#################################################################################### #################################################################################### #################################################################################### ### ### ### ### ### TRIANGULATIONS OF AKBULUT-KIRBY SPHERES ### ### by Frank H. Lutz and Mimi Tsuruga ### ### http://matsguru.com/research/AKspheres.html ### ### ### ### name of example: ### ### ### ### AK_II_018 ### ### ### ### ### ### description: ### ### ### ### Type 2 construction of triangulation of Akbulut-Kirby sphere ### ### ### ### ### ### properties: ### ### ### ### f=(1040,15654,52236,62700,25080) ### ### 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:=[ [0,1,2,5,521],[0,1,2,35,551],[0,1,2,518,521],[0,1,2,518,551], [0,1,4,5,521],[0,1,4,262,778],[0,1,4,520,521],[0,1,4,520,778], [0,1,34,35,551],[0,1,34,250,508],[0,1,34,250,766],[0,1,34,292,508], [0,1,34,550,551],[0,1,34,550,766],[0,1,249,250,508],[0,1,249,250,766], [0,1,249,507,508],[0,1,249,507,1023],[0,1,249,765,766],[0,1,249,765,1023], [0,1,259,262,778],[0,1,259,292,508],[0,1,259,507,508],[0,1,259,507,1023], [0,1,259,775,778],[0,1,259,775,1023],[0,1,517,518,521],[0,1,517,518,551], [0,1,517,520,521],[0,1,517,520,778],[0,1,517,550,551],[0,1,517,550,766], [0,1,517,765,766],[0,1,517,765,1023],[0,1,517,775,778],[0,1,517,775,1023], [0,2,5,26,284],[2,5,26,284,800],[0,2,5,26,542],[2,5,26,542,800], [0,2,5,263,284],[2,5,263,284,800],[2,5,263,779,800],[0,2,5,521,542], [2,5,521,542,800],[2,5,521,779,800],[0,2,26,29,287],[2,26,29,287,803], [0,2,26,29,545],[2,26,29,545,803],[0,2,26,284,287],[2,26,284,287,803], [2,26,284,800,803],[0,2,26,542,545],[2,26,542,545,803],[2,26,542,800,803], [0,2,29,253,511],[0,2,29,253,769],[0,2,29,287,511],[0,2,29,545,769], [0,2,35,253,511],[0,2,35,253,769],[0,2,35,293,511],[0,2,35,551,769], [0,2,260,263,284],[2,260,263,284,800],[2,260,263,779,800],[0,2,260,284,287], [2,260,284,287,803],[2,260,284,800,803],[0,2,260,287,511],[0,2,260,293,511], [2,260,776,779,800],[2,260,776,800,803],[0,2,518,521,542],[2,518,521,542,800], [2,518,521,779,800],[0,2,518,542,545],[2,518,542,545,803],[2,518,542,800,803], [0,2,518,545,769],[0,2,518,551,769],[2,518,776,779,800],[2,518,776,800,803], [0,3,4,5,521],[0,3,4,262,778],[0,3,4,520,521],[0,3,4,520,778], [0,3,5,26,284],[0,3,5,26,542],[0,3,5,263,284],[0,3,5,521,542], [0,3,24,26,284],[0,3,24,26,542],[0,3,24,282,284],[0,3,24,282,798], [0,3,24,540,542],[0,3,24,540,798],[0,3,261,262,778],[0,3,261,263,284], [0,3,261,282,284],[0,3,261,282,798],[0,3,261,777,778],[0,3,261,777,798], [0,3,519,520,521],[0,3,519,520,778],[0,3,519,521,542],[0,3,519,540,542], [0,3,519,540,798],[0,3,519,777,778],[0,3,519,777,798],[0,24,26,29,287], [0,24,26,29,545],[0,24,26,284,287],[0,24,26,542,545],[0,24,27,29,287], [0,24,27,29,545],[0,24,27,285,287],[0,24,27,285,801],[0,24,27,543,545], [0,24,27,543,801],[0,24,282,284,287],[0,24,282,285,287],[0,24,282,285,801], [0,24,282,798,801],[0,24,540,542,545],[0,24,540,543,545],[0,24,540,543,801], [0,24,540,798,801],[0,27,29,253,511],[0,27,29,253,769],[0,27,29,287,511], [0,27,29,545,769],[0,27,246,250,508],[0,27,246,250,766],[0,27,246,253,511], [0,27,246,253,769],[0,27,246,504,508],[0,27,246,504,511],[0,27,246,762,766], [0,27,246,762,769],[0,27,249,250,508],[0,27,249,250,766],[0,27,249,507,508], [0,27,249,507,1023],[0,27,249,765,766],[0,27,249,765,1023],[0,27,285,287,511], [0,27,285,504,508],[0,27,285,504,511],[0,27,285,507,508],[0,27,285,507,1023], [0,27,285,801,1023],[0,27,543