151,152,302,305,341],[151,152,302,335,445],[151,152,302,338,341], [151,152,302,338,448],[151,152,302,444,445],[151,152,302,444,448],[1,151,154,155,191], [151,154,155,191,341],[151,154,155,305,341],[1,151,154,189,191],[151,154,189,191,341], [1,151,154,189,339],[151,154,189,339,341],[151,154,304,305,341],[1,151,154,304,339], [151,154,304,339,341],[1,151,184,185,295],[151,184,185,295,445],[151,184,185,335,445], [1,151,184,289,292],[151,184,289,292,442],[1,151,184,289,295],[151,184,289,295,445], [151,184,289,439,442],[151,184,289,439,445],[151,184,334,335,445],[151,184,334,439,442], [151,184,334,439,445],[1,151,186,188,191],[151,186,188,191,341],[1,151,186,188,298], [151,186,188,298,448],[151,186,188,338,341],[151,186,188,338,448],[1,151,186,189,191], [151,186,189,191,341],[1,151,186,189,339],[151,186,189,339,341],[1,151,186,289,292], [151,186,289,292,442],[1,151,186,289,295],[151,186,289,295,445],[151,186,289,439,442], [151,186,289,439,445],[1,151,186,291,292],[151,186,291,292,442],[1,151,186,291,441], [151,186,291,441,442],[1,151,186,294,295],[151,186,294,295,445],[1,151,186,294,298], [151,186,294,298,448],[151,186,294,444,445],[151,186,294,444,448],[151,186,336,338,341], [151,186,336,338,448],[1,151,186,336,339],[151,186,336,339,341],[151,186,336,439,442], [151,186,336,439,445],[1,151,186,336,441],[151,186,336,441,442],[151,186,336,444,445], [151,186,336,444,448],[1,301,302,305,341],[151,301,302,305,341],[1,301,302,335,445], [151,301,302,335,445],[1,301,302,338,341],[151,301,302,338,341],[1,301,302,338,448], [151,301,302,338,448],[1,301,302,444,445],[151,301,302,444,445],[1,301,302,444,448], [151,301,302,444,448],[1,301,304,305,341],[151,301,304,305,341],[1,151,301,304,339], [1,301,304,339,341],[151,301,304,339,341],[1,301,334,335,445],[151,301,334,335,445], [1,301,334,439,442],[151,301,334,439,442],[1,301,334,439,445],[151,301,334,439,445], [1,301,336,338,341],[151,301,336,338,341],[1,301,336,338,448],[151,301,336,338,448], [1,151,301,336,339],[1,301,336,339,341],[151,301,336,339,341],[1,301,336,439,442], [151,301,336,439,442],[1,301,336,439,445],[151,301,336,439,445],[1,151,301,336,441], [1,301,336,441,442],[151,301,336,441,442],[1,301,336,444,445],[151,301,336,444,445], [1,301,336,444,448],[151,301,336,444,448],[2,29,144,145,295],[2,29,144,145,445], [2,29,144,148,298],[2,29,144,148,448],[2,29,144,294,295],[2,29,144,294,298], [2,29,144,444,445],[2,29,144,444,448],[2,29,146,148,298],[2,29,146,148,448], [2,29,146,296,298],[2,29,146,296,446],[2,29,146,446,448],[2,29,179,294,295], [2,29,179,294,298],[2,29,179,296,298],[2,29,179,296,446],[2,29,329,444,445], [2,29,329,444,448],[2,29,179,329,446],[2,29,329,446,448],[2,38,146,148,298], [2,38,146,148,448],[2,38,146,296,298],[2,38,146,296,446],[2,38,146,446,448], [2,38,188,296,298],[2,38,188,296,446],[2,38,188,338,446],[2,38,338,446,448], [2,152,179,294,295],[152,179,294,295,445],[2,152,179,294,298],[152,179,294,298,448], [152,179,294,444,445],[152,179,294,444,448],[2,152,179,296,298],[152,179,296,298,448], [2,152,179,296,446],[152,179,296,446,448],[152,179,329,444,445],[152,179,329,444,448], [2,152,179,329,446],[152,179,329,446,448],[2,152,188,296,298],[152,188,296,298,448], [2,152,188,296,446],[152,188,296,446,448],[2,152,188,338,446],[152,188,338,446,448], [2,302,329,444,445],[152,302,329,444,445],[2,302,329,444,448],[152,302,329,444,448], [2,152,302,329,446],[2,302,329,446,448],[152,302,329,446,448],[2,152,302,338,446], [2,302,338,446,448],[152,302,338,446,448],[3,4,5,8,308],[3,4,5,305,308], [3,4,7,8,308],[3,4,7,142,292],[3,4,7,142,442],[3,4,7,157,292], [3,4,7,307,308],[3,4,7,307,442],[3,4,141,142,292],[3,4,141,142,442], [3,4,141,291,292],[3,4,141,291,441],[3,4,141,441,442],[3,4,154,157,292], [3,4,154,291,292],[3,4,154,291,441],[3,4,304,305,308],[3,4,304,307,308], [3,4,304,307,442],[3,4,154,304,441],[3,4,304,441,442],[3,5,8,23,173], [3,5,8,23,323],[5,8,23,173,323],[3,5,8,158,173],[5,8,158,173,323], [3,5,8,308,323],[5,8,158,308,323],[3,5,23,26,176],[3,5,23,26,326], [5,23,26,176,326],[3,5,23,173,176],[5,23,173,176,326],[3,5,23,323,326], [5,23,173,323,326],[3,5,155,158,173],[5,155,158,173,323],[5,155,158,308,323], [3,5,155,173,176],[5,155,173,176,326],[5,155,173,323,326],[3,5,305,308,323], [5,155,305,308,323],[3,5,305,323,326],[5,155,305,323,326],[3,6,7,8,308], [3,6,7,142,292],[3,6,7,142,442],[3,6,7,157,292],[3,6,7,307,308], [3,6,7,307,442],[3,6,8,23,173],[3,6,8,23,323],[3,6,8,158,173], [3,6,8,308,323],[3,6,21,23,173],[3,6,21,23,323],[3,6,21,142,292], [3,6,21,142,442],[3,6,21,171,173],[3,6,21,171,292],[3,6,21,321,323], [3,6,21,321,442],[3,6,156,157,292],[3,6,156,158,173],[3,6,156,171,173], [3,6,156,171,292],[3,6,306,307,308],[3,6,306,307,442],[3,6,306,308,323], [3,6,306,321,323],[3,6,306,321,442],[3,21,23,26,176],[3,21,23,26,326], [3,21,23,173,176],[3,21,23,323,326],[3,21,24,26,176],[3,21,24,26,326], [3,21,24,142