#################################################################################### #################################################################################### #################################################################################### ### ### ### ### ### TRIANGULATIONS OF AKBULUT-KIRBY SPHERES ### ### by Frank H. Lutz and Mimi Tsuruga ### ### http://matsguru.com/research/AKspheres.html ### ### ### ### name of example: ### ### ### ### AK_III_013 ### ### ### ### ### ### description: ### ### ### ### Type 3 construction of triangulation of Akbulut-Kirby sphere ### ### ### ### ### ### properties: ### ### ### ### f=(602,8652,28608,34260,13704) ### ### 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:=[ [0,1,2,5,401],[0,1,2,35,431],[0,1,2,398,401],[0,1,2,398,431], [0,1,4,5,401],[0,1,4,202,400],[0,1,4,400,401],[0,1,34,35,431], [0,1,34,190,388],[0,1,34,190,586],[0,1,34,232,388],[0,1,34,430,431], [0,1,34,430,586],[0,1,189,190,388],[0,1,189,190,586],[0,1,189,387,388], [0,1,189,387,585],[0,1,189,585,586],[0,1,199,202,400],[0,1,199,232,388], [0,1,199,387,388],[0,1,199,387,585],[0,1,397,398,401],[0,1,397,398,431], [0,1,199,397,400],[0,1,397,400,401],[0,1,397,430,431],[0,1,397,430,586], [0,1,199,397,585],[0,1,397,585,586],[0,2,5,26,224],[0,2,5,26,422], [2,5,26,224,422],[0,2,5,203,224],[2,5,203,224,422],[0,2,5,401,422], [2,5,203,401,422],[0,2,26,29,227],[0,2,26,29,425],[2,26,29,227,425], [0,2,26,224,227],[2,26,224,227,425],[0,2,26,422,425],[2,26,224,422,425], [0,2,29,193,391],[0,2,29,193,589],[0,2,29,227,391],[0,2,29,425,589], [0,2,35,193,391],[0,2,35,193,589],[0,2,35,233,391],[0,2,35,431,589], [0,2,200,203,224],[2,200,203,224,422],[2,200,203,401,422],[0,2,200,224,227], [2,200,224,227,425],[2,200,224,422,425],[0,2,200,227,391],[0,2,200,233,391], [0,2,398,401,422],[2,200,398,401,422],[0,2,398,422,425],[2,200,398,422,425], [0,2,398,425,589],[0,2,398,431,589],[0,3,4,5,401],[0,3,4,202,400], [0,3,4,400,401],[0,3,5,26,224],[0,3,5,26,422],[0,3,5,203,224], [0,3,5,401,422],[0,3,24,26,224],[0,3,24,26,422],[0,3,24,222,224], [0,3,24,222,420],[0,3,24,420,422],[0,3,201,202,400],[0,3,201,203,224], [0,3,201,222,224],[0,3,201,222,420],[0,3,201,399,400],[0,3,399,400,401], [0,3,399,401,422],[0,3,201,399,420],[0,3,399,420,422],[0,24,26,29,227], [0,24,26,29,425],[0,24,26,224,227],[0,24,26,422,425],[0,24,27,29,227], [0,24,27,29,425],[0,24,27,225,227],[0,24,27,225,423],[0,24,27,423,425], [0,24,222,224,227],[0,24,222,225,227],[0,24,222,225,423],[0,24,420,422,425], [0,24,222,420,423],[0,24,420,423,425],[0,27,29,193,391],[0,27,29,193,589], [0,27,29,227,391],[0,27,29,425,589],[0,27,186,190,388],[0,27,186,190,586], [0,27,186,193,391],[0,27,186,193,589],[0,27,186,384,388],[0,27,186,384,391], [0,27,186,582,586],[0,27,186,582,589],[0,27,189,190,388],[0,27,189,190,586], [0,27,189,387,388],[0,27,189,387,585],[0,27,189,585,586],[0,27,225,227,391], [0,27,225,384,388],[0,27,225,384,391],[0,27,225,387,388],[0,27,225,387,585], [0,27,423,425,589],[0,27,423,582,586],[0,27,423,582,589],[0,27,225,423,585], [0,27,423,585,586],[0,33,34,35,431],[0,33,34,190,388],[0,33,34,190,586], [0,33,34,232,388],[0,33,34,430,431],[0,33,34,430,586],[0,33,35,193,391], [0,33,35,193,589],[0,33,35,233,391],[0,33,35,431,589],[0,33,186,190,388], [0,33,186,190,586],[0,33,186,193,391],[0,33,186,193,589],[0,33,186,384,388], [0,33,186,384,391],[0,33,186,582,586],[0,33,186,582,589],[0,33,231,232,388], [0,33,231,233,391],[0,33,231,384,388],[0,33,231,384,391],[0,33,429,430,431], [0,33,429,430,586],[0,33,429,431,589],[0,33,429,582,586],[0,33,429,582,589], [198,199,200,203,401],[198,199,200,233,431],[198,199,200,398,401],[198,199,200,398,431], [198,199,202,203,401],[0,198,199,202,400],[198,199,202,400,401],[198,199,232,233,431], [0,198,199,232,388],[198,199,232,388,586],[198,199,232,430,431],[198,199,232