,545,769],[0,27,543,762,766],[0,27,543,762,769], [0,27,543,765,766],[0,27,543,765,1023],[0,27,543,801,1023],[0,33,34,35,551], [0,33,34,250,508],[0,33,34,250,766],[0,33,34,292,508],[0,33,34,550,551], [0,33,34,550,766],[0,33,35,253,511],[0,33,35,253,769],[0,33,35,293,511], [0,33,35,551,769],[0,33,246,250,508],[0,33,246,250,766],[0,33,246,253,511], [0,33,246,253,769],[0,33,246,504,508],[0,33,246,504,511],[0,33,246,762,766], [0,33,246,762,769],[0,33,291,292,508],[0,33,291,293,511],[0,33,291,504,508], [0,33,291,504,511],[0,33,549,550,551],[0,33,549,550,766],[0,33,549,551,769], [0,33,549,762,766],[0,33,549,762,769],[258,259,260,263,779],[258,259,260,293,809], [258,259,260,776,779],[258,259,260,776,809],[258,259,262,263,779],[0,258,259,262,778], [258,259,262,778,779],[258,259,292,293,809],[0,258,259,292,508],[258,259,292,508,1024], [258,259,292,808,809],[258,259,292,808,1024],[0,258,259,507,508],[258,259,507,508,1024], [0,258,259,507,1023],[258,259,507,1023,1024],[258,259,775,776,779],[258,259,775,776,809], [0,258,259,775,778],[258,259,775,778,779],[258,259,775,808,809],[258,259,775,808,1024], [0,258,259,775,1023],[258,259,775,1023,1024],[0,258,260,263,284],[258,260,263,284,800], [258,260,263,779,800],[0,258,260,284,287],[258,260,284,287,803],[258,260,284,800,803], [0,258,260,287,511],[258,260,287,511,1027],[258,260,287,803,1027],[0,258,260,293,511], [258,260,293,511,1027],[258,260,293,809,1027],[258,260,776,779,800],[258,260,776,800,803], [258,260,776,803,1027],[258,260,776,809,1027],[258,261,262,263,779],[0,258,261,262,778], [258,261,262,778,779],[0,258,261,263,284],[258,261,263,284,800],[258,261,263,779,800], [0,258,261,282,284],[258,261,282,284,800],[0,258,261,282,798],[258,261,282,798,800], [0,258,261,777,778],[258,261,777,778,779],[258,261,777,779,800],[0,258,261,777,798], [258,261,777,798,800],[0,258,282,284,287],[258,282,284,287,803],[258,282,284,800,803], [0,258,282,285,287],[258,282,285,287,803],[0,258,282,285,801],[258,282,285,801,803], [258,282,798,800,803],[0,258,282,798,801],[258,282,798,801,803],[0,258,285,287,511], [258,285,287,511,1027],[258,285,287,803,1027],[0,258,285,504,508],[258,285,504,508,1024], [0,258,285,504,511],[258,285,504,511,1027],[258,285,504,1020,1024],[258,285,504,1020,1027], [0,258,285,507,508],[258,285,507,508,1024],[0,258,285,507,1023],[258,285,507,1023,1024], [258,285,801,803,1027],[258,285,801,1020,1024],[258,285,801,1020,1027],[0,258,285,801,1023], [258,285,801,1023,1024],[258,291,292,293,809],[0,258,291,292,508],[258,291,292,508,1024], [258,291,292,808,809],[258,291,292,808,1024],[0,258,291,293,511],[258,291,293,511,1027], [258,291,293,809,1027],[0,258,291,504,508],[258,291,504,508,1024],[0,258,291,504,511], [258,291,504,511,1027],[258,291,504,1020,1024],[258,291,504,1020,1027],[258,291,807,808,809], [258,291,807,808,1024],[258,291,807,809,1027],[258,291,807,1020,1024],[258,291,807,1020,1027], [258,774,775,776,779],[258,774,775,776,809],[0,258,774,775,778],[258,774,775,778,779], [258,774,775,808,809],[258,774,775,808,1024],[0,258,774,775,1023],[258,774,775,1023,1024], [258,774,776,779,800],[258,774,776,800,803],[258,774,776,803,1027],[258,774,776,809,1027], [0,258,774,777,778],[258,774,777,778,779],[258,774,777,779,800],[0,258,774,777,798], [258,774,777,798,800],[258,774,798,800,803],[0,258,774,798,801],[258,774,798,801,803], [258,774,801,803,1027],[258,774,801,1020,1024],[258,774,801,1020,1027],[0,258,774,801,1023], [258,774,801,1023,1024],[258,774,807,808,809],[258,774,807,808,1024],[258,774,807,809,1027], [258