#################################################################################### #################################################################################### #################################################################################### ### ### ### ### ### TRIANGULATIONS OF AKBULUT-KIRBY SPHERES ### ### by Frank H. Lutz and Mimi Tsuruga ### ### http://matsguru.com/research/AKspheres.html ### ### ### ### name of example: ### ### ### ### AK_III_008 ### ### ### ### ### ### description: ### ### ### ### Type 3 construction of triangulation of Akbulut-Kirby sphere ### ### ### ### ### ### properties: ### ### ### ### f=(422,6072,20088,24060,9624) ### ### 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:=[ [0,1,2,5,281],[0,1,2,35,311],[0,1,2,278,281],[0,1,2,278,311], [0,1,4,5,281],[0,1,4,142,280],[0,1,4,280,281],[0,1,34,35,311], [0,1,34,130,268],[0,1,34,130,406],[0,1,34,172,268],[0,1,34,310,311], [0,1,34,310,406],[0,1,129,130,268],[0,1,129,130,406],[0,1,129,267,268], [0,1,129,267,405],[0,1,129,405,406],[0,1,139,142,280],[0,1,139,172,268], [0,1,139,267,268],[0,1,139,267,405],[0,1,277,278,281],[0,1,277,278,311], [0,1,139,277,280],[0,1,277,280,281],[0,1,277,310,311],[0,1,277,310,406], [0,1,139,277,405],[0,1,277,405,406],[0,2,5,26,164],[0,2,5,26,302], [2,5,26,164,302],[0,2,5,143,164],[2,5,143,164,302],[0,2,5,281,302], [2,5,143,281,302],[0,2,26,29,167],[0,2,26,29,305],[2,26,29,167,305], [0,2,26,164,167],[2,26,164,167,305],[0,2,26,302,305],[2,26,164,302,305], [0,2,29,133,271],[0,2,29,133,409],[0,2,29,167,271],[0,2,29,305,409], [0,2,35,133,271],[0,2,35,133,409],[0,2,35,173,271],[0,2,35,311,409], [0,2,140,143,164],[2,140,143,164,302],[2,140,143,281,302],[0,2,140,164,167], [2,140,164,167,305],[2,140,164,302,305],[0,2,140,167,271],[0,2,140,173,271], [0,2,278,281,302],[2,140,278,281,302],[0,2,278,302,305],[2,140,278,302,305], [0,2,278,305,409],[0,2,278,311,409],[0,3,4,5,281],[0,3,4,142,280], [0,3,4,280,281],[0,3,5,26,164],[0,3,5,26,302],[0,3,5,143,164], [0,3,5,281,302],[0,3,24,26,164],[0,3,24,26,302],[0,3,24,162,164], [0,3,24,162,300],[0,3,24,300,302],[0,3,141,142,280],[0,3,141,143,164], [0,3,141,162,164],[0,3,141,162,300],[0,3,141,279,280],[0,3,279,280,281], [0,3,279,281,302],[0,3,141,279,300],[0,3,279,300,302],[0,24,26,29,167], [0,24,26,29,305],[0,24,26,164,167],[0,24,26,302,305],[0,24,27,29,167], [0,24,27,29,305],[0,24,27,165,167],[0,24,27,165,303],[0,24,27,303,305], [0,24,162,164,167],[0,24,162,165,167],[0,24,162,165,303],[0,24,300,302,305], [0,24,162,300,303],[0,24,300,303,305],[0,27,29,133,271],[0,27,29,133,409], [0,27,29,167,271],[0,27,29,305,409],[0,27,126,130,268],[0,27,126,130,406], [0,27,126,133,271],[0,27,126,133,409],[0,27,126,264,268],[0,27,126,264,271], [0,27,126,402,406],[0,27,126,402,409],[0,27,129,130,268],[0,27,129,130,406], [0,27,129,267,268],[0,27,129,267,405],[0,27,129,405,406],[0,27,165,167,271], [0,27,165,264,268],[0,27,165,264,271],[0,27,165,267,268],[0,27,165,267,405], [0,27,303,305,409],[0,27,303,402,406],[0,27,303,402,409],[0,27,165,303,405], [0,27,303,405,406],[0,33,34,35,311],[0,33,34,130,268],[0,33,34,130,406], [0,33,34,172,268],[0,33,34,310,311],[0,33,34,310,406],[0,33,35,133,271], [0,33,35,133,409],[0,33,35,173,271],[0,33,35,311,409],[0,33,126,130,268], [0,33,126,130,406],[0,33,126,133,271],[0,33,126,133,409],[0,33,126,264,268