,430,586], [0,198,199,387,388],[198,199,387,388,586],[0,198,199,387,585],[198,199,387,585,586], [198,199,397,398,401],[198,199,397,398,431],[0,198,199,397,400],[198,199,397,400,401], [198,199,397,430,431],[198,199,397,430,586],[0,198,199,397,585],[198,199,397,585,586], [0,198,200,203,224],[198,200,203,224,422],[198,200,203,401,422],[0,198,200,224,227], [198,200,224,227,425],[198,200,224,422,425],[0,198,200,227,391],[198,200,227,391,589], [198,200,227,425,589],[0,198,200,233,391],[198,200,233,391,589],[198,200,233,431,589], [198,200,398,401,422],[198,200,398,422,425],[198,200,398,425,589],[198,200,398,431,589], [198,201,202,203,401],[0,198,201,202,400],[198,201,202,400,401],[0,198,201,203,224], [198,201,203,224,422],[198,201,203,401,422],[0,198,201,222,224],[198,201,222,224,422], [0,198,201,222,420],[198,201,222,420,422],[0,198,201,399,400],[198,201,399,400,401], [198,201,399,401,422],[0,198,201,399,420],[198,201,399,420,422],[0,198,222,224,227], [198,222,224,227,425],[198,222,224,422,425],[0,198,222,225,227],[198,222,225,227,425], [0,198,222,225,423],[198,222,225,423,425],[198,222,420,422,425],[0,198,222,420,423], [198,222,420,423,425],[0,198,225,227,391],[198,225,227,391,589],[198,225,227,425,589], [0,198,225,384,388],[198,225,384,388,586],[0,198,225,384,391],[198,225,384,391,589], [198,225,384,582,586],[198,225,384,582,589],[0,198,225,387,388],[198,225,387,388,586], [0,198,225,387,585],[198,225,387,585,586],[198,225,423,425,589],[198,225,423,582,586], [198,225,423,582,589],[0,198,225,423,585],[198,225,423,585,586],[198,231,232,233,431], [0,198,231,232,388],[198,231,232,388,586],[198,231,232,430,431],[198,231,232,430,586], [0,198,231,233,391],[198,231,233,391,589],[198,231,233,431,589],[0,198,231,384,388], [198,231,384,388,586],[0,198,231,384,391],[198,231,384,391,589],[198,231,384,582,586], [198,231,384,582,589],[198,231,429,430,431],[198,231,429,430,586],[198,231,429,431,589], [198,231,429,582,586],[198,231,429,582,589],[0,396,397,398,401],[198,396,397,398,401], [0,396,397,398,431],[198,396,397,398,431],[0,198,396,397,400],[0,396,397,400,401], [198,396,397,400,401],[0,396,397,430,431],[198,396,397,430,431],[0,396,397,430,586], [198,396,397,430,586],[0,198,396,397,585],[0,396,397,585,586],[198,396,397,585,586], [0,396,398,401,422],[198,396,398,401,422],[0,396,398,422,425],[198,396,398,422,425], [0,396,398,425,589],[198,396,398,425,589],[0,396,398,431,589],[198,396,398,431,589], [0,198,396,399,400],[0,396,399,400,401],[198,396,399,400,401],[0,396,399,401,422], [198,396,399,401,422],[0,198,396,399,420],[0,396,399,420,422],[198,396,399,420,422], [0,396,420,422,425],[198,396,420,422,425],[0,198,396,420,423],[0,396,420,423,425], [198,396,420,423,425],[0,396,423,425,589],[198,396,423,425,589],[0,396,423,582,586], [198,396,423,582,586],[0,396,423,582,589],[198,396,423,582,589],[0,198,396,423,585], [0,396,423,585,586],[198,396,423,585,586],[0,396,429,430,431],[198,396,429,430,431], [0,396,429,430,586],[198,396,429,430,586],[0,396,429,431,589],[198,396,429,431,589], [0,396,429,582,586],[198,396,429,582,586],[0,396,429,582,589],[198,396,429,582,589], [1,2,5,41,239],[1,2,5,41,437],[2,5,41,239,437],[1,2,5,203,239], [2,5,203,239,437],[1,2,5,401,437],[2,5,203,401,437],[1,2,35,193,391], [1,2,35,193,589],[1,2,35,233,391],[1,2,35,431,589],[1,2,38,41,239], [1,2,38,41,437],[2,38,41,239,437],[1,2,38,196,394],[1,2,38,196,592], [1,2,38,236,239],[2,38,236,239,437],[1,2,38,236,394],[1,2,38,434,437], [2,38,236,434,437],[1,2,38,434,592],[1,2,192,193,391],[1,2,192,193,589], [1,2,192,196,394],[1,2,192,196,592],[1,2,192,390,391],[1,2,192,390,394], [1,2,192,588,589],[1,2,192,588,592],[1,2,200,203,239],[2,200,203,239,437], [2,200,203,401,437],[1,2,200,233,391],[1,2,200,236,239],[2,200,236,239,437], [1,2,200,236,394],[2,200,236,434,437],[1,2,200,390,391],[1,2,200,390