,292],[3,21,24,142,442],[3,21,24,174,176],[3,21,24,174,292], [3,21,24,324,326],[3,21,24,324,442],[3,21,171,173,176],[3,21,171,174,176], [3,21,171,174,292],[3,21,321,323,326],[3,21,321,324,326],[3,21,321,324,442], [3,24,141,142,292],[3,24,141,142,442],[3,24,141,291,292],[3,24,141,291,441], [3,24,141,441,442],[3,24,174,291,292],[3,24,174,291,441],[3,24,174,324,441], [3,24,324,441,442],[153,154,155,158,308],[153,154,155,305,308],[153,154,157,158,308], [3,153,154,157,292],[153,154,157,292,442],[153,154,157,307,308],[153,154,157,307,442], [3,153,154,291,292],[153,154,291,292,442],[3,153,154,291,441],[153,154,291,441,442], [153,154,304,305,308],[153,154,304,307,308],[153,154,304,307,442],[3,153,154,304,441], [153,154,304,441,442],[3,153,155,158,173],[153,155,158,173,323],[153,155,158,308,323], [3,153,155,173,176],[153,155,173,176,326],[153,155,173,323,326],[153,155,305,308,323], [153,155,305,323,326],[153,156,157,158,308],[3,153,156,157,292],[153,156,157,292,442], [153,156,157,307,308],[153,156,157,307,442],[3,153,156,158,173],[153,156,158,173,323], 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[1,4,5,155,450],[0,1,4,154,450],[1,4,154,155,450],[1,34,35,185,450], [0,1,34,184,450],[1,34,184,185,450],[1,151,152,155,450],[1,151,152,185,450], [0,1,151,154,450],[1,151,154,155,450],[0,1,151,184,450],[1,151,184,185,450], [0,3,5,155,450],[0,3,4,154,450],[0,3,153,154,450],[0,3,153,155,450], [0,33,35,185,450],[0,33,34,184,450],[0,33,183,184,450],[0,33,183,185,450], [0,150,152,155,450],[150,151,152,155,450],[0,150,152,185,450],[150,151,152,185,450], [0,150,151,154,450],[150,151,154,155,450],[0,150,151,184,450],[150,151,184,185,450], [0,150,153,154,450],[0,150,153,155,450],[150,153,154,155,450],[0,150,183,184,450], [0,150,183,185,450],[150,183,184,185,450],[3,5,8,158,450],[4,5,8,158,450], [3,5,155,158,450],[4,5,155,158,450],[4,7,8,158,450],[3,4,7,157,450], [4,7,157,158,450],[4,154,155,158,450],[3,4,154,157,450],[4,154,157,158,450], [3,6,8,158,450],[3,6,7,157,450],[3,6,156,157,450],[3,6,156,158,450], [3,153,155,158,450],[153,154,155,158,450],[3,153,154,157,450],[153,154,157,158,450], [3,153,156,157,450],[3,153,156,158,450],[153,156,157,158,450],[6,8,11,161,450], [7,8,11,161,450],[6,8,158,161,450],[7,8,158,161,450],[7,10,11,161,450], [6,7,10,160,450],[7,10,160,161,450],[7,157,158,161,450],[6,7,157,160,450], [7,157,160,161,450],[6,9,11,161,450],[6,9,10,160,450],[6,9,159,160,450], [6,9,159,161,450],[6,156,158,161,450],[156,157,158,161,450],[6,156,157,160,450], [156,157,160,161,450],[6,156,159,160,450],[6,156,159,161,450],[156,159,160,161,450], [9,11,14,164,450],[10,11,14,164,450],[9,11,161,164,450],[10,11,161,164,450], [10,13,14,164,450],[9,10,13,163,450],[10,13,163,164,450],[10,160,161,164,450], [9,10,160,163,450],[10,160,163,164,450],[9,12,14,164,450],[9,12,13,163,450], [9,12,162,163,450],[9,12,162,164,450],[9,159,161,164,450],[159,160,161,164,450], [9,159,160,163,450],[159,160,163,164,450],[9,159,162,163,450],[9,159,162,164,450], [159,162,163,164,450],[12,14,17,167,450],[13,14,17,167,450],[12,14,164,167,450], 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[19,169,172,173,450],[18,21,23,173,450],[18,21,22,172,450],[18,21,171,172,450], [18,21,171,173,450],[18,168,170,173,450],[168,169,170,173,450],[18,168,169,172,450], [168,169,172,173,450],[18,168,171,172,450],[18,168,171,173,450],[168,171,172,173,450], [21,23,26,176,450],[22,23,26,176,450],[21,23,173,176,450],[22,23,173,176,450], [22,25,26,176,450],[21,22,25,175,450],[22,25,175,176,450],[22,172,173,176,450], [21,22,172,175,450],[22,172,175,176,450],[21,24,26,176,450],[21,24,25,175,450], [21,24,174,175,450],[21,24,174,176,450],[21,171,173,176,450],[171,172,173,176,450], [21,171,172,175,450],[171,172,175,176,450],[21,171,174,175,450],[21,171,174,176,450], [171,174,175,176,450],[24,26,29,179,450],[25,26,29,179,450],[24,26,176,179,450], [25,26,176,179,450],[25,28,29,179,450],[24,25,28,178,450],[25,28,178,179,450], [25,175,176,179,450],[24,25,175,178,450],[25,175,178,179,450],[24,27,29,179,450], [24,27,28,178,450],[24,27,177,178,450],[24,27,177,179,450],[24,174,176,179,450], [174,175,176,179,450],[24,174,175,178,450],[174,175,178,179,450],[24,174,177,178,450], [24,174,177,179,450],[174,177,178,179,450],[27,29,32,182,450],[28,29,32,182,450], [27,29,179,182,450],[28,29,179,182,450],[28,31,32,182,450],[27,28,31,181,450], [28,31,181,182,450],[28,178,179,182,450],[27,28,178,181,450],[28,178,181,182,450], [27,30,32,182,450],[27,30,31,181,450],[27,30,180,181,450],[27,30,180,182,450], [27,177,179,182,450],[177,178,179,182,450],[27,177,178,181,450],[177,178,181,182,450], [27,177,180,181,450],[27,177,180,182,450],[177,180,181,182,450],[30,32,35,185,450], [31,32,35,185,450],[30,32,182,185,450],[31,32,182,185,450],[31,34,35,185,450], [30,31,34,184,450],[31,34,184,185,450],[31,181,182,185,450],[30,31,181,184,450], [31,181,184,185