], [0,33,126,264,271],[0,33,126,402,406],[0,33,126,402,409],[0,33,171,172,268], [0,33,171,173,271],[0,33,171,264,268],[0,33,171,264,271],[0,33,309,310,311], [0,33,309,310,406],[0,33,309,311,409],[0,33,309,402,406],[0,33,309,402,409], [138,139,140,143,281],[138,139,140,173,311],[138,139,140,278,281],[138,139,140,278,311], [138,139,142,143,281],[0,138,139,142,280],[138,139,142,280,281],[138,139,172,173,311], [0,138,139,172,268],[138,139,172,268,406],[138,139,172,310,311],[138,139,172,310,406], [0,138,139,267,268],[138,139,267,268,406],[0,138,139,267,405],[138,139,267,405,406], [138,139,277,278,281],[138,139,277,278,311],[0,138,139,277,280],[138,139,277,280,281], [138,139,277,310,311],[138,139,277,310,406],[0,138,139,277,405],[138,139,277,405,406], [0,138,140,143,164],[138,140,143,164,302],[138,140,143,281,302],[0,138,140,164,167], [138,140,164,167,305],[138,140,164,302,305],[0,138,140,167,271],[138,140,167,271,409], [138,140,167,305,409],[0,138,140,173,271],[138,140,173,271,409],[138,140,173,311,409], [138,140,278,281,302],[138,140,278,302,305],[138,140,278,305,409],[138,140,278,311,409], [138,141,142,143,281],[0,138,141,142,280],[138,141,142,280,281],[0,138,141,143,164], [138,141,143,164,302],[138,141,143,281,302],[0,138,141,162,164],[138,141,162,164,302], [0,138,141,162,300],[138,141,162,300,302],[0,138,141,279,280],[138,141,279,280,281], [138,141,279,281,302],[0,138,141,279,300],[138,141,279,300,302],[0,138,162,164,167], [138,162,164,167,305],[138,162,164,302,305],[0,138,162,165,167],[138,162,165,167,305], [0,138,162,165,303],[138,162,165,303,305],[138,162,300,302,305],[0,138,162,300,303], [138,162,300,303,305],[0,138,165,167,271],[138,165,167,271,409],[138,165,167,305,409], [0,138,165,264,268],[138,165,264,268,406],[0,138,165,264,271],[138,165,264,271,409], [138,165,264,402,406],[138,165,264,402,409],[0,138,165,267,268],[138,165,267,268,406], [0,138,165,267,405],[138,165,267,405,406],[138,165,303,305,409],[138,165,303,402,406], [138,165,303,402,409],[0,138,165,303,405],[138,165,303,405,406],[138,171,172,173,311], [0,138,171,172,268],[138,171,172,268,406],[138,171,172,310,311],[138,171,172,310,406], [0,138,171,173,271],[138,171,173,271,409],[138,171,173,311,409],[0,138,171,264,268], [138,171,264,268,406],[0,138,171,264,271],[138,171,264,271,409],[138,171,264,402,406], [138,171,264,402,409],[138,171,309,310,311],[138,171,309,310,406],[138,171,309,311,409], [138,171,309,402,406],[138,171,309,402,409],[0,276,277,278,281],[138,276,277,278,281], [0,276,277,278,311],[138,276,277,278,311],[0,138,276,277,280],[0,276,277,280,281], [138,276,277,280,281],[0,276,277,310,311],[138,276,277,310,311],[0,276,277,310,406], [138,276,277,310,406],[0,138,276,277,405],[0,276,277,405,406],[138,276,277,405,406], [0,276,278,281,302],[138,276,278,281,302],[0,276,278,302,305],[138,276,278,302,305], [0,276,278,305,409],[138,276,278,305,409],[0,276,278,311,409],[138,276,278,311,409], [0,138,276,279,280],[0,276,279,280,281],[138,276,279,280,281],[0,276,279,281,302], [138,276,279,281,302],[0,138,276,279,300],[0,276,279,300,302],[138,276,279,300,302], [0,276,300,302,305],[138,276,300,302,305],[0,138,276,300,303],[0,276,300,303,305], [138,276,300,303,305],[0,276,303,305,409],[138,276,303,305,409],[0,276,303,402,406], [138,276,303,402,406],[0,276,303,402,409],[138,276,303,402,409],[0,138,276,303