,394], [1,2,398,401,437],[2,200,398,401,437],[1,2,398,431,589],[1,2,398,434,437], [2,200,398,434,437],[1,2,398,434,592],[1,2,398,588,589],[1,2,398,588,592], [1,4,5,41,239],[1,4,5,41,437],[1,4,5,203,239],[1,4,5,401,437], [1,4,39,41,239],[1,4,39,41,437],[1,4,39,237,239],[1,4,39,237,435], [1,4,39,435,437],[1,4,202,203,239],[1,4,202,237,239],[1,4,202,237,435], [1,4,400,401,437],[1,4,202,400,435],[1,4,400,435,437],[1,34,35,193,391], [1,34,35,193,589],[1,34,35,233,391],[1,34,35,431,589],[1,34,187,190,388], [1,34,187,190,586],[1,34,187,193,391],[1,34,187,193,589],[1,34,187,385,388], [1,34,187,385,391],[1,34,187,583,586],[1,34,187,583,589],[1,34,232,233,391], [1,34,232,385,388],[1,34,232,385,391],[1,34,430,431,589],[1,34,430,583,586], [1,34,430,583,589],[1,36,38,41,239],[1,36,38,41,437],[1,36,38,196,394], [1,36,38,196,592],[1,36,38,236,239],[1,36,38,236,394],[1,36,38,434,437], [1,36,38,434,592],[1,36,39,41,239],[1,36,39,41,437],[1,36,39,237,239], [1,36,39,237,435],[1,36,39,435,437],[1,36,187,190,388],[1,36,187,190,586], [1,36,187,193,391],[1,36,187,193,589],[1,36,187,385,388],[1,36,187,385,391], [1,36,187,583,586],[1,36,187,583,589],[1,36,189,190,388],[1,36,189,190,586], [1,36,189,387,388],[1,36,189,387,585],[1,36,189,585,586],[1,36,192,193,391], [1,36,192,193,589],[1,36,192,196,394],[1,36,192,196,592],[1,36,192,390,391], [1,36,192,390,394],[1,36,192,588,589],[1,36,192,588,592],[1,36,234,236,239], [1,36,234,236,394],[1,36,234,237,239],[1,36,234,237,435],[1,36,234,385,388], [1,36,234,385,391],[1,36,234,387,388],[1,36,234,387,585],[1,36,234,390,391], [1,36,234,390,394],[1,36,432,434,437],[1,36,432,434,592],[1,36,234,432,435], [1,36,432,435,437],[1,36,432,583,586],[1,36,432,583,589],[1,36,234,432,585], [1,36,432,585,586],[1,36,432,588,589],[1,36,432,588,592],[1,199,200,203,239], [199,200,203,239,437],[199,200,203,401,437],[1,199,200,233,391],[199,200,233,391,589], [199,200,233,431,589],[1,199,200,236,239],[199,200,236,239,437],[1,199,200,236,394], [199,200,236,394,592],[199,200,236,434,437],[199,200,236,434,592],[1,199,200,390,391], [199,200,390,391,589],[1,199,200,390,394],[199,200,390,394,592],[199,200,390,588,589], [199,200,390,588,592],[199,200,398,401,437],[199,200,398,431,589],[199,200,398,434,437], [199,200,398,434,592],[199,200,398,588,589],[199,200,398,588,592],[1,199,202,203,239], [199,202,203,239,437],[199,202,203,401,437],[1,199,202,237,239],[199,202,237,239,437], [1,199,202,237,435],[199,202,237,435,437],[199,202,400,401,437],[1,199,202,400,435], [199,202,400,435,437],[1,199,232,233,391],[199,232,233,391,589],[199,232,233,431,589], [1,199,232,385,388],[199,232,385,388,586],[1,199,232,385,391],[199,232,385,391,589], [199,232,385,583,586],[199,232,385,583,589],[199,232,430,431,589],[199,232,430,583,586], [199,232,430,583,589],[1,199,234,236,239],[199,234,236,239,437],[1,199,234,236,394], [199,234,236,394,592],[199,234,236,434,437],[199,234,236,434,592],[1,199,234,237,239], [199,234,237,239,437],[1,199,234,237,435],[199,234,237,435,437],[1,199,234,385,388], [199,234,385,388,586],[1,199,234,385,391],[199,234,385,391,589],[199,234,385,583,586], [199,234,385,583,589],[1,199,234,387,388],[199,234,387,388,586],[1,199,234,387,585], [199,234,387,585,586],[1,199,234,390,391],[199,234,390,391,589],[1,199,234,390,394], [199,234,390,394,592],[199,234,390,588,589],[199,234,390,588,592],[199,234,432,434,437], [199,234,432,434,592],[1,199,234,432,435],[199,234,432,435,437],[199,234,432,583,586], [199,234,432,583,589],[1,199,234,432,585],[199,234,432,585,586],[199,234,432,588,589], [199,234,432,588,592],[1,397,398,401,437],[199,397,398,401,437],[1,397,398,431,589], [199,397,398,431,589],[1,397,398,434,437],[199,397,398,434,437],[1,397,398,434,592], [199,397,398,434,592],[1,397,398,588,589],[199,397,398,588,589],[1,397,398,588,592], [199,397,398,588,592],