#################################################################################### #################################################################################### #################################################################################### ### ### ### ### ### TRIANGULATIONS OF AKBULUT-KIRBY SPHERES ### ### by Frank H. Lutz and Mimi Tsuruga ### ### http://matsguru.com/research/AKspheres.html ### ### ### ### name of example: ### ### ### ### AK_II_013 ### ### ### ### ### ### description: ### ### ### ### Type 2 construction of triangulation of Akbulut-Kirby sphere ### ### ### ### ### ### properties: ### ### ### ### f=(800,12054,40236,48300,19320) ### ### 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],[0,1,4,202,598],[0,1,4,400,401],[0,1,4,400,598], [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],[0,1,189,387,783],[0,1,189,585,586],[0,1,189,585,783], [0,1,199,202,598],[0,1,199,232,388],[0,1,199,387,388],[0,1,199,387,783], [0,1,199,595,598],[0,1,199,595,783],[0,1,397,398,401],[0,1,397,398,431], [0,1,397,400,401],[0,1,397,400,598],[0,1,397,430,431],[0,1,397,430,586], [0,1,397,585,586],[0,1,397,585,783],[0,1,397,595,598],[0,1,397,595,783], [0,2,5,26,224],[2,5,26,224,620],[0,2,5,26,422],[2,5,26,422,620], [0,2,5,203,224],[2,5,203,224,620],[2,5,203,599,620],[0,2,5,401,422], [2,5,401,422,620],[2,5,401,599,620],[0,2,26,29,227],[2,26,29,227,623], [0,2,26,29,425],[2,26,29,425,623],[0,2,26,224,227],[2,26,224,227,623], [2,26,224,620,623],[0,2,26,422,425],[2,26,422,425,623],[2,26,422,620,623], [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],[2,200,203,224,620],[2,200,203,599,620],[0,2,200,224,227], [2,200,224,227,623],[2,200,224,620,623],[0,2,200,227,391],[0,2,200,233,391], [2,200,596,599,620],[2,200,596,620,623],[0,2,398,401,422],[2,398,401,422,620], [2,398,401,599,620],[0,2,398,422,425],[2,398,422,425,623],[2,398,422,620,623], [0,2,398,425,589],[0,2,398,431,589],[2,398,596,599,620],[2,398,596,620,623], [0,3,4,5,401],[0,3,4,202,598],[0,3,4,400,401],[0,3,4,400,598], [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],[0,3,24,222,618], [0,3,24,420,422],[0,3,24,420,618],[0,3,201,202,598],[0,3,201,203,224], [0,3,201,222,224],[0,3,201,222,618],[0,3,201,597,598],[0,3,201,597,618], [0,3,399,400,401],[0,3,399,400,598],[0,3,399,401,422],[0,3,399,420,422], [0,3,399,420,618],[0,3,399,597,598],[0,3,399,597,618],[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],[0,24,27,225,621],[0,24,27,423,425], [0,24,27,423,621],[0,24,222,224,227],[0,24,222,225,227],[0,24,222,225,621], [0,24,222,618,621],[0,24,420,422,425],[0,24,420,423,425],[0,24,420,423,621], [0,24,420,618,621],[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], [0,27,189,387,783],[0,27,189,585,586],[0,27,189,585,783],[0,27,225,227,391], [0,27,225,384,388],[0,27,225,384,391],[0,27,225,387,388],[0,27,225,387,783], [0,27,225,621,783],[0,27,423,425,589],[0,27,423,582,586],[0,27,423,582,589], [0,27,423,585,586],[