#################################################################################### #################################################################################### #################################################################################### ### ### ### ### ### TRIANGULATIONS OF AKBULUT-KIRBY SPHERES ### ### by Frank H. Lutz and Mimi Tsuruga ### ### http://matsguru.com/research/AKspheres.html ### ### ### ### name of example: ### ### ### ### AK_I_007 ### ### ### ### ### ### description: ### ### ### ### Type 1 construction of triangulation of Akbulut-Kirby sphere ### ### ### ### ### ### properties: ### ### ### ### f=(516,7974,26756,32160,12864) ### ### 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:=[ [0,1,2,5,131],[0,1,2,5,252],[1,2,5,252,510],[1,2,5,263,510], [0,1,2,35,161],[0,1,2,35,252],[1,2,35,252,510],[1,2,35,293,510], [0,1,2,128,131],[0,1,2,128,161],[1,2,260,263,510],[1,2,260,293,510], [0,1,4,5,131],[0,1,4,5,252],[0,1,4,252,510],[1,4,5,252,510], [1,4,5,263,510],[0,1,4,130,131],[0,1,4,130,388],[0,1,4,262,510], [1,4,262,263,510],[0,1,4,262,388],[0,1,34,35,161],[0,1,34,35,252], [0,1,34,252,510],[1,34,35,252,510],[1,34,35,293,510],[0,1,34,118,244], [0,1,34,118,376],[0,1,34,160,161],[0,1,34,160,244],[0,1,34,292,510], [1,34,292,293,510],[0,1,34,292,376],[0,1,117,118,244],[0,1,117,118,376], [0,1,117,243,244],[0,1,117,243,501],[0,1,117,375,376],[0,1,117,375,501], [0,1,127,128,131],[0,1,127,128,161],[0,1,127,130,131],[0,1,127,130,388], [0,1,127,160,161],[0,1,127,160,244],[0,1,127,243,244],[0,1,127,243,501], [0,1,127,385,388],[0,1,127,385,501],[1,259,260,263,510],[1,259,260,293,510], [0,1,259,262,510],[1,259,262,263,510],[0,1,259,262,388],[0,1,259,292,510], [1,259,292,293,510],[0,1,259,292,376],[0,1,259,375,376],[0,1,259,375,501], [0,1,259,385,388],[0,1,259,385,501],[0,2,5,26,152],[2,5,26,152,410], [0,2,5,26,284],[2,5,26,284,410],[0,2,5,131,152],[2,5,131,152,410], [2,5,131,389,410],[0,2,5,252,253],[0,2,5,253,511],[2,5,252,253,511], [2,5,252,510,511],[0,2,5,263,284],[2,5,263,284,410],[2,5,263,389,410], [0,2,5,263,511],[2,5,263,510,511],[0,2,26,29,155],[2,26,29,155,413], [0,2,26,29,287],[2,26,29,287,413],[0,2,26,152,155],[2,26,152,155,413], [2,26,152,410,413],[0,2,26,284,287],[2,26,284,287,413],[2,26,284,410,413], [0,2,29,121,247],[0,2,29,121,379],[0,2,29,155,247],[0,2,29,287,379], [0,2,35,121,247],[0,2,35,121,379],[0,2,35,161,247],[0,2,35,252,253], [0,2,35,253,511],[2,35,252,253,511],[2,35,252,510,511],[0,2,35,293,379], [0,2,35,293,511],[2,35,293,510,511],[0,2,128,131,152],[2,128,131,152,410], [2,128,131,389,410],[0,2,128,152,155],[2,128,152,155,413],[2,128,152,410,413], [0,2,128,155,247],[0,2,128,161,247],[2,128,386,389,410],[2,128,386,410,413], [0,2,260,263,284],[2,260,263,284,410],[2,260,263,389,410],[0,2,260,263,511], [2,260,263,510,511],[0,2,260,284,287],[2,260,284,287,413],[2,260,284,410,413], [0,2,260,287,379],[0,2,260,293,379],[0,2,260,293,511],[2,260,293,510,511], [2,260,386,389,410],[2,260,386,410,413],[0,3,4,5,131],[0,3,4,5,252], [0,3,4,252,510],[0,3,4,130,131],[0,3,4,130,388],[0,3,4,262,510], [0,3,4,262,388],[0,3,5,26,152],[0,3,5,26,284],[0,3,5,131,152], [0,3,5,252,253],[0,3,5,253,511],[0,3,5,263,284],[0,3,5,263,511], [0,3,24,26,152],[0,3,24,26,284],[0,3,24,150,152],[0,3,24,150,408], [0,3,24,282,284],[0,3,24,282,408],[0,3,129,130,131],[0,3,129,130,388], [0,3,129,131,152],[0,3,129,150,152],[0,3,129,150,408],[0,3,129,387,388], [0,3,129,387,408],[0,3,252,253,254],[0,3,252,254,512],[0,3,253,254,512], [0,3,253,511,512],[0,3,252,510,512],[0,3,261,262,510],[0,3,261,262,388], [0,3,261,263,284],[0,3,261,263,511],[0,3,261,282,284],[0,3,261,282,408], [0,3,261,387,388],[0,3,261,387,408],[0,3,261,510,512],[0,3,261,511,512], [0,24,26,29,155],[0,24,26,29,287],[0,24,26,152,155],[0,24,26,284,287], [0,24,27,29,155],[0,24,27,29,287],[0,24,27,153,155],[0,24,27,153,411], [0,24,27,285,287],[0,24,27,285,411],[0,24,150,152,155],[0,24