[1,397,400,401,437],[199,397,400,401,437],[1,199,397,400,435], [1,397,400,435,437],[199,397,400,435,437],[1,397,430,431,589],[199,397,430,431,589], [1,397,430,583,586],[199,397,430,583,586],[1,397,430,583,589],[199,397,430,583,589], [1,397,432,434,437],[199,397,432,434,437],[1,397,432,434,592],[199,397,432,434,592], [1,199,397,432,435],[1,397,432,435,437],[199,397,432,435,437],[1,397,432,583,586], [199,397,432,583,586],[1,397,432,583,589],[199,397,432,583,589],[1,199,397,432,585], [1,397,432,585,586],[199,397,432,585,586],[1,397,432,588,589],[199,397,432,588,589], [1,397,432,588,592],[199,397,432,588,592],[2,29,192,193,391],[2,29,192,193,589], [2,29,192,196,394],[2,29,192,196,592],[2,29,192,390,391],[2,29,192,390,394], [2,29,192,588,589],[2,29,192,588,592],[2,29,194,196,394],[2,29,194,196,592], [2,29,194,392,394],[2,29,194,392,590],[2,29,194,590,592],[2,29,227,390,391], [2,29,227,390,394],[2,29,227,392,394],[2,29,227,392,590],[2,29,425,588,589], [2,29,425,588,592],[2,29,227,425,590],[2,29,425,590,592],[2,38,194,196,394], [2,38,194,196,592],[2,38,194,392,394],[2,38,194,392,590],[2,38,194,590,592], [2,38,236,392,394],[2,38,236,392,590],[2,38,236,434,590],[2,38,434,590,592], [2,200,227,390,391],[200,227,390,391,589],[2,200,227,390,394],[200,227,390,394,592], [200,227,390,588,589],[200,227,390,588,592],[2,200,227,392,394],[200,227,392,394,592], [2,200,227,392,590],[200,227,392,590,592],[200,227,425,588,589],[200,227,425,588,592], [2,200,227,425,590],[200,227,425,590,592],[2,200,236,392,394],[200,236,392,394,592], [2,200,236,392,590],[200,236,392,590,592],[2,200,236,434,590],[200,236,434,590,592], [2,398,425,588,589],[200,398,425,588,589],[2,398,425,588,592],[200,398,425,588,592], [2,200,398,425,590],[2,398,425,590,592],[200,398,425,590,592],[2,200,398,434,590], [2,398,434,590,592],[200,398,434,590,592],[3,4,5,8,404],[3,4,5,401,404], [3,4,7,8,404],[3,4,7,190,388],[3,4,7,190,586],[3,4,7,205,388], [3,4,7,403,404],[3,4,7,403,586],[3,4,189,190,388],[3,4,189,190,586], [3,4,189,387,388],[3,4,189,387,585],[3,4,189,585,586],[3,4,202,205,388], [3,4,202,387,388],[3,4,202,387,585],[3,4,400,401,404],[3,4,400,403,404], [3,4,400,403,586],[3,4,202,400,585],[3,4,400,585,586],[3,5,8,23,221], [3,5,8,23,419],[5,8,23,221,419],[3,5,8,206,221],[5,8,206,221,419], [3,5,8,404,419],[5,8,206,404,419],[3,5,23,26,224],[3,5,23,26,422], [5,23,26,224,422],[3,5,23,221,224],[5,23,221,224,422],[3,5,23,419,422], [5,23,221,419,422],[3,5,203,206,221],[5,203,206,221,419],[5,203,206,404,419], [3,5,203,221,224],[5,203,221,224,422],[5,203,221,419,422],[3,5,401,404,419], [5,203,401,404,419],[3,5,401,419,422],[5,203,401,419,422],[3,6,7,8,404], [3,6,7,190,388],[3,6,7,190,586],[3,6,7,205,388],[3,6,7,403,404], [3,6,7,403,586],[3,6,8,23,221],[3,6,8,23,419],[3,6,8,206,221], [3,6,8,404,419],[3,6,21,23,221],[3,6,21,23,419],[3,6,21,190,388], [3,6,21,190,586],[3,6,21,219,221],[3,6,21,219,388],[3,6,21,417,419], [3,6,21,417,586],[3,6,204,205,388],[3,6,204,206,221],[3,6,204,219,221], [3,6,204,219,388],[3,6,402,403,404],[3,6,402,403,586],[3,6,402,404,419], [3,6,402,417,419],[3,6,402,417,586],[3,21,23,26,224],[3,21,23,26,422], [3,21,23,221,224],[3,21,23,419,422],[3,21,24,26,224],[3,21,24,26,422], [3,21,24,190,388],[3,21,24,190,586],[3,21,24,222,224],[3,21,24,222,388], [3,21,24,420,422],[3,21,24,420,586],[3,21,219,221,224],[3,21,219,222,224], [3,21,219,222,388],[3,21,417,419,422],[3,21,417,420,422],[3,21,417,420,586], [3,24,189,190,388],[3,24,189,190,586],[3,24,189,387,388],[3,24,189,387,585], [3,24,189,585,586],[3,24,222,387,388],[3,24,222,387,585],[3,24,222,420,585], [3,24,420,585,586],[201,202,203,206,404],[201,202,203,401,404],[201,202,205,206,404], [3,201,202,205,388],[201,202,205,388,586],[201,202,205,403,404],[201,202,205,403,586], [3,201,202,387,388],[201,202,387,388,586],[3,201,202,387,585],[201,202,387,585,586], [201,202,400,401,404],[201,202,400,403,404],[201,202,400,403,586],[3,201,202,400,585], [201,202,400,585,586],[3,201,203,206,221],[201,203,206,221,419],[201,203,206,404,419], [3,201,203,221,224],[201,203,221,224,422],[201,203,221,419,422],[201,203,401,404,419], [201,203,401,419,422],[201,204,205,206,404],[3,201,204,205,388],[201,204,205,388,586], [201,204,205,403,404],[201,204,205,403,586],[3,201,204,206,221],[201,204,206,221,419], 