0,27,423,585,783],[0,27,423,621,783],[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],[198,199,200,203,599],[198,199,200,233,629], [198,199,200,596,599],[198,199,200,596,629],[198,199,202,203,599],[0,198,199,202,598], [198,199,202,598,599],[198,199,232,233,629],[0,198,199,232,388],[198,199,232,388,784], [198,199,232,628,629],[198,199,232,628,784],[0,198,199,387,388],[198,199,387,388,784], [0,198,199,387,783],[198,199,387,783,784],[198,199,595,596,599],[198,199,595,596,629], [0,198,199,595,598],[198,199,595,598,599],[198,199,595,628,629],[198,199,595,628,784], [0,198,199,595,783],[198,199,595,783,784],[0,198,200,203,224],[198,200,203,224,620], [198,200,203,599,620],[0,198,200,224,227],[198,200,224,227,623],[198,200,224,620,623], [0,198,200,227,391],[198,200,227,391,787],[198,200,227,623,787],[0,198,200,233,391], [198,200,233,391,787],[198,200,233,629,787],[198,200,596,599,620],[198,200,596,620,623], [198,200,596,623,787],[198,200,596,629,787],[198,201,202,203,599],[0,198,201,202,598], [198,201,202,598,599],[0,198,201,203,224],[198,201,203,224,620],[198,201,203,599,620], [0,198,201,222,224],[198,201,222,224,620],[0,198,201,222,618],[198,201,222,618,620], [0,198,201,597,598],[198,201,597,598,599],[198,201,597,599,620],[0,198,201,597,618], [198,201,597,618,620],[0,198,222,224,227],[198,222,224,227,623],[198,222,224,620,623], [0,198,222,225,227],[198,222,225,227,623],[0,198,222,225,621],[198,222,225,621,623], [198,222,618,620,623],[0,198,222,618,621],[198,222,618,621,623],[0,198,225,227,391], [198,225,227,391,787],[198,225,227,623,787],[0,198,225,384,388],[198,225,384,388,784], [0,198,225,384,391],[198,225,384,391,787],[198,225,384,780,784],[198,225,384,780,787], [0,198,225,387,388],[198,225,387,388,784],[0,198,225,387,783],[198,225,387,783,784], [198,225,621,623,787],[198,225,621,780,784],[198,225,621,780,787],[0,198,225,621,783], [198,225,621,783,784],[198,231,232,233,629],[0,198,231,232,388],[198,231,232,388,784], [198,231,232,628,629],[198,231,232,628,784],[0,198,231,233,391],[198,231,233,391,787], [198,231,233,629,787],[0,198,231,384,388],[198,231,384,388,784],[0,198,231,384,391], [198,231,384,391,787],[198,231,384,780,784],[198,231,384,780,787],[198,231,627,628,629], [198,231,627,628,784],[198,231,627,629,787],[198,231,627,780,784],[198,231,627,780,787], [198,594,595,596,599],[198,594,595,596,629],[0,198,594,595,598],[198,594,595,598,599], [198,594,595,628,629],[198,594,595,628,784],[0,198,594,595,783],[198,594,595,783,784], [198,594,596,599,620],[198,594,596,620,623],[198,594,596,623,787],[198,594,596,629,787], [0,198,594,597,598],[198,594,597,598,599],[198,594,597,599,620],[0,198,594,597,618], [198,594,597,618,620],[198,594,618,620,623],[0,198,594,618,621],[198,594,618,621,623], [198,594,621,623,787],[198,594,621,780,784],[198,594,621,780,787],[0,198,594,621,783], [198,594,621,783,784],[198,594,627,628,629],[198,594,627,628,784],[198,594,627,629,787], [198,594,627,780,784],[198