,150,153,155], [0,24,150,153,411],[0,24,150,408,411],[0,24,282,284,287],[0,24,282,285,287], [0,24,282,285,411],[0,24,282,408,411],[0,27,29,121,247],[0,27,29,121,379], [0,27,29,155,247],[0,27,29,287,379],[0,27,114,118,244],[0,27,114,118,376], [0,27,114,121,247],[0,27,114,121,379],[0,27,114,240,244],[0,27,114,240,247], [0,27,114,372,376],[0,27,114,372,379],[0,27,117,118,244],[0,27,117,118,376], [0,27,117,243,244],[0,27,117,243,501],[0,27,117,375,376],[0,27,117,375,501], [0,27,153,155,247],[0,27,153,240,244],[0,27,153,240,247],[0,27,153,243,244], [0,27,153,243,501],[0,27,153,411,501],[0,27,285,287,379],[0,27,285,372,376], [0,27,285,372,379],[0,27,285,375,376],[0,27,285,375,501],[0,27,285,411,501], [0,33,34,35,161],[0,33,34,35,252],[0,33,34,252,510],[0,33,34,118,244], [0,33,34,118,376],[0,33,34,160,161],[0,33,34,160,244],[0,33,34,292,510], [0,33,34,292,376],[0,33,35,121,247],[0,33,35,121,379],[0,33,35,161,247], [0,33,35,252,253],[0,33,35,253,511],[0,33,35,293,379],[0,33,35,293,511], [0,33,114,118,244],[0,33,114,118,376],[0,33,114,121,247],[0,33,114,121,379], [0,33,114,240,244],[0,33,114,240,247],[0,33,114,372,376],[0,33,114,372,379], [0,33,159,160,161],[0,33,159,160,244],[0,33,159,161,247],[0,33,159,240,244], [0,33,159,240,247],[0,33,252,253,254],[0,33,252,254,512],[0,33,253,254,512], [0,33,253,511,512],[0,33,252,510,512],[0,33,291,292,510],[0,33,291,292,376], [0,33,291,293,379],[0,33,291,293,511],[0,33,291,372,376],[0,33,291,372,379], [0,33,291,510,512],[0,33,291,511,512],[0,126,127,128,131],[126,127,128,131,389], [0,126,127,128,161],[126,127,128,161,419],[126,127,128,386,389],[126,127,128,386,419], [0,126,127,130,131],[126,127,130,131,389],[0,126,127,130,388],[126,127,130,388,389], [0,126,127,160,161],[126,127,160,161,419],[0,126,127,160,244],[126,127,160,244,502], [126,127,160,418,419],[126,127,160,418,502],[0,126,127,243,244],[126,127,243,244,502], [0,126,127,243,501],[126,127,243,501,502],[126,127,385,386,389],[126,127,385,386,419], [0,126,127,385,388],[126,127,385,388,389],[126,127,385,418,419],[126,127,385,418,502], [0,126,127,385,501],[126,127,385,501,502],[0,126,128,131,152],[126,128,131,152,410], [126,128,131,389,410],[0,126,128,152,155],[126,128,152,155,413],[126,128,152,410,413], [0,126,128,155,247],[126,128,155,247,505],[126,128,155,413,505],[0,126,128,161,247], [126,128,161,247,505],[126,128,161,419,505],[126,128,386,389,410],[126,128,386,410,413], [126,128,386,413,505],[126,128,386,419,505],[0,126,129,130,131],[126,129,130,131,389], [0,126,129,130,388],[126,129,130,388,389],[0,126,129,131,152],[126,129,131,152,410], [126,129,131,389,410],[0,126,129,150,152],[126,129,150,152,410],[0,126,129,150,408], [126,129,150,408,410],[0,126,129,387,388],[126,129,387,388,389],[126,129,387,389,410], [0,126,129,387,408],[126,129,387,408,410],[0,126,150,152,155],[126,150,152,155,413], [126,150,152,410,413],[0,126,150,153,155],[126,150,153,155,413],[0,126,150,153,411], [126,150,153,411,413],[126,150,408,410,413],[0,126,150,408,411],[126,150,408,411,413], [0,126,153,155,247],[126,153,155,247,505],[126,153,155,413,505],[0,126,153,240,244], [126,153,240,244,502],[0,126,153,240,247],[126,153,240,247,505],[126,153,240,498,502], [126,153,240,498,505],[0,126,153,243,244],[126,153,243,244,502],[0,126,153,243,501], [126,153,243,501,502],[126,153,411,413,505],[126,153,411,498,502],[126,153,411,498,505], [0,126,153,411,501],[126,153,411,501,502],[0,126,159,160,161],[126,159,160,161,419], [0,126,159,160,244],[126,159,160,244,502],[126,159,160,418,419],[126,159,160,418,502], [0,126,159,161,247],[126,159,161,247,505],[126,159,161,419,505],[0,126,159,240,244], [126,159,240,244,502],[0,126,159,240,247],[126,159,240,247,505],[126,159,240,498,502], [126,159,240,498,505],[126,159,417,418,419],[126,159,417,418,502],[126,159,417,419,505], [126,159,417,498,502],[126,159,417,498,505],[126,384,385,386,389],[126,384,385,386,419], [0,126,384,385,388],[126,384,385,388,