,774,807,1020,1024],[258,774,807,1020,1027],[0,516,517,518,521],[516,517,518,521,779], [0,516,517,518,551],[516,517,518,551,809],[516,517,518,776,779],[516,517,518,776,809], [0,516,517,520,521],[516,517,520,521,779],[0,516,517,520,778],[516,517,520,778,779], [0,516,517,550,551],[516,517,550,551,809],[0,516,517,550,766],[516,517,550,766,1024], [516,517,550,808,809],[516,517,550,808,1024],[0,516,517,765,766],[516,517,765,766,1024], [0,516,517,765,1023],[516,517,765,1023,1024],[516,517,775,776,779],[516,517,775,776,809], [0,516,517,775,778],[516,517,775,778,779],[516,517,775,808,809],[516,517,775,808,1024], [0,516,517,775,1023],[516,517,775,1023,1024],[0,516,518,521,542],[516,518,521,542,800], [516,518,521,779,800],[0,516,518,542,545],[516,518,542,545,803],[516,518,542,800,803], [0,516,518,545,769],[516,518,545,769,1027],[516,518,545,803,1027],[0,516,518,551,769], [516,518,551,769,1027],[516,518,551,809,1027],[516,518,776,779,800],[516,518,776,800,803], [516,518,776,803,1027],[516,518,776,809,1027],[0,516,519,520,521],[516,519,520,521,779], [0,516,519,520,778],[516,519,520,778,779],[0,516,519,521,542],[516,519,521,542,800], [516,519,521,779,800],[0,516,519,540,542],[516,519,540,542,800],[0,516,519,540,798], [516,519,540,798,800],[0,516,519,777,778],[516,519,777,778,779],[516,519,777,779,800], [0,516,519,777,798],[516,519,777,798,800],[0,516,540,542,545],[516,540,542,545,803], [516,540,542,800,803],[0,516,540,543,545],[516,540,543,545,803],[0,516,540,543,801], [516,540,543,801,803],[516,540,798,800,803],[0,516,540,798,801],[516,540,798,801,803], [0,516,543,545,769],[516,543,545,769,1027],[516,543,545,803,1027],[0,516,543,762,766], [516,543,762,766,1024],[0,516,543,762,769],[516,543,762,769,1027],[516,543,762,1020,1024], [516,543,762,1020,1027],[0,516,543,765,766],[516,543,765,766,1024],[0,516,543,765,1023], [516,543,765,1023,1024],[516,543,801,803,1027],[516,543,801,1020,1024],[516,543,801,1020,1027], [0,516,543,801,1023],[516,543,801,1023,1024],[0,516,549,550,551],[516,549,550,551,809], [0,516,549,550,766],[516,549,550,766,1024],[516,549,550,808,809],[516,549,550,808,1024], [0,516,549,551,769],[516,549,551,769,1027],[516,549,551,809,1027],[0,516,549,762,766], [516,549,762,766,1024],[0,516,549,762,769],[516,549,762,769,1027],[516,549,762,1020,1024], [516,549,762,1020,1027],[516,549,807,808,809],[516,549,807,808,1024],[516,549,807,809,1027], [516,549,807,1020,1024],[516,549,807,1020,1027],[516,774,775,776,779],[516,774,775,776,809], [0,516,774,775,778],[516,774,775,778,779],[516,774,775,808,809],[516,774,775,808,1024], [0,516,774,775,1023],[516,774,775,1023,1024],[516,774,776,779,800],[516,774,776,800,803], [516,774,776,803,1027],[516,774,776,809,1027],[0,516,774,777,778],[516,774,777,778,779], [516,774,777,779,800],[0,516,774,777,798],[516,774,777,798,800],[516,774,798,800,803], [0,516,774,798,801],[516,774,798,801,803],[516,774,801,803,1027],[516,774,801,1020,1024], [516,774,801,1020,1027],[0,516,774,801,1023],[516,774,801,1023,1024],[516,774,807,808,809], [516,774,807,808,1024],[516,774,807,809,1027],[516,774,807,1020,1024],[516,774,807,1020,1027], [1,2,5,41,299],[2,5,41,299,815],[1,2,5,41,557],[2,5,41,557,815], [1,2,5,263,299],[2,5,263,299,815],[2,5,263,779,815],[1,2,5,521,557], [2,5,521,557,815],[2,5,521,779,815],[1,2,35,253,511],[1,2,35,253,769], [1,2,35,293,511],[1,2,35,551,769],[1,2,38,41,299],[2,38,41,299,815], [1,2,38,41,557],[2,38,41,557,815],[1,2,38,256,514],[1,2,38,256,772], [1,2,38,296,299],[2,38,296,299,815],[1,2,38,296,514],[2,38,296,812