,594,627,780,787],[0,396,397,398,401],[396,397,398,401,599], [0,396,397,398,431],[396,397,398,431,629],[396,397,398,596,599],[396,397,398,596,629], [0,396,397,400,401],[396,397,400,401,599],[0,396,397,400,598],[396,397,400,598,599], [0,396,397,430,431],[396,397,430,431,629],[0,396,397,430,586],[396,397,430,586,784], [396,397,430,628,629],[396,397,430,628,784],[0,396,397,585,586],[396,397,585,586,784], [0,396,397,585,783],[396,397,585,783,784],[396,397,595,596,599],[396,397,595,596,629], [0,396,397,595,598],[396,397,595,598,599],[396,397,595,628,629],[396,397,595,628,784], [0,396,397,595,783],[396,397,595,783,784],[0,396,398,401,422],[396,398,401,422,620], [396,398,401,599,620],[0,396,398,422,425],[396,398,422,425,623],[396,398,422,620,623], [0,396,398,425,589],[396,398,425,589,787],[396,398,425,623,787],[0,396,398,431,589], [396,398,431,589,787],[396,398,431,629,787],[396,398,596,599,620],[396,398,596,620,623], [396,398,596,623,787],[396,398,596,629,787],[0,396,399,400,401],[396,399,400,401,599], [0,396,399,400,598],[396,399,400,598,599],[0,396,399,401,422],[396,399,401,422,620], [396,399,401,599,620],[0,396,399,420,422],[396,399,420,422,620],[0,396,399,420,618], [396,399,420,618,620],[0,396,399,597,598],[396,399,597,598,599],[396,399,597,599,620], [0,396,399,597,618],[396,399,597,618,620],[0,396,420,422,425],[396,420,422,425,623], [396,420,422,620,623],[0,396,420,423,425],[396,420,423,425,623],[0,396,420,423,621], [396,420,423,621,623],[396,420,618,620,623],[0,396,420,618,621],[396,420,618,621,623], [0,396,423,425,589],[396,423,425,589,787],[396,423,425,623,787],[0,396,423,582,586], [396,423,582,586,784],[0,396,423,582,589],[396,423,582,589,787],[396,423,582,780,784], [396,423,582,780,787],[0,396,423,585,586],[396,423,585,586,784],[0,396,423,585,783], [396,423,585,783,784],[396,423,621,623,787],[396,423,621,780,784],[396,423,621,780,787], [0,396,423,621,783],[396,423,621,783,784],[0,396,429,430,431],[396,429,430,431,629], [0,396,429,430,586],[396,429,430,586,784],[396,429,430,628,629],[396,429,430,628,784], [0,396,429,431,589],[396,429,431,589,787],[396,429,431,629,787],[0,396,429,582,586], [396,429,582,586,784],[0,396,429,582,589],[396,429,582,589,787],[396,429,582,780,784], [396,429,582,780,787],[396,429,627,628,629],[396,429,627,628,784],[396,429,627,629,787], [396,429,627,780,784],[396,429,627,780,787],[396,594,595,596,599],[396,594,595,596,629], [0,396,594,595,598],[396,594,595,598,599],[396,594,595,628,629],[396,594,595,628,784], [0,396,594,595,783],[396,594,595,783,784],[396,594,596,599,620],[396,594,596,620,623], [396,594,596,623,787],[396,594,596,629,787],[0,396,594,597,598],[396,594,597,598,599], [396,594,597,599,620],[0,396,594,597,618],[396,594,597,618,620],[396,594,618,620,623], [0,396,594,618,621],[396,594,618,621,623],[396,594,621,623,787],[396,594,621,780,784], [396,594,621,780,787],[0,396,594,621,783],[396,594,621,783,784],[396,594,627,628,629], [396,594,627,628,784],[396