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[219,222,223,224,422],[21,219,222,223,388],[219,222,223,388,586],[219,222,223,421,422], [219,222,223,421,586],[219,222,420,421,422],[219,222,420,421,586],[21,417,418,419,422], [219,417,418,419,422],[21,417,418,421,422],[219,417,418,421,422],[21,417,418,421,586], [219,417,418,421,586],[21,219,417,418,584],[21,417,418,584,586],[219,417,418,584,586], [21,417,420,421,422],[219,417,420,421,422],[21,417,420,421,586],[219,417,420,421,586], [22,25,26,190,388],[22,25,26,190,586],[22,25,26,224,388],[22,25,26,422,586], [22,25,223,224,388],[22,25,421,422,586],[22,26,188,190,388],[22,26,188,190,586], [22,26,188,386,388],[22,26,188,386,584],[22,26,188,584,586],[22,26,224,386,388], [22,26,224,386,584],[22,26,224,422,584],[22,26,422,584,586],[22,220,223,224,388], [220,223,224,388,586],[220,223,224,422,586],[220,223,421,422,586],[22,220,224,386,388], [220,224,386,388,586],[22,220,224,386,584],[220,224,386,584,586],[22,220,224,422,584], [220,224,422,584,586],[22,418,421,422,586],[220,418,421,422,586],[22,220,418,422,584], [22,418,422,584,586],[220,418,422,584,586],[24,25,26,29,425],[24,25,26,422,425], [24,25,28,29,425],[24,25,28,226,424],[24,25,28,424,425],[24,25,189,190,388], [24,25,189,190,586],[24,25,189,387,388],[24,25,189,387,585],[24,25,189,585,586], [24,25,223,226,424],[24,25,223,387,388],[24,25,223,387,585],[24,25,421,422,425], [24,25,223,421,424],[24,25,421,424,425],[24,25,223,421,585],[24,25,421,585,586], [24,27,28,29,425],[24,27,28,226,424],[24,27,28,424,425],[24,27,225,226,424], [24,27,225,423,424],[24,27,423,424,425],[222,223,224,227,425],[222,223,224,422,425], [222,223,226,227,425],[24,222,223,226,424],[222,223,226,424,425],[24,222,223,387,388], [222,223,387,388,586],[24,222,223,387,585],[222,223,387,585,586],[222,223,421,422,425], [24,222,223,421,424],[222,223,421,424,425],[24,222,223,421,585],[222,223,421,585,586], [222,225,226,227,425],[24,222,225,226,424],[222,225,226,424,425],[24,222,225,423,424], [222,225,423,424,425],[24,420,421,422,425],[222,420,421,422,425],[24,222,420,421,424], [24,420,421,424,425],[222,420,421,424,425],[24,222,420,421,585],[24,420,421,585,586], [222,420,421,585,586],[24,222,420,423,424],[24,420,423,424,425],[222,420,423,424,425], [27,28,29,32,428],[27,28,29,425,428],[27,28,31,32,428],[27,28,31,190,388], [27,28,31,190,586],[27,28,31,229,388],[27,28,31,427,428],[27,28,31,427,586], [27,28,189,190,388],[27,28,189,190,586],[27,28,189,387,388],[27,28,189,387,585], [27,28,189,585,586],[27,28,226,229,388],[27,28,226,387,388],[27,28,226,387,585], [27,28,424,425,428],[27,28,424,427,428],[27,28,424,427,586],[27,28,226,424,585], [27,28,424,585,586],[27,29,32,193,391],[27,29,32,193,589],[27,29,32,230,391], [27,29,32,428,589],[27,29,227,230,391],[27,29,425,428,589],[27,30,31,32,428], [27,30,31,190,388],[27,30,31,190,586],[27,30,31,229,388],[27,30,31,427,428], [27,30,31,427,586],[27,30,32,193,391],[27,30,32,193,589],[27,30,32,230,391], 