,815], [1,2,38,554,557],[2,38,554,557,815],[1,2,38,554,772],[2,38,554,812,815], [1,2,252,253,511],[1,2,252,253,769],[1,2,252,256,514],[1,2,252,256,772], [1,2,252,510,511],[1,2,252,510,514],[1,2,252,768,769],[1,2,252,768,772], [1,2,260,263,299],[2,260,263,299,815],[2,260,263,779,815],[1,2,260,293,511], [1,2,260,296,299],[2,260,296,299,815],[1,2,260,296,514],[2,260,296,812,815], [1,2,260,510,511],[1,2,260,510,514],[2,260,776,779,815],[2,260,776,812,815], [1,2,518,521,557],[2,518,521,557,815],[2,518,521,779,815],[1,2,518,551,769], [1,2,518,554,557],[2,518,554,557,815],[1,2,518,554,772],[2,518,554,812,815], [1,2,518,768,769],[1,2,518,768,772],[2,518,776,779,815],[2,518,776,812,815], [1,4,5,41,299],[1,4,5,41,557],[1,4,5,263,299],[1,4,5,521,557], [1,4,39,41,299],[1,4,39,41,557],[1,4,39,297,299],[1,4,39,297,813], [1,4,39,555,557],[1,4,39,555,813],[1,4,262,263,299],[1,4,262,297,299], [1,4,262,297,813],[1,4,262,778,813],[1,4,520,521,557],[1,4,520,555,557], [1,4,520,555,813],[1,4,520,778,813],[1,34,35,253,511],[1,34,35,253,769], [1,34,35,293,511],[1,34,35,551,769],[1,34,247,250,508],[1,34,247,250,766], [1,34,247,253,511],[1,34,247,253,769],[1,34,247,505,508],[1,34,247,505,511], [1,34,247,763,766],[1,34,247,763,769],[1,34,292,293,511],[1,34,292,505,508], [1,34,292,505,511],[1,34,550,551,769],[1,34,550,763,766],[1,34,550,763,769], [1,36,38,41,299],[1,36,38,41,557],[1,36,38,256,514],[1,36,38,256,772], [1,36,38,296,299],[1,36,38,296,514],[1,36,38,554,557],[1,36,38,554,772], [1,36,39,41,299],[1,36,39,41,557],[1,36,39,297,299],[1,36,39,297,813], [1,36,39,555,557],[1,36,39,555,813],[1,36,247,250,508],[1,36,247,250,766], [1,36,247,253,511],[1,36,247,253,769],[1,36,247,505,508],[1,36,247,505,511], [1,36,247,763,766],[1,36,247,763,769],[1,36,249,250,508],[1,36,249,250,766], [1,36,249,507,508],[1,36,249,507,1023],[1,36,249,765,766],[1,36,249,765,1023], [1,36,252,253,511],[1,36,252,253,769],[1,36,252,256,514],[1,36,252,256,772], [1,36,252,510,511],[1,36,252,510,514],[1,36,252,768,769],[1,36,252,768,772], [1,36,294,296,299],[1,36,294,296,514],[1,36,294,297,299],[1,36,294,297,813], [1,36,294,505,508],[1,36,294,505,511],[1,36,294,507,508],[1,36,294,507,1023], [1,36,294,510,511],[1,36,294,510,514],[1,36,294,810,813],[1,36,294,810,1023], [1,36,552,554,557],[1,36,552,554,772],[1,36,552,555,557],[1,36,552,555,813], [1,36,552,763,766],[1,36,552,763,769],[1,36,552,765,766],[1,36,552,765,1023], [1,36,552,768,769],[1,36,552,768,772],[1,36,552,810,813],[1,36,552,810,1023], [1,259,260,263,299],[259,260,263,299,815],[259,260,263,779,815],[1,259,260,293,511], [259,260,293,511,1027],[259,260,293,809,1027],[1,259,260,296,299],[259,260,296,299,815], [1,259,260,296,514],[259,260,296,514,1030],[259,260,296,812,815],[259,260,296,812,1030], [1,259,260,510,511],[259,260,510,511,1027],[1,259,260,510,514],[259,260,510,514,1030], [259,260,510,1026,1027],[259,260,510,1026,1030],[259,260,776,779,815],[259,260,776,809,1027], [259,260,776,812,815],[259,260,776,812,1030],[259,260,776,1026,1027],[259,260,776,1026,1030], [1,259,262,263,299],[259,262,263,299,815],[259,262,263,779,815],[1,259,262,297,299], [259,262,297,299,815],[1,259,262,297,813],[259,262,297,813,815],[259,262,778,779,815], [1,259,262,778,813],[259,262,778,813,815],[1,259,292,293,511],[259,292,293,511,1027], [259,292,293,809,1027],[1,259,292,505,508],[259,292,505,508,1024],[1,259,292,505,511], [259,292,505,511,1027],[259,292,505,1021,1024],[259,292,505,1021,1027],[259,292,808,809,1027], [259,292,808,1021,1024],[259,292,808,1021,1027],