,405], [0,276,303,405,406],[138,276,303,405,406],[0,276,309,310,311],[138,276,309,310,311], [0,276,309,310,406],[138,276,309,310,406],[0,276,309,311,409],[138,276,309,311,409], [0,276,309,402,406],[138,276,309,402,406],[0,276,309,402,409],[138,276,309,402,409], [1,2,5,41,179],[1,2,5,41,317],[2,5,41,179,317],[1,2,5,143,179], [2,5,143,179,317],[1,2,5,281,317],[2,5,143,281,317],[1,2,35,133,271], [1,2,35,133,409],[1,2,35,173,271],[1,2,35,311,409],[1,2,38,41,179], [1,2,38,41,317],[2,38,41,179,317],[1,2,38,136,274],[1,2,38,136,412], [1,2,38,176,179],[2,38,176,179,317],[1,2,38,176,274],[1,2,38,314,317], [2,38,176,314,317],[1,2,38,314,412],[1,2,132,133,271],[1,2,132,133,409], [1,2,132,136,274],[1,2,132,136,412],[1,2,132,270,271],[1,2,132,270,274], [1,2,132,408,409],[1,2,132,408,412],[1,2,140,143,179],[2,140,143,179,317], [2,140,143,281,317],[1,2,140,173,271],[1,2,140,176,179],[2,140,176,179,317], [1,2,140,176,274],[2,140,176,314,317],[1,2,140,270,271],[1,2,140,270,274], [1,2,278,281,317],[2,140,278,281,317],[1,2,278,311,409],[1,2,278,314,317], [2,140,278,314,317],[1,2,278,314,412],[1,2,278,408,409],[1,2,278,408,412], [1,4,5,41,179],[1,4,5,41,317],[1,4,5,143,179],[1,4,5,281,317], [1,4,39,41,179],[1,4,39,41,317],[1,4,39,177,179],[1,4,39,177,315], [1,4,39,315,317],[1,4,142,143,179],[1,4,142,177,179],[1,4,142,177,315], [1,4,280,281,317],[1,4,142,280,315],[1,4,280,315,317],[1,34,35,133,271], [1,34,35,133,409],[1,34,35,173,271],[1,34,35,311,409],[1,34,127,130,268], [1,34,127,130,406],[1,34,127,133,271],[1,34,127,133,409],[1,34,127,265,268], [1,34,127,265,271],[1,34,127,403,406],[1,34,127,403,409],[1,34,172,173,271], [1,34,172,265,268],[1,34,172,265,271],[1,34,310,311,409],[1,34,310,403,406], [1,34,310,403,409],[1,36,38,41,179],[1,36,38,41,317],[1,36,38,136,274], [1,36,38,136,412],[1,36,38,176,179],[1,36,38,176,274],[1,36,38,314,317], [1,36,38,314,412],[1,36,39,41,179],[1,36,39,41,317],[1,36,39,177,179], [1,36,39,177,315],[1,36,39,315,317],[1,36,127,130,268],[1,36,127,130,406], [1,36,127,133,271],[1,36,127,133,409],[1,36,127,265,268],[1,36,127,265,271], [1,36,127,403,406],[1,36,127,403,409],[1,36,129,130,268],[1,36,129,130,406], [1,36,129,267,268],[1,36,129,267,405],[1,36,129,405,406],[1,36,132,133,271], [1,36,132,133,409],[1,36,132,136,274],[1,36,132,136,412],[1,36,132,270,271], [1,36,132,270,274],[1,36,132,408,409],[1,36,132,408,412],[1,36,174,176,179], [1,36,174,176,274],[1,36,174,177,179],[1,36,174,177,315],[1,36,174,265,268], [1,36,174,265,271],[1,36,174,267,268],[1,36,174,267,405],[1,36,174,270,271], [1,36,174,270,274],[1,36,312,314,317],[1,36,312,314,412],[1,36,174,312,315], [1,36,312,315,317],[1,36,312,403,406],[1,36,312,403,409],[1,36,174,312,405], [1,36,312,405,406],[1,36,312,408,409],[1,36,312,408,412],[1,139,140,143,179], [139,140,143,179,317],[139,140,143,281,317],[1,139,140,173,271],[139,140,173,271,409], [139,140,173,311,409],[1,139,140,176,179],[139,140,176,179,317],[1,139,140,176,274], [139,140,176,274,412],[139,140,176,314,317],[139,140,176,314,412],[1,139,140,270,271], [139,140,270,271,409],[1,139,140,270,274],[139,140,270,274,412],[139,140,270,408,409], [139,140,270,408,412],[139,140,278,281,317],[139,140,278,311,409],[139,140,278,314,317], [139,140,278,314,412],[139,140,278,408,409],[139,140,278,408,412],[1,139,142,143,179], [139,142,143,179,317],[139,142,