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[15,18,20,218,594],[15,18,19,217,594],[15,18,216,217,594],[15,18,216,218,594], [15,213,215,218,594],[213,214,215,218,594],[15,213,214,217,594],[213,214,217,218,594], [15,213,216,217,594],[15,213,216,218,594],[213,216,217,218,594],[18,20,23,221,594], [19,20,23,221,594],[18,20,218,221,594],[19,20,218,221,594],[19,22,23,221,594], [18,19,22,220,594],[19,22,220,221,594],[19,217,218,221,594],[18,19,217,220,594], [19,217,220,221,594],[18,21,23,221,594],[18,21,22,220,594],[18,21,219,220,594], [18,21,219,221,594],[18,216,218,221,594],[216,217,218,221,594],[18,216,217,220,594], [216,217,220,221,594],[18,216,219,220,594],[18,216,219,221,594],[216,219,220,221,594], [21,23,26,224,594],[22,23,26,224,594],[21,23,221,224,594],[22,23,221,224,594], [22,25,26,224,594],[21,22,25,223,594],[22,25,223,224,594],[22,220,221,224,594], [21,22,220,223,594],[22,220,223,224,594],[21,24,26,224,594],[21,24,25,223,594], [21,24,222,223,594],[21,24,222,224,594],[21,219,221,224,594],[219,220,221,224,594], [21,219,220,223,594],[219,220,223,224,594],[21,219,222,223,594],[21,219,222,224,594], [219,222,223,224,594],[24,26,29,227,594],[25,26,29,227,594],[24,26,224,227,594], [25,26,224,227,594],[25,28,29,227,594],[24,25,28,226,594],[25,28,226,227,594], [25,223,224,227,594],[24,25,223,226,594],[25,223,226,227,594],[24,27,29,227,594], [24,27,28,226,594],[24,27,225,226,594],[24,27,225,227,594],[24,222,224,227,594], [222,223,224,227,594],[24,222,223,226,594],[222,223,226,227,594],[24,222,225,226,594], [24,222,225,227,594],[222,225,226,227,594],[27,29,32,230,594],[28,29,32,230,594], [27,29,227,230,594],[28,29,227,230,594],[28,31,32,230,594],[27,28,31,229,594], [28,31,229,230,594],[28,226,227,230,594],[27,28,226,229,594],[28,226,229,230,594], [27,30,32,230,594],[27,30,31,229,594],[27,30,228,229,594],[27,30,228,230,594], [27,225,227,230,594],[225,226,227,230,594],[27,225,226,229,594],[225,226,229,230,594], [27,225,228,229,594],[27,225,228,230,594],[225,228,229,230,594],[30,32,35,233,594], [31,32,35,233,594],[30,32,230,233,594],[31,32,230,233,594],[31,34,35,233,594], [30,31,34,232,594],[31,34,232,233,594],[31,229,230,233,594],[30,31,229,232,594], [31,229,232,233,594],[30,33,35,233,594],[30,33,34,232,594],[30,33,231,232,594], [30,33,231,233,594],[30,228,230,233,594],[228,229,230,233,594],[30,228,229,232,594], [228,229,232,233,594],[30,228,231,232,594],[30,228,231,233,594],[228,231,232,233,594], [0,1,2,5,595],[1,2,5,594,595],[0,1,2,35,595],[1,2,35,594,595], [0,1,4,5,595],[0,1,4,594,595],[1,4,5,594,595],[0,1,34,35,595], [0,1,34,594,595],[1,34,35,594,595],[0,3,4,5,595],[0,3,4,594,595], [0,33,34,35,595],[0,33,34,594,595],[3,4,5,8,595],[4,5,8,594,595], [3,4,7,8,595],[3,4,7,594,595],[4,7,8,594,595],[3,6,7,8,595], [3,6,7,594,595],[6,7,8,11,595],[7,8,11,594,595],[6,7,10,11,595], [6,7,10,594,595],[7,10,11,594,595],[6,9,10,11,595],[6,9,10,594,595], [9,10,11,14,595],[10,11,14,594,595],[9,10,13,14,595],[9,10,13,594,595], [10,13,14,594,595],[9,12,13,14,595],[9,12,13,594,595],[12,13,14,17,595], [13,14,17,594,595],[12,13,16,17,595],[12,13,16,594,595],[13,16,17,594,595], [12,15,16,17,595],[12,15,16,594,595],[15,16,17,20,595],[16,17,20,594,595], [15,16,19,20,595],[15,16,19,594,595],[16,19,20,594,595],[15,18,19,20,595], [15,18,19,594,595],[18,19,20,23,595],[19,20,23,594,595],[18,19,22,23,595], [18,19,22,594,595],[19,22,23,594,595],[18,21,22,23,595],[18,21,22,594,595], [21,22,23,26,595],[22,23,26,594,595],[21,22,25,26,595],[21,22,25,594,595], [22,25,26,594,595],[21,24,25,26,595],[21,24,25,594,595],[24,25,26,29,595], [25,26,29,594,595],[24,25,28,29,595],[24,25,28,594,595],[25,28,29,594,595], [24,27,28,29,595],[24,27,28,594,595],[27,28,29,32,595],[28,29,32,594,595], [27,28,31,32,595],[27,28,31,594,595],[28,31,32,594,595],[27,30,31,32,595], [27,30,31,594,595],[30,31,32,35,595],[31,32,35,594,595],[30,31,34,35,595], [30,31,34,594,595],[31,34,35,594,595],[30,33,34,35,595],[30,33,34,594,595], [0,2,5,594,596],[0,2,5,595,596],[2,5,594,595,596],[0,2,35,594,596], [0,2,35,595,596],[2,35,594,595,596],[0,3,5,594,596],[0,3,5,595,596], [0,33,35,594,596],[0,33,35,595,596],[3,5,8,594,596],[3,5,8,595,596], [5,8,594,595,596],[3,6,8,594,596],[3,6,8,595,596],[6,8,11,594