#################################################################################### #################################################################################### #################################################################################### ### ### ### ### ### TRIANGULATIONS OF AKBULUT-KIRBY SPHERES ### ### by Frank H. Lutz and Mimi Tsuruga ### ### http://matsguru.com/research/AKspheres.html ### ### ### ### name of example: ### ### ### ### AK_III_012 ### ### ### ### ### ### description: ### ### ### ### Type 3 construction of triangulation of Akbulut-Kirby sphere ### ### ### ### ### ### properties: ### ### ### ### f=(566,8136,26904,32220,12888) ### ### 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:=[ [0,1,2,5,377],[0,1,2,35,407],[0,1,2,374,377],[0,1,2,374,407], [0,1,4,5,377],[0,1,4,190,376],[0,1,4,376,377],[0,1,34,35,407], [0,1,34,178,364],[0,1,34,178,550],[0,1,34,220,364],[0,1,34,406,407], [0,1,34,406,550],[0,1,177,178,364],[0,1,177,178,550],[0,1,177,363,364], [0,1,177,363,549],[0,1,177,549,550],[0,1,187,190,376],[0,1,187,220,364], [0,1,187,363,364],[0,1,187,363,549],[0,1,373,374,377],[0,1,373,374,407], [0,1,187,373,376],[0,1,373,376,377],[0,1,373,406,407],[0,1,373,406,550], [0,1,187,373,549],[0,1,373,549,550],[0,2,5,26,212],[0,2,5,26,398], [2,5,26,212,398],[0,2,5,191,212],[2,5,191,212,398],[0,2,5,377,398], [2,5,191,377,398],[0,2,26,29,215],[0,2,26,29,401],[2,26,29,215,401], [0,2,26,212,215],[2,26,212,215,401],[0,2,26,398,401],[2,26,212,398,401], [0,2,29,181,367],[0,2,29,181,553],[0,2,29,215,367],[0,2,29,401,553], [0,2,35,181,367],[0,2,35,181,553],[0,2,35,221,367],[0,2,35,407,553], [0,2,188,191,212],[2,188,191,212,398],[2,188,191,377,398],[0,2,188,212,215], [2,188,212,215,401],[2,188,212,398,401],[0,2,188,215,367],[0,2,188,221,367], [0,2,374,377,398],[2,188,374,377,398],[0,2,374,398,401],[2,188,374,398,401], [0,2,374,401,553],[0,2,374,407,553],[0,3,4,5,377],[0,3,4,190,376], [0,3,4,376,377],[0,3,5,26,212],[0,3,5,26,398],[0,3,5,191,212], [0,3,5,377,398],[0,3,24,26,212],[0,3,24,26,398],[0,3,24,210,212], [0,3,24,210,396],[0,3,24,396,398],[0,3,189,190,376],[0,3,189,191,212], [0,3,189,210,212],[0,3,189,210,396],[0,3,189,375,376],[0,3,375,376,377], [0,3,375,377,398],[0,3,189,375,396],[0,3,375,396,398],[0,24,26,29,215], [0,24,26,29,401],[0,24,26,212,215],[0,24,26,398,401],[0,24,27,29,215], [0,24,27,29,401],[0,24,27,213,215],[0,24,27,213,399],[0,24,27,399,401], [0,24,210,212,215],[0,24,210,213,215],[0,24,210,213,399],[0,24,396,398,401], [0,24,210,396,399],[0,24,396,399,401],[0,27,29,181,367],[0,27,29,181,553], [0,27,29,215,367],[0,27,29,401,553],[0,27,174,178,364],[0,27,174,178,550], [0,27,174,181,367],[0,27,174,181,553],[0,27,174,360,364],[0,27,174,360,367], [0,27,174,546,550],[0,27,174,546,553],[0,27,177,178,364],[0,27,177,178,550], [0,27,177,363,364],[0,27,177,363,549],[0,27,177,549,550],[0,27,213,215,367], [0,27,213,360,364],[0,27,213,360,367],[0,27,213,363,364],[0,27,213,363,549], [0,27,399,401,553],[0,27,399,546,550],[0,27,399,546,553],[0,27,213,399,549], [0,27,399,549,550],[0,33,34,35,407],[0,33,34,178,364],[0,33,34,178,550], [0,33,34,220,364],[0