389],[126,384,385,418,419],[126,384,385,418,502], [0,126,384,385,501],[126,384,385,501,502],[126,384,386,389,410],[126,384,386,410,413], [126,384,386,413,505],[126,384,386,419,505],[0,126,384,387,388],[126,384,387,388,389], [126,384,387,389,410],[0,126,384,387,408],[126,384,387,408,410],[126,384,408,410,413], [0,126,384,408,411],[126,384,408,411,413],[126,384,411,413,505],[126,384,411,498,502], [126,384,411,498,505],[0,126,384,411,501],[126,384,411,501,502],[126,384,417,418,419], [126,384,417,418,502],[126,384,417,419,505],[126,384,417,498,502],[126,384,417,498,505], [258,259,260,263,389],[258,259,260,263,510],[258,259,260,293,419],[258,259,260,293,510], [258,259,260,386,389],[258,259,260,386,419],[258,259,262,263,389],[0,258,259,262,510], [258,259,262,263,510],[0,258,259,262,388],[258,259,262,388,389],[258,259,292,293,419], [0,258,259,292,510],[258,259,292,293,510],[0,258,259,292,376],[258,259,292,376,502], [258,259,292,418,419],[258,259,292,418,502],[0,258,259,375,376],[258,259,375,376,502], [0,258,259,375,501],[258,259,375,501,502],[258,259,385,386,389],[258,259,385,386,419], [0,258,259,385,388],[258,259,385,388,389],[258,259,385,418,419],[258,259,385,418,502], [0,258,259,385,501],[258,259,385,501,502],[0,258,260,263,284],[258,260,263,284,410], [258,260,263,389,410],[0,258,260,263,511],[258,260,263,510,511],[0,258,260,284,287], [258,260,284,287,413],[258,260,284,410,413],[0,258,260,287,379],[258,260,287,379,505], [258,260,287,413,505],[0,258,260,293,379],[258,260,293,379,505],[258,260,293,419,505], [0,258,260,293,511],[258,260,293,510,511],[258,260,386,389,410],[258,260,386,410,413], [258,260,386,413,505],[258,260,386,419,505],[258,261,262,263,389],[0,258,261,262,510], [258,261,262,263,510],[0,258,261,262,388],[258,261,262,388,389],[0,258,261,263,284], [258,261,263,284,410],[258,261,263,389,410],[0,258,261,263,511],[258,261,263,510,511], [0,258,261,282,284],[258,261,282,284,410],[0,258,261,282,408],[258,261,282,408,410], [0,258,261,387,388],[258,261,387,388,389],[258,261,387,389,410],[0,258,261,387,408], [258,261,387,408,410],[0,258,261,510,512],[0,258,261,511,512],[258,261,510,511,512], [0,258,282,284,287],[258,282,284,287,413],[258,282,284,410,413],[0,258,282,285,287], [258,282,285,287,413],[0,258,282,285,411],[258,282,285,411,413],[258,282,408,410,413], [0,258,282,408,411],[258,282,408,411,413],[0,258,285,287,379],[258,285,287,379,505], [258,285,287,413,505],[0,258,285,372,376],[258,285,372,376,502],[0,258,285,372,379], [258,285,372,379,505],[258,285,372,498,502],[258,285,372,498,505],[0,258,285,375,376], [258,285,375,376,502],[0,258,285,375,501],[258,285,375,501,502],[258,285,411,413,505], [258,285,411,498,502],[258,285,411,498,505],[0,258,285,411,501],[258,285,411,501,502], [258,291,292,293,419],[0,258,291,292,510],[258,291,292,293,510],[0,258,291,292,376], [258,291,292,376,502],[258,291,292,418,419],[258,291,292,418,502],[0,258,291,293,379], [258,291,293,379,505],[258,291,293,419,505],[0,258,291,293,511],[258,291,293,510,511], [0,258,291,372,376],[258,291,372,376,502],[0,258,291,372,379],[258,291,372,379,505], [258,291,372,498,502],[258,291,372,498,505],[258,291,417,418,419],[258,291,417,418,502], [258,291,417,419,505],[258,291,417,498,502],[258,291,417,498,505],[0,258,291,510,512], [0,258,291,511,512],[258,291,510,511,512],[258,384,385,386,389],[258,384,385,386,419], [0,258,384,385,388],[258,384,385,388,389],[258,384,385,418,419],[258,384,385,418,502], [0,258,384,385,501],[258,384,385,501,502],[258,384,386,389,410],[258,384,386,410,413], [258,384,386,413,505],[258,384,386,419,505],[0,258,384,387,388],[258,384,387,388,389], [258,384,387,389,410],[0,258,384,387,408],[258,384,387,408,410],[258,384,408,410,413], [0,258,384,408,411],[258,384,408,411,413],[258,384,411,413,505],[258,384,411,498,502], [258,384,411,498,505],[0,258,384,411,501],[258,384,411,501,502],[258,384,417,418,419], [258,384,417,418,502],[258,384,417,419,505],[258