,594,627,629,787],[396,594,627,780,784],[396,594,627,780,787], [1,2,5,41,239],[2,5,41,239,635],[1,2,5,41,437],[2,5,41,437,635], [1,2,5,203,239],[2,5,203,239,635],[2,5,203,599,635],[1,2,5,401,437], [2,5,401,437,635],[2,5,401,599,635],[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],[2,38,41,239,635], [1,2,38,41,437],[2,38,41,437,635],[1,2,38,196,394],[1,2,38,196,592], [1,2,38,236,239],[2,38,236,239,635],[1,2,38,236,394],[2,38,236,632,635], [1,2,38,434,437],[2,38,434,437,635],[1,2,38,434,592],[2,38,434,632,635], [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],[2,200,203,239,635],[2,200,203,599,635],[1,2,200,233,391], [1,2,200,236,239],[2,200,236,239,635],[1,2,200,236,394],[2,200,236,632,635], [1,2,200,390,391],[1,2,200,390,394],[2,200,596,599,635],[2,200,596,632,635], [1,2,398,401,437],[2,398,401,437,635],[2,398,401,599,635],[1,2,398,431,589], [1,2,398,434,437],[2,398,434,437,635],[1,2,398,434,592],[2,398,434,632,635], [1,2,398,588,589],[1,2,398,588,592],[2,398,596,599,635],[2,398,596,632,635], [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],[1,4,39,237,633], [1,4,39,435,437],[1,4,39,435,633],[1,4,202,203,239],[1,4,202,237,239], [1,4,202,237,633],[1,4,202,598,633],[1,4,400,401,437],[1,4,400,435,437], [1,4,400,435,633],[1,4,400,598,633],[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],[1,36,39,237,633], [1,36,39,435,437],[1,36,39,435,633],[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],[1,36,189,387,783],[1,36,189,585,586],[1,36,189,585,783], [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],[1,36,234,237,633], [1,36,234,385,388],[1,36,234,385,391],[1,36,234,387,388],[1,36,234,387,783], [1,36,234,390,391],[1,36,234,390,394],[1,36,234,630,633],[1,36,234,630,783], [1,36,432,434,437],[1,36,432,434,592],[1,36,432,435,437],[1,36,432,435,633], [1,36,432,583,586],[1,36,432,583,589],[1,36,432,585,586],[1,36,432,585,783], 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[183,184,195,591,592],[183,184,195,591,789],[183,184,382,393,394],[183,184,382,393,789], [183,184,382,778,789],[183,184,580,591,592],[183,184,580,591,789],[183,184,580,778,789], [183,185,195,196,394],[183,185,195,196,592],[183,185,195,393,394],[183,185,195,393,789], [183,185,195,591,592],[183,185,195,591,789],[183,185,383,393,394],[183,185,383,393,789], [183,185,383,779,789],[183,185,581,591,592],[183,185,581,591,789],[183,185,581,779,789], [183,381,382,393,394],[381,382,393,394,790],[183,381,382,393,789],[381,382,393,789,790], [183,381,382,778,789],[381,382,778,789,790],[183,381,383,393,394],[381,383,393,394,790], [183,381,383,393,789],[381,383,393,789,790],[183,381,383,779,789],[381,383,779,789,790], [183,381,777,778,789],[381,777,778,789,790],[183,381,777,779,789],[381,777,779,789,790], [183,579,580,591,592],[579,580,591,592,790],[183,579,580,591,789],[579,580,591,789,790], [183,579,580,778,789],[579,580,778,789,790],[183,579,581,591,592],[579,581,591,592,790], [183,579,581,591,789