[1,259,294,296,299],[259,294,296,299,815], [1,259,294,296,514],[259,294,296,514,1030],[259,294,296,812,815],[259,294,296,812,1030], [1,259,294,297,299],[259,294,297,299,815],[1,259,294,297,813],[259,294,297,813,815], [1,259,294,505,508],[259,294,505,508,1024],[1,259,294,505,511],[259,294,505,511,1027], [259,294,505,1021,1024],[259,294,505,1021,1027],[1,259,294,507,508],[259,294,507,508,1024], [1,259,294,507,1023],[259,294,507,1023,1024],[1,259,294,510,511],[259,294,510,511,1027], [1,259,294,510,514],[259,294,510,514,1030],[259,294,510,1026,1027],[259,294,510,1026,1030], [259,294,810,812,815],[259,294,810,812,1030],[1,259,294,810,813],[259,294,810,813,815], [259,294,810,1021,1024],[259,294,810,1021,1027],[1,259,294,810,1023],[259,294,810,1023,1024], 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[171,429,431,434,1036],[429,430,431,434,1036],[171,429,430,433,1036],[429,430,433,434,1036], [171,429,432,433,1036],[171,429,432,434,1036],[429,432,433,434,1036],[174,176,179,437,1036], [175,176,179,437,1036],[174,176,434,437,1036],[175,176,434,437,1036],[175,178,179,437,1036], [174,175,178,436,1036],[175,178,436,437,1036],[175,433,434,437,1036],[174,175,433,436,1036], [175,433,436,437,1036],[174,177,179,437,1036],[174,177,178,436,1036],[174,177,435,436,1036], [174,177,435,437,1036],[174,432,434,437,1036],[432,433,434,437,1036],[174,432,433,436,1036], [432,433,436,437,1036],[174,432,435,436,1036],[174,432,435,437,1036],[432,435,436,437,1036], [177,179,182,440,1036],[178,179,182,440,1036],[177,179,437,440,1036],[178,179,437,440,1036], [178,181,182,440,1036],[177,178,181,439,1036],[178,181,439,440,1036],[178,436,437,440,1036], [177,178,436,439,1036],[178,436,439,440,1036],[177,180,182,440,1036],[177,180,181,439,1036], 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[183,186,188,446,1036],[183,186,187,445,1036],[183,186,444,445,1036],[183,186,444,446,1036], [183,441,443,446,1036],[441,442,443,446,1036],[183,441,442,445,1036],[441,442,445,446,1036], [183,441,444,445,1036],[183,441,444,446,1036],[441,444,445,446,1036],[186,188,191,449,1036], [187,188,191,449,1036],[186,188,446,449,1036],[187,188,446,449,1036],[187,190,191,449,1036], [186,187,190,448,1036],[187,190,448,449,1036],[187,445,446,449,1036],[186,187,445,448,1036], [187,445,448,449,1036],[186,189,191,449,1036],[186,189,190,448,1036],[186,189,447,448,1036], [186,189,447,449,1036],[186,444,446,449,1036],[444,445,446,449,1036],[186,444,445,448,1036], [444,445,448,449,1036],[186,444,447,448,1036],[186,444,447,449,1036],[444,447,448,449,1036], [189,191,194,452,1036],[190,191,194,452,1036],[189,191,449,452,1036],[190,191,449,452,1036], [190,193,194,452,1036],[189,190,193,451,1036],[190,193,451,452,1036],[190,448,449,452,1036], [189,190,448,451,1036],[190,448,451,452,1036],[189,192,194,452,1036],[189,192,193,451,1036], [189,192,450,451,1036],[189,192,450,452,1036],[189,447,449,452,1036],[447,448,449,452,1036], [189,447,448,451,1036],[447,448,451,452,1036],[189,447,450,451,1036],[189,447,450,452,1036], [447,450,451,452,1036],[192,194,197,455,1036],[193,194,197,455,1036],[192,194,452,455,1036], [193,194,452,455,1036],[193,196,197,455,1036],[192,193,196,454,1036],[193,196,454,455,1036], [193,451,452,455,1036],[192,193,451,454,1036],[193,451,454,455,1036],[192,195,197,455,1036], [192,195,196,454,1036],[192,195,453,454,1036],[192,195,453,455,1036],[192,450,452,455,1036], [450,451,452,455,1036],[192,450,451,454,1036],[450,451,454,455,1036],[192,450,453,454,1036], [192,450,453,455,1036],[450,453,454,455,1