143,281,317],[1,139,142,177,179],[139,142,177,179,317], [1,139,142,177,315],[139,142,177,315,317],[139,142,280,281,317],[1,139,142,280,315], [139,142,280,315,317],[1,139,172,173,271],[139,172,173,271,409],[139,172,173,311,409], [1,139,172,265,268],[139,172,265,268,406],[1,139,172,265,271],[139,172,265,271,409], [139,172,265,403,406],[139,172,265,403,409],[139,172,310,311,409],[139,172,310,403,406], [139,172,310,403,409],[1,139,174,176,179],[139,174,176,179,317],[1,139,174,176,274], [139,174,176,274,412],[139,174,176,314,317],[139,174,176,314,412],[1,139,174,177,179], [139,174,177,179,317],[1,139,174,177,315],[139,174,177,315,317],[1,139,174,265,268], [139,174,265,268,406],[1,139,174,265,271],[139,174,265,271,409],[139,174,265,403,406], [139,174,265,403,409],[1,139,174,267,268],[139,174,267,268,406],[1,139,174,267,405], [139,174,267,405,406],[1,139,174,270,271],[139,174,270,271,409],[1,139,174,270,274], [139,174,270,274,412],[139,174,270,408,409],[139,174,270,408,412],[139,174,312,314,317], [139,174,312,314,412],[1,139,174,312,315],[139,174,312,315,317],[139,174,312,403,406], [139,174,312,403,409],[1,139,174,312,405],[139,174,312,405,406],[139,174,312,408,409], [139,174,312,408,412],[1,277,278,281,317],[139,277,278,281,317],[1,277,278,311,409], [139,277,278,311,409],[1,277,278,314,317],[139,277,278,314,317],[1,277,278,314,412], [139,277,278,314,412],[1,277,278,408,409],[139,277,278,408,409],[1,277,278,408,412], [139,277,278,408,412],[1,277,280,281,317],[139,277,280,281,317],[1,139,277,280,315], [1,277,280,315,317],[139,277,280,315,317],[1,277,310,311,409],[139,277,310,311,409], [1,277,310,403,406],[139,277,310,403,406],[1,277,310,403,409],[139,277,310,403,409], [1,277,312,314,317],[139,277,312,314,317],[1,277,312,314,412],[139,277,312,314,412], [1,139,277,312,315],[1,277,312,315,317],[139,277,312,315,317],[1,277,312,403,406], [139,277,312,403,406],[1,277,312,403,409],[139,277,312,403,409],[1,139,277,312,405], [1,277,312,405,406],[139,277,312,405,406],[1,277,312,408,409],[139,277,312,408,409], [1,277,312,408,412],[139,277,312,408,412],[2,29,132,133,271],[2,29,132,133,409], [2,29,132,136,274],[2,29,132,136,412],[2,29,132,270,271],[2,29,132,270,274], [2,29,132,408,409],[2,29,132,408,412],[2,29,134,136,274],[2,29,134,136,412], [2,29,134,272,274],[2,29,134,272,410],[2,29,134,410,412],[2,29,167,270,271], [2,29,167,270,274],[2,29,167,272,274],[2,29,167,272,410],[2,29,305,408,409], [2,29,305,408,412],[2,29,167,305,410],[2,29,305,410,412],[2,38,134,136,274], [2,38,134,136,412],[2,38,134,272,274],[2,38,134,272,410],[2,38,134,410,412], [2,38,176,272,274],[2,38,176,272,410],[2,38,176,314,410],[2,38,314,410,412], [2,140,167,270,271],[140,167,270,271,409],[2,140,167,270,274],[140,167,270,274,412], [140,167,270,408,409],[140,167,270,408,412],[2,140,167,272,274],[140,167,272,274,412], [2,140,167,272,410],[140,167,272,410,412],[140,167,305,408,409],[140,167,305,408,412], [2,140,167,305,410],[140,167,305,410,412],[2,140,176,272,274],[140,176,272,274,412], [2,140,176,272,410],[140,176,272,410,412],[2,140,176,314,410],[140,176,314,410,412], [2,278,305,408,409],[140,278,305,408,409],[2,278,305,408,412],[140,278,305,408,412], [2,140,278,305,410],[2,278,305,410,412],[140,278,305,410,412],[2,140,278,314,410], [2,278,314,410,412],[140,278,314,410,412],[3,4,5,8,284],[3,4,5,281,284], [3,4,