,33,34,406,407],[0,33,34,406,550],[0,33,35,181,367], [0,33,35,181,553],[0,33,35,221,367],[0,33,35,407,553],[0,33,174,178,364], [0,33,174,178,550],[0,33,174,181,367],[0,33,174,181,553],[0,33,174,360,364], [0,33,174,360,367],[0,33,174,546,550],[0,33,174,546,553],[0,33,219,220,364], [0,33,219,221,367],[0,33,219,360,364],[0,33,219,360,367],[0,33,405,406,407], [0,33,405,406,550],[0,33,405,407,553],[0,33,405,546,550],[0,33,405,546,553], [186,187,188,191,377],[186,187,188,221,407],[186,187,188,374,377],[186,187,188,374,407], [186,187,190,191,377],[0,186,187,190,376],[186,187,190,376,377],[186,187,220,221,407], [0,186,187,220,364],[186,187,220,364,550],[186,187,220,406,407],[186,187,220,406,550], [0,186,187,363,364],[186,187,363,364,550],[0,186,187,363,549],[186,187,363,549,550], [186,187,373,374,377],[186,187,373,374,407],[0,186,187,373,376],[186,187,373,376,377], [186,187,373,406,407],[186,187,373,406,550],[0,186,187,373,549],[186,187,373,549,550], [0,186,188,191,212],[186,188,191,212,398],[186,188,191,377,398],[0,186,188,212,215], [186,188,212,215,401],[186,188,212,398,401],[0,186,188,215,367],[186,188,215,367,553], [186,188,215,401,553],[0,186,188,221,367],[186,188,221,367,553],[186,188,221,407,553], [186,188,374,377,398],[186,188,374,398,401],[186,188,374,401,553],[186,188,374,407,553], [186,189,190,191,377],[0,186,189,190,376],[186,189,190,376,377],[0,186,189,191,212], [186,189,191,212,398],[186,189,191,377,398],[0,186,189,210,212],[186,189,210,212,398], [0,186,189,210,396],[186,189,210,396,398],[0,186,189,375,376],[186,189,375,376,377], [186,189,375,377,398],[0,186,189,375,396],[186,189,375,396,398],[0,186,210,212,215], [186,210,212,215,401],[186,210,212,398,401],[0,186,210,213,215],[186,210,213,215,401], [0,186,210,213,399],[186,210,213,399,401],[186,210,396,398,401],[0,186,210,396,399], [186,210,396,399,401],[0,186,213,215,367],[186,213,215,367,553],[186,213,215,401,553], [0,186,213,360,364],[186,213,360,364,550],[0,186,213,360,367],[186,213,360,367,553], [186,213,360,546,550],[186,213,360,546,553],[0,186,213,363,364],[186,213,363,364,550], [0,186,213,363,549],[186,213,363,549,550],[186,213,399,401,553],[186,213,399,546,550], [186,213,399,546,553],[0,186,213,399,549],[186,213,399,549,550],[186,219,220,221,407], [0,186,219,220,364],[186,219,220,364,550],[186,219,220,406,407],[186,219,220,406,550], [0,186,219,221,367],[186,219,221,367,553],[186,219,221,407,553],[0,186,219,360,364], [186,219,360,364,550],[0,186,219,360,367],[186,219,360,367,553],[186,219,360,546,550], [186,219,360,546,553],[186,219,405,406,407],[186,219,405,406,550],[186,219,405,407,553], [186,219,405,546,550],[186,219,405,546,553],[0,372,373,374,377],[186,372,373,374,377], [0,372,373,374,407],[186,372,373,374,407],[0,186,372,373,376],[0,372,373,376,377], [186,372,373,376,377],[0,372,373,406,407],[186,372,373,406,407],[0,372,373,406,550], [186,372,373,406,550],[0,186,372,373,549],[0,372,373,549,550],[186,372,373,549,550], [0,372,374,377,398],[186,372,374,377,398],[0,372,374,398,401],[186,372,374,398,401], [0,372,374,401,553],[186,372,374,401,553],[0,372,374,407,553],[186,372,374,407,553], [0,186,372,375