,384,417,498,502],[258,384,417,498,505], [1,2,5,41,167],[2,5,41,167,425],[1,2,5,41,299],[2,5,41,299,425], [1,2,5,131,167],[2,5,131,167,425],[2,5,131,389,425],[1,2,5,263,299], [2,5,263,299,425],[2,5,263,389,425],[1,2,35,121,247],[1,2,35,121,379], [1,2,35,161,247],[1,2,35,293,379],[1,2,38,41,167],[2,38,41,167,425], [1,2,38,41,299],[2,38,41,299,425],[1,2,38,124,250],[1,2,38,124,382], [1,2,38,164,167],[2,38,164,167,425],[1,2,38,164,250],[2,38,164,422,425], [1,2,38,296,299],[2,38,296,299,425],[1,2,38,296,382],[2,38,296,422,425], [1,2,120,121,247],[1,2,120,121,379],[1,2,120,124,250],[1,2,120,124,382], [1,2,120,246,247],[1,2,120,246,250],[1,2,120,378,379],[1,2,120,378,382], [1,2,128,131,167],[2,128,131,167,425],[2,128,131,389,425],[1,2,128,161,247], [1,2,128,164,167],[2,128,164,167,425],[1,2,128,164,250],[2,128,164,422,425], [1,2,128,246,247],[1,2,128,246,250],[2,128,386,389,425],[2,128,386,422,425], [1,2,260,263,299],[2,260,263,299,425],[2,260,263,389,425],[1,2,260,293,379], [1,2,260,296,299],[2,260,296,299,425],[1,2,260,296,382],[2,260,296,422,425], [1,2,260,378,379],[1,2,260,378,382],[2,260,386,389,425],[2,260,386,422,425], [1,4,5,41,167],[1,4,5,41,299],[1,4,5,131,167],[1,4,5,263,299], [1,4,39,41,167],[1,4,39,41,299],[1,4,39,165,167],[1,4,39,165,423], [1,4,39,297,299],[1,4,39,297,423],[1,4,130,131,167],[1,4,130,165,167], [1,4,130,165,423],[1,4,130,388,423],[1,4,262,263,299],[1,4,262,297,299], [1,4,262,297,423],[1,4,262,388,423],[1,34,35,121,247],[1,34,35,121,379], [1,34,35,161,247],[1,34,35,293,379],[1,34,115,118,244],[1,34,115,118,376], [1,34,115,121,247],[1,34,115,121,379],[1,34,115,241,244],[1,34,115,241,247], [1,34,115,373,376],[1,34,115,373,379],[1,34,160,161,247],[1,34,160,241,244], [1,34,160,241,247],[1,34,292,293,379],[1,34,292,373,376],[1,34,292,373,379], [1,36,38,41,167],[1,36,38,41,299],[1,36,38,124,250],[1,36,38,124,382], [1,36,38,164,167],[1,36,38,164,250],[1,36,38,296,299],[1,36,38,296,382], [1,36,39,41,167],[1,36,39,41,299],[1,36,39,165,167],[1,36,39,165,423], [1,36,39,297,299],[1,36,39,297,423],[1,36,115,118,244],[1,36,115,118,376], [1,36,115,121,247],[1,36,115,121,379],[1,36,115,241,244],[1,36,115,241,247], [1,36,115,373,376],[1,36,115,373,379],[1,36,117,118,244],[1,36,117,118,376], [1,36,117,243,244],[1,36,117,243,501],[1,36,117,375,376],[1,36,117,375,501], [1,36,120,121,247],[1,36,120,121,379],[1,36,120,124,250],[1,36,120,124,382], [1,36,120,246,247],[1,36,120,246,250],[1,36,120,378,379],[1,36,120,378,382], [1,36,162,164,167],[1,36,162,164,250],[1,36,162,165,167],[1,36,162,165,423], [1,36,162,241,244],[1,36,162,241,247],[1,36,162,243,244],[1,36,162,243,501], [1,36,162,246,247],[1,36,162,246,250],[1,36,162,420,423],[1,36,162,420,501], [1,36,294,296,299],[1,36,294,296,382],[1,36,294,297,299],[1,36,294,297,423], [1,36,294,373,376],[1,36,294,373,379],[1,36,294,375,376],[1,36,294,375,501], [1,36,294,378,379],[1,36,294,378,382],[1,36,294,420,423],[1,36,294,420,501], [1,127,128,131,167],[127,128,131,167,425],[127,128,131,389,425],[1,127,128,161,247], [127,128,161,247,505],[127,128,161,419,505],[1,127,128,164,167],[127,128,164,167,425], [1,127,128,164,250],[127,128,164,250,508],[127,128,164,422,425],[127,128,164,422,508], [1,127,128,246,247],[127,128,246,247,505],[1,127,128,246,250],[127,128,246,250,508], [127,128,246,504,505],[127,128,246,504,508],[127,128,386,389,425],[127,128,386,419,505], [127,128,386,422,425],[127,128,386,422,508],[127,128,386,504,505],[127,128,386,504,508], [1,127,130,131,167],[127,130,131,167,425],[127,130,131,389,425],[1,127,130,165,167], [127,130,165,167,425],[1,127,130,165,423],[127,130,165,423,425],[127,130,388,389,425], [1,127,130,388,423],[127,130,388,423,425],[1,127,160,161,247],[127,160,161,247,505], [127,160,161,419,505],[1,127,160,241,244],[127,160,241,244,502],[1,127,160,241,247], [127,160,241,247,505],[127,160,241,499,502],[127,160,241,499,505],[127,160,418,419,505], 