7,8,284],[3,4,7,130,268],[3,4,7,130,406],[3,4,7,145,268], [3,4,7,283,284],[3,4,7,283,406],[3,4,129,130,268],[3,4,129,130,406], [3,4,129,267,268],[3,4,129,267,405],[3,4,129,405,406],[3,4,142,145,268], [3,4,142,267,268],[3,4,142,267,405],[3,4,280,281,284],[3,4,280,283,284], [3,4,280,283,406],[3,4,142,280,405],[3,4,280,405,406],[3,5,8,23,161], [3,5,8,23,299],[5,8,23,161,299],[3,5,8,146,161],[5,8,146,161,299], [3,5,8,284,299],[5,8,146,284,299],[3,5,23,26,164],[3,5,23,26,302], [5,23,26,164,302],[3,5,23,161,164],[5,23,161,164,302],[3,5,23,299,302], [5,23,161,299,302],[3,5,143,146,161],[5,143,146,161,299],[5,143,146,284,299], [3,5,143,161,164],[5,143,161,164,302],[5,143,161,299,302],[3,5,281,284,299], [5,143,281,284,299],[3,5,281,299,302],[5,143,281,299,302],[3,6,7,8,284], [3,6,7,130,268],[3,6,7,130,406],[3,6,7,145,268],[3,6,7,283,284], [3,6,7,283,406],[3,6,8,23,161],[3,6,8,23,299],[3,6,8,146,161], [3,6,8,284,299],[3,6,21,23,161],[3,6,21,23,299],[3,6,21,130,268], [3,6,21,130,406],[3,6,21,159,161],[3,6,21,159,268],[3,6,21,297,299], [3,6,21,297,406],[3,6,144,145,268],[3,6,144,146,161],[3,6,144,159,161], [3,6,144,159,268],[3,6,282,283,284],[3,6,282,283,406],[3,6,282,284,299], [3,6,282,297,299],[3,6,282,297,406],[3,21,23,26,164],[3,21,23,26,302], [3,21,23,161,164],[3,21,23,299,302],[3,21,24,26,164],[3,21,24,26,302], [3,21,24,130,268],[3,21,24,130,406],[3,21,24,162,164],[3,21,24,162,268], [3,21,24,300,302],[3,21,24,300,406],[3,21,159,161,164],[3,21,159,162,164], [3,21,159,162,268],[3,21,297,299,302],[3,21,297,300,302],[3,21,297,300,406], [3,24,129,130,268],[3,24,129,130,406],[3,24,129,267,268],[3,24,129,267,405], [3,24,129,405,406],[3,24,162,267,268],[3,24,162,267,405],[3,24,162,300,405], [3,24,300,405,406],[141,142,143,146,284],[141,142,143,281,284],[141,142,145,146,284], [3,141,142,145,268],[141,142,145,268,406],[141,142,145,283,284],[141,142,145,283,406], [3,141,142,267,268],[141,142,267,268,406],[3,141,142,267,405],[141,142,267,405,406], [141,142,280,281,284],[141,142,280,283,284],[141,142,280,283,406],[3,141,142,280,405], [141,142,280,405,406],[3,141,143,146,161],[141,143,146,161,299],[141,143,146,284,299], [3,141,143,161,164],[141,143,161,164,302],[141,143,161,299,302],[141,143,281,284,299], [141,143,281,299,302],[141,144,145,146,284],[3,141,144,145,268],[141,144,145,268,406], [141,144,145,283,284],[141,144,145,283,406],[3,141,144,146,161],[141,144,146,161,299], 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[27,29,167,170,414],[28,29,167,170,414],[28,31,32,170,414],[27,28,31,169,414], [28,31,169,170,414],[28,166,167,170,414],[27,28,166,169,414],[28,166,169,170,414], [27,30,32,170,414],[27,30,31,169,414],[27,30,168,169,414],[27,30,168,170,414], [27,165,167,170,414],[165,166,167,170,414],[27,165,166,169,414],[165,166,169,170,414], [27,165,168,169,414],[27,165,168,170,414],[165,168,169,170,414],[30,32,35,173,414], [31,32,35,173,414],[30,32,170,173,414],[31,32,170,173,414],[31,34,35,173,414], [30,31,34,172,414],[31,34,172,173,414],[31,169,170,173,414],[30,31,169,172,414], [31,169,172,173,414],[30,33,35,173,414],[30,33,34,172,414],[30,33,171,172,414], [30,33,171,173,414],[30,168,170,173,414],[168,169,170,173,414],[30,168,169,172,414], [168,169,172,173,414],[30,168,171,172,414],[30,168,171,173,414],[168,171,172,173,414], [0,1,2,5,415],[1,2,5,414,415],[0,1,2,35,415],[