,450],[30,33,35,185,450],[30,33,34,184,450],[30,33,183,184,450], [30,33,183,185,450],[30,180,182,185,450],[180,181,182,185,450],[30,180,181,184,450], [180,181,184,185,450],[30,180,183,184,450],[30,180,183,185,450],[180,183,184,185,450], [0,1,2,5,451],[1,2,5,450,451],[0,1,2,35,451],[1,2,35,450,451], [0,1,4,5,451],[0,1,4,450,451],[1,4,5,450,451],[0,1,34,35,451], [0,1,34,450,451],[1,34,35,450,451],[0,3,4,5,451],[0,3,4,450,451], [0,33,34,35,451],[0,33,34,450,451],[3,4,5,8,451],[4,5,8,450,451], [3,4,7,8,451],[3,4,7,450,451],[4,7,8,450,451],[3,6,7,8,451], [3,6,7,450,451],[6,7,8,11,451],[7,8,11,450,451],[6,7,10,11,451], [6,7,10,450,451],[7,10,11,450,451],[6,9,10,11,451],[6,9,10,450,451], [9,10,11,14,451],[10,11,14,450,451],[9,10,13,14,451],[9,10,13,450,451], [10,13,14,450,451],[9,12,13,14,451],[9,12,13,450,451],[12,13,14,17,451], [13,14,17,450,451],[12,13,16,17,451],[12,13,16,450,451],[13,16,17,450,451], [12,15,16,17,451],[12,15,16,450,451],[15,16,17,20,451],[16,17,20,450,451], [15,16,19,20,451],[15,16,19,450,451],[16,19,20,450,451],[15,18,19,20,451], [15,18,19,450,451],[18,19,20,23,451],[19,20,23,450,451],[18,19,22,23,451], [18,19,22,450,451],[19,22,23,450,451],[18,21,22,23,451],[18,21,22,450,451], [21,22,23,26,451],[22,23,26,450,451],[21,22,25,26,451],[21,22,25,450,451], [22,25,26,450,451],[21,24,25,26,451],[21,24,25,450,451],[24,25,26,29,451], [25,26,29,450,451],[24,25,28,29,451],[24,25,28,450,451],[25,28,29,450,451], [24,27,28,29,451],[24,27,28,450,451],[27,28,29,32,451],[28,29,32,450,451], [27,28,31,32,451],[27,28,31,450,451],[28,31,32,450,451],[27,30,31,32,451], [27,30,31,450,451],[30,31,32,35,451],[31,32,35,450,451],[30,31,34,35,451], [30,31,34,450,451],[31,34,35,450,451],[30,33,34,35,451],[30,33,34,450,451], [0,2,5,450,452],[0,2,5,451,452],[2,5,450,451,452],[0,2,35,450,452], [0,2,35,451,452],[2,35,450,451,452],[0,3,5,450,452],[0,3,5,451,452], [0,33,35,450,452],[0,33,35,451,452],[3,5,8,450,452],[3,5,8,451,452], [5,8,450,451,452],[3,6,8,450,452],[3,6,8,451,452],[6,8,11,450,452], [6,8,11,451,452],[8,11,450,451,452],[6,9,11,450,452],[6,9,11,451,452], [9,11,14,450,452],[9,11,14,451,452],[11,14,450,451,452],[9,12,14,450,452], [9,12,14,451,452],[12,14,17,450,452],[12,14,17,451,452],[14,17,450,451,452], [12,15,17,450,452],[12,15,17,451,452],[15,17,20,450,452],[15,17,20,451,452], [17,20,450,451,452],[15,18,20,450,452],[15,18,20,451,452],[18,20,23,450,452], [18,20,23,451,452],[20,23,450,451,452],[18,21,23,450,452],[18,21,23,451,452], [21,23,26,450,452],[21,23,26,451,452],[23,26,450,451,452],[21,24,26,450,452], [21,24,26,451,452],[24,26,29,450,452],[24,26,29,451,452],[26,29,450,451,452], [24,27,29,450,452],[24,27,29,451,452],[27,29,32,450,452],[27,29,32,451,452], [29,32,450,451,452],[27,30,32,450,452],[27,30,32,451,452],[30,32,35,450,452], [30,32,35,451,452],[32,35,450,451,452],[30,33,35,450,452],[30,33,35,451,452], [0,3,450,451,453],[0,3,450,452,453],[0,3,451,452,453],[0,33,450,451,453], [0,33,450,452,453],[0,33,451,452,453],[3,6,450,451,453],[3,6,450,452,453], [3,6,451,452,453],[6,9,450,451,453],[6,9,450,452,453],[6,9,451,452,453], [9,12,450,451,453],[9,12,450,452,453],[9,12,451,452,453],[12,15,450,451,453], [12,15,450,452,453],[12,15,451,452,453],[15,18,450,451,453],[15,18,450,452,453], [15,18,451,452,453],[18,21,450,451,453],[18,21,450,452,453],[18,21,451,452,453], [21,24,450,451,453],[21,24,450,452,453],[21,24,451,452,453],[24,27,450,451,453], [24,27,450,452,453],[24,27,451,452,453],[27,30,450,451,453],[27,30,450,452,453], [27,30,451,452,453],[30,33,450,451,453],[30,33,450,452,453],[30,33,451,452,453], [36,38,41,191,454],[37,38,41,191,454],[36,38,137,287,454],[37,38,137,287,454], [36,38,188,191,454],[37,38,188,191,454],[36,38,188,287,454],[37,38,188,287,454], [37,40,41,191,454],[36,37,40,190,454],[37,40,190,191,454],[37,136,137,287,454], [36,37,136,286,454],[37,136,286,287,454],[37,187,188,191,454],[37,187,188,287,454], [36,37,187,190,454],[37,187,190,191,454],[36,37,187,286,454],[37,187,286,287,454], [36,39,41,191,454],[36,39,40,190,454],[36,39,189,190,454],[36,39,189,191,454], [36,135,137,287,454],[36,135,136,286,454],[36,135,285,286,454],[36,135,285,287,454], [36,186,188,191,454],[186,187,188,191,454],[36,186,188,287,454],[186,187,188,287,454], [36,186,187,190,454],[186,187,190,191,454],[36,186,187,286,454],[186,187,286,287,454], [36,186,189,190,454],[36,186,189,191,454],[186,189,190,191,454],[36,186,285,286,454], [36,186,285,287,454],[186,285,286,287,454],[39,41,44,194,454],[40,41,44,194,454], [39,41,191,194,454],[40,41,191,194,454],[40,43,44,194,454],[39,40,43,193,454], [40,43,193,194,454],[40,190,191,194,454],[39,40,190,193,454],[40,190,193,194,454], [39,42,44,194,454],[39,42,43,193,454],[39,42,192,193,454],[39,42,192,194,454], [39,189,191,194,454],[189,190,191,194,454],[39,189,190,193,454],[189,190,193,194,454], [39,189,192,193,454],[39,189,192,194,454],