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[3,21,24,150,244],[3,21,24,282,284],[3,21,24,282,376],[3,21,147,149,152], [3,21,147,150,152],[3,21,147,150,244],[3,21,279,281,284],[3,21,279,282,284], [3,21,279,282,376],[3,24,117,118,244],[3,24,117,118,376],[3,24,117,243,244], [3,24,117,243,501],[3,24,117,375,376],[3,24,117,375,501],[3,24,150,243,244], [3,24,150,243,501],[3,24,150,408,501],[3,24,282,375,376],[3,24,282,375,501], [3,24,282,408,501],[3,129,130,131,134],[129,130,131,134,392],[129,130,131,389,392], [3,129,130,133,134],[129,130,133,134,392],[3,129,130,133,244],[129,130,133,244,502], [129,130,133,391,392],[129,130,133,391,502],[3,129,130,243,244],[129,130,243,244,502], [3,129,130,243,501],[129,130,243,501,502],[129,130,388,389,392],[129,130,388,391,392], [129,130,388,391,502],[3,129,130,388,501],[129,130,388,501,502],[3,129,131,134,149], [129,131,134,149,407],[129,131,134,392,407],[3,129,131,149,152],[129,131,149,152,410], [129,131,149,407,410],[129,131,389,392,407],[129,131,389,407,410],[3,129,132,133,134], 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[44,170,176,248,250],[170,176,248,250,508],[44,170,176,248,506],[170,176,248,506,508], [44,170,176,434,506],[170,176,434,506,508],[44,170,428,434,506],[170,428,434,506,508], [44,302,308,380,382],[302,308,380,382,508],[44,302,308,380,506],[302,308,380,506,508], [44,302,308,434,506],[302,308,434,506,508],[44,302,428,434,506],[302,428,434,506,508], [45,46,47,50,176],[45,46,47,50,255],[46,47,50,255,513],[46,47,50,308,513], [45,46,47,173,176],[46,47,305,308,513],[45,46,49,50,176],[45,46,49,50,255], [45,46,49,255,513],[46,49,50,255,513],[46,49,50,308,513],[45,46,49,175,176], [45,46,49,175,433],[45,46,49,307,513],[46,49,307,308,513],[45,46,49,307,433], [45,46,172,173,176],[45,46,172,175,176],[45,46,172,175,433],[45,46,172,430,433], [46,304,305,308,513],[45,46,304,307,513],[46,304,307,308,513],[45,46,304,307,433], [45,46,304,430,433],[45,47,50,255,256],[45,47,50,256,514],[47,50,255,256,514], [47,50,255,513,514],[45,47,50,308,514],[47,50,308,513,514],[45,47,305,308,514], [47,305,308,513,514],[45,48,49,50,176],[45,48,49,50,255],[45,48,49,255,513], [45,48,49,175,176],[45,48,49,175,433],[45,48,49,307,513],[45,48,49,307,433], [45,48,50,255,256],[45,48,50,256,514],[45,48,50,308,514],[45,48,174,175,176], [45,48,174,175,433],[45,48,174,432,433],[45,48,255,256,257],[45,48,255,257,515], [45,48,256,257,515],[45,48,256,514,515],[45,48,255,513,515],[45,48,306,307,513], [45,48,306,307,433],[45,48,306,308,514],[45,48,306,432,433],[45,48,306,513,515], [45,48,306,514,515],[45,171,172,173,176],[171,172,173,176,434],[171,172,173,431,434], [45,171,172,175,176],[171,172,175,176,434],[45,171,172,175,433],[171,172,175,433,434], [171,172,430,431,434],[45,171,172,430,433],[171,172,430,433,434],[45,171,174,175,176], [171,174,175,176,434],[45,171,174,175,433],[171,174,175,433,434],[45,171,174,432,433], [171,174,432,433,434],[171,429,430,431,434],[45,171,429,430,433],[171,429,430,433,434], [45,171,429,432,433],[171,429,432,433,434],[303,304,305,308,434],[303,304,305,308,513], [303,304,305,431,434],[303,304,307,308,434],[45,303,304,307,513],[303,304,307,308,513], [45,303,304,307,433],[303,304,307,433,434],[303,304,430,431,434],[45,303,304,430,433], [303,304,430,433,434],[45,303,305,308,514],[303,305,308,513,514],[303,306,307,308,434], [45,303,306,307,513],[303,306,307,308,513],[45,303,306,307,433],[303,306,307,433,434], [45,303,306,308,514],[303,306,308,513,514],[45,303,306,432,433],[303,306,432,433,434], [45,303,306,513,515],[45,303,306,514,515],[303,306,513,514,515],[303,429,430,431,434], [45,303,429,430,433],[303,429,430,433,434],[45,303,429,432,433],[303,429,432,433,434], [46,47,50,56,182],[46,47,50,56,314],[46,47,50,176,182],[46,47,50,308,314], [46,47,53,56,182],[46,47,53,56,314],[46,47,53,179,182],[46,47,53,311,314], [46,47,173,176,182],[46,47,173,179,182],[46,47,305,308,314],[46,47,305,311,314], [46,49,50,56,182],[46,49