],[579,581,591,789,790],[183,579,581,779,789],[579,581,779,789,790], [183,579,777,778,789],[579,777,778,789,790],[183,579,777,779,789],[579,777,779,789,790], [0,2,5,203,792],[1,2,5,203,792],[0,2,35,233,792],[1,2,35,233,792], [0,2,200,203,792],[1,2,200,203,792],[0,2,200,233,792],[1,2,200,233,792], [1,4,5,203,792],[0,1,4,202,792],[1,4,202,203,792],[1,34,35,233,792], [0,1,34,232,792],[1,34,232,233,792],[1,199,200,203,792],[1,199,200,233,792], [0,1,199,202,792],[1,199,202,203,792],[0,1,199,232,792],[1,199,232,233,792], [0,3,5,203,792],[0,3,4,202,792],[0,3,201,202,792],[0,3,201,203,792], [0,33,35,233,792],[0,33,34,232,792],[0,33,231,232,792],[0,33,231,233,792], [0,198,200,203,792],[198,199,200,203,792],[0,198,200,233,792],[198,199,200,233,792], [0,198,199,202,792],[198,199,202,203,792],[0,198,199,232,792],[198,199,232,233,792], [0,198,201,202,792],[0,198,201,203,792],[198,201,202,203,792],[0,198,231,232,792], [0,198,231,233,792],[198,231,232,233,792],[3,5,8,206,792],[4,5,8,206,792], [3,5,203,206,792],[4,5,203,206,792],[4,7,8,206,792],[3,4,7,205,792], [4,7,205,206,792],[4,202,203,206,792],[3,4,202,205,792],[4,202,205,206,792], [3,6,8,206,792],[3,6,7,205,792],[3,6,204,205,792],[3,6,204,206,792], [3,201,203,206,792],[201,202,203,206,792],[3,201,202,205,792],[201,202,205,206,792], [3,201,204,205,792],[3,201,204,206,792],[201,204,205,206,792],[6,8,11,209,792], [7,8,11,209,792],[6,8,206,209,792],[7,8,206,209,792],[7,10,11,209,792], [6,7,10,208,792],[7,10,208,209,792],[7,205,206,209,792],[6,7,205,208,792], [7,205,208,209,792],[6,9,11,209,792],[6,9,10,208,792],[6,9,207,208,792], [6,9,207,209,792],[6,204,206,209,792],[204,205,206,209,792],[6,204,205,208,792], [204,205,208,209,792],[6,204,207,208,792],[6,204,207,209,792],[204,207,208,209,792], [9,11,14,212,792],[10,11,14,212,792],[9,11,209,212,792],[10,11,209,212,792], [10,13,14,212,792],[9,10,13,211,792],[10,13,211,212,792],[10,208,209,212,792], [9,10,208,211,792],[10,208,211,212,792],[9,12,14,212,792],[9,12,13,211,792], [9,12,210,211,792],[9,12,210,212,792],[9,207,209,212,792],[207,208,209,212,792], [9,207,208,211,792],[207,208,211,212,792],[9,207,210,211,792],[9,207,210,212,792], [207,210,211,212,792],[12,14,17,215,792],[13,14,17,215,792],[12,14,212,215,792], [13,14,212,215,792],[13,16,17,215,792],[12,13,16,214,792],[13,16,214,215,792], [13,211,212,215,792],[12,13,211,214,792],[13,211,214,215,792],[12,15,17,215,792], [12,15,16,214,792],[12,15,213,214,792],[12,15,213,215,792],[12,210,212,215,792], [210,211,212,215,792],[12,210,211,214,792],[210,211,214,215,792],[12,210,213,214,792], [12,210,213,215,792],[210,213,214,215,792],[15,17,20,218,792],[16,17,20,218,792], [15,17,215,218,792],[16,17,215,218,792],[16,19,20,218,792],[15,16,19,217,792], [16,19,217,218,792],[16,214,215,218,792],[15,16,214,217,792],[16,214,217,218,792], [15,18,20,218,792],[15,18,19,217,792],[15,18,216,217,792],[15,18,216,218,792], [15,213,215,218,792],[213,214,215,218,792],[15,213