#################################################################################### #################################################################################### #################################################################################### ### ### ### ### ### TRIANGULATIONS OF AKBULUT-KIRBY SPHERES ### ### by Frank H. Lutz and Mimi Tsuruga ### ### http://matsguru.com/research/AKspheres.html ### ### ### ### name of example: ### ### ### ### AK_II_007 ### ### ### ### ### ### description: ### ### ### ### Type 2 construction of triangulation of Akbulut-Kirby sphere ### ### ### ### ### ### properties: ### ### ### ### f=(512,7734,25836,31020,12408) ### ### 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:=[ [0,1,2,5,257],[0,1,2,35,287],[0,1,2,254,257],[0,1,2,254,287], [0,1,4,5,257],[0,1,4,130,382],[0,1,4,256,257],[0,1,4,256,382], [0,1,34,35,287],[0,1,34,118,244],[0,1,34,118,370],[0,1,34,160,244], [0,1,34,286,287],[0,1,34,286,370],[0,1,117,118,244],[0,1,117,118,370], [0,1,117,243,244],[0,1,117,243,495],[0,1,117,369,370],[0,1,117,369,495], [0,1,127,130,382],[0,1,127,160,244],[0,1,127,243,244],[0,1,127,243,495], [0,1,127,379,382],[0,1,127,379,495],[0,1,253,254,257],[0,1,253,254,287], [0,1,253,256,257],[0,1,253,256,382],[0,1,253,286,287],[0,1,253,286,370], [0,1,253,369,370],[0,1,253,369,495],[0,1,253,379,382],[0,1,253,379,495], [0,2,5,26,152],[2,5,26,152,404],[0,2,5,26,278],[2,5,26,278,404], [0,2,5,131,152],[2,5,131,152,404],[2,5,131,383,404],[0,2,5,257,278], [2,5,257,278,404],[2,5,257,383,404],[0,2,26,29,155],[2,26,29,155,407], [0,2,26,29,281],[2,26,29,281,407],[0,2,26,152,155],[2,26,152,155,407], [2,26,152,404,407],[0,2,26,278,281],[2,26,278,281,407],[2,26,278,404,407], [0,2,29,121,247],[0,2,29,121,373],[0,2,29,155,247],[0,2,29,281,373], [0,2,35,121,247],[0,2,35,121,373],[0,2,35,161,247],[0,2,35,287,373], [0,2,128,131,152],[2,128,131,152,404],[2,128,131,383,404],[0,2,128,152,155], [2,128,152,155,407],[2,128,152,404,407],[0,2,128,155,247],[0,2,128,161,247], [2,128,380,383,404],[2,128,380,404,407],[0,2,254,257,278],[2,254,257,278,404], [2,254,257,383,404],[0,2,254,278,281],[2,254,278,281,407],[2,254,278,404,407], [0,2,254,281,373],[0,2,254,287,373],[2,254,380,383,404],[2,254,380,404,407], [0,3,4,5,257],[0,3,4,130,382],[0,3,4,256,257],[0,3,4,256,382], [0,3,5,26,152],[0,3,5,26,278],[0,3,5,131,152],[0,3,5,257,278], [0,3,24,26,152],[0,3,24,26,278],[0,3,24,150,152],[0,3,24,150,402], [0,3,24,276,278],[0,3,24,276,402],[0,3,129,130,382],[0,3,129,131,152], [0,3,129,150,152],[0,3,129,150,402],[0,3,129,381,382],[0,3,129,381,402], [0,3,255,256,257],[0,3,255,256,382],[0,3,255,257,278],[0,3,255,276,278], [0,3,255,276,402],[0,3,255,381,382],[0,3,255,381,402],[0,24,26,29,155], [0,24,26,29,281],[0,24,26,152,155],[0,24,26,278,281],[0,24,27,29,155], [0,24,27,29,281],[0,24,27,153,155],[0,24,27,153,405],[0,24,27,279,281], [0,24,27,279,405],[0,24,150,152,155],[0,24,150,153,155],[0,24,150,153,405], [0,24,150,402,405],[0,24,276,278,281],[0,24,276,279,281],[0,24,276,279,405], [0,24,276,402,405],[0,27,29,121,247],[0,27,29,121,373],[0,27,29,155,247], [0,27,29,281,373],[0,27,114,118,244],[0,27,114,118,370],[0,27,114,121,247], [0,27,114,121,373],[0,27,114,240,244],[0,27,114,240,247],[0,27,114,366,370], [0,27,114