,50,56,314],[46,49,50,176,182],[46,49,50,308,314], [46,49,54,56,182],[46,49,54,56,314],[46,49,54,180,182],[46,49,54,180,438], [46,49,54,312,314],[46,49,54,312,438],[46,49,175,176,182],[46,49,175,180,182], [46,49,175,180,438],[46,49,175,433,438],[46,49,307,308,314],[46,49,307,312,314], [46,49,307,312,438],[46,49,307,433,438],[46,51,53,56,182],[46,51,53,56,314], [46,51,53,179,182],[46,51,53,311,314],[46,51,54,56,182],[46,51,54,56,314], [46,51,54,180,182],[46,51,54,180,438],[46,51,54,312,314],[46,51,54,312,438], [46,51,177,179,182],[46,51,177,180,182],[46,51,177,180,438],[46,51,177,435,438], [46,51,309,311,314],[46,51,309,312,314],[46,51,309,312,438],[46,51,309,435,438], [46,172,173,176,182],[172,173,176,182,440],[172,173,176,434,440],[46,172,173,179,182], [172,173,179,182,440],[172,173,179,437,440],[172,173,431,434,440],[172,173,431,437,440], [46,172,175,176,182],[172,175,176,182,440],[172,175,176,434,440],[46,172,175,180,182], [172,175,180,182,440],[46,172,175,180,438],[172,175,180,438,440],[172,175,433,434,440], [46,172,175,433,438],[172,175,433,438,440],[46,172,177,179,182],[172,177,179,182,440], [172,177,179,437,440],[46,172,177,180,182],[172,177,180,182,440],[46,172,177,180,438], [172,177,180,438,440],[172,177,435,437,440],[46,172,177,435,438],[172,177,435,438,440], [172,430,431,434,440],[172,430,431,437,440],[172,430,433,434,440],[46,172,430,433,438], [172,430,433,438,440],[172,430,435,437,440],[46,172,430,435,438],[172,430,435,438,440], [46,304,305,308,314],[304,305,308,314,440],[304,305,308,434,440],[46,304,305,311,314], [304,305,311,314,440],[304,305,311,437,440],[304,305,431,434,440],[304,305,431,437,440], [46,304,307,308,314],[304,307,308,314,440],[304,307,308,434,440],[46,304,307,312,314], [304,307,312,314,440],[46,304,307,312,438],[304,307,312,438,440],[304,307,433,434,440], [46,304,307,433,438],[304,307,433,438,440],[46,304,309,311,314],[304,309,311,314,440], [304,309,311,437,440],[46,304,309,312,314],[304,309,312,314,440],[46,304,309,312,438], [304,309,312,438,440],[304,309,435,437,440],[46,304,309,435,438],[304,309,435,438,440], [304,430,431,434,440],[304,430,431,437,440],[304,430,433,434,440],[46,304,430,433,438], [304,430,433,438,440],[304,430,435,437,440],[46,304,430,435,438],[304,430,435,438,440], [47,50,56,124,250],[47,50,56,124,382],[47,50,56,182,250],[47,50,56,314,382], [47,50,176,182,250],[47,50,308,314,382],[47,53,56,124,250],[47,53,56,124,382], [47,53,56,182,250],[47,53,56,314,382],[47,53,123,124,250],[47,53,123,124,382], [47,53,123,249,250],[47,53,123,249,507],[47,53,123,381,382],[47,53,123,381,507], [47,53,179,182,250],[47,53,179,249,250],[47,53,179,249,507],[47,53,179,437,507], [47,53,311,314,382],[47,53,311,381,382],[47,53,311,381,507],[47,53,311,437,507], [47,173,176,182,250],[173,176,182,250,508],[173,176,182,440,508],[173,176,434,440,508], [47,173,179,182,250],[173,179,182,250,508],[173,179,182,440,508],[47,173,179,249,250], [173,179,249,250,508],[47,173,179,249,507],[173,179,249,507,508],[173,179,437,440,508], [47,173,179,437,507],[173,179,437,507,508],[173,431,434,440,508],[173,431,437,440,508], [47,173,431,437,507],[173,431,437,507,508],[47,305,308,314,382],[305,308,314,382,508], [305,308,314,440,508],[305,308,434,440,508],[47,305,311,314,382],[305,311,314,382,508], [305,311,314,440,508],[47,305,311,381,382],[305,311,381,382,508],[47,305,311,381,507], [305,311,381,507,508],[305,311,437,440,508],[47,305,311,437,507],[305,311,437,507,508], [305,431,434,440,508],[305,431,437,440,508],[47,305,431,437,507],[305,431,437,507,508], [48,49,50,53,179],[48,49,50,53,255],[49,50,53,255,513],[49,50,53,311,513], [48,49,50,176,179],[49,50,308,311,513],[48,49,52,53,179],[48,49,52,53,255], [48,49,52,255,513],[49,52,53,255,513],[49,52,53,311,513],[48,49,52,178,179], [48,49,52,178,436],[48,49,52,310,513],[49,52,310,311,513],[48,49,52,310,436], [48,49,175,176,179],[48,49,175,178,179],[48,49,175,178,436],[48,49,175,433,436], [49,307,308,311,513],[48,49,307,310,513],[49,307,310,311,513],[48,49,307,310,436], [48,49,307,433,436],[48,50,53,255,256],[48,50,53,256,514],[50,53,255,256,514], [50,53,255,513,514],[48,50,53,311,514],[50,53,311,513,514],[48,50,308,311,514], [50,308,311,513,514],[48,51,52,53,179],[48,51,52,53,255],[48,51,52,255,513], [48,51,52,178,179],[48,51,52,178,436],[48,51,52,310,513],[48,51,52,310,436], [48,51,53,255,256],[48,51,53,256,514],[48,51,53,311,514],[48,51,177,178,179], [48,51,177,178,436],[48,51,177,435,436],[48,51,255,256,257],[48,51,255,257,515], [48,51,256,257,515],[48,51,256,514,515],[48,51,255,513,515],[48,51,309,310,513], [48,51,309,310,436],[48,51,309,311,514],[48,51,309,435,436],[48,51,309,513,515], [48,51,309,514,515],[48,174,175,176,179],[174,175,176,179,437],[174,175,176,434,437], [48,174,175,178,179],[174,175,178,179,437],[48,174,175,178,436],[174,175,178,436,437], [174,175,433,434,437],[48,174,175,433,436],[174,175,433,436,437],[48,174,177,178,179], [174,177,178,179,437],[48,174,177,178,436],[174,177,178,436,437],[48,174,177,435,436], [174,177,435,436,437],[174,432,433,434,437],[48,174,432,433,436],[174,432,433,436,437], [48,174,432,435,436],[174,432,435,436,437],[306,307,308,311,437],[306,307,308,311,513], [306,307,308,434,437],[306,307,310,311,437],[48,306,307,310,513],[306,307,310,311,513], [48,306,307,310,436],[306,307,310,436,437],[306,307,433,434,437],[48,306,307,433,436], [306,307,433,436,437],[48,306,308,311,514],[306,308,311,513,514],[306,309,310,311,437], [48,306,309,310,513],[306,309,310,311,513],[48,306,309,310,436],[306,309,310,436,437], [48,306,309,311,514],[306,309,311,513,514],[48,306,309,435,436],[306,309,435,436,437], [48,306,309,513,515],[48,306,309,514,515],[306,309,513,514,515],[306,432,433,434,437], [48,306,432,433,436],[306,432,433,436,437],[48,306,432,435,436],[306,432,435,436,437], [49,50,53,59,185],[50,53,59,185,443],[49,50,53,59,317],[50,53,59,317,443], [49,50,53,179,185],[50,53,179,185,443],[50,53,179,437,443],[49,50,53,311,317], [50,53,311,317,443],[50,53,311,437,443],[49,50,56,59,185],[50,56,59,185,443], [49,50,56,59,317],[50,56,59,317,443],[49,50,56,182,185],[50,56,182,185,443], [50,56,182,440,443],[49,50,56,314,317],[50,56,314,317,443],[50,56,314,440,443], [49,50,176,179,185],[50,176,179,185,443],[50,176,179,437,443],[49,50,176,182,185], [50,176,182,185,443],[50,176,182,440,443],[50,176,434,437,443],[50,176,434,440,443], [49,50,308,311,317],[50,308,311,317,443],[50,308,311,437,443],[49,50,308,314,317], [50,308,314,317,443],[50,308,314,440,443],[50,308,434,437,443],[50,308,434,440,443], [49,52,53,59,185],[49,52,53,59,317],[49,52,53,179,185],[49,52,53,311,317], [49,52,57,59,185],[49,52,57,59,317],[49,52,57,183,185],[49,52,57,183,441], [49,52,57,315,317],[49,52,57,315,441],[49,52,178,179,185],[49,52,178,183,185], [49,52,178,183,441],[49,52,178,436,441],[49,52,310,311,317],[49,52,310,315,317], [49,52,310,315,441],[49,52,310,436,441],[49,54,56,59,185],[49,54,56,59,317], [49,54,56,182,185],[49,54,56,314,317],[49,54,57,59,185],[49,54,57,59,317], [49,54,57,183,185],[49,54,57,183,441],[49,54,57,315,317],[49,54,57,315,441], [49,54,180,182,185],[49,54,180,183,185],[49,54,180,183,441],[49,54,180,438,441], [49,54,312,314,317],[49,54,312,315,317],[49,54,312,315,441],[49,54,312,438,441], [49,175,176,179,185],[175,176,179,185,443],[175,176,179,437,443],[49,175,176,182,185], [175,176,182,185,443],[175,176,182,440,443],[175,176,434,437,443],[175,176,434,440,443], [49,175,178,179,185],[175,178,179,185,443],[175,178,179,437,443],[49,175,178,183,185], [175,178,183,185,443],[49,175,178,183,441],[175,178,183,441,443],[175,178,436,437,443], [49,175,178,436,441],[175,178,436,441,443],[49,175,180,182,185],[175,180,182,185,443], [175,180,182,440,443],[49,175,180,183,185],[175,180,183,185,443],[49,175,180,183,441], [175,180,183,441,443],[175,180,438,440,443],[49,175,180,438,441],[175,180,438,441,443], [175,433,434,437