#################################################################################### #################################################################################### #################################################################################### ### ### ### ### ### TRIANGULATIONS OF AKBULUT-KIRBY SPHERES ### ### by Frank H. Lutz and Mimi Tsuruga ### ### http://matsguru.com/research/AKspheres.html ### ### ### ### name of example: ### ### ### ### AK_III_019 ### ### ### ### ### ### description: ### ### ### ### Type 3 construction of triangulation of Akbulut-Kirby sphere ### ### ### ### ### ### properties: ### ### ### ### f=(818,11748,38832,46500,18600) ### ### 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:=[ [0,1,2,5,545],[0,1,2,35,575],[0,1,2,542,545],[0,1,2,542,575], [0,1,4,5,545],[0,1,4,274,544],[0,1,4,544,545],[0,1,34,35,575], [0,1,34,262,532],[0,1,34,262,802],[0,1,34,304,532],[0,1,34,574,575], [0,1,34,574,802],[0,1,261,262,532],[0,1,261,262,802],[0,1,261,531,532], [0,1,261,531,801],[0,1,261,801,802],[0,1,271,274,544],[0,1,271,304,532], [0,1,271,531,532],[0,1,271,531,801],[0,1,541,542,545],[0,1,541,542,575], [0,1,271,541,544],[0,1,541,544,545],[0,1,541,574,575],[0,1,541,574,802], [0,1,271,541,801],[0,1,541,801,802],[0,2,5,26,296],[0,2,5,26,566], [2,5,26,296,566],[0,2,5,275,296],[2,5,275,296,566],[0,2,5,545,566], [2,5,275,545,566],[0,2,26,29,299],[0,2,26,29,569],[2,26,29,299,569], [0,2,26,296,299],[2,26,296,299,569],[0,2,26,566,569],[2,26,296,566,569], [0,2,29,265,535],[0,2,29,265,805],[0,2,29,299,535],[0,2,29,569,805], [0,2,35,265,535],[0,2,35,265,805],[0,2,35,305,535],[0,2,35,575,805], [0,2,272,275,296],[2,272,275,296,566],[2,272,275,545,566],[0,2,272,296,299], [2,272,296,299,569],[2,272,296,566,569],[0,2,272,299,535],[0,2,272,305,535], [0,2,542,545,566],[2,272,542,545,566],[0,2,542,566,569],[2,272,542,566,569], [0,2,542,569,805],[0,2,542,575,805],[0,3,4,5,545],[0,3,4,274,544], [0,3,4,544,545],[0,3,5,26,296],[0,3,5,26,566],[0,3,5,275,296], [0,3,5,545,566],[0,3,24,26,296],[0,3,24,26,566],[0,3,24,294,296], [0,3,24,294,564],[0,3,24,564,566],[0,3,273,274,544],[0,3,273,275,296], [0,3,273,294,296],[0,3,273,294,564],[0,3,273,543,544],[0,3,543,544,545], [0,3,543,545,566],[0,3,273,543,564],[0,3,543,564,566],[0,24,26,29,299], [0,24,26,29,569],[0,24,26,296,299],[0,24,26,566,569],[0,24,27,29,299], [0,24,27,29,569],[0,24,27,297,299],[0,24,27,297,567],[0,24,27,567,569], [0,24,294,296,299],[0,24,294,297,299],[0,24,294,297,567],[0,24,564,566,569], [0,24,294,564,567],[0,24,564,567,569],[0,27,29,265,535],[0,27,29,265,805], [0,27,29,299,535],[0,27,29,569,805],[0,27,258,262,532],[0,27,258,262,802], [0,27,258,265,535],[0,27,258,265,805],[0,27,258,528,532],[0,27,258,528,535], [0,27,258,798,802],[0,27,258,798,805],[0,27,261,262,532],[0,27,261,262,802], [0,27,261,531,532],[0,27,261,531,801],[0,27,261,801,802],[0,27,297,299,535], [0,27,297,528,532],[0,27,297,528,535],[0,27,297,531,532],[0,27,297,531,801], [0,27,567,569,805],[0,27,567,798,802],[0,27,567,798,805],[0,27,297,567,801], [0,27,567,801,802],[0,33,34,35,575],[0,33,34,262,532],[0,33,34,262,802], [0,33,34,304,532],[0,33,34,574,575],[0,33,34,574,802],[0,33,35,265,535], [0,33,35,265,805],[0,33,35,305,535],[0,33,35,575,805],[0,33,258,262,532], [0,33,258,262,802],[0,33,258,265,535],[0,33,258,265,805],[0,33,258,528,532], [0,33,258,528,535],[0,33,258,798,802],[0,33,258,798,805],[0,33,303,304,532], [0,33,303,305,535],[0,33,303,528,532],[0,33,303,528,535],[0,33,573,574,575], [0,33,573,574,802],[0,33,573,575,805],[0,33,573,798,802],[0,33,573,798,805], [270,271,272