,376],[0,372,375,376,377],[186,372,375,376,377],[0,372,375,377,398], [186,372,375,377,398],[0,186,372,375,396],[0,372,375,396,398],[186,372,375,396,398], [0,372,396,398,401],[186,372,396,398,401],[0,186,372,396,399],[0,372,396,399,401], [186,372,396,399,401],[0,372,399,401,553],[186,372,399,401,553],[0,372,399,546,550], [186,372,399,546,550],[0,372,399,546,553],[186,372,399,546,553],[0,186,372,399,549], [0,372,399,549,550],[186,372,399,549,550],[0,372,405,406,407],[186,372,405,406,407], [0,372,405,406,550],[186,372,405,406,550],[0,372,405,407,553],[186,372,405,407,553], [0,372,405,546,550],[186,372,405,546,550],[0,372,405,546,553],[186,372,405,546,553], [1,2,5,41,227],[1,2,5,41,413],[2,5,41,227,413],[1,2,5,191,227], [2,5,191,227,413],[1,2,5,377,413],[2,5,191,377,413],[1,2,35,181,367], [1,2,35,181,553],[1,2,35,221,367],[1,2,35,407,553],[1,2,38,41,227], [1,2,38,41,413],[2,38,41,227,413],[1,2,38,184,370],[1,2,38,184,556], [1,2,38,224,227],[2,38,224,227,413],[1,2,38,224,370],[1,2,38,410,413], [2,38,224,410,413],[1,2,38,410,556],[1,2,180,181,367],[1,2,180,181,553], [1,2,180,184,370],[1,2,180,184,556],[1,2,180,366,367],[1,2,180,366,370], [1,2,180,552,553],[1,2,180,552,556],[1,2,188,191,227],[2,188,191,227,413], [2,188,191,377,413],[1,2,188,221,367],[1,2,188,224,227],[2,188,224,227,413], [1,2,188,224,370],[2,188,224,410,413],[1,2,188,366,367],[1,2,188,366,370], [1,2,374,377,413],[2,188,374,377,413],[1,2,374,407,553],[1,2,374,410,413], [2,188,374,410,413],[1,2,374,410,556],[1,2,374,552,553],[1,2,374,552,556], [1,4,5,41,227],[1,4,5,41,413],[1,4,5,191,227],[1,4,5,377,413], [1,4,39,41,227],[1,4,39,41,413],[1,4,39,225,227],[1,4,39,225,411], [1,4,39,411,413],[1,4,190,191,227],[1,4,190,225,227],[1,4,190,225,411], [1,4,376,377,413],[1,4,190,376,411],[1,4,376,411,413],[1,34,35,181,367], [1,34,35,181,553],[1,34,35,221,367],[1,34,35,407,553],[1,34,175,178,364], [1,34,175,178,550],[1,34,175,181,367],[1,34,175,181,553],[1,34,175,361,364], [1,34,175,361,367],[1,34,175,547,550],[1,34,175,547,553],[1,34,220,221,367], [1,34,220,361,364],[1,34,220,361,367],[1,34,406,407,553],[1,34,406,547,550], [1,34,406,547,553],[1,36,38,41,227],[1,36,38,41,413],[1,36,38,184,370], [1,36,38,184,556],[1,36,38,224,227],[1,36,38,224,370],[1,36,38,410,413], [1,36,38,410,556],[1,36,39,41,227],[1,36,39,41,413],[1,36,39,225,227], [1,36,39,225,411],[1,36,39,411,413],[1,36,175,178,364],[1,36,175,178,550], [1,36,175,181,367],[1,36,175,181,553],[1,36,175,361,364],[1,36,175,361,367], [1,36,175,547,550],[1,36,175,547,553],[1,36,177,178,364],[1,36,177,178,550], [1,36,177,363,364],[1,36,177,363,549],[1,36,177,549,550],[1,36,180,181,367], [1,36,180,181,553],[1,36,180,184,370],[1,36,180,184,556],[1,36,180,366,367], [1,36,180,366,370],[1,36,180,552,553],[1,36,180,552,556],[1,36,222,224,227], [1,36,222,224,370],[1,36,222,225,227],[1,36,222,225,411],[1,36,222,361,364], [1,36,222,361,367],[1,36,222,363,364],[1,36,222,363,549],[1,36,222,366,367], [1,36,222,366,370],[1,36,408,410,413],[1,36,408,410,556],[1,36,222,408,411], [1,36,408,411,413],[1,36,408,547,550],[1,36,408,547,553],[1,36,222,408,549], [1,36,408,549,550],[1,36,408