,596], [6,8,11,595,596],[8,11,594,595,596],[6,9,11,594,596],[6,9,11,595,596], [9,11,14,594,596],[9,11,14,595,596],[11,14,594,595,596],[9,12,14,594,596], [9,12,14,595,596],[12,14,17,594,596],[12,14,17,595,596],[14,17,594,595,596], [12,15,17,594,596],[12,15,17,595,596],[15,17,20,594,596],[15,17,20,595,596], [17,20,594,595,596],[15,18,20,594,596],[15,18,20,595,596],[18,20,23,594,596], [18,20,23,595,596],[20,23,594,595,596],[18,21,23,594,596],[18,21,23,595,596], [21,23,26,594,596],[21,23,26,595,596],[23,26,594,595,596],[21,24,26,594,596], [21,24,26,595,596],[24,26,29,594,596],[24,26,29,595,596],[26,29,594,595,596], [24,27,29,594,596],[24,27,29,595,596],[27,29,32,594,596],[27,29,32,595,596], [29,32,594,595,596],[27,30,32,594,596],[27,30,32,595,596],[30,32,35,594,596], [30,32,35,595,596],[32,35,594,595,596],[30,33,35,594,596],[30,33,35,595,596], [0,3,594,595,597],[0,3,594,596,597],[0,3,595,596,597],[0,33,594,595,597], [0,33,594,596,597],[0,33,595,596,597],[3,6,594,595,597],[3,6,594,596,597], [3,6,595,596,597],[6,9,594,595,597],[6,9,594,596,597],[6,9,595,596,597], [9,12,594,595,597],[9,12,594,596,597],[9,12,595,596,597],[12,15,594,595,597], [12,15,594,596,597],[12,15,595,596,597],[15,18,594,595,597],[15,18,594,596,597], [15,18,595,596,597],[18,21,594,595,597],[18,21,594,596,597],[18,21,595,596,597], [21,24,594,595,597],[21,24,594,596,597],[21,24,595,596,597],[24,27,594,595,597], [24,27,594,596,597],[24,27,595,596,597],[27,30,594,595,597],[27,30,594,596,597], [27,30,595,596,597],[30,33,594,595,597],[30,33,594,596,597],[30,33,595,596,597], [36,38,41,239,598],[37,38,41,239,598],[36,38,185,383,598],[37,38,185,383,598], [36,38,236,239,598],[37,38,236,239,598],[36,38,236,383,598],[37,38,236,383,598], [37,40,41,239,598],[36,37,40,238,598],[37,40,238,239,598],[37,184,185,383,598], [36,37,184,382,598],[37,184,382,383,598],[37,235,236,239,598],[37,235,236,383,598], [36,37,235,238,598],[37,235,238,239,598],[36,37,235,382,598],[37,235,382,383,598], [36,39,41,239,598],[36,39,40,238,598],[36,39,237,238,598],[36,39,237,239,598], [36,183,185,383,598],[36,183,184,382,598],[36,183,381,382,598],[36,183,381,383,598], [36,234,236,239,598],[234,235,236,239,598],[36,234,236,383,598],[234,235,236,383,598], [36,234,235,238,598],[234,235,238,239,598],[36,234,235,382,598],[234,235,382,383,598], [36,234,237,238,598],[36,234,237,239,598],[234,237,238,239,598],[36,234,381,382,598], [36,234,381,383,598],[234,381,382,383,598],[39,41,44,242,598],[40,41,44,242,598], [39,41,239,242,598],[40,41,239,242,598],[40,43,44,242,598],[39,40,43,241,598], [40,43,241,242,598],[40,238,239,242,598],[39,40,238,241,598],[40,238,241,242,598], [39,42,44,242,598],[39,42,43,241,598],[39,42,240,241,598],[39,42,240,242,598], [39,237,239,242,598],[237,238,239,242,598],[39,237,238,241,598],[237,238,241,242,598], [39,237,240,241,598],[39,237,240,242,598],[237,240,241,242,598],[42,44,47,245,598], [43,44,47,245,598],[42,44,242,245,598],[43,44,242,245,598],[43,46,47,245,598], [42,43,46,244,598],[43,46,244,245,598],[43,241,242,245,598],[42,43,241,244,598], [43,241,244,245,598],[42,45,47,245,598],[42,45,46,244,598],[42,45,243,244,598], [42,45,243,245,598],[42,240,242,245,598],[240,241,242,245,598],[42,240,241,244,598], [240,241,244,245,598],[42,240,243,244,598],[42,240,243,245,598],[240,243,244,245,598], [45,47,50,248,598],[46,47,50,248,598],[45,47,245,248,598],[46,47,245,248,598], [46,49,50,248,598],[45,46,49,247,598],[46,49,247,248,598],[46,244,245,248,598], [45,46,244,247,598],[46,244,247,248,598],[45,48,50,248,598],[45,48,49,247,598], [45,48,246,247,598],[45,48,246,248,598],[45,243,245,248,598],[243,244,245,248,598], [45,243,244,247,598],[243,244,247,248,598],[45,243,246,247,598],[45,243,246,248,598], [243,246,247,248,598],[48,50,53,251,598],[49,50,53,251,598],[48,50,248,251,598], [49,50,248,251,598],[49,