,275,545],[270,271,272,305,575],[270,271,272,542,545],[270,271,272,542,575], [270,271,274,275,545],[0,270,271,274,544],[270,271,274,544,545],[270,271,304,305,575], [0,270,271,304,532],[270,271,304,532,802],[270,271,304,574,575],[270,271,304,574,802], [0,270,271,531,532],[270,271,531,532,802],[0,270,271,531,801],[270,271,531,801,802], [270,271,541,542,545],[270,271,541,542,575],[0,270,271,541,544],[270,271,541,544,545], [270,271,541,574,575],[270,271,541,574,802],[0,270,271,541,801],[270,271,541,801,802], [0,270,272,275,296],[270,272,275,296,566],[270,272,275,545,566],[0,270,272,296,299], [270,272,296,299,569],[270,272,296,566,569],[0,270,272,299,535],[270,272,299,535,805], [270,272,299,569,805],[0,270,272,305,535],[270,272,305,535,805],[270,272,305,575,805], [270,272,542,545,566],[270,272,542,566,569],[270,272,542,569,805],[270,272,542,575,805], [270,273,274,275,545],[0,270,273,274,544],[270,273,274,544,545],[0,270,273,275,296], [270,273,275,296,566],[270,273,275,545,566],[0,270,273,294,296],[270,273,294,296,566], [0,270,273,294,564],[270,273,294,564,566],[0,270,273,543,544],[270,273,543,544,545], [270,273,543,545,566],[0,270,273,543,564],[270,273,543,564,566],[0,270,294,296,299], [270,294,296,299,569],[270,294,296,566,569],[0,270,294,297,299],[270,294,297,299,569], [0,270,294,297,567],[270,294,297,567,569],[270,294,564,566,569],[0,270,294,564,567], [270,294,564,567,569],[0,270,297,299,535],[270,297,299,535,805],[270,297,299,569,805], [0,270,297,528,532],[270,297,528,532,802],[0,270,297,528,535],[270,297,528,535,805], [270,297,528,798,802],[270,297,528,798,805],[0,270,297,531,532],[270,297,531,532,802], [0,270,297,531,801],[270,297,531,801,802],[270,297,567,569,805],[270,297,567,798,802], [270,297,567,798,805],[0,270,297,567,801],[270,297,567,801,802],[270,303,304,305,575], [0,270,303,304,532],[270,303,304,532,802],[270,303,304,574,575],[270,303,304,574,802], [0,270,303,305,535],[270,303,305,535,805],[270,303,305,575,805],[0,270,303,528,532], [270,303,528,532,802],[0,270,303,528,535],[270,303,528,535,805],[270,303,528,798,802], [270,303,528,798,805],[270,303,573,574,575],[270,303,573,574,802],[270,303,573,575,805], [270,303,573,798,802],[270,303,573,798,805],[0,540,541,542,545],[270,540,541,542,545], [0,540,541,542,575],[270,540,541,542,575],[0,270,540,541,544],[0,540,541,544,545], [270,540,541,544,545],[0,540,541,574,575],[270,540,541,574,575],[0,540,541,574,802], [270,540,541,574,802],[0,270,540,541,801],[0,540,541,801,802],[270,540,541,801,802], [0,540,542,545,566],[270,540,542,545,566],[0,540,542,566,569],[270,540,542,566,569], [0,540,542,569,805],[270,540,542,569,805],[0,540,542,575,805],[270,540,542,575,805], [0,270,540,543,544],[0,540,543,544,545],[270,540,543,544,545],[0,540,543,545,566], [270,540,543,545,566],[0,270,540,543,564],[0,540,543,564,566],[270,540,543,564,566], [0,540,564,566,569],[270,540,564,566,569],[0,270,540,564,567],[0,540,564,567,569], [270,540,564,567,569],[0,540,567,569,805],[270,540,567,569,805],[0,540,567,798,802], [270,540,567,798,802],[0,540,567,798,805],[270,540,567,798,805],[0,270,540,567,801], [0,540,567,801,802],[270,540,567,801,802],[0,540,573,574,575],[270,540,573,574,575], [0,540,573,574,802],[270,540,573,574,802],[0,540,573,575,805],[270,540,573,575,805], [0,540,573,798,802],[270,540,573,798,802],[0,540,573,798,805],[270,540,573,798,805], [1,2,5,41,311],[1,2,5,41,581],[2,5,41,311,581],[1,2,5,275,311], [2,5,275,311,581],[1,2,5,545,581],[2,5,275,545,581],[1,2,35,265,535], [1,2,35,265,805],[1,2,35,305,535],[1,2,35,575,805],[1,2,38,41,311], [1,2,38,41,581],[2,38,41,311,