,552,553],[1,36,408,552,556],[1,187,188,191,227], [187,188,191,227,413],[187,188,191,377,413],[1,187,188,221,367],[187,188,221,367,553], [187,188,221,407,553],[1,187,188,224,227],[187,188,224,227,413],[1,187,188,224,370], [187,188,224,370,556],[187,188,224,410,413],[187,188,224,410,556],[1,187,188,366,367], [187,188,366,367,553],[1,187,188,366,370],[187,188,366,370,556],[187,188,366,552,553], [187,188,366,552,556],[187,188,374,377,413],[187,188,374,407,553],[187,188,374,410,413], [187,188,374,410,556],[187,188,374,552,553],[187,188,374,552,556],[1,187,190,191,227], [187,190,191,227,413],[187,190,191,377,413],[1,187,190,225,227],[187,190,225,227,413], [1,187,190,225,411],[187,190,225,411,413],[187,190,376,377,413],[1,187,190,376,411], [187,190,376,411,413],[1,187,220,221,367],[187,220,221,367,553],[187,220,221,407,553], [1,187,220,361,364],[187,220,361,364,550],[1,187,220,361,367],[187,220,361,367,553], [187,220,361,547,550],[187,220,361,547,553],[187,220,406,407,553],[187,220,406,547,550], [187,220,406,547,553],[1,187,222,224,227],[187,222,224,227,413],[1,187,222,224,370], [187,222,224,370,556],[187,222,224,410,413],[187,222,224,410,556],[1,187,222,225,227], [187,222,225,227,413],[1,187,222,225,411],[187,222,225,411,413],[1,187,222,361,364], [187,222,361,364,550],[1,187,222,361,367],[187,222,361,367,553],[187,222,361,547,550], [187,222,361,547,553],[1,187,222,363,364],[187,222,363,364,550],[1,187,222,363,549], [187,222,363,549,550],[1,187,222,366,367],[187,222,366,367,553],[1,187,222,366,370], [187,222,366,370,556],[187,222,366,552,553],[187,222,366,552,556],[187,222,408,410,413], [187,222,408,410,556],[1,187,222,408,411],[187,222,408,411,413],[187,222,408,547,550], [187,222,408,547,553],[1,187,222,408,549],[187,222,408,549,550],[187,222,408,552,553], [187,222,408,552,556],[1,373,374,377,413],[187,373,374,377,413],[1,373,374,407,553], [187,373,374,407,553],[1,373,374,410,413],[187,373,374,410,413],[1,373,374,410,556], [187,373,374,410,556],[1,373,374,552,553],[187,373,374,552,553],[1,373,374,552,556], [187,373,374,552,556],[1,373,376,377,413],[187,373,376,377,413],[1,187,373,376,411], [1,373,376,411,413],[187,373,376,411,413],[1,373,406,407,553],[187,373,406,407,553], [1,373,406,547,550],[187,373,406,547,550],[1,373,406,547,553],[187,373,406,547,553], [1,373,408,410,413],[187,373,408,410,413],[1,373,408,410,556],[187,373,408,410,556], [1,187,373,408,411],[1,373,408,411,413],[187,373,408,411,413],[1,373,408,547,550], [187,373,408,547,550],[1,373,408,547,553],[187,373,408,547,553],[1,187,373,408,549], [1,373,408,549,550],[187,373,408,549,550],[1,373,408,552,553],[187,373,408,552,553], [1,373,408,552,556],[187,373,408,552,556],[2,29,180,181,367],[2,29,180,181,553], [2,29,180,184,370],[2,29,180,184,556],[2,29,180,366,367],[2,29,180,366,370], [2,29,180,552,553],[2,29,180,552,556],[2,29,182,184,370],[2,29,182,184,556], [2,29,182,368,370],[2,29,182,368,554],[2,29,182,554,556],[2,29,215,366,367], [2,29,215,366,370],[2,29,215,368,370],[2,29,215,368,554],[2,29,401,552,553], [2,29,401,552,556],[2,29,215,401,554],[2,29,401,554,556],[2,38,182,184,370], [2,38,182,184,556],[2,38,182