036],[195,197,200,458,1036],[196,197,200,458,1036], [195,197,455,458,1036],[196,197,455,458,1036],[196,199,200,458,1036],[195,196,199,457,1036], [196,199,457,458,1036],[196,454,455,458,1036],[195,196,454,457,1036],[196,454,457,458,1036], [195,198,200,458,1036],[195,198,199,457,1036],[195,198,456,457,1036],[195,198,456,458,1036], [195,453,455,458,1036],[453,454,455,458,1036],[195,453,454,457,1036],[453,454,457,458,1036], [195,453,456,457,1036],[195,453,456,458,1036],[453,456,457,458,1036],[198,200,203,461,1036], [199,200,203,461,1036],[198,200,458,461,1036],[199,200,458,461,1036],[199,202,203,461,1036], [198,199,202,460,1036],[199,202,460,461,1036],[199,457,458,461,1036],[198,199,457,460,1036], [199,457,460,461,1036],[198,201,203,461,1036],[198,201,202,460,1036],[198,201,459,460,1036], [198,201,459,461,1036],[198,456,458,461,1036],[456,457,458,461,1036],[198,456,457,460,1036], [456,457,460,461,1036],[198,456,459,460,1036],[198,456,459,461,1036],[456,459,460,461,1036], [201,203,206,464,1036],[202,203,206,464,1036],[201,203,461,464,1036],[202,203,461,464,1036], [202,205,206,464,1036],[201,202,205,463,1036],[202,205,463,464,1036],[202,460,461,464,1036], [201,202,460,463,1036],[202,460,463,464,1036],[201,204,206,464,1036],[201,204,205,463,1036], [201,204,462,463,1036],[201,204,462,464,1036],[201,459,461,464,1036],[459,460,461,464,1036], [201,459,460,463,1036],[459,460,463,464,1036],[201,459,462,463,1036],[201,459,462,464,1036], [459,462,463,464,1036],[204,206,209,467,1036],[205,206,209,467,1036],[204,206,464,467,1036], [205,206,464,467,1036],[205,208,209,467,1036],[204,205,208,466,1036],[205,208,466,467,1036], [205,463,464,467,1036],[204,205,463,466,1036],[205,463,466,467,1036],[204,207,209,467,1036], [204,207,208,466,1036],[204,207,465,466,1036],[204,207,465,467,1036],[204,462,464,467,1036], [462,463,464,467,1036],[204,462,463,466,1036],[462,463,466,467,1036],[204,462,465,466,1036], [204,462,465,467,1036],[462,465,466,467,1036],[207,209,212,470,1036],[208,209,212,470,1036], [207,209,467,470,1036],[208,209,467,470,1036],[208,211,212,470,1036],[207,208,211,469,1036], [208,211,469,470,1036],[208,466,467,470,1036],[207,208,466,469,1036],[208,466,469,470,1036], [207,210,212,470,1036],[207,210,211,469,1036],[207,210,468,469,1036],[207,210,468,470,1036], [207,465,467,470,1036],[465,466,467,470,1036],[207,465,466,469,1036],[465,466,469,470,1036], [207,465,468,469,1036],[207,465,468,470,1036],[465,468,469,470,1036],[210,212,215,473,1036], [211,212,215,473,1036],[210,212,470,473,1036],[211,212,470,473,1036],[211,214,215,473,1036], [210,211,214,472,1036],[211,214,472,473,1036],[211,469,470,473,1036],[210,211,469,472,1036], [211,469,472,473,1036],[210,213,215,473,1036],[210,213,214,472,1036],[210,213,471,472,1036], [210,213,471,473,1036],[210,468,470,473,1036],[468,469,470,473,1036],[210,468,469,472,1036], [468,469,472,473,1036],[210,468,471,472,1036],[210,468,471,473,1036],[468,471,472,473,1036], [213,215,218,476,1036],[214,215,218,476,1036],[213,215,473,476,1036],[214,215,473,476,1036], [214,217,218,476,1036],[213,214,217,475,1036],[214,217,475,476,1036],[214,472,473,476,1036], [213,214,472,475,1036],[214,472,475,476,1036],[213,216,218,476,1036],[213,216,217,475,1036], [213,216,474,475,1036],[213,216,474,476,1036],[213,471,473,476,1036],[471,472,473,476,1036], [213,471,472,475,1036],[471,472,475,476,1036],[213,471,474,475,1036],[213,471,474,476,1036], [471,474,475,476,1036],[216,218,221,479,1036],[217,218,221,479,1036],[216,218,476,479,1036], [217,218,476,479,1