,366,373],[0,27,117,118,244],[0,27,117,118,370],[0,27,117,243,244], [0,27,117,243,495],[0,27,117,369,370],[0,27,117,369,495],[0,27,153,155,247], [0,27,153,240,244],[0,27,153,240,247],[0,27,153,243,244],[0,27,153,243,495], [0,27,153,405,495],[0,27,279,281,373],[0,27,279,366,370],[0,27,279,366,373], [0,27,279,369,370],[0,27,279,369,495],[0,27,279,405,495],[0,33,34,35,287], [0,33,34,118,244],[0,33,34,118,370],[0,33,34,160,244],[0,33,34,286,287], [0,33,34,286,370],[0,33,35,121,247],[0,33,35,121,373],[0,33,35,161,247], [0,33,35,287,373],[0,33,114,118,244],[0,33,114,118,370],[0,33,114,121,247], [0,33,114,121,373],[0,33,114,240,244],[0,33,114,240,247],[0,33,114,366,370], [0,33,114,366,373],[0,33,159,160,244],[0,33,159,161,247],[0,33,159,240,244], [0,33,159,240,247],[0,33,285,286,287],[0,33,285,286,370],[0,33,285,287,373], [0,33,285,366,370],[0,33,285,366,373],[126,127,128,131,383],[126,127,128,161,413], [126,127,128,380,383],[126,127,128,380,413],[126,127,130,131,383],[0,126,127,130,382], [126,127,130,382,383],[126,127,160,161,413],[0,126,127,160,244],[126,127,160,244,496], [126,127,160,412,413],[126,127,160,412,496],[0,126,127,243,244],[126,127,243,244,496], [0,126,127,243,495],[126,127,243,495,496],[126,127,379,380,383],[126,127,379,380,413], [0,126,127,379,382],[126,127,379,382,383],[126,127,379,412,413],[126,127,379,412,496], [0,126,127,379,495],[126,127,379,495,496],[0,126,128,131,152],[126,128,131,152,404], [126,128,131,383,404],[0,126,128,152,155],[126,128,152,155,407],[126,128,152,404,407], [0,126,128,155,247],[126,128,155,247,499],[126,128,155,407,499],[0,126,128,161,247], [126,128,161,247,499],[126,128,161,413,499],[126,128,380,383,404],[126,128,380,404,407], [126,128,380,407,499],[126,128,380,413,499],[126,129,130,131,383],[0,126,129,130,382], [126,129,130,382,383],[0,126,129,131,152],[126,129,131,152,404],[126,129,131,383,404], [0,126,129,150,152],[126,129,150,152,404],[0,126,129,150,402],[126,129,150,402,404], [0,126,129,381,382],[126,129,381,382,383],[126,129,381,383,404],[0,126,129,381,402], [126,129,381,402,404],[0,126,150,152,155],[126,150,152,155,407],[126,150,152,404,407], [0,126,150,153,155],[126,150,153,155,407],[0,126,150,153,405],[126,150,153,405,407], [126,150,402,404,407],[0,126,150,402,405],[126,150,402,405,407],[0,126,153,155,247], [126,153,155,247,499],[126,153,155,407,499],[0,126,153,240,244],[126,153,240,244,496], [0,126,153,240,247],[126,153,240,247,499],[126,153,240,492,496],[126,153,240,492,499], [0,126,153,243,244],[126,153,243,244,496],[0,126,153,243,495],[126,153,243,495,496], [126,153,405,407,499],[126,153,405,492,496],[126,153,405,492,499],[0,126,153,405,495], [126,153,405,495,496],[126,159,160,161,413],[0,126,159,160,244],[126,159,160,244,496], [126,159,160,412,413],[126,159,160,412,496],[0,126,159,161,247],[126,159,161,247,499], [126,159,161,413,499],[0,126,159,240,244],[126,159,240,244,496],[0,126,159,240,247], [126,159,240,247,499],[126,159,240,492,496],[126,159,240,492,499],[126,159,411,412,413], [126,159,411,412,496],[126,159,411,413,499],[126,159,411,492,496],[126,159,411,492,499], [126,378,379,380,383],[126,378,379,380,413],[0,126,378,379,382],[126,378,379,382,383], [126,378,379,412,413],[126,378,379,412,496],[0,126,378,379,495],[126,378,379,495,496], [126,378,380,383,404],[126,378,380,404,407],[126,378,380,407,499],[126,378,380,413,499], [0,126,378,381,382],[126,378,381,382,383],[126,378,381,383,404],[0,126,378,381,402], [126,378,381,402,404],[126,378,402,404,407],[0,126,378,402,405],[126,378,402,405,407], [126,378,405,407,499],[126,378,405,492,496],[126,378,405,492,499],[0,126,378,405,495], [126,378,405,495,496],[126,378,411,412,413],[126,378,411,412,496],[126,378,411,413,499], [126,378,411,492,496],[126,378,411,492,499],[0,252,253,254,257],[252,253,254,257,383], [0,252,253,254,287],[252,253,254,287,413],[252,253,254,380,383],[252,253,254,380,413], [0,252,253,256,257],[252,253,256,257,383],[0,252,253,256,382],[252,253,256,382,383], [0,252,253,286,287],[252,253,286,287,413],[0,252,253,286,370],[252,253,286,370,496], [252,253,286,412,413],[252,253,286,412,496],[0,252,253,369,370],[252,253,369,370,496], [0,252,253,369,495],[252,253,369,495,496],[252,253,379,380,383],[252,253,379,380,413], [0,252,253,379,382],[252,253,379,382,383],[252,253,379,412,413],[252,253,379,412,496], [0,252,253,379,495],[252,253,379,495,496],[0,252,254,257,278],[252,254,257,278,404], [252,254,257,383,404],[0,252,254,278,281],[252,254,278,281,407],[252,254,278,404,407], [0,252,254,281,373],[252,254,281,373,499],[252,254,281,407,499],[0,252,254,287,373], [252,254,287,373,499],[252,254,287,413,499],[252,254,380,383,404],[252,254,380,404,407], [252,254,380,407,499],[252,254,380,413,499],[0,252,255,256,257],[252,255,256,257,383], [0,252,255,256,382],[252,255,256,382,383],[0,252,255,257,278],[252,255,257,278,404], [252,255,257,383,404],[0,252,255,276,278],[252,255,276,278,404],[0,252,255,276,402], [252,255,276,402,404],[0,252,255,381,382],[252,255,381,382,383],[252,255,381,383,404], [0,252,255,381,402],[252,255,381,402,404],[0,252,276,278,281],[252,276,278,281,407], [252,276,278,404,407],[0,252,276,279,281],[252,276,279,281,407],[0,252,276,279,405], [252,276,279,405,407],[252,276,402,404,407],[0,252,276,402,405],[252,276,402,405,407], [0,252,279,281,373],[252,279,281,373,499],[252,279,281,407,499],[0,252,279,366,370], [252,279,366,370,496],[0,252,279,366,373],[252,279,366,373,499],[252,279,366,492,496], [252,279,366,492,499],[0,252,279,369,370],[252,279,369,370,496],[0,252,279,369,495], [252,279,369,495,496],[252,279,405,407,499],[252,279,405,492,496],[252,279,405,492,499], [0,252,279,405,495],[252,279,405,495,496],[0,252,285,286,287],[252,285,286,287,413], [0,252,285,286,370],[252,285,286,370,496],[252,285,286,412,413],[252,285,286,412,496], [0,252,285,287,373],[252,285,287,373,499],[252,285,287,413,499],[0,252,285,366,370], [252,285,366,370,496],[0,252,285,366,373],[252,285,366,373,499],[252,285,366,492,496], [252,285,366,492,499],[252,285,411,412,413],[252,285,411,412,496],[252,285,411,413,499], [252,285,411,492,496],[252,285,411,492,499],[252,378,379,380,383],[252,378,379,380,413], [0,252,378,379,382],[252,378,379,382,383],[252,378,379,412,413],[252,378,379,412,496], [0,252,378,379,495],[252,378,379,495,496],[252,378,380,383,404],[252,378,380,404,407], [252,378,380,407,499],[252,378,380,413,499],[0,252,378,381,382],[252,378,381,382,383], [252,378,381,383,404],[0,252,378,381,402],[252,378,381,402,404],[252,378,402,404,407], [0,252,378,402,405],[252,378,402,405,407],[