581],[1,2,38,268,538],[1,2,38,268,808], [1,2,38,308,311],[2,38,308,311,581],[1,2,38,308,538],[1,2,38,578,581], [2,38,308,578,581],[1,2,38,578,808],[1,2,264,265,535],[1,2,264,265,805], [1,2,264,268,538],[1,2,264,268,808],[1,2,264,534,535],[1,2,264,534,538], [1,2,264,804,805],[1,2,264,804,808],[1,2,272,275,311],[2,272,275,311,581], [2,272,275,545,581],[1,2,272,305,535],[1,2,272,308,311],[2,272,308,311,581], [1,2,272,308,538],[2,272,308,578,581],[1,2,272,534,535],[1,2,272,534,538], [1,2,542,545,581],[2,272,542,545,581],[1,2,542,575,805],[1,2,542,578,581], [2,272,542,578,581],[1,2,542,578,808],[1,2,542,804,805],[1,2,542,804,808], [1,4,5,41,311],[1,4,5,41,581],[1,4,5,275,311],[1,4,5,545,581], [1,4,39,41,311],[1,4,39,41,581],[1,4,39,309,311],[1,4,39,309,579], [1,4,39,579,581],[1,4,274,275,311],[1,4,274,309,311],[1,4,274,309,579], [1,4,544,545,581],[1,4,274,544,579],[1,4,544,579,581],[1,34,35,265,535], [1,34,35,265,805],[1,34,35,305,535],[1,34,35,575,805],[1,34,259,262,532], [1,34,259,262,802],[1,34,259,265,535],[1,34,259,265,805],[1,34,259,529,532], [1,34,259,529,535],[1,34,259,799,802],[1,34,259,799,805],[1,34,304,305,535], [1,34,304,529,532],[1,34,304,529,535],[1,34,574,575,805],[1,34,574,799,802], [1,34,574,799,805],[1,36,38,41,311],[1,36,38,41,581],[1,36,38,268,538], [1,36,38,268,808],[1,36,38,308,311],[1,36,38,308,538],[1,36,38,578,581], [1,36,38,578,808],[1,36,39,41,311],[1,36,39,41,581],[1,36,39,309,311], [1,36,39,309,579],[1,36,39,579,581],[1,36,259,262,532],[1,36,259,262,802], [1,36,259,265,535],[1,36,259,265,805],[1,36,259,529,532],[1,36,259,529,535], [1,36,259,799,802],[1,36,259,799,805],[1,36,261,262,532],[1,36,261,262,802], [1,36,261,531,532],[1,36,261,531,801],[1,36,261,801,802],[1,36,264,265,535], [1,36,264,265,805],[1,36,264,268,538],[1,36,264,268,808],[1,36,264,534,535], [1,36,264,534,538],[1,36,264,804,805],[1,36,264,804,808],[1,36,306,308,311], [1,36,306,308,538],[1,36,306,309,311],[1,36,306,309,579],[1,36,306,529,532], [1,36,306,529,535],[1,36,306,531,532],[1,36,306,531,801],[1,36,306,534,535], [1,36,306,534,538],[1,36,576,578,581],[1,36,576,578,808],[1,36,306,576,579], [1,36,576,579,581],[1,36,576,799,802],[1,36,576,799,805],[1,36,306,576,801], [1,36,576,801,802],[1,36,576,804,805],[1,36,576,804,808],[1,271,272,275,311], [271,272,275,311,581],[271,272,275,545,581],[1,271,272,305,535],[271,272,305,535,805], [271,272,305,575,805],[1,271,272,308,311],[271,272,308,311,581],[1,271,272,308,538], [271,272,308,538,808],[271,272,308,578,581],[271,272,308,578,808],[1,271,272,534,535], [271,272,534,535,805],[1,271,272,534,538],[271,272,534,538,808],[271,272,534,804,805], [271,272,534,804,808],[271,272,542,545,581],[271,272,542,575,805],[271,272,542,578,581], [271,272,542,578,808],[271,272,542,804,805],[271,272,542,804,808],[1,271,274,275,311], [271,274,275,311,581],[271,274,275,545,581],[1,271,274,309,311],[271,274,309,311,581], [1,271,274,309,579],[271,274,309,579,581],[271,274,544,545,581],[1,271,274,544,579], [271,274,544,579,581],[1,271,304,305,535],[271,304,305,535,805],[271,304,305,575,805], [1,271,304,529,532],[271,304,529,532,802],[1,271,304,529,535],[271,304,529,535,805], [271,304,529,799,802],[271,304,529,799,805],[271,304,574,575,805],[271,304,574,799,802], [271,304,574,799,805],[1,271,306,308,311],[271,306,308,311,581],[1,271,306,308,538], [271,306,308,538,808],[271,306,308,578,581],[271,306,308,578,808],[1,271,306,309,311], [271,306,309,311,581],[1,271,306,309,579],[271,306,309,579,581],[1,271,306,529,532], [271,306,529,532,802],[1,271,306,529,535],[271,306,529,535,805],[271,306,529,799,