,214,217,792],[213,214,217,218,792], [15,213,216,217,792],[15,213,216,218,792],[213,216,217,218,792],[18,20,23,221,792], [19,20,23,221,792],[18,20,218,221,792],[19,20,218,221,792],[19,22,23,221,792], [18,19,22,220,792],[19,22,220,221,792],[19,217,218,221,792],[18,19,217,220,792], [19,217,220,221,792],[18,21,23,221,792],[18,21,22,220,792],[18,21,219,220,792], [18,21,219,221,792],[18,216,218,221,792],[216,217,218,221,792],[18,216,217,220,792], [216,217,220,221,792],[18,216,219,220,792],[18,216,219,221,792],[216,219,220,221,792], [21,23,26,224,792],[22,23,26,224,792],[21,23,221,224,792],[22,23,221,224,792], [22,25,26,224,792],[21,22,25,223,792],[22,25,223,224,792],[22,220,221,224,792], [21,22,220,223,792],[22,220,223,224,792],[21,24,26,224,792],[21,24,25,223,792], [21,24,222,223,792],[21,24,222,224,792],[21,219,221,224,792],[219,220,221,224,792], [21,219,220,223,792],[219,220,223,224,792],[21,219,222,223,792],[21,219,222,224,792], [219,222,223,224,792],[24,26,29,227,792],[25,26,29,227,792],[24,26,224,227,792], [25,26,224,227,792],[25,28,29,227,792],[24,25,28,226,792],[25,28,226,227,792], [25,223,224,227,792],[24,25,223,226,792],[25,223,226,227,792],[24,27,29,227,792], [24,27,28,226,792],[24,27,225,226,792],[24,27,225,227,792],[24,222,224,227,792], [222,223,224,227,792],[24,222,223,226,792],[222,223,226,227,792],[24,222,225,226,792], [24,222,225,227,792],[222,225,226,227,792],[27,29,32,230,792],[28,29,32,230,792], [27,29,227,230,792],[28,29,227,230,792],[28,31,32,230,792],[27,28,31,229,792], [28,31,229,230,792],[28,226,227,230,792],[27,28,226,229,792],[28,226,229,230,792], [27,30,32,230,792],[27,30,31,229,792],[27,30,228,229,792],[27,30,228,230,792], [27,225,227,230,792],[225,226,227,230,792],[27,225,226,229,792],[225,226,229,230,792], [27,225,228,229,792],[27,225,228,230,792],[225,228,229,230,792],[30,32,35,233,792], [31,32,35,233,792],[30,32,230,233,792],[31,32,230,233,792],[31,34,35,233,792], [30,31,34,232,792],[31,34,232,233,792],[31,229,230,233,792],[30,31,229,232,792], [31,229,232,233,792],[30,33,35,233,792],[30,33,34,232,792],[30,33,231,232,792], [30,33,231,233,792],[30,228,230,233,792],[228,229,230,233,792],[30,228,229,232,792], [228,229,232,233,792],[30,228,231,232,792],[30,228,231,233,792],[228,231,232,233,792], [0,1,2,5,793],[1,2,5,792,793],[0,1,2,35,793],[1,2,35,792,793], [0,1,4,5,793],[0,1,4,792,793],[1,4,5,792,793],[0,1,34,35,793], [0,1,34,792,793],[1,34,35,792,793],[0,3,4,5,793],[0,3,4,792,793], [0,33,34,35,793],[0,33,34,792,793],[3,4,5,8,793],[4,5,8,792,793], [3,4,7,8,793],[3,4,7,792,793],[4,7,8,792,793],[3,6,7,8,793], [3,6,7,792,793],[6,7,8,11,793],[7,8,11,792,793],[6,7,10,11,793], [6,7,10,792,793],[7,10,11,792,793],[6,9,10,11,793],[6,9,10,792,793], [9,10,11,14,793],[10,11,14,792,793],[9,10,13,14,793],[9,10,13,792,793], [10,13,14,792,793],[9,12,13,14,793],[9,12,13,792,793],[12,13,14,17,793], [13,14,17,792,793],[12,13,16,17,793],[12,13,16,792,793],[13,16,17,792,793], [12,15,16