[189,192,193,194,454],[42,44,47,197,454], [43,44,47,197,454],[42,44,194,197,454],[43,44,194,197,454],[43,46,47,197,454], [42,43,46,196,454],[43,46,196,197,454],[43,193,194,197,454],[42,43,193,196,454], [43,193,196,197,454],[42,45,47,197,454],[42,45,46,196,454],[42,45,195,196,454], [42,45,195,197,454],[42,192,194,197,454],[192,193,194,197,454],[42,192,193,196,454], [192,193,196,197,454],[42,192,195,196,454],[42,192,195,197,454],[192,195,196,197,454], [45,47,50,200,454],[46,47,50,200,454],[45,47,197,200,454],[46,47,197,200,454], [46,49,50,200,454],[45,46,49,199,454],[46,49,199,200,454],[46,196,197,200,454], [45,46,196,199,454],[46,196,199,200,454],[45,48,50,200,454],[45,48,49,199,454], [45,48,198,199,454],[45,48,198,200,454],[45,195,197,200,454],[195,196,197,200,454], [45,195,196,199,454],[195,196,199,200,454],[45,195,198,199,454],[45,195,198,200,454], [195,198,199,200,454],[48,50,53,203,454],[49,50,53,203,454],[48,50,200,203,454], [49,50,200,203,454],[49,52,53,203,454],[48,49,52,202,454],[49,52,202,203,454], [49,199,200,203,454],[48,49,199,202,454],[49,199,202,203,454],[48,51,53,203,454], [48,51,52,202,454],[48,51,201,202,454],[48,51,201,203,454],[48,198,200,203,454], [198,199,200,203,454],[48,198,199,202,454],[198,199,202,203,454],[48,198,201,202,454], [48,198,201,203,454],[198,201,202,203,454],[51,53,56,206,454],[52,53,56,206,454], [51,53,203,206,454],[52,53,203,206,454],[52,55,56,206,454],[51,52,55,205,454], [52,55,205,206,454],[52,202,203,206,454],[51,52,202,205,454],[52,202,205,206,454], [51,54,56,206,454],[51,54,55,205,454],[51,54,204,205,454],[51,54,204,206,454], [51,201,203,206,454],[201,202,203,206,454],[51,201,202,205,454],[201,202,205,206,454], [51,201,204,205,454],[51,201,204,206,454],[201,204,205,206,454],[54,56,59,209,454], [55,56,59,209,454],[54,56,206,209,454],[55,56,206,209,454],[55,58,59,209,454], [54,55,58,208,454],[55,58,208,209,454],[55,205,206,209,454],[54,55,205,208,454], [55,205,208,209,454],[54,57,59,209,454],[54,57,58,208,454],[54,57,207,208,454], [54,57,207,209,454],[54,204,206,209,454],[204,205,206,209,454],[54,204,205,208,454], [204,205,208,209,454],[54,204,207,208,454],[54,204,207,209,454],[204,207,208,209,454], [57,59,62,212,454],[58,59,62,212,454],[57,59,209,212,454],[58,59,209,212,454], [58,61,62,212,454],[57,58,61,211,454],[58,61,211,212,454],[58,208,209,212,454], [57,58,208,211,454],[58,208,211,212,454],[57,60,62,212,454],[57,60,61,211,454], [57,60,210,211,454],[57,60,210,212,454],[57,207,209,212,454],[207,208,209,212,454], [57,207,208,211,454],[207,208,211,212,454],[57,207,210,211,454],[57,207,210,212,454], [207,210,211,212,454],[60,62,65,215,454],[61,62,65,215,454],[60,62,212,215,454], [61,62,212,215,454],[61,64,65,215,454],[60,61,64,214,454],[61,64,214,215,454], [61,211,212,215,454],[60,61,211,214,454],[61,211,214,215,454],[60,63,65,215,454], [60,63,64,214,454],[60,63,213,214,454],[60,63,213,215,454],[60,210,212,215,454], [210,211,212,215,454],[60,210,211,214,454],[210,211,214,215,454],[60,210,213,214,454], [60,210,213,215,454],[210,213,214,215,454],[63,65,68,218,454],[64,65,68,218,454], [63,65,215,218,454],[64,65,215,218,454],[64,67,68,218,454],[63,64,67,217,454], [64,67,217,218,454],[64,214,215,218,454],[63,64,214,217,454],[64,214,217,218,454], [63,66,68,218,454],[63,66,67,217,454],[63,66,216,217,454],[63,66,216,218,454], [63,213,215,218,454],[213,214,215,218,454],[63,213,214,217,454],[213,214,217,218,454], [63,213,216,217,454],[63,213,216,218,454],[213,216,217,218,454],[66,68,71,221,454], [67,68,71,221,454],[66,68,218,221,454],[67,68,218,221,454],[67,70,71,221,454], [66,67,70,220,454],[67,70,220,221,454],[67,217,218,221,454],[66,67,217,220,454], [67,217,220,221,454],[66,69,71,221,454],[66,69,70,220,454],[66,69,219,220,454], [66,69,219,221,454],[66,216,218,221,454],[216,217,218,221,454],[66,216,217,220,454], [216,217,220,221,454],[66,216,219,220,454],[66,216,219,221,454],[216,219,220,221,454], [69,71,74,224,454],[70,71,74,224,454],[69,71,221,224,454],[70,71,221,224,454], [70,73,74,224,454],[69,70,73,223,454],[70,73,223,224,454],[70,220,221,224,454], [69,70,220,223,454],[70,220,223,224,454],[69,72,74,224,454],[69,72,73,223,454], [69,72,222,223,454],[69,72,222,224,454],[69,219,221,224,454],[219,220,221,224,454], [69,219,220,223,454],[219,220,223,224,454],[69,219,222,223,454],[69,219,222,224,454], [219,222,223,224,454],[72,74,77,227,454],[73,74,77,227,454],[72,74,224,227,454], [73,74,224,227,454],[73,76,77,227,454],[72,73,76,226,454],[73,76,226,227,454], [73,223,224,227,454],[72,73,223,226,454],[73,223,226,227,454],[72,75,77,227,454], [72,75,76,226,454],[72,75,225,226,454],[72,75,225,227,454],[72,222,224,227,454], [222,223,224,227,454],[72,222,223,226,454],[222,223,226,227,454],[72,222,225,226,454], [72,222,225,227,454],[222,225,226,227,454],[75,77,80,230,454],[76,77,80,230,454], [75,77,227,230,454],[76,77,227,230,454],