802], [271,306,529,799,805],[1,271,306,531,532],[271,306,531,532,802],[1,271,306,531,801], [271,306,531,801,802],[1,271,306,534,535],[271,306,534,535,805],[1,271,306,534,538], [271,306,534,538,808],[271,306,534,804,805],[271,306,534,804,808],[271,306,576,578,581], [271,306,576,578,808],[1,271,306,576,579],[271,306,576,579,581],[271,306,576,799,802], [271,306,576,799,805],[1,271,306,576,801],[271,306,576,801,802],[271,306,576,804,805], [271,306,576,804,808],[1,541,542,545,581],[271,541,542,545,581],[1,541,542,575,805], [271,541,542,575,805],[1,541,542,578,581],[271,541,542,578,581],[1,541,542,578,808], [271,541,542,578,808],[1,541,542,804,805],[271,541,542,804,805],[1,541,542,804,808], [271,541,542,804,808],[1,541,544,545,581],[271,541,544,545,581],[1,271,541,544,579], [1,541,544,579,581],[271,541,544,579,581],[1,541,574,575,805],[271,541,574,575,805], [1,541,574,799,802],[271,541,574,799,802],[1,541,574,799,805],[271,541,574,799,805], [1,541,576,578,581],[271,541,576,578,581],[1,541,576,578,808],[271,541,576,578,808], [1,271,541,576,579],[1,541,576,579,581],[271,541,576,579,581],[1,541,576,799,802], [271,541,576,799,802],[1,541,576,799,805],[271,541,576,799,805],[1,271,541,576,801], [1,541,576,801,802],[271,541,576,801,802],[1,541,576,804,805],[271,541,576,804,805], [1,541,576,804,808],[271,541,576,804,808],[2,29,264,265,535],[2,29,264,265,805], [2,29,264,268,538],[2,29,264,268,808],[2,29,264,534,535],[2,29,264,534,538], [2,29,264,804,805],[2,29,264,804,808],[2,29,266,268,538],[2,29,266,268,808], [2,29,266,536,538],[2,29,266,536,806],[2,29,266,806,808],[2,29,299,534,535], [2,29,299,534,538],[2,29,299,536,538],[2,29,299,536,806],[2,29,569,804,805], [2,29,569,804,808],[2,29,299,569,806],[2,29,569,806,808],[2,38,266,268,538], [2,38,266,268,808],[2,38,266,536,538],[2,38,266,536,806],[2,38,266,806,808], [2,38,308,536,538],[2,38,308,536,806],[2,38,308,578,806],[2,38,578,806,808], [2,272,299,534,535],[272,299,534,535,805],[2,272,299,534,538],[272,299,534,538,808], [272,299,534,804,805],[272,299,534,804,808],[2,272,299,536,538],[272,299,536,538,808], 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[130,133,134,404,814],[129,130,133,403,814],[130,133,403,404,814],[130,400,401,404,814], [129,130,400,403,814],[130,400,403,404,814],[129,132,134,404,814],[129,132,133,403,814], [129,132,402,403,814],[129,132,402,404,814],[129,399,401,404,814],[399,400,401,404,814], [129,399,400,403,814],[399,400,403,404,814],[129,399,402,403,814],[129,399,402,404,814], [399,402,403,404,814],[132,134,137,407,814],[133,134,137,407,814],[132,134,404,407,814], [133,134,404,407,814],[133,136,137,407,814],[132,133,136,406,814],[133,136,406,407,814], [133,403,404,407,814],[132,133,403,406,814],[133,403,406,407,814],[132,135,137,407,814], [132,135,136,406,814],[132,135,405,406,814],[132,135,405,407,814],[132,402,404,407,814], [402,403,404,407,814],[132,402,403,406,814],[402,403,406,407,814],[132,402,405,406,814], [132,402,405,407,814],[402,405,406,407,814],[135,137,140,410,814],[136,137,140,410,814], [135,137,407,410,814],[136,137,407,410,814],[136,139,140,410,814],[135,136,139,409,814], [136,139,409,410,814],[136,406,407,410,814],[135,136,406,409,814],[136,406,409,410,814], [135,138,140,410,814],[135,138,139,409,814],[135,138,408,409,814],[135,138,408,410,814], [135,405,407,410,814],[405,406,407,410,814],[135,405,406,409,814],[405,406,409,410,814], [135,405,408,409,814],[135,405,408,410,814],[405,408,409,410,814],[138,140,143,413,814], [139,140,143,413,814],[138,140,410,413,814],[139,140,410,413,814],[139,142,143,413,814], [138,139,142,412