,17,793],[12,15,16,792,793],[15,16,17,20,793],[16,17,20,792,793], [15,16,19,20,793],[15,16,19,792,793],[16,19,20,792,793],[15,18,19,20,793], [15,18,19,792,793],[18,19,20,23,793],[19,20,23,792,793],[18,19,22,23,793], [18,19,22,792,793],[19,22,23,792,793],[18,21,22,23,793],[18,21,22,792,793], [21,22,23,26,793],[22,23,26,792,793],[21,22,25,26,793],[21,22,25,792,793], [22,25,26,792,793],[21,24,25,26,793],[21,24,25,792,793],[24,25,26,29,793], [25,26,29,792,793],[24,25,28,29,793],[24,25,28,792,793],[25,28,29,792,793], [24,27,28,29,793],[24,27,28,792,793],[27,28,29,32,793],[28,29,32,792,793], [27,28,31,32,793],[27,28,31,792,793],[28,31,32,792,793],[27,30,31,32,793], [27,30,31,792,793],[30,31,32,35,793],[31,32,35,792,793],[30,31,34,35,793], [30,31,34,792,793],[31,34,35,792,793],[30,33,34,35,793],[30,33,34,792,793], [0,2,5,792,794],[0,2,5,793,794],[2,5,792,793,794],[0,2,35,792,794], [0,2,35,793,794],[2,35,792,793,794],[0,3,5,792,794],[0,3,5,793,794], [0,33,35,792,794],[0,33,35,793,794],[3,5,8,792,794],[3,5,8,793,794], [5,8,792,793,794],[3,6,8,792,794],[3,6,8,793,794],[6,8,11,792,794], [6,8,11,793,794],[8,11,792,793,794],[6,9,11,792,794],[6,9,11,793,794], [9,11,14,792,794],[9,11,14,793,794],[11,14,792,793,794],[9,12,14,792,794], [9,12,14,793,794],[12,14,17,792,794],[12,14,17,793,794],[14,17,792,793,794], [12,15,17,792,794],[12,15,17,793,794],[15,17,20,792,794],[15,17,20,793,794], [17,20,792,793,794],[15,18,20,792,794],[15,18,20,793,794],[18,20,23,792,794], [18,20,23,793,794],[20,23,792,793,794],[18,21,23,792,794],[18,21,23,793,794], [21,23,26,792,794],[21,23,26,793,794],[23,26,792,793,794],[21,24,26,792,794], [21,24,26,793,794],[24,26,29,792,794],[24,26,29,793,794],[26,29,792,793,794], [24,27,29,792,794],[24,27,29,793,794],[27,29,32,792,794],[27,29,32,793,794], [29,32,792,793,794],[27,30,32,792,794],[27,30,32,793,794],[30,32,35,792,794], [30,32,35,793,794],[32,35,792,793,794],[30,33,35,792,794],[30,33,35,793,794], [0,3,792,793,795],[0,3,792,794,795],[0,3,793,794,795],[0,33,792,793,795], [0,33,792,794,795],[0,33,793,794,795],[3,6,792,793,795],[3,6,792,794,795], [3,6,793,794,795],[6,9,792,793,795],[6,9,792,794,795],[6,9,793,794,795], [9,12,792,793,795],[9,12,792,794,795],[9,12,793,794,795],[12,15,792,793,795], [12,15,792,794,795],[12,15,793,794,795],[15,18,792,793,795],[15,18,792,794,795], [15,18,793,794,795],[18,21,792,793,795],[18,21,792,794,795],[18,21,793,794,795], [21,24,792,793,795],[21,24,792,794,795],[21,24,793,794,795],[24,27,792,793,795], [24,27,792,794,795],[24,27,793,794,795],[27,30,792,793,795],[27,30,792,794,795], [27,30,793,794,795],[30,33,792,793,795],[30,33,792,794,795],[30,33,793,794,795], [36,38,41,239,796],[37,38,41,239,796],[36,38,185,383,796],[37,38,185,383,796], [36,38,236,239,796],[37,38,236,239,796],[36,38,236,383,796],[37,38,236,383,796], [37,40,41,239,796],[36,37,40,238,796],[37,40,238,239,796],[37,184,185,383,796], [36,37,184,382,796],[37,184,382,383,796],[37,235,236,239