036],[217,220,221,479,1036],[216,217,220,478,1036],[217,220,478,479,1036], [217,475,476,479,1036],[216,217,475,478,1036],[217,475,478,479,1036],[216,219,221,479,1036], [216,219,220,478,1036],[216,219,477,478,1036],[216,219,477,479,1036],[216,474,476,479,1036], [474,475,476,479,1036],[216,474,475,478,1036],[474,475,478,479,1036],[216,474,477,478,1036], [216,474,477,479,1036],[474,477,478,479,1036],[219,221,224,482,1036],[220,221,224,482,1036], [219,221,479,482,1036],[220,221,479,482,1036],[220,223,224,482,1036],[219,220,223,481,1036], [220,223,481,482,1036],[220,478,479,482,1036],[219,220,478,481,1036],[220,478,481,482,1036], [219,222,224,482,1036],[219,222,223,481,1036],[219,222,480,481,1036],[219,222,480,482,1036], [219,477,479,482,1036],[477,478,479,482,1036],[219,477,478,481,1036],[477,478,481,482,1036], [219,477,480,481,1036],[219,477,480,482,1036],[477,480,481,482,1036],[222,224,227,485,1036], [223,224,227,485,1036],[222,224,482,485,1036],[223,224,482,485,1036],[223,226,227,485,1036], [222,223,226,484,1036],[223,226,484,485,1036],[223,481,482,485,1036],[222,223,481,484,1036], [223,481,484,485,1036],[222,225,227,485,1036],[222,225,226,484,1036],[222,225,483,484,1036], [222,225,483,485,1036],[222,480,482,485,1036],[480,481,482,485,1036],[222,480,481,484,1036], [480,481,484,485,1036],[222,480,483,484,1036],[222,480,483,485,1036],[480,483,484,485,1036], [225,227,230,488,1036],[226,227,230,488,1036],[225,227,485,488,1036],[226,227,485,488,1036], [226,229,230,488,1036],[225,226,229,487,1036],[226,229,487,488,1036],[226,484,485,488,1036], [225,226,484,487,1036],[226,484,487,488,1036],[225,228,230,488,1036],[225,228,229,487,1036], [225,228,486,487,1036],[225,228,486,488,1036],[225,483,485,488,1036],[483,484,485,488,1036], [225,483,484,487,1036],[483,484,487,488,1036],[225,483,486,487,1036],[225,483,486,488,1036], [483,486,487,488,1036],[228,230,233,491,1036],[229,230,233,491,1036],[228,230,488,491,1036], [229,230,488,491,1036],[229,232,233,491,1036],[228,229,232,490,1036],[229,232,490,491,1036], [229,487,488,491,1036],[228,229,487,490,1036],[229,487,490,491,1036],[228,231,233,491,1036], [228,231,232,490,1036],[228,231,489,490,1036],[228,231,489,491,1036],[228,486,488,491,1036], [486,487,488,491,1036],[228,486,487,490,1036],[486,487,490,491,1036],[228,486,489,490,1036], [228,486,489,491,1036],[486,489,490,491,1036],[231,233,236,494,1036],[232,233,236,494,1036], [231,233,491,494,1036],[232,233,491,494,1036],[232,235,236,494,1036],[231,232,235,493,1036], [232,235,493,494,1036],[232,490,491,494,1036],[231,232,490,493,1036],[232,490,493,494,1036], [231,234,236,494,1036],[231,234,235,493,1036],[231,234,492,493,1036],[231,234,492,494,1036], [231,489,491,494,1036],[489,490,491,494,1036],[231,489,490,493,1036],[489,490,493,494,1036], [231,489,492,493,1036],[231,489,492,494,1036],[489,492,493,494,1036],[234,236,239,497,1036], [235,236,239,497,1036],[234,236,494,497,1036],[235,236,494,497,1036],[235,238,239,497,1036], [234,235,238,496,1036],[235,238,496,497,1036],[235,493,494,497,1036],[234,235,493,496,1036], [235,493,496,497,1036],[234,237,239,497,1036],[234,237,238,496,1036],[234,237,495,496,1036], [234,237,495,497,1036],[234,492,494,497,1036],[492,493,494,497,1036],[234,492,493,496,1036], [492,493,496,497,1036],[234,492,495,496,1036],[234,492,495,497,1036],[492,495,496,497,1036], [237,239,242,500,1036],[238,239,242,500,1036],[237,239,497,500,1036],[238,239,497,500,1036], [238,241,242,500,1036],[237,238,241,499,1036],[238,241,499,500,1036],[238,496,497,500,1036