[76,79,80,230,454],[75,76,79,229,454], [76,79,229,230,454],[76,226,227,230,454],[75,76,226,229,454],[76,226,229,230,454], [75,78,80,230,454],[75,78,79,229,454],[75,78,228,229,454],[75,78,228,230,454], [75,225,227,230,454],[225,226,227,230,454],[75,225,226,229,454],[225,226,229,230,454], [75,225,228,229,454],[75,225,228,230,454],[225,228,229,230,454],[78,80,83,233,454], [79,80,83,233,454],[78,80,230,233,454],[79,80,230,233,454],[79,82,83,233,454], [78,79,82,232,454],[79,82,232,233,454],[79,229,230,233,454],[78,79,229,232,454], [79,229,232,233,454],[78,81,83,233,454],[78,81,82,232,454],[78,81,231,232,454], [78,81,231,233,454],[78,228,230,233,454],[228,229,230,233,454],[78,228,229,232,454], [228,229,232,233,454],[78,228,231,232,454],[78,228,231,233,454],[228,231,232,233,454], [81,83,86,236,454],[82,83,86,236,454],[81,83,233,236,454],[82,83,233,236,454], [82,85,86,236,454],[81,82,85,235,454],[82,85,235,236,454],[82,232,233,236,454], [81,82,232,235,454],[82,232,235,236,454],[81,84,86,236,454],[81,84,85,235,454], [81,84,234,235,454],[81,84,234,236,454],[81,231,233,236,454],[231,232,233,236,454], [81,231,232,235,454],[231,232,235,236,454],[81,231,234,235,454],[81,231,234,236,454], [231,234,235,236,454],[84,86,89,239,454],[85,86,89,239,454],[84,86,236,239,454], [85,86,236,239,454],[85,88,89,239,454],[84,85,88,238,454],[85,88,238,239,454], [85,235,236,239,454],[84,85,235,238,454],[85,235,238,239,454],[84,87,89,239,454], [84,87,88,238,454],[84,87,237,238,454],[84,87,237,239,454],[84,234,236,239,454], [234,235,236,239,454],[84,234,235,238,454],[234,235,238,239,454],[84,234,237,238,454], [84,234,237,239,454],[234,237,238,239,454],[87,89,92,242,454],[88,89,92,242,454], [87,89,239,242,454],[88,89,239,242,454],[88,91,92,242,454],[87,88,91,241,454], [88,91,241,242,454],[88,238,239,242,454],[87,88,238,241,454],[88,238,241,242,454], [87,90,92,242,454],[87,90,91,241,454],[87,90,240,241,454],[87,90,240,242,454], [87,237,239,242,454],[237,238,239,242,454],[87,237,238,241,454],[237,238,241,242,454], [87,237,240,241,454],[87,237,240,242,454],[237,240,241,242,454],[90,92,95,245,454], [91,92,95,245,454],[90,92,242,245,454],[91,92,242,245,454],[91,94,95,245,454], [90,91,94,244,454],[91,94,244,245,454],[91,241,242,245,454],[90,91,241,244,454], [91,241,244,245,454],[90,93,95,245,454],[90,93,94,244,454],[90,93,243,244,454], [90,93,243,245,454],[90,240,242,245,454],[240,241,242,245,454],[90,240,241,244,454], [240,241,244,245,454],[90,240,243,244,454],[90,240,243,245,454],[240,243,244,245,454], [93,95,98,248,454],[94,95,98,248,454],[93,95,245,248,454],[94,95,245,248,454], [94,97,98,248,454],[93,94,97,247,454],[94,97,247,248,454],[94,244,245,248,454], [93,94,244,247,454],[94,244,247,248,454],[93,96,98,248,454],[93,96,97,247,454], [93,96,246,247,454],[93,96,246,248,454],[93,243,245,248,454],[243,244,245,248,454], [93,243,244,247,454],[243,244,247,248,454],[93,243,246,247,454],[93,243,246,248,454], [243,246,247,248,454],[96,98,101,251,454],[97,98,101,251,454],[96,98,248,251,454], [97,98,248,251,454],[97,100,101,251,454],[96,97,100,250,454],[97,100,250,251,454], [97,247,248,251,454],[96,97,247,250,454],[97,247,250,251,454],[96,99,101,251,454], [96,99,100,250,454],[96,99,249,250,454],[96,99,249,251,454],[96,246,248,251,454], [246,247,248,251,454],[96,246,247,250,454],[246,247,250,251,454],[96,246,249,250,454], [96,246,249,251,454],[246,249,250,251,454],[99,101,104,254,454],[100,101,104,254,454], [99,101,251,254,454],[100,101,251,254,454],[100,103,104,254,454],[99,100,103,253,454], [100,103,253,254,454],[100,250,251,254,454],[99,100,250,253,454],[100,250,253,254,454], [99,102,104,254,454],[99,102,103,253,454],[99,102,252,253,454],[99,102,252,254,454], [99,249,251,254,454],[249,250,251,254,454],[99,249,250,253,454],[249,250,253,254,454], [99,249,252,253,454],[99,249,252,254,454],[249,252,253,254,454],[102,104,107,257,454], [103,104,107,257,454],[102,104,254,257,454],[103,104,254,257,454],[103,106,107,257,454], [102,103,106,256,454],[103,106,256,257,454],[103,253,254,257,454],[102,103,253,256,454], [103,253,256,257,454],[102,105,107,257,454],[102,105,106,256,454],[102,105,255,256,454], [102,105,255,257,454],[102,252,254,257,454],[252,253,254,257,454],[102,252,253,256,454], [252,253,256,257,454],[102,252,255,256,454],[102,252,255,257,454],[252,255,256,257,454], [105,107,110,260,454],[106,107,110,260,454],[105,107,257,260,454],[106,107,257,260,454], [106,109,110,260,454],[105,106,109,259,454],[106,109,259,260,454],[106,256,257,260,454], [105,106,256,259,454],[106,256,259,260,454],[105,108,110,260,454],[105,108,109,259,454], [105,108,258,259,454],[105,108,258,260,454],[105,255,257,260,454],[255,256,257,260,454], [105,255,256,259,454],[255,256,259,260,454],[105,255,258,259,454],[105,255,258,260,454], [255,258,259,260,454],[108,110,113,263,454],[109,110,113,263,454],[108,110,260,263,454], [109,110,