,443],[175,433,434,440,443],[175,433,436,437,443],[49,175,433,436,441], [175,433,436,441,443],[175,433,438,440,443],[49,175,433,438,441],[175,433,438,441,443], [49,307,308,311,317],[307,308,311,317,443],[307,308,311,437,443],[49,307,308,314,317], [307,308,314,317,443],[307,308,314,440,443],[307,308,434,437,443],[307,308,434,440,443], [49,307,310,311,317],[307,310,311,317,443],[307,310,311,437,443],[49,307,310,315,317], [307,310,315,317,443],[49,307,310,315,441],[307,310,315,441,443],[307,310,436,437,443], [49,307,310,436,441],[307,310,436,441,443],[49,307,312,314,317],[307,312,314,317,443], [307,312,314,440,443],[49,307,312,315,317],[307,312,315,317,443],[49,307,312,315,441], [307,312,315,441,443],[307,312,438,440,443],[49,307,312,438,441],[307,312,438,441,443], [307,433,434,437,443],[307,433,434,440,443],[307,433,436,437,443],[49,307,433,436,441], [307,433,436,441,443],[307,433,438,440,443],[49,307,433,438,441],[307,433,438,441,443], [50,56,122,124,250],[50,56,122,124,382],[50,56,122,248,250],[50,56,122,248,506], [50,56,122,380,382],[50,56,122,380,506],[50,56,182,248,250],[50,56,182,248,506], [50,56,182,440,506],[50,56,314,380,382],[50,56,314,380,506],[50,56,314,440,506], [50,176,182,248,250],[176,182,248,250,508],[50,176,182,248,506],[176,182,248,506,508], [50,176,182,440,506],[176,182,440,506,508],[50,176,434,440,506],[176,434,440,506,508], [50,308,314,380,382],[308,314,380,382,508],[50,308,314,380,506],[308,314,380,506,508], [50,308,314,440,506],[308,314,440,506,508],[50,308,434,440,506],[308,434,440,506,508], [51,52,53,56,182],[51,52,53,56,255],[52,53,56,255,513],[52,53,56,314,513], [51,52,53,179,182],[52,53,311,314,513],[51,52,55,56,182],[51,52,55,56,255], [51,52,55,255,513],[52,55,56,255,513],[52,55,56,314,513],[51,52,55,181,182], [51,52,55,181,439],[51,52,55,313,513],[52,55,313,314,513],[51,52,55,313,439], [51,52,178,179,182],[51,52,178,181,182],[51,52,178,181,439],[51,52,178,436,439], [52,310,311,314,513],[51,52,310,313,513],[52,310,313,314,513],[51,52,310,313,439], [51,52,310,436,439],[51,53,56,255,256],[51,53,56,256,514],[53,56,255,256,514], [53,56,255,513,514],[51,53,56,314,514],[53,56,314,513,514],[51,53,311,314,514], [53,311,314,513,514],[51,54,55,56,182],[51,54,55,56,255],[51,54,55,255,513], [51,54,55,181,182],[51,54,55,181,439],[51,54,55,313,513],[51,54,55,313,439], [51,54,56,255,256],[51,54,56,256,514],[51,54,56,314,514],[51,54,180,181,182], [51,54,180,181,439],[51,54,180,438,439],[51,54,255,256,257],[51,54,255,257,515], [51,54,256,257,515],[51,54,256,514,515],[51,54,255,513,515],[51,54,312,313,513], [51,54,312,313,439],[51,54,312,314,514],[51,54,312,438,439],[51,54,312,513,515], [51,54,312,514,515],[51,177,178,179,182],[177,178,179,182,440],[177,178,179,437,440], [51,177,178,181,182],[177,178,181,182,440],[51,177,178,181,439],[177,178,181,439,440], [177,178,436,437,440],[51,177,178,436,439],[177,178,436,439,440],[51,177,180,181,182], [177,180,181,182,440],[51,177,180,181,439],[177,180,181,439,440],[51,177,180,438,439], [177,180,438,439,440],[177,435,436,437,440],[51,177,435,436,439],[177,435,436,439,440], [51,177,435,438,439],[177,435,438,439,440],[309,310,311,314,440],[309,310,311,314,513], [309,310,311,437,440],[309,310,313,314,440],[51,309,310,313,513],[309,310,313,314,513], [51,309,310,313,439],[309,310,313,439,440],[309,310,436,437,440],[51,309,310,436,439], [309,310,436,439,440],[51,309,311,314,514],[309,311,314,513,514],[309,312,313,314,440], [51,309,312,313,513],[309,312,313,314,513],[51,309,312,313,439],[309,312,313,439,440], [51,309,312,314,514],[309,312,314,513,514],[51,309,312,438,439],[309,312,438,439,440], [51,309,312,513,515],[51,309,312,514,515],[309,312,513,514,515],[309,435,436,437,440], [51,309,435,436,439],[309,435,436,439,440],[51,309,435,438,439],[309,435,438,439,440], [52,53,56,62,188],[52,53,56,62,320],[52,53,56,182,188],[52,53,56,314,320], 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