], [237,238,496,499,1036],[238,496,499,500,1036],[237,240,242,500,1036],[237,240,241,499,1036], [237,240,498,499,1036],[237,240,498,500,1036],[237,495,497,500,1036],[495,496,497,500,1036], [237,495,496,499,1036],[495,496,499,500,1036],[237,495,498,499,1036],[237,495,498,500,1036], [495,498,499,500,1036],[240,242,245,503,1036],[241,242,245,503,1036],[240,242,500,503,1036], [241,242,500,503,1036],[241,244,245,503,1036],[240,241,244,502,1036],[241,244,502,503,1036], [241,499,500,503,1036],[240,241,499,502,1036],[241,499,502,503,1036],[240,243,245,503,1036], [240,243,244,502,1036],[240,243,501,502,1036],[240,243,501,503,1036],[240,498,500,503,1036], [498,499,500,503,1036],[240,498,499,502,1036],[498,499,502,503,1036],[240,498,501,502,1036], [240,498,501,503,1036],[498,501,502,503,1036],[36,37,38,41,1037],[37,38,41,1036,1037], [36,37,38,245,1037],[37,38,245,1036,1037],[36,37,40,41,1037],[36,37,40,1036,1037], [37,40,41,1036,1037],[36,37,244,245,1037],[36,37,244,1036,1037],[37,244,245,1036,1037], [36,39,40,41,1037],[36,39,40,1036,1037],[36,243,244,245,1037],[36,243,244,1036,1037], [39,40,41,44,1037],[40,41,44,1036,1037],[39,40,43,44,1037],[39,40,43,1036,1037], [40,43,44,1036,1037],[39,42,43,44,1037],[39,42,43,1036,1037],[42,43,44,47,1037], [43,44,47,1036,1037],[42,43,46,47,1037],[42,43,46,1036,1037],[43,46,47,1036,1037], [42,45,46,47,1037],[42,45,46,1036,1037],[45,46,47,50,1037],[46,47,50,1036,1037], [45,46,49,50,1037],[45,46,49,1036,1037],[46,49,50,1036,1037],[45,48,49,50,1037], [45,48,49,1036,1037],[48,49,50,53,1037],[49,50,53,1036,1037],[48,49,52,53,1037], [48,49,52,1036,1037],[49,52,53,1036,1037],[48,51,52,53,1037],[48,51,52,1036,1037], [51,52,53,56,1037],[52,53,56,1036,1037],[51,52,55,56,1037],[51,52,55,1036,1037], [52,55,56,1036,1037],[51,54,55,56,1037],[51,54,55,1036,1037],[54,55,56,59,1037], [55,56,59,1036,1037],[54,55,58,59,1037],[54,55,58,1036,1037],[55,58,59,1036,1037], [54,57,58,59,1037],[54,57,58,1036,1037],[57,58,59,62,1037],[58,59,62,1036,1037], [57,58,61,62,1037],[57,58,61,1036,1037],[58,61,62,1036,1037],[57,60,61,62,1037], [57,60,61,1036,1037],[60,61,62,65,1037],[61,62,65,1036,1037],[60,61,64,65,1037], [60,61,64,1036,1037],[61,64,65,1036,1037],[60,63,64,65,1037],[60,63,64,1036,1037], [63,64,65,68,1037],[64,65,68,1036,1037],[63,64,67,68,1037],[63,64,67,1036,1037], [64,67,68,1036,1037],[63,66,67,68,1037],[63,66,67,1036,1037],[66,67,68,71,1037], [67,68,71,1036,1037],[66,67,70,71,1037],[66,67,70,1036,1037],[67,70,71,1036,1037], [66,69,70,71,1037],[66,69,70,1036,1037],[69,70,71,74,1037],[70,71,74,1036,1037], [69,70,73,74,1037],[69,70,73,1036,1037],[70,73,74,1036,1037],[69,72,73,74,1037], [69,72,73,1036,1037],[72,73,74,77,1037],[73,74,77,1036,1037],[72,73,76,77,1037], [72,73,76,1036,1037],[73,76,77,1036,1037],[72,75,76,77,1037],[72,75,76,1036,1037], [75,76,77,80,1037],[76,77,80,1036,1037],[75,76,79,80,1037],[75,76,79,1036,1037], [76,79,80,1036,1037],[75,78,79,80,1037],[75,78,79,1036,1037],[78,79,80,83,1037], [79,80,83,1036,1037],[78,79,82,83,1037],[78,79,82,1036,1037],[79,82,83,1036,1037], [78,81,82,83,1037],[78,81,82,1036,1037],[81,82,83,86,1037],[82,83,86,1036,1037], [81,82,85,86,1037],[81,82,85,1036,1037],[82,85,86,1036,1037],[81,84,85,86,1037], [81,84,85,1036,1037],[84,85,86,89,1037],[85,86,89,1036,1037],[84,85,88,89,1037], [84,85,88,1036,1037],[85,88,89,1036,1037],[84,87,88,89,1037],[84,87,88,1036,1037], [87,88,89,92,1037],[88,89,92,1036,1037],[87,88,91,92,1037],[87,88,91,1036,1037], 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