,814],[139,142,412,413,814],[139,409,410,413,814],[138,139,409,412,814], [139,409,412,413,814],[138,141,143,413,814],[138,141,142,412,814],[138,141,411,412,814], [138,141,411,413,814],[138,408,410,413,814],[408,409,410,413,814],[138,408,409,412,814], [408,409,412,413,814],[138,408,411,412,814],[138,408,411,413,814],[408,411,412,413,814], [141,143,146,416,814],[142,143,146,416,814],[141,143,413,416,814],[142,143,413,416,814], [142,145,146,416,814],[141,142,145,415,814],[142,145,415,416,814],[142,412,413,416,814], [141,142,412,415,814],[142,412,415,416,814],[141,144,146,416,814],[141,144,145,415,814], [141,144,414,415,814],[141,144,414,416,814],[141,411,413,416,814],[411,412,413,416,814], [141,411,412,415,814],[411,412,415,416,814],[141,411,414,415,814],[141,411,414,416,814], [411,414,415,416,814],[144,146,149,419,814],[145,146,149,419,814],[144,146,416,419,814], [145,146,416,419,814],[145,148,149,419,814],[144,145,148,418,814],[145,148,418,419,814], [145,415,416,419,814],[144,145,415,418,814],[145,415,418,419,814],[144,147,149,419,814], [144,147,148,418,814],[144,147,417,418,814],[144,147,417,419,814],[144,414,416,419,814], [414,415,416,419,814],[144,414,415,418,814],[414,415,418,419,814],[144,414,417,418,814], [144,414,417,419,814],[414,417,418,419,814],[147,149,152,422,814],[148,149,152,422,814], [147,149,419,422,814],[148,149,419,422,814],[148,151,152,422,814],[147,148,151,421,814], [148,151,421,422,814],[148,418,419,422,814],[147,148,418,421,814],[148,418,421,422,814], [147,150,152,422,814],[147,150,151,421,814],[147,150,420,421,814],[147,150,420,422,814], [147,417,419,422,814],[417,418,419,422,814],[147,417,418,421,814],[417,418,421,422,814], [147,417,420,421,814],[147,417,420,422,814],[417,420,421,422,814],[150,152,155,425,814], [151,152,155,425,814],[150,152,422,425,814],[151,152,422,425,814],[151,154,155,425,814], [150,151,154,424,814],[151,154,424,425,814],[151,421,422,425,814],[150,151,421,424,814], [151,421,424,425,814],[150,153,155,425,814],[150,153,154,424,814],[150,153,423,424,814], [150,153,423,425,814],[150,420,422,425,814],[420,421,422,425,814],[150,420,421,424,814], [420,421,424,425,814],[150,420,423,424,814],[150,420,423,425,814],[420,423,424,425,814], [153,155,158,428,814],[154,155,158,428,814],[153,155,425,428,814],[154,155,425,428,814], [154,157,158,428,814],[153,154,157,427,814],[154,157,427,428,814],[154,424,425,428,814], [153,154,424,427,814],[154,424,427,428,814],[153,156,158,428,814],[153,156,157,427,814], [153,156,426,427,814],[153,156,426,428,814],[153,423,425,428,814],[423,424,425,428,814], [153,423,424,427,814],[423,424,427,428,814],[153,423,426,427,814],[153,423,426,428,814], [423,426,427,428,814],[156,158,161,431,814],[157,158,161,431,814],[156,158,428,431,814], [157,158,428,431,814],[157,160,161,431,814],[156,157,160,430,814],[157,160,430,431,814], [157,427,428,431,814],[156,157,427,430,814],[157,427,430,431,814],[156,159,161,431,814], [156,159,160,430,814],[156,159,429,430,814],[156,159,429,431,814],[156,426,428,431,814], [426,427,428,431,814],[156,426,427,430,814],[426,427,430,431,814],[156,426,429,430,814], [156,426,429,431,814],[426,429,430,431,814],[159,161,164,434,814],[160,161,164,434,814], [159,161,431,434,814],[160,161,431,434,814],[160,163,164,434,814],[159,160,163,433,814], [160,163,433,434,814],[160,430,431,434,814],[159,160,430,433,814],[160,430,433,434,814], [159,162,164,434,814],[159,162,163,433,814],[159,162,432,433,814],[159,162,432,434,814], [159,429,431,434,814],[429,430,431,434,814],[159,429,430,433,814],[429,430,433,434,814], [159,429,432,433,814],[159