,368,370],[2,38,182,368,554],[2,38,182,554,556], [2,38,224,368,370],[2,38,224,368,554],[2,38,224,410,554],[2,38,410,554,556], [2,188,215,366,367],[188,215,366,367,553],[2,188,215,366,370],[188,215,366,370,556], [188,215,366,552,553],[188,215,366,552,556],[2,188,215,368,370],[188,215,368,370,556], [2,188,215,368,554],[188,215,368,554,556],[188,215,401,552,553],[188,215,401,552,556], [2,188,215,401,554],[188,215,401,554,556],[2,188,224,368,370],[188,224,368,370,556], [2,188,224,368,554],[188,224,368,554,556],[2,188,224,410,554],[188,224,410,554,556], [2,374,401,552,553],[188,374,401,552,553],[2,374,401,552,556],[188,374,401,552,556], [2,188,374,401,554],[2,374,401,554,556],[188,374,401,554,556],[2,188,374,410,554], [2,374,410,554,556],[188,374,410,554,556],[3,4,5,8,380],[3,4,5,377,380], [3,4,7,8,380],[3,4,7,178,364],[3,4,7,178,550],[3,4,7,193,364], [3,4,7,379,380],[3,4,7,379,550],[3,4,177,178,364],[3,4,177,178,550], [3,4,177,363,364],[3,4,177,363,549],[3,4,177,549,550],[3,4,190,193,364], [3,4,190,363,364],[3,4,190,363,549],[3,4,376,377,380],[3,4,376,379,380], [3,4,376,379,550],[3,4,190,376,549],[3,4,376,549,550],[3,5,8,23,209], [3,5,8,23,395],[5,8,23,209,395],[3,5,8,194,209],[5,8,194,209,395], [3,5,8,380,395],[5,8,194,380,395],[3,5,23,26,212],[3,5,23,26,398], 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[44,416,422,554,556],[230,416,422,554,556],[45,46,47,50,422],[45,46,47,419,422], [45,46,49,50,422],[45,46,49,235,421],[45,46,49,421,422],[45,46,232,235,421], [45,46,418,419,422],[45,46,232,418,421],[45,46,418,421,422],[45,48,49,50,422], [45,48,49,235,421],[45,48,49,421,422],[45,48,234,235,421],[45,48,234,420,421], [45,48,420,421,422],[231,232,233,236,422],[231,232,233,419,422],[231,232,235,236,422], [45,231,232,235,421],[231,232,235,421,422],[231,232,418,419,422],[45,231,232,418,421], [231,232,418,421,422],[231,234,235,236,422],[45,231,234,235,421],[231,234,235,421,422], [45,231,234,420,421],[231,234,420,421,422],[45,417,418,419,422],[231,417,418,419,422], [45,231,417,418,421],[45,417,418,421,422],[231,417,418,421,422],[45,231,417,420,421], [45,417,420,421,422],[231,417,420,421,422],[46,47,50,56,242],[46,47,50,56,428], [46,47,50,236,242],[46,47,50,422,428],[46,47,53,56,242],[46,47,53,56,428], [46,47,53,239,242],[46,47,53,425,428],[46,47,233,236,242],[46,47,233,239,242], 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[47,53,425,428,556],[47,53,239,425,555],[47,53,425,555,556],[47,233,236,242,370], [233,236,242,370,556],[233,236,242,428,556],[233,236,422,428,556],[47,233,239,242,370], [233,239,242,370,556],[233,239,242,428,556],[47,233,239,369,370],[233,239,369,370,556], [47,233,239,369,555],[233,239,369,555,556],[233,239,425,428,556],[47,233,239,425,555], [233,239,425,555,556],[47,419,422,428,556],[233,419,422,428,556],[47,419,425,428,556], [233,419,425,428,556],[47,233,419,425,555],[47,419,425,555,556],[233,419,425,555,556], [48,49,50,53,425],[48,49,50,422,425],[48,49,52,53,425],[48,49,52,238,424], [48,49,52,424,425],[48,49,235,238,424],[48,49,421,422,425],[48,49,235,421,424], [48,49,421,424,425],[48,51,52,53,425],[48,51,52,238,424],[48,51,52,424,425], [48,51,237,238,424],[48,51,237,423,424],[48,51,423,424,425],[234,235,236,239,425], [234,235,236,422,425],[234,235,238,239,425],[48,234,235,238,424],[234,235,238,424,425], 