1,2,35,414,415], [0,1,4,5,415],[0,1,4,414,415],[1,4,5,414,415],[0,1,34,35,415], [0,1,34,414,415],[1,34,35,414,415],[0,3,4,5,415],[0,3,4,414,415], [0,33,34,35,415],[0,33,34,414,415],[3,4,5,8,415],[4,5,8,414,415], [3,4,7,8,415],[3,4,7,414,415],[4,7,8,414,415],[3,6,7,8,415], [3,6,7,414,415],[6,7,8,11,415],[7,8,11,414,415],[6,7,10,11,415], [6,7,10,414,415],[7,10,11,414,415],[6,9,10,11,415],[6,9,10,414,415], [9,10,11,14,415],[10,11,14,414,415],[9,10,13,14,415],[9,10,13,414,415], [10,13,14,414,415],[9,12,13,14,415],[9,12,13,414,415],[12,13,14,17,415], [13,14,17,414,415],[12,13,16,17,415],[12,13,16,414,415],[13,16,17,414,415], [12,15,16,17,415],[12,15,16,414,415],[15,16,17,20,415],[16,17,20,414,415], [15,16,19,20,415],[15,16,19,414,415],[16,19,20,414,415],[15,18,19,20,415], [15,18,19,414,415],[18,19,20,23,415],[19,20,23,414,415],[18,19,22,23,415], [18,19,22,414,415],[19,22,23,414,415],[18,21,22,23,415],[18,21,22,414,415], [21,22,23,26,415],[22,23,26,414,415],[21,22,25,26,415],[21,22,25,414,415], [22,25,26,414,415],[21,24,25,26,415],[21,24,25,414,415],[24,25,26,29,415], [25,26,29,414,415],[24,25,28,29,415],[24,25,28,414,415],[25,28,29,414,415], [24,27,28,29,415],[24,27,28,414,415],[27,28,29,32,415],[28,29,32,414,415], [27,28,31,32,415],[27,28,31,414,415],[28,31,32,414,415],[27,30,31,32,415], [27,30,31,414,415],[30,31,32,35,415],[31,32,35,414,415],[30,31,34,35,415], [30,31,34,414,415],[31,34,35,414,415],[30,33,34,35,415],[30,33,34,414,415], [0,2,5,414,416],[0,2,5,415,416],[2,5,414,415,416],[0,2,35,414,416], [0,2,35,415,416],[2,35,414,415,416],[0,3,5,414,416],[0,3,5,415,416], [0,33,35,414,416],[0,33,35,415,416],[3,5,8,414,416],[3,5,8,415,416], [5,8,414,415,416],[3,6,8,414,416],[3,6,8,415,416],[6,8,11,414,416], [6,8,11,415,416],[8,11,414,415,416],[6,9,11,414,416],[6,9,11,415,416], [9,11,14,414,416],[9,11,14,415,416],[11,14,414,415,416],[9,12,14,414,416], [9,12,14,415,416],[12,14,17,414,416],[12,14,17,415,416],[14,17,414,415,416], [12,15,17,414,416],[12,15,17,415,416],[15,17,20,414,416],[15,17,20,415,416], [17,20,414,415,416],[15,18,20,414,416],[15,18,20,415,416],[18,20,23,414,416], [18,20,23,415,416],[20,23,414,415,416],[18,21,23,414,416],[18,21,23,415,416], [21,23,26,414,416],[21,23,26,415,416],[23,26,414,415,416],[21,24,26,414,416], [21,24,26,415,416],[24,26,29,414,416],[24,26,29,415,416],[26,29,414,415,416], [24,27,29,414,416],[24,27,29,415,416],[27,29,32,414,416],[27,29,32,415,416], [29,32,414,415,416],[27,30,32,414,416],[27,30,32,415,416],[30,32,35,414,416], [30,32,35,415,416],[32,35,414,415,416],[30,33,35,414,416],[30,33,35,415,416], [0,3,414,415,417],[0,3,414,416,417],[0,3,415,416,417],[0,33,414,415,417], [0,33,414,416,417],[0,33,415,416,417],[3,6,414,415,417],[3,6,414,416,417], [3,6,415,416,417],[6,9,414,415,417],[6,9,414,416,417],[6,9,415,416,417], [9,12,414,415,417],[9,12,414,416,417],[9,12,415,416,417],[12,15,414,415,417], [12,15,414,416,417],[12,15,415,416,417],[15,18,414,415,417],[15,18,414,416,417], 