52,53,251,598],[48,49,52,250,598],[49,52,250,251,598], [49,247,248,251,598],[48,49,247,250,598],[49,247,250,251,598],[48,51,53,251,598], [48,51,52,250,598],[48,51,249,250,598],[48,51,249,251,598],[48,246,248,251,598], [246,247,248,251,598],[48,246,247,250,598],[246,247,250,251,598],[48,246,249,250,598], [48,246,249,251,598],[246,249,250,251,598],[51,53,56,254,598],[52,53,56,254,598], [51,53,251,254,598],[52,53,251,254,598],[52,55,56,254,598],[51,52,55,253,598], [52,55,253,254,598],[52,250,251,254,598],[51,52,250,253,598],[52,250,253,254,598], [51,54,56,254,598],[51,54,55,253,598],[51,54,252,253,598],[51,54,252,254,598], [51,249,251,254,598],[249,250,251,254,598],[51,249,250,253,598],[249,250,253,254,598], [51,249,252,253,598],[51,249,252,254,598],[249,252,253,254,598],[54,56,59,257,598], [55,56,59,257,598],[54,56,254,257,598],[55,56,254,257,598],[55,58,59,257,598], [54,55,58,256,598],[55,58,256,257,598],[55,253,254,257,598],[54,55,253,256,598], [55,253,256,257,598],[54,57,59,257,598],[54,57,58,256,598],[54,57,255,256,598], [54,57,255,257,598],[54,252,254,257,598],[252,253,254,257,598],[54,252,253,256,598], [252,253,256,257,598],[54,252,255,256,598],[54,252,255,257,598],[252,255,256,257,598], [57,59,62,260,598],[58,59,62,260,598],[57,59,257,260,598],[58,59,257,260,598], [58,61,62,260,598],[57,58,61,259,598],[58,61,259,260,598],[58,256,257,260,598], [57,58,256,259,598],[58,256,259,260,598],[57,60,62,260,598],[57,60,61,259,598], [57,60,258,259,598],[57,60,258,260,598],[57,255,257,260,598],[255,256,257,260,598], [57,255,256,259,598],[255,256,259,260,598],[57,255,258,259,598],[57,255,258,260,598], [255,258,259,260,598],[60,62,65,263,598],[61,62,65,263,598],[60,62,260,263,598], [61,62,260,263,598],[61,64,65,263,598],[60,61,64,262,598],[61,64,262,263,598], [61,259,260,263,598],[60,61,259,262,598],[61,259,262,263,598],[60,63,65,263,598], [60,63,64,262,598],[60,63,261,262,598],[60,63,261,263,598],[60,258,260,263,598], [258,259,260,263,598],[60,258,259,262,598],[258,259,262,263,598],[60,258,261,262,598], [60,258,261,263,598],[258,261,262,263,598],[63,65,68,266,598],[64,65,68,266,598], [63,65,263,266,598],[64,65,263,266,598],[64,67,68,266,598],[63,64,67,265,598], [64,67,265,266,598],[64,262,263,266,598],[63,64,262,265,598],[64,262,265,266,598], [63,66,68,266,598],[63,66,67,265,598],[63,66,264,265,598],[63,66,264,266,598], [63,261,263,266,598],[261,262,263,266,598],[63,261,262,265,598],[261,262,265,266,598], [63,261,264,265,598],[63,261,264,266,598],[261,264,265,266,598],[66,68,71,269,598], [67,68,71,269,598],[66,68,266,269,598],[67,68,266,269,598],[67,70,71,269,598], [66,67,70,268,598],[67,70,268,269,598],[67,265,266,269,598],[66,67,265,268,598], [67,265,268,269,598],[66,69,71,269,598],[66,69,70,268,598],[66,69,267,268,598], [66,69,267,269,598],[66,264,266,269,598],[264,265,266,269,598],[66,264,265,268,598], [264,265,268,269,598],[66,264,267,268,598],[66,264,267,269,598],[264,267,268,269,598], [69,71,74,272,598],[70,71,74,272,598],[69,71,269,272,598],[70,71,269,272,598], [70,73,74,272,598],[69,70,73,271,598],[70,73,271,272,598],[70,268,269,272,598], [69,70,268,271,598],[70,268,271,272,598],[69,72,74,272,598],[69,72,73,271,598], [69,72,270,271,598],[69,72,270,272,598],[69,267,269,272,598],[267,268,269,272,598], [69,267,268,271,598],[267,268,271,272,598],[69,267,270,271,598],[69,267,270,272,598], [267,270,271,272,598],[72,74,77,275,598],[73,74,77,275,598],[72,74,272,275,598], [73,74,272,275,598],[73,76,77,275,598],[72,73,76,274,598],[73,76,274,275,598], [73,271,272,275,598],[72,73,271,274,598],[73,271,274,275,598],[72,75,77,275,598], [72,75,76,274,598],[72,75,273,274,598],[72,75,273,275,598],[72,270,272,275,598], [270,271,272,275,598],[72,270,271,274,598],[270,271,274,275,598],[72,270,273,274,598], 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