260,263,454],[109,112,113,263,454],[108,109,112,262,454],[109,112,262,263,454], [109,259,260,263,454],[108,109,259,262,454],[109,259,262,263,454],[108,111,113,263,454], [108,111,112,262,454],[108,111,261,262,454],[108,111,261,263,454],[108,258,260,263,454], [258,259,260,263,454],[108,258,259,262,454],[258,259,262,263,454],[108,258,261,262,454], [108,258,261,263,454],[258,261,262,263,454],[111,113,116,266,454],[112,113,116,266,454], [111,113,263,266,454],[112,113,263,266,454],[112,115,116,266,454],[111,112,115,265,454], [112,115,265,266,454],[112,262,263,266,454],[111,112,262,265,454],[112,262,265,266,454], [111,114,116,266,454],[111,114,115,265,454],[111,114,264,265,454],[111,114,264,266,454], [111,261,263,266,454],[261,262,263,266,454],[111,261,262,265,454],[261,262,265,266,454], [111,261,264,265,454],[111,261,264,266,454],[261,264,265,266,454],[114,116,119,269,454], [115,116,119,269,454],[114,116,266,269,454],[115,116,266,269,454],[115,118,119,269,454], [114,115,118,268,454],[115,118,268,269,454],[115,265,266,269,454],[114,115,265,268,454], [115,265,268,269,454],[114,117,119,269,454],[114,117,118,268,454],[114,117,267,268,454], [114,117,267,269,454],[114,264,266,269,454],[264,265,266,269,454],[114,264,265,268,454], [264,265,268,269,454],[114,264,267,268,454],[114,264,267,269,454],[264,267,268,269,454], [117,119,122,272,454],[118,119,122,272,454],[117,119,269,272,454],[118,119,269,272,454], [118,121,122,272,454],[117,118,121,271,454],[118,121,271,272,454],[118,268,269,272,454], [117,118,268,271,454],[118,268,271,272,454],[117,120,122,272,454],[117,120,121,271,454], [117,120,270,271,454],[117,120,270,272,454],[117,267,269,272,454],[267,268,269,272,454], [117,267,268,271,454],[267,268,271,272,454],[117,267,270,271,454],[117,267,270,272,454], [267,270,271,272,454],[120,122,125,275,454],[121,122,125,275,454],[120,122,272,275,454], [121,122,272,275,454],[121,124,125,275,454],[120,121,124,274,454],[121,124,274,275,454], [121,271,272,275,454],[120,121,271,274,454],[121,271,274,275,454],[120,123,125,275,454], [120,123,124,274,454],[120,123,273,274,454],[120,123,273,275,454],[120,270,272,275,454], [270,271,272,275,454],[120,270,271,274,454],[270,271,274,275,454],[120,270,273,274,454], [120,270,273,275,454],[270,273,274,275,454],[123,125,128,278,454],[124,125,128,278,454], [123,125,275,278,454],[124,125,275,278,454],[124,127,128,278,454],[123,124,127,277,454], [124,127,277,278,454],[124,274,275,278,454],[123,124,274,277,454],[124,274,277,278,454], [123,126,128,278,454],[123,126,127,277,454],[123,126,276,277,454],[123,126,276,278,454], [123,273,275,278,454],[273,274,275,278,454],[123,273,274,277,454],[273,274,277,278,454], [123,273,276,277,454],[123,273,276,278,454],[273,276,277,278,454],[126,128,131,281,454], [127,128,131,281,454],[126,128,278,281,454],[127,128,278,281,454],[127,130,131,281,454], [126,127,130,280,454],[127,130,280,281,454],[127,277,278,281,454],[126,127,277,280,454], [127,277,280,281,454],[126,129,131,281,454],[126,129,130,280,454],[126,129,279,280,454], [126,129,279,281,454],[126,276,278,281,454],[276,277,278,281,454],[126,276,277,280,454], [276,277,280,281,454],[126,276,279,280,454],[126,276,279,281,454],[276,279,280,281,454], [129,131,134,284,454],[130,131,134,284,454],[129,131,281,284,454],[130,131,281,284,454], [130,133,134,284,454],[129,130,133,283,454],[130,133,283,284,454],[130,280,281,284,454], [129,130,280,283,454],[130,280,283,284,454],[129,132,134,284,454],[129,132,133,283,454], [129,132,282,283,454],[129,132,282,284,454],[129,279,281,284,454],[279,280,281,284,454], [129,279,280,283,454],[279,280,283,284,454],[129,279,282,283,454],[129,279,282,284,454], [279,282,283,284,454],[132,134,137,287,454],[133,134,137,287,454],[132,134,284,287,454], [133,134,284,287,454],[133,136,137,287,454],[132,133,136,286,454],[133,136,286,287,454], [133,283,284,287,454],[132,133,283,286,454],[133,283,286,287,454],[132,135,137,287,454], [132,135,136,286,454],[132,135,285,286,454],[132,135,285,287,454],[132,282,284,287,454], [282,283,284,287,454],[132,282,283,286,454],[282,283,286,287,454],[132,282,285,286,454], [132,282,285,287,454],[282,285,286,287,454],[36,37,38,41,455],[37,38,41,454,455], [36,37,38,137,455],[37,38,137,454,455],[36,37,40,41,455],[36,37,40,454,455], [37,40,41,454,455],[36,37,136,137,455],[36,37,136,454,455],[37,136,137,454,455], [36,39,40,41,455],[36,39,40,454,455],[36,135,136,137,455],[36,135,136,454,455], [39,40,41,44,455],[40,41,44,454,455],[39,40,43,44,455],[39,40,43,454,455], [40,43,44,454,455],[39,42,43,44,455],[39,42,43,454,455],[42,43,44,47,455], [43,44,47,454,455],[42,43,46,47,455],[42,43,46,454,455],[43,46,47,454,455], [42,45,46,47,455],[42,45,46,454,455],[45,46,47,50,455],[46,47,50,454,455], [45,46,49,50,455],[45,46,49,454,455],[46,49,50,454,455],[45,48,49,50,455], [45,48,49,454,455],[48,49,50,53,455],[49,50,53,454,455],[48,49,52