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[36,174,175,178,418],[174,175,178,179,418],[36,174,175,262,418],[174,175,262,263,418], [36,174,177,178,418],[36,174,177,179,418],[174,177,178,179,418],[36,174,261,262,418], [36,174,261,263,418],[174,261,262,263,418],[39,41,44,182,418],[40,41,44,182,418], [39,41,179,182,418],[40,41,179,182,418],[40,43,44,182,418],[39,40,43,181,418], [40,43,181,182,418],[40,178,179,182,418],[39,40,178,181,418],[40,178,181,182,418], [39,42,44,182,418],[39,42,43,181,418],[39,42,180,181,418],[39,42,180,182,418], [39,177,179,182,418],[177,178,179,182,418],[39,177,178,181,418],[177,178,181,182,418], [39,177,180,181,418],[39,177,180,182,418],[177,180,181,182,418],[42,44,47,185,418], [43,44,47,185,418],[42,44,182,185,418],[43,44,182,185,418],[43,46,47,185,418], [42,43,46,184,418],[43,46,184,185,418],[43,181,182,185,418],[42,43,181,184,418], [43,181,184,185,418],[42,45,47,185,418],[42,45,46,184,418],[42,45,183,184,418], [42,45,183,185,418],[42,180,182,185,418],[180,181,182,185,418],[42,180,181,184,418], [180,181,184,185,418],[42,180,183,184,418],[42,180,183,185,418],[180,183,184,185,418], [45,47,50,188,418],[46,47,50,188,418],[45,47,185,188,418],[46,47,185,188,418], [46,49,50,188,418],[45,46,49,187,418],[46,49,187,188,418],[46,184,185,188,418], [45,46,184,187,418],[46,184,187,188,418],[45,48,50,188,418],[45,48,49,187,418], [45,48,186,187,418],[45,48,186,188,418],[45,183,185,188,418],[183,184,185,188,418], [45,183,184,187,418],[183,184,187,188,418],[45,183,186,187,418],[45,183,186,188,418], [183,186,187,188,418],[48,50,53,191,418],[49,50,53,191,418],[48,50,188,191,418], [49,50,188,191,418],[49,52,53,191,418],[48,49,52,190,418],[49,52,190,191,418], [49,187,188,191,418],[48,49,187,190,418],[49,187,190,191,418],[48,51,53,191,418], [48,51,52,190,418],[48,51,189,190,418],[48,51,189,191,418],[48,186,188,191,418], [186,187,188,191,418],[48,186,187,190,418],[186,187,190,191,418],[48,186,189,190,418], [48,186,189,191,418],[186,189,190,191,418],[51,53,56,194,418],[52,53,56,194,418], [51,53,191,194,418],[52,53,191,194,418],[52,55,56,194,418],[51,52,55,193,418], [52,55,193,194,418],[52,190,191,194,418],[51,52,190,193,418],[52,190,193,194,418], [51,54,56,194,418],[51,54,55,193,418],[51,54,192,193,418],[51,54,192,194,418], [51,189,191,194,418],[189,190,191,194,418],[51,189,190,193,418],[189,190,193,194,418], [51,189,192,193,418],[51,189,192,194,418],[189,192,193,194,418],[54,56,59,197,418], [55,56,59,197,418],[54,56,194,197,418],[55,56,194,197,418],[55,58,59,197,418], [54,55,58,196,418],[55,58,196,197,418],[55,193,194,197,418],[54,55,193,196,418], [55,193,196,197,418],[54,57,59,197,418],[54,57,58,196,418],[54,57,195,196,418], [54,57,195,197,418],[54,192,194,197,418],[192,193,194,197,418],[54,192,193,196,418], [192,193,196,197,418],[54,192,195,196,418],[54,192,195,197,418],[192,195,196,197,418], [57,59,62,200,418],[58,59,62,200,418],[57,59,197,200,418],[58,59,197,200,418], [58,61,62,200,418],[57,58,61,199,418],[58,61,199,200,418],[58,196,197,200,418], [57,58,196,199,418],[58,196,199,200,418],[57,60,62,200,418],[57,60,61,199,418], [57,60,198,199,418],[57,60,198,200,418],[57,195,197,200,418],[195,196,197,200,418], [57,195,196,199,418],[195,196,199,200,418],[57,195,198,199,418],[57,195,198,200,418], [195,198,199,200,418],[60,62,65,203,418],[61,62,65,203,418],[60,62,200,203,418], [61,62,200,203,418],[61,64,65,203,418],[60,61,64,202,418],[61,64,202,203,418], [61,199,200,203,418],[60,61,199,202,418],[61,199,202,203,418],[60,63,65,203,418], [60,63,64,202,418],[60,63,201,202,418],[60,63,201,203,418],[60,198,200,203,418], [198,199,200,203,418],[60,198,199,202,418],[198,199,202,203,418],[60,198,201,202,418], [60,198,201,203