,429,432,434,814],[429,432,433,434,814],[162,164,167,437,814], [163,164,167,437,814],[162,164,434,437,814],[163,164,434,437,814],[163,166,167,437,814], [162,163,166,436,814],[163,166,436,437,814],[163,433,434,437,814],[162,163,433,436,814], [163,433,436,437,814],[162,165,167,437,814],[162,165,166,436,814],[162,165,435,436,814], [162,165,435,437,814],[162,432,434,437,814],[432,433,434,437,814],[162,432,433,436,814], [432,433,436,437,814],[162,432,435,436,814],[162,432,435,437,814],[432,435,436,437,814], [165,167,170,440,814],[166,167,170,440,814],[165,167,437,440,814],[166,167,437,440,814], [166,169,170,440,814],[165,166,169,439,814],[166,169,439,440,814],[166,436,437,440,814], [165,166,436,439,814],[166,436,439,440,814],[165,168,170,440,814],[165,168,169,439,814], [165,168,438,439,814],[165,168,438,440,814],[165,435,437,440,814],[435,436,437,440,814], [165,435,436,439,814],[435,436,439,440,814],[165,435,438,439,814],[165,435,438,440,814], [435,438,439,440,814],[168,170,173,443,814],[169,170,173,443,814],[168,170,440,443,814], [169,170,440,443,814],[169,172,173,443,814],[168,169,172,442,814],[169,172,442,443,814], [169,439,440,443,814],[168,169,439,442,814],[169,439,442,443,814],[168,171,173,443,814], [168,171,172,442,814],[168,171,441,442,814],[168,171,441,443,814],[168,438,440,443,814], [438,439,440,443,814],[168,438,439,442,814],[438,439,442,443,814],[168,438,441,442,814], [168,438,441,443,814],[438,441,442,443,814],[171,173,176,446,814],[172,173,176,446,814], [171,173,443,446,814],[172,173,443,446,814],[172,175,176,446,814],[171,172,175,445,814], [172,175,445,446,814],[172,442,443,446,814],[171,172,442,445,814],[172,442,445,446,814], [171,174,176,446,814],[171,174,175,445,814],[171,174,444,445,814],[171,174,444,446,814], [171,441,443,446,814],[441,442,443,446,814],[171,441,442,445,814],[441,442,445,446,814], [171,441,444,445,814],[171,441,444,446,814],[441,444,445,446,814],[174,176,179,449,814], [175,176,179,449,814],[174,176,446,449,814],[175,176,446,449,814],[175,178,179,449,814], [174,175,178,448,814],[175,178,448,449,814],[175,445,446,449,814],[174,175,445,448,814], [175,445,448,449,814],[174,177,179,449,814],[174,177,178,448,814],[174,177,447,448,814], [174,177,447,449,814],[174,444,446,449,814],[444,445,446,449,814],[174,444,445,448,814], [444,445,448,449,814],[174,444,447,448,814],[174,444,447,449,814],[444,447,448,449,814], [177,179,182,452,814],[178,179,182,452,814],[177,179,449,452,814],[178,179,449,452,814], [178,181,182,452,814],[177,178,181,451,814],[178,181,451,452,814],[178,448,449,452,814], [177,178,448,451,814],[178,448,451,452,814],[177,180,182,452,814],[177,180,181,451,814], [177,180,450,451,814],[177,180,450,452,814],[177,447,449,452,814],[447,448,449,452,814], [177,447,448,451,814],[447,448,451,452,814],[177,447,450,451,814],[177,447,450,452,814], [447,450,451,452,814],[180,182,185,455,814],[181,182,185,455,814],[180,182,452,455,814], [181,182,452,455,814],[181,184,185,455,814],[180,181,184,454,814],[181,184,454,455,814], [181,451,452,455,814],[180,181,451,454,814],[181,451,454,455,814],[180,183,185,455,814], [180,183,184,454,814],[180,183,453,454,814],[180,183,453,455,814],[180,450,452,455,814], [450,451,452,455,814],[180,450,451,454,814],[450,451,454,455,814],[180,450,453,454,814], [180,450,453,455,814],[450,453,454,455,814],[183,185,188,458,814],[184,185,188,458,814], [183,185,455,458,814],[184,185,455,458,814],[184,187,188,458,814],[183,184,187,457,814], [184,187,457,458,814],[184,454,455,458,814],[183,184,454,457,814],[184,454,457,458,814], [183,186,188,458,814],[183,186,187