,53,455], [48,49,52,454,455],[49,52,53,454,455],[48,51,52,53,455],[48,51,52,454,455], [51,52,53,56,455],[52,53,56,454,455],[51,52,55,56,455],[51,52,55,454,455], [52,55,56,454,455],[51,54,55,56,455],[51,54,55,454,455],[54,55,56,59,455], [55,56,59,454,455],[54,55,58,59,455],[54,55,58,454,455],[55,58,59,454,455], [54,57,58,59,455],[54,57,58,454,455],[57,58,59,62,455],[58,59,62,454,455], [57,58,61,62,455],[57,58,61,454,455],[58,61,62,454,455],[57,60,61,62,455], [57,60,61,454,455],[60,61,62,65,455],[61,62,65,454,455],[60,61,64,65,455], [60,61,64,454,455],[61,64,65,454,455],[60,63,64,65,455],[60,63,64,454,455], [63,64,65,68,455],[64,65,68,454,455],[63,64,67,68,455],[63,64,67,454,455], [64,67,68,454,455],[63,66,67,68,455],[63,66,67,454,455],[66,67,68,71,455], [67,68,71,454,455],[66,67,70,71,455],[66,67,70,454,455],[67,70,71,454,455], [66,69,70,71,455],[66,69,70,454,455],[69,70,71,74,455],[70,71,74,454,455], [69,70,73,74,455],[69,70,73,454,455],[70,73,74,454,455],[69,72,73,74,455], [69,72,73,454,455],[72,73,74,77,455],[73,74,77,454,455],[72,73,76,77,455], [72,73,76,454,455],[73,76,77,454,455],[72,75,76,77,455],[72,75,76,454,455], [75,76,77,80,455],[76,77,80,454,455],[75,76,79,80,455],[75,76,79,454,455], [76,79,80,454,455],[75,78,79,80,455],[75,78,79,454,455],[78,79,80,83,455], [79,80,83,454,455],[78,79,82,83,455],[78,79,82,454,455],[79,82,83,454,455], [78,81,82,83,455],[78,81,82,454,455],[81,82,83,86,455],[82,83,86,454,455], [81,82,85,86,455],[81,82,85,454,455],[82,85,86,454,455],[81,84,85,86,455], [81,84,85,454,455],[84,85,86,89,455],[85,86,89,454,455],[84,85,88,89,455], [84,85,88,454,455],[85,88,89,454,455],[84,87,88,89,455],[84,87,88,454,455], [87,88,89,92,455],[88,89,92,454,455],[87,88,91,92,455],[87,88,91,454,455], [88,91,92,454,455],[87,90,91,92,455],[87,90,91,454,455],[90,91,92,95,455], [91,92,95,454,455],[90,91,94,95,455],[90,91,94,454,455],[91,94,95,454,455], [90,93,94,95,455],[90,93,94,454,455],[93,94,95,98,455],[94,95,98,454,455], [93,94,97,98,455],[93,94,97,454,455],[94,97,98,454,455],[93,96,97,98,455], [93,96,97,454,455],[96,97,98,101,455],[97,98,101,454,455],[96,97,100,101,455], [96,97,100,454,455],[97,100,101,454,455],[96,99,100,101,455],[96,99,100,454,455], [99,100,101,104,455],[100,101,104,454,455],[99,100,103,104,455],[99,100,103,454,455], [100,103,104,454,455],[99,102,103,104,455],[99,102,103,454,455],[102,103,104,107,455], [103,104,107,454,455],[102,103,106,107,455],[102,103,106,454,455],[103,106,107,454,455], [102,105,106,107,455],[102,105,106,454,455],[105,106,107,110,455],[106,107,110,454,455], [105,106,109,110,455],[105,106,109,454,455],[106,109,110,454,455],[105,108,109,110,455], [105,108,109,454,455],[108,109,110,113,455],[109,110,113,454,455],[108,109,112,113,455], [108,109,112,454,455],[109,112,113,454,455],[108,111,112,113,455],[108,111,112,454,455], [111,112,113,116,455],[112,113,116,454,455],[111,112,115,116,455],[111,112,115,454,455], [112,115,116,454,455],[111,114,115,116,455],[111,114,115,454,455],[114,115,116,119,455], [115,116,119,454,455],[114,115,118,119,455],[114,115,118,454,455],[115,118,119,454,455], [114,117,118,119,455],[114,117,118,454,455],[117,118,119,122,455],[118,119,122,454,455], [117,118,121,122,455],[117,118,121,454,455],[118,121,122,454,455],[117,120,121,122,455], [117,120,121,454,455],[120,121,122,125,455],[121,122,125,454,455],[120,121,124,125,455], [120,121,124,454,455],[121,124,125,454,455],[120,123,124,125,455],[120,123,124,454,455], [123,124,125,128,455],[124,125,128,454,455],[123,124,127,128,455],[123,124,127,454,455], [124,127,128,454,455],[123,126,127,128,455],[123,126,127,454,455],[126,127,128,131,455], [127,128,131,454,455],[126,127,130,131,455],[126,127,130,454,455],[127,130,131,454,455], [126,129,130,131,455],[126,129,130,454,455],[129,130,131,134,455],[130,131,134,454,455], [129,130,133,134,455],[129,130,133,454,455],[130,133,134,454,455],[129,132,133,134,455], [129,132,133,454,455],[132,133,134,137,455],[133,134,137,454,455],[132,133,136,137,455], [132,133,136,454,455],[133,136,137,454,455],[132,135,136,137,455],[132,135,136,454,455], [36,38,41,454,456],[36,38,41,455,456],[38,41,454,455,456],[36,38,137,454,456], [36,38,137,455,456],[38,137,454,455,456],[36,39,41,454,456],[36,39,41,455,456], [36,135,137,454,456],[36,135,137,455,456],[39,41,44,454,456],[39,41,44,455,456], [41,44,454,455,456],[39,42,44,454,456],[39,42,44,455,456],[42,44,47,454,456], [42,44,47,455,456],[44,47,454,455,456],[42,45,47,454,456],[42,45,47,455,456], [45,47,50,454,456],[45,47,50,455,456],[47,50,454,455,456],[45,48,50,454,456], [45,48,50,455,456],[48,50,53,454,456],[48,50,53,455,456],[50,53,454,455,456], [48,51,53,454,456],[48,51,53,455,456],[51,53,56,454,456],[51,53,56,455,456], [53,56,454,455,456],[51,54,56,454,456],[51,54,56,455,456],[54,56,59,454,456], [54,56,59,455,456],[56,59,454,455,456],[54,57,59,454,456],[54,57,59,455