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[49,52,57,429,431],[49,52,238,239,245],[49,52,238,243,245],[49,52,238,243,429], [49,52,424,425,431],[49,52,238,424,429],[49,52,424,429,431],[49,54,56,59,245], [49,54,56,59,431],[49,54,56,242,245],[49,54,56,428,431],[49,54,57,59,245], [49,54,57,59,431],[49,54,57,243,245],[49,54,57,243,429],[49,54,57,429,431], [49,54,240,242,245],[49,54,240,243,245],[49,54,240,243,429],[49,54,426,428,431], [49,54,240,426,429],[49,54,426,429,431],[49,235,236,239,245],[235,236,239,245,431], [235,236,239,425,431],[49,235,236,242,245],[235,236,242,245,431],[235,236,242,428,431], [235,236,422,425,431],[235,236,422,428,431],[49,235,238,239,245],[235,238,239,245,431], [235,238,239,425,431],[49,235,238,243,245],[235,238,243,245,431],[49,235,238,243,429], [235,238,243,429,431],[235,238,424,425,431],[49,235,238,424,429],[235,238,424,429,431], [49,235,240,242,245],[235,240,242,245,431],[235,240,242,428,431],[49,235,240,243,245], [235,240,243,245,431],[49,235,240,243,429],[235,240,243,429,431],[235,240,426,428,431], [49,235,240,426,429],[235,240,426,429,431],[49,421,422,425,431],[235,421,422,425,431], [49,421,422,428,431],[235,421,422,428,431],[49,421,424,425,431],[235,421,424,425,431], [49,235,421,424,429],[49,421,424,429,431],[235,421,424,429,431],[49,421,426,428,431], [235,421,426,428,431],[49,235,421,426,429],[49,421,426,429,431],[235,421,426,429,431], [50,56,182,184,370],[50,56,182,184,556],[50,56,182,368,370],[50,56,182,368,554], [50,56,182,554,556],[50,56,242,368,370],[50,56,242,368,554],[50,56,242,428,554], [50,56,428,554,556],[50,236,242,368,370],[236,242,368,370,556],[50,236,242,368,554], [236,242,368,554,556],[50,236,242,428,554],[236,242,428,554,556],[50,236,422,428,554], [50,422,428,554,556],[236,422,428,554,556],[51,52,53,56,428],[51,52,53,425,428], [51,52,55,56,428],[51,52,55,241,427],[51,52,55,427,428],[51,52,238,241,427], [51,52,424,425,428],[51,52,238,424,427],[51,52,424,427,428],[51,54,55,56,428], [51,54,55,241,427],[51,54,55,427,428],[51,54,240,241,427],[51,54,240,426,427], 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[52,424,425,428,434],[238,424,425,428,434],[52,424,425,431,434],[238,424,425,431,434], [52,424,427,428,434],[238,424,427,428,434],[52,238,424,427,432],[52,424,427,432,434], [238,424,427,432,434],[52,424,429,431,434],[238,424,429,431,434],[52,238,424,429,432], [52,424,429,432,434],[238,424,429,432,434],[53,56,62,184,370],[53,56,62,184,556], [53,56,62,248,370],[53,56,62,434,556],[53,56,242,248,370],[53,56,428,434,556], [53,59,62,184,370],[53,59,62,184,556],[53,59,62,248,370],[53,59,62,434,556], [53,59,183,184,370],[53,59,183,184,556],[53,59,183,369,370],[53,59,183,369,555], [53,59,183,555,556],[53,59,245,248,370],[53,59,245,369,370],[53,59,245,369,555], [53,59,431,434,556],[53,59,245,431,555],[53,59,431,555,556],[53,239,242,248,370], [239,242,248,370,556],[239,242,248,434,556],[239,242,428,434,556],[53,239,245,248,370], [239,245,248,370,556],[239,245,248,434,556],[53,239,245,369,370],[239,245,369,370,556], 