,457,814],[183,186,456,457,814],[183,186,456,458,814], [183,453,455,458,814],[453,454,455,458,814],[183,453,454,457,814],[453,454,457,458,814], [183,453,456,457,814],[183,453,456,458,814],[453,456,457,458,814],[186,188,191,461,814], [187,188,191,461,814],[186,188,458,461,814],[187,188,458,461,814],[187,190,191,461,814], [186,187,190,460,814],[187,190,460,461,814],[187,457,458,461,814],[186,187,457,460,814], [187,457,460,461,814],[186,189,191,461,814],[186,189,190,460,814],[186,189,459,460,814], [186,189,459,461,814],[186,456,458,461,814],[456,457,458,461,814],[186,456,457,460,814], [456,457,460,461,814],[186,456,459,460,814],[186,456,459,461,814],[456,459,460,461,814], [189,191,194,464,814],[190,191,194,464,814],[189,191,461,464,814],[190,191,461,464,814], [190,193,194,464,814],[189,190,193,463,814],[190,193,463,464,814],[190,460,461,464,814], [189,190,460,463,814],[190,460,463,464,814],[189,192,194,464,814],[189,192,193,463,814], [189,192,462,463,814],[189,192,462,464,814],[189,459,461,464,814],[459,460,461,464,814], [189,459,460,463,814],[459,460,463,464,814],[189,459,462,463,814],[189,459,462,464,814], [459,462,463,464,814],[192,194,197,467,814],[193,194,197,467,814],[192,194,464,467,814], [193,194,464,467,814],[193,196,197,467,814],[192,193,196,466,814],[193,196,466,467,814], [193,463,464,467,814],[192,193,463,466,814],[193,463,466,467,814],[192,195,197,467,814], [192,195,196,466,814],[192,195,465,466,814],[192,195,465,467,814],[192,462,464,467,814], [462,463,464,467,814],[192,462,463,466,814],[462,463,466,467,814],[192,462,465,466,814], [192,462,465,467,814],[462,465,466,467,814],[195,197,200,470,814],[196,197,200,470,814], [195,197,467,470,814],[196,197,467,470,814],[196,199,200,470,814],[195,196,199,469,814], [196,199,469,470,814],[196,466,467,470,814],[195,196,466,469,814],[196,466,469,470,814], [195,198,200,470,814],[195,198,199,469,814],[195,198,468,469,814],[195,198,468,470,814], [195,465,467,470,814],[465,466,467,470,814],[195,465,466,469,814],[465,466,469,470,814], [195,465,468,469,814],[195,465,468,470,814],[465,468,469,470,814],[198,200,203,473,814], [199,200,203,473,814],[198,200,470,473,814],[199,200,470,473,814],[199,202,203,473,814], [198,199,202,472,814],[199,202,472,473,814],[199,469,470,473,814],[198,199,469,472,814], [199,469,472,473,814],[198,201,203,473,814],[198,201,202,472,814],[198,201,471,472,814], [198,201,471,473,814],[198,468,470,473,814],[468,469,470,473,814],[198,468,469,472,814], [468,469,472,473,814],[198,468,471,472,814],[198,468,471,473,814],[468,471,472,473,814], [201,203,206,476,814],[202,203,206,476,814],[201,203,473,476,814],[202,203,473,476,814], [202,205,206,476,814],[201,202,205,475,814],[202,205,475,476,814],[202,472,473,476,814], [201,202,472,475,814],[202,472,475,476,814],[201,204,206,476,814],[201,204,205,475,814], [201,204,474,475,814],[201,204,474,476,814],[201,471,473,476,814],[471,472,473,476,814], [201,471,472,475,814],[471,472,475,476,814],[201,471,474,475,814],[201,471,474,476,814], [471,474,475,476,814],[204,206,209,479,814],[205,206,209,479,814],[204,206,476,479,814], [205,206,476,479,814],[205,208,209,479,814],[204,205,208,478,814],[205,208,478,479,814], [205,475,476,479,814],[204,205,475,478,814],[205,475,478,479,814],[204,207,209,479,814], [204,207,208,478,814],[204,207,477,478,814],[204,207,477,479,814],[204,474,476,479,814], [474,475,476,479,814],[204,474,475,478,814],[474,475,478,479,814],[204,474,477,478,814], [204,474,477,479,814],[474,477,478,479,814],[207,209,212,482,814],[208,209,212,482,814], [207,209,479,482,814],[208,209,479,482,814],