,456], [57,59,62,454,456],[57,59,62,455,456],[59,62,454,455,456],[57,60,62,454,456], [57,60,62,455,456],[60,62,65,454,456],[60,62,65,455,456],[62,65,454,455,456], [60,63,65,454,456],[60,63,65,455,456],[63,65,68,454,456],[63,65,68,455,456], [65,68,454,455,456],[63,66,68,454,456],[63,66,68,455,456],[66,68,71,454,456], [66,68,71,455,456],[68,71,454,455,456],[66,69,71,454,456],[66,69,71,455,456], [69,71,74,454,456],[69,71,74,455,456],[71,74,454,455,456],[69,72,74,454,456], [69,72,74,455,456],[72,74,77,454,456],[72,74,77,455,456],[74,77,454,455,456], [72,75,77,454,456],[72,75,77,455,456],[75,77,80,454,456],[75,77,80,455,456], [77,80,454,455,456],[75,78,80,454,456],[75,78,80,455,456],[78,80,83,454,456], [78,80,83,455,456],[80,83,454,455,456],[78,81,83,454,456],[78,81,83,455,456], [81,83,86,454,456],[81,83,86,455,456],[83,86,454,455,456],[81,84,86,454,456], [81,84,86,455,456],[84,86,89,454,456],[84,86,89,455,456],[86,89,454,455,456], [84,87,89,454,456],[84,87,89,455,456],[87,89,92,454,456],[87,89,92,455,456], [89,92,454,455,456],[87,90,92,454,456],[87,90,92,455,456],[90,92,95,454,456], [90,92,95,455,456],[92,95,454,455,456],[90,93,95,454,456],[90,93,95,455,456], [93,95,98,454,456],[93,95,98,455,456],[95,98,454,455,456],[93,96,98,454,456], [93,96,98,455,456],[96,98,101,454,456],[96,98,101,455,456],[98,101,454,455,456], [96,99,101,454,456],[96,99,101,455,456],[99,101,104,454,456],[99,101,104,455,456], [101,104,454,455,456],[99,102,104,454,456],[99,102,104,455,456],[102,104,107,454,456], [102,104,107,455,456],[104,107,454,455,456],[102,105,107,454,456],[102,105,107,455,456], [105,107,110,454,456],[105,107,110,455,456],[107,110,454,455,456],[105,108,110,454,456], [105,108,110,455,456],[108,110,113,454,456],[108,110,113,455,456],[110,113,454,455,456], [108,111,113,454,456],[108,111,113,455,456],[111,113,116,454,456],[111,113,116,455,456], [113,116,454,455,456],[111,114,116,454,456],[111,114,116,455,456],[114,116,119,454,456], [114,116,119,455,456],[116,119,454,455,456],[114,117,119,454,456],[114,117,119,455,456], [117,119,122,454,456],[117,119,122,455,456],[119,122,454,455,456],[117,120,122,454,456], [117,120,122,455,456],[120,122,125,454,456],[120,122,125,455,456],[122,125,454,455,456], [120,123,125,454,456],[120,123,125,455,456],[123,125,128,454,456],[123,125,128,455,456], [125,128,454,455,456],[123,126,128,454,456],[123,126,128,455,456],[126,128,131,454,456], [126,128,131,455,456],[128,131,454,455,456],[126,129,131,454,456],[126,129,131,455,456], [129,131,134,454,456],[129,131,134,455,456],[131,134,454,455,456],[129,132,134,454,456], [129,132,134,455,456],[132,134,137,454,456],[132,134,137,455,456],[134,137,454,455,456], [132,135,137,454,456],[132,135,137,455,456],[36,39,454,455,457],[36,39,454,456,457], [36,39,455,456,457],[36,135,454,455,457],[36,135,454,456,457],[36,135,455,456,457], [39,42,454,455,457],[39,42,454,456,457],[39,42,455,456,457],[42,45,454,455,457], [42,45,454,456,457],[42,45,455,456,457],[45,48,454,455,457],[45,48,454,456,457], [45,48,455,456,457],[48,51,454,455,457],[48,51,454,456,457],[48,51,455,456,457], [51,54,454,455,457],[51,54,454,456,457],[51,54,455,456,457],[54,57,454,455,457], [54,57,454,456,457],[54,57,455,456,457],[57,60,454,455,457],[57,60,454,456,457], [57,60,455,456,457],[60,63,454,455,457],[60,63,454,456,457],[60,63,455,456,457], [63,66,454,455,457],[63,66,454,456,457],[63,66,455,456,457],[66,69,454,455,457], [66,69,454,456,457],[66,69,455,456,457],[69,72,454,455,457],[69,72,454,456,457], [69,72,455,456,457],[72,75,454,455,457],[72,75,454,456,457],[72,75,455,456,457], [75,78,454,455,457],[75,78,454,456,457],[75,78,455,456,457],[78,81,454,455,457], [78,81,454,456,457],[78,81,455,456,457],[81,84,454,455,457],[81,84,454,456,457], [81,84,455,456,457],[84,87,454,455,457],[84,87,454,456,457],[84,87,455,456,457], [87,90,454,455,457],[87,90,454,456,457],[87,90,455,456,457],[90,93,454,455,457], [90,93,454,456,457],[90,93,455,456,457],[93,96,454,455,457],[93,96,454,456,457], [93,96,455,456,457],[96,99,454,455,457],[96,99,454,456,457],[96,99,455,456,457], [99,102,454,455,457],[99,102,454,456,457],[99,102,455,456,457],[102,105,454,455,457], [102,105,454,456,457],[102,105,455,456,457],[105,108,454,455,457],[105,108,454,456,457], [105,108,455,456,457],[108,111,454,455,457],[108,111,454,456,457],[108,111,455,456,457], [111,114,454,455,457],[111,114,454,456,457],[111,114,455,456,457],[114,117,454,455,457], [114,117,454,456,457],[114,117,455,456,457],[117,120,454,455,457],[117,120,454,456,457], [117,120,455,456,457],[120,123,454,455,457],[120,123,454,456,457],[120,123,455,456,457], [123,126,454,455,457],[123,126,454,456,457],[123,126,455,456,457],[126,129,454,455,457], [126,129,454,456,457],[126,129,455,456,457],[129,132,454,455,457],[129,132,454,456,457], [129,132,455,456,457],[132,135,454,455,457],[132,135,454,456,457],[132,135,455,456,457] ];