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[6,8,11,559,560],[8,11,558,559,560],[6,9,11,558,560],[6,9,11,559,560], [9,11,14,558,560],[9,11,14,559,560],[11,14,558,559,560],[9,12,14,558,560], [9,12,14,559,560],[12,14,17,558,560],[12,14,17,559,560],[14,17,558,559,560], [12,15,17,558,560],[12,15,17,559,560],[15,17,20,558,560],[15,17,20,559,560], [17,20,558,559,560],[15,18,20,558,560],[15,18,20,559,560],[18,20,23,558,560], [18,20,23,559,560],[20,23,558,559,560],[18,21,23,558,560],[18,21,23,559,560], [21,23,26,558,560],[21,23,26,559,560],[23,26,558,559,560],[21,24,26,558,560], [21,24,26,559,560],[24,26,29,558,560],[24,26,29,559,560],[26,29,558,559,560], [24,27,29,558,560],[24,27,29,559,560],[27,29,32,558,560],[27,29,32,559,560], [29,32,558,559,560],[27,30,32,558,560],[27,30,32,559,560],[30,32,35,558,560], [30,32,35,559,560],[32,35,558,559,560],[30,33,35,558,560],[30,33,35,559,560], [0,3,558,559,561],[0,3,558,560,561],[0,3,559,560,561],[0,33,558,559,561], [0,33,558,560,561],[0,33,559,560,561],[3,6,558,559,561],[3,6,558,560,561], [3,6,559,560,561],[6,9,558,559,561],[6,9,558,560,561],[6,9,559,560,561], [9,12,558,559,561],[9,12,558,560,561],[9,12,559,560,561],[12,15,558,559,561], [12,15,558,560,561],[12,15,559,560,561],[15,18,558,559,561],[15,18,558,560,561], [15,18,559,560,561],[18,21,558,559,561],[18,21,558,560,561],[18,21,559,560,561], [21,24,558,559,561],[21,24,558,560,561],[21,24,559,560,561],[24,27,558,559,561], [24,27,558,560,561],[24,27,559,560,561],[27,30,558,559,561],[27,30,558,560,561], [27,30,559,560,561],[30,33,558,559,561],[30,33,558,560,561],[30,33,559,560,561], [36,38,41,227,562],[37,38,41,227,562],[36,38,173,359,562],[37,38,173,359,562], [36,38,224,227,562],[37,38,224,227,562],[36,38,224,359,562],[37,38,224,359,562], [37,40,41,227,562],[36,37,40,226,562],[37,40,226,227,562],[37,172,173,359,562], [36,37,172,358,562],[37,172,358,359,562],[37,223,224,227,562],[37,223,224,359,562], [36,37,223,226,562],[37,223,226,227,562],[36,37,223,358,562],[37,223,358,359,562], 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[42,43,46,232,562],[43,46,232,233,562],[43,229,230,233,562],[42,43,229,232,562], [43,229,232,233,562],[42,45,47,233,562],[42,45,46,232,562],[42,45,231,232,562], [42,45,231,233,562],[42,228,230,233,562],[228,229,230,233,562],[42,228,229,232,562], [228,229,232,233,562],[42,228,231,232,562],[42,228,231,233,562],[228,231,232,233,562], [45,47,50,236,562],[46,47,50,236,562],[45,47,233,236,562],[46,47,233,236,562], [46,49,50,236,562],[45,46,49,235,562],[46,49,235,236,562],[46,232,233,236,562], [45,46,232,235,562],[46,232,235,236,562],[45,48,50,236,562],[45,48,49,235,562], [45,48,234,235,562],[45,48,234,236,562],[45,231,233,236,562],[231,232,233,236,562], [45,231,232,235,562],[231,232,235,236,562],[45,231,234,235,562],[45,231,234,236,562], [231,234,235,236,562],[48,50,53,239,562],[49,50,53,239,562],[48,50,236,239,562], [49,50,236,239,562],[49,52,53,239,562],[48,49,52,238,562],[49,52,238,239,562], [49,235,236,239,562],[48,49,235,238,562],[49,235,238,239,562],[48,51,53,239,562], 