,418],[198,201,202,203,418],[63,65,68,206,418],[64,65,68,206,418], [63,65,203,206,418],[64,65,203,206,418],[64,67,68,206,418],[63,64,67,205,418], [64,67,205,206,418],[64,202,203,206,418],[63,64,202,205,418],[64,202,205,206,418], [63,66,68,206,418],[63,66,67,205,418],[63,66,204,205,418],[63,66,204,206,418], [63,201,203,206,418],[201,202,203,206,418],[63,201,202,205,418],[201,202,205,206,418], [63,201,204,205,418],[63,201,204,206,418],[201,204,205,206,418],[66,68,71,209,418], [67,68,71,209,418],[66,68,206,209,418],[67,68,206,209,418],[67,70,71,209,418], [66,67,70,208,418],[67,70,208,209,418],[67,205,206,209,418],[66,67,205,208,418], [67,205,208,209,418],[66,69,71,209,418],[66,69,70,208,418],[66,69,207,208,418], [66,69,207,209,418],[66,204,206,209,418],[204,205,206,209,418],[66,204,205,208,418], [204,205,208,209,418],[66,204,207,208,418],[66,204,207,209,418],[204,207,208,209,418], [69,71,74,212,418],[70,71,74,212,418],[69,71,209,212,418],[70,71,209,212,418], [70,73,74,212,418],[69,70,73,211,418],[70,73,211,212,418],[70,208,209,212,418], [69,70,208,211,418],[70,208,211,212,418],[69,72,74,212,418],[69,72,73,211,418], [69,72,210,211,418],[69,72,210,212,418],[69,207,209,212,418],[207,208,209,212,418], [69,207,208,211,418],[207,208,211,212,418],[69,207,210,211,418],[69,207,210,212,418], [207,210,211,212,418],[72,74,77,215,418],[73,74,77,215,418],[72,74,212,215,418], [73,74,212,215,418],[73,76,77,215,418],[72,73,76,214,418],[73,76,214,215,418], [73,211,212,215,418],[72,73,211,214,418],[73,211,214,215,418],[72,75,77,215,418], [72,75,76,214,418],[72,75,213,214,418],[72,75,213,215,418],[72,210,212,215,418], [210,211,212,215,418],[72,210,211,214,418],[210,211,214,215,418],[72,210,213,214,418], [72,210,213,215,418],[210,213,214,215,418],[75,77,80,218,418],[76,77,80,218,418], [75,77,215,218,418],[76,77,215,218,418],[76,79,80,218,418],[75,76,79,217,418], [76,79,217,218,418],[76,214,215,218,418],[75,76,214,217,418],[76,214,217,218,418], [75,78,80,218,418],[75,78,79,217,418],[75,78,216,217,418],[75,78,216,218,418], [75,213,215,218,418],[213,214,215,218,418],[75,213,214,217,418],[213,214,217,218,418], [75,213,216,217,418],[75,213,216,218,418],[213,216,217,218,418],[78,80,83,221,418], [79,80,83,221,418],[78,80,218,221,418],[79,80,218,221,418],[79,82,83,221,418], [78,79,82,220,418],[79,82,220,221,418],[79,217,218,221,418],[78,79,217,220,418], [79,217,220,221,418],[78,81,83,221,418],[78,81,82,220,418],[78,81,219,220,418], [78,81,219,221,418],[78,216,218,221,418],[216,217,218,221,418],[78,216,217,220,418], [216,217,220,221,418],[78,216,219,220,418],[78,216,219,221,418],[216,219,220,221,418], [81,83,86,224,418],[82,83,86,224,418],[81,83,221,224,418],[82,83,221,224,418], [82,85,86,224,418],[81,82,85,223,418],[82,85,223,224,418],[82,220,221,224,418], [81,82,220,223,418],[82,220,223,224,418],[81,84,86,224,418],[81,84,85,223,418], [81,84,222,223,418],[81,84,222,224,418],[81,219,221,224,418],[219,220,221,224,418], [81,219,220,223,418],[219,220,223,224,418],[81,219,222,223,418],[81,219,222,224,418], [219,222,223,224,418],[84,86,89,227,418],[85,86,89,227,418],[84,86,224,227,418], [85,86,224,227,418],[85,88,89,227,418],[84,85,88,226,418],[85,88,226,227,418], [85,223,224,227,418],[84,85,223,226,418],[85,223,226,227,418],[84,87,89,227,418], 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