[208,211,212,482,814],[207,208,211,481,814], [208,211,481,482,814],[208,478,479,482,814],[207,208,478,481,814],[208,478,481,482,814], [207,210,212,482,814],[207,210,211,481,814],[207,210,480,481,814],[207,210,480,482,814], [207,477,479,482,814],[477,478,479,482,814],[207,477,478,481,814],[477,478,481,482,814], [207,477,480,481,814],[207,477,480,482,814],[477,480,481,482,814],[210,212,215,485,814], [211,212,215,485,814],[210,212,482,485,814],[211,212,482,485,814],[211,214,215,485,814], [210,211,214,484,814],[211,214,484,485,814],[211,481,482,485,814],[210,211,481,484,814], [211,481,484,485,814],[210,213,215,485,814],[210,213,214,484,814],[210,213,483,484,814], [210,213,483,485,814],[210,480,482,485,814],[480,481,482,485,814],[210,480,481,484,814], [480,481,484,485,814],[210,480,483,484,814],[210,480,483,485,814],[480,483,484,485,814], [213,215,218,488,814],[214,215,218,488,814],[213,215,485,488,814],[214,215,485,488,814], [214,217,218,488,814],[213,214,217,487,814],[214,217,487,488,814],[214,484,485,488,814], [213,214,484,487,814],[214,484,487,488,814],[213,216,218,488,814],[213,216,217,487,814], [213,216,486,487,814],[213,216,486,488,814],[213,483,485,488,814],[483,484,485,488,814], [213,483,484,487,814],[483,484,487,488,814],[213,483,486,487,814],[213,483,486,488,814], [483,486,487,488,814],[216,218,221,491,814],[217,218,221,491,814],[216,218,488,491,814], [217,218,488,491,814],[217,220,221,491,814],[216,217,220,490,814],[217,220,490,491,814], [217,487,488,491,814],[216,217,487,490,814],[217,487,490,491,814],[216,219,221,491,814], [216,219,220,490,814],[216,219,489,490,814],[216,219,489,491,814],[216,486,488,491,814], [486,487,488,491,814],[216,486,487,490,814],[486,487,490,491,814],[216,486,489,490,814], [216,486,489,491,814],[486,489,490,491,814],[219,221,224,494,814],[220,221,224,494,814], [219,221,491,494,814],[220,221,491,494,814],[220,223,224,494,814],[219,220,223,493,814], [220,223,493,494,814],[220,490,491,494,814],[219,220,490,493,814],[220,490,493,494,814], [219,222,224,494,814],[219,222,223,493,814],[219,222,492,493,814],[219,222,492,494,814], [219,489,491,494,814],[489,490,491,494,814],[219,489,490,493,814],[489,490,493,494,814], [219,489,492,493,814],[219,489,492,494,814],[489,492,493,494,814],[222,224,227,497,814], [223,224,227,497,814],[222,224,494,497,814],[223,224,494,497,814],[223,226,227,497,814], [222,223,226,496,814],[223,226,496,497,814],[223,493,494,497,814],[222,223,493,496,814], [223,493,496,497,814],[222,225,227,497,814],[222,225,226,496,814],[222,225,495,496,814], [222,225,495,497,814],[222,492,494,497,814],[492,493,494,497,814],[222,492,493,496,814], [492,493,496,497,814],[222,492,495,496,814],[222,492,495,497,814],[492,495,496,497,814], [225,227,230,500,814],[226,227,230,500,814],[225,227,497,500,814],[226,227,497,500,814], [226,229,230,500,814],[225,226,229,499,814],[226,229,499,500,814],[226,496,497,500,814], [225,226,496,499,814],[226,496,499,500,814],[225,228,230,500,814],[225,228,229,499,814], [225,228,498,499,814],[225,228,498,500,814],[225,495,497,500,814],[495,496,497,500,814], [225,495,496,499,814],[495,496,499,500,814],[225,495,498,499,814],[225,495,498,500,814], [495,498,499,500,814],[228,230,233,503,814],[229,230,233,503,814],[228,230,500,503,814], [229,230,500,503,814],[229,232,233,503,814],[228,229,232,502,814],[229,232,502,503,814], [229,499,500,503,814],[228,229,499,502,814],[229,499,502,503,814],[228,231,233,503,814], [228,231,232,502,814],[228,231,501,502,814],[228,231,501,503,814],[228,498,500,503,814], 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