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[69,70,256,259,562],[70,256,259,260,562],[69,72,74,260,562],[69,72,73,259,562], [69,72,258,259,562],[69,72,258,260,562],[69,255,257,260,562],[255,256,257,260,562], [69,255,256,259,562],[255,256,259,260,562],[69,255,258,259,562],[69,255,258,260,562], [255,258,259,260,562],[72,74,77,263,562],[73,74,77,263,562],[72,74,260,263,562], [73,74,260,263,562],[73,76,77,263,562],[72,73,76,262,562],[73,76,262,263,562], [73,259,260,263,562],[72,73,259,262,562],[73,259,262,263,562],[72,75,77,263,562], [72,75,76,262,562],[72,75,261,262,562],[72,75,261,263,562],[72,258,260,263,562], [258,259,260,263,562],[72,258,259,262,562],[258,259,262,263,562],[72,258,261,262,562], [72,258,261,263,562],[258,261,262,263,562],[75,77,80,266,562],[76,77,80,266,562], [75,77,263,266,562],[76,77,263,266,562],[76,79,80,266,562],[75,76,79,265,562], [76,79,265,266,562],[76,262,263,266,562],[75,76,262,265,562],[76,262,265,266,562], [75,78,80,266,562],[75,78,79,265,562],[75,78,264,265,562],[75,78,264,266,562], [75,261,263,266,562],[261,262,263,266,562],[75,261,262,265,562],[261,262,265,266,562], [75,261,264,265,562],[75,261,264,266,562],[261,264,265,266,562],[78,80,83,269,562], [79,80,83,269,562],[78,80,266,269,562],[79,80,266,269,562],[79,82,83,269,562], [78,79,82,268,562],[79,82,268,269,562],[79,265,266,269,562],[78,79,265,268,562], [79,265,268,269,562],[78,81,83,269,562],[78,81,82,268,562],[78,81,267,268,562], [78,81,267,269,562],[78,264,266,269,562],[264,265,266,269,562],[78,264,265,268,562], [264,265,268,269,562],[78,264,267,268,562],[78,264,267,269,562],[264,267,268,269,562], [81,83,86,272,562],[82,83,86,272,562],[81,83,269,272,562],[82,83,269,272,562], [82,85,86,272,562],[81,82,85,271,562],[82,85,271,272,562],[82,268,269,272,562], [81,82,268,271,562],[82,268,271,272,562],[81,84,86,272,562],[81,84,85,271,562], [81,84,270,271,562],[81,84,270,272,562],[81,267,269,272,562],[267,268,269,272,562], [81,267,268,271,562],[267,268,271,272,562],[81,267,270,271,562],[81,267,270,272,562], 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[90,91,94,280,562],[91,94,280,281,562],[91,277,278,281,562],[90,91,277,280,562], [91,277,280,281,562],[90,93,95,281,562],[90,93,94,280,562],[90,93,279,280,562], [90,93,279,281,562],[90,276,278,281,562],[276,277,278,281,562],[90,276,277,280,562], [276,277,280,281,562],[90,276,279,280,562],[90,276,279,281,562],[276,279,280,281,562], [93,95,98,284,562],[94,95,98,284,562],[93,95,281,284,562],[94,95,281,284,562], [94,97,98,284,562],[93,94,97,283,562],[94,97,283,284,562],[94,280,281,284,562], [93,94,280,283,562],[94,280,283,284,562],[93,96,98,284,562],[93,96,97,283,562], [93,96,282,283,562],[93,96,282,284,562],[93,279,281,284,562],[279,280,281,284,562], [93,279,280,283,562],[279,280,283,284,562],[93,279,282,283,562],[93,279,282,284,562], [279,282,283,284,562],[96,98,101,287,562],[97,98,101,287,562],[96,98,284,287,562], [97,98,284,287,562],[97,100,101,287,562],[96,97,100,286,562],[97,100,286,287,562], [97,283,284,287,562],[96,97,283,286,562],[97,283,286,287,562],[96,99,101,287,562], 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