,796],[37,235,236,383,796], [36,37,235,238,796],[37,235,238,239,796],[36,37,235,382,796],[37,235,382,383,796], [36,39,41,239,796],[36,39,40,238,796],[36,39,237,238,796],[36,39,237,239,796], [36,183,185,383,796],[36,183,184,382,796],[36,183,381,382,796],[36,183,381,383,796], [36,234,236,239,796],[234,235,236,239,796],[36,234,236,383,796],[234,235,236,383,796], [36,234,235,238,796],[234,235,238,239,796],[36,234,235,382,796],[234,235,382,383,796], [36,234,237,238,796],[36,234,237,239,796],[234,237,238,239,796],[36,234,381,382,796], [36,234,381,383,796],[234,381,382,383,796],[39,41,44,242,796],[40,41,44,242,796], [39,41,239,242,796],[40,41,239,242,796],[40,43,44,242,796],[39,40,43,241,796], [40,43,241,242,796],[40,238,239,242,796],[39,40,238,241,796],[40,238,241,242,796], [39,42,44,242,796],[39,42,43,241,796],[39,42,240,241,796],[39,42,240,242,796], [39,237,239,242,796],[237,238,239,242,796],[39,237,238,241,796],[237,238,241,242,796], [39,237,240,241,796],[39,237,240,242,796],[237,240,241,242,796],[42,44,47,245,796], [43,44,47,245,796],[42,44,242,245,796],[43,44,242,245,796],[43,46,47,245,796], [42,43,46,244,796],[43,46,244,245,796],[43,241,242,245,796],[42,43,241,244,796], [43,241,244,245,796],[42,45,47,245,796],[42,45,46,244,796],[42,45,243,244,796], [42,45,243,245,796],[42,240,242,245,796],[240,241,242,245,796],[42,240,241,244,796], [240,241,244,245,796],[42,240,243,244,796],[42,240,243,245,796],[240,243,244,245,796], [45,47,50,248,796],[46,47,50,248,796],[45,47,245,248,796],[46,47,245,248,796], [46,49,50,248,796],[45,46,49,247,796],[46,49,247,248,796],[46,244,245,248,796], [45,46,244,247,796],[46,244,247,248,796],[45,48,50,248,796],[45,48,49,247,796], [45,48,246,247,796],[45,48,246,248,796],[45,243,245,248,796],[243,244,245,248,796], [45,243,244,247,796],[243,244,247,248,796],[45,243,246,247,796],[45,243,246,248,796], 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[54,55,58,256,796],[55,58,256,257,796],[55,253,254,257,796],[54,55,253,256,796], [55,253,256,257,796],[54,57,59,257,796],[54,57,58,256,796],[54,57,255,256,796], [54,57,255,257,796],[54,252,254,257,796],[252,253,254,257,796],[54,252,253,256,796], [252,253,256,257,796],[54,252,255,256,796],[54,252,255,257,796],[252,255,256,257,796], [57,59,62,260,796],[58,59,62,260,796],[57,59,257,260,796],[58,59,257,260,796], [58,61,62,260,796],[57,58,61,259,796],[58,61,259,260,796],[58,256,257,260,796], [57,58,256,259,796],[58,256,259,260,796],[57,60,62,260,796],[57,60,61,259,796], [57,60,258,259,796],[57,60,258,260,796],[57,255,257,260,796],[255,256,257,260,796], [57,255,256,259,796],[255,256,259,260,796],[57,255,258,259,796],[57,255,258,260,796], [255,258,259,260,796],[60,62,65,263,796],[61,62,65,263,796],[60,62,260,263,796], [61,62,260,263,796],[61,64,65,263,796],[60,61,64,262,796],[61,64,262,263,796], [61,259,260,263,796],[60,61,259,262,796],[61,259,262,263,796],[60,63,65,263,796], 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