252,378,405,407,499],[252,378,405,492,496], [252,378,405,492,499],[0,252,378,405,495],[252,378,405,495,496],[252,378,411,412,413], [252,378,411,412,496],[252,378,411,413,499],[252,378,411,492,496],[252,378,411,492,499], [1,2,5,41,167],[2,5,41,167,419],[1,2,5,41,293],[2,5,41,293,419], [1,2,5,131,167],[2,5,131,167,419],[2,5,131,383,419],[1,2,5,257,293], [2,5,257,293,419],[2,5,257,383,419],[1,2,35,121,247],[1,2,35,121,373], [1,2,35,161,247],[1,2,35,287,373],[1,2,38,41,167],[2,38,41,167,419], [1,2,38,41,293],[2,38,41,293,419],[1,2,38,124,250],[1,2,38,124,376], [1,2,38,164,167],[2,38,164,167,419],[1,2,38,164,250],[2,38,164,416,419], [1,2,38,290,293],[2,38,290,293,419],[1,2,38,290,376],[2,38,290,416,419], [1,2,120,121,247],[1,2,120,121,373],[1,2,120,124,250],[1,2,120,124,376], [1,2,120,246,247],[1,2,120,246,250],[1,2,120,372,373],[1,2,120,372,376], [1,2,128,131,167],[2,128,131,167,419],[2,128,131,383,419],[1,2,128,161,247], [1,2,128,164,167],[2,128,164,167,419],[1,2,128,164,250],[2,128,164,416,419], [1,2,128,246,247],[1,2,128,246,250],[2,128,380,383,419],[2,128,380,416,419], [1,2,254,257,293],[2,254,257,293,419],[2,254,257,383,419],[1,2,254,287,373], [1,2,254,290,293],[2,254,290,293,419],[1,2,254,290,376],[2,254,290,416,419], [1,2,254,372,373],[1,2,254,372,376],[2,254,380,383,419],[2,254,380,416,419], [1,4,5,41,167],[1,4,5,41,293],[1,4,5,131,167],[1,4,5,257,293], [1,4,39,41,167],[1,4,39,41,293],[1,4,39,165,167],[1,4,39,165,417], [1,4,39,291,293],[1,4,39,291,417],[1,4,130,131,167],[1,4,130,165,167], [1,4,130,165,417],[1,4,130,382,417],[1,4,256,257,293],[1,4,256,291,293], [1,4,256,291,417],[1,4,256,382,417],[1,34,35,121,247],[1,34,35,121,373], [1,34,35,161,247],[1,34,35,287,373],[1,34,115,118,244],[1,34,115,118,370], [1,34,115,121,247],[1,34,115,121,373],[1,34,115,241,244],[1,34,115,241,247], [1,34,115,367,370],[1,34,115,367,373],[1,34,160,161,247],[1,34,160,241,244], [1,34,160,241,247],[1,34,286,287,373],[1,34,286,367,370],[1,34,286,367,373], [1,36,38,41,167],[1,36,38,41,293],[1,36,38,124,250],[1,36,38,124,376], [1,36,38,164,167],[1,36,38,164,250],[1,36,38,290,293],[1,36,38,290,376], [1,36,39,41,167],[1,36,39,41,293],[1,36,39,165,167],[1,36,39,165,417], [1,36,39,291,293],[1,36,39,291,417],[1,36,115,118,244],[1,36,115,118,370], [1,36,115,121,247],[1,36,115,121,373],[1,36,115,241,244],[1,36,115,241,247], [1,36,115,367,370],[1,36,115,367,373],[1,36,117,118,244],[1,36,117,118,370], [1,36,117,243,244],[1,36,117,243,495],[1,36,117,369,370],[1,36,117,369,495], [1,36,120,121,247],[1,36,120,121,373],[1,36,120,124,250],[1,36,120,124,376], [1,36,120,246,247],[1,36,120,246,250],[1,36,120,372,373],[1,36,120,372,376], [1,36,162,164,167],[1,36,162,164,250],[1,36,162,165,167],[1,36,162,165,417], [1,36,162,241,244],[1,36,162,241,247],[1,36,162,243,244],[1,36,162,243,495], [1,36,162,246,247],[1,36,162,246,250],[1,36,162,414,417],[1,36,162,414,495], [1,36,288,290,293],[1,36,288,290,376],[1,36,288,291,293],[1,36,288,291,417], [1,36,288,367,370],[1,36,288,367,373],[1,36,288,369,370],[1,36,288,369,495], [1,36,288,372,373],[1,36,288,372,376],[1,36,288,414,417],[1,36,288,414,495], [1,127,128,131,167],[127,128,131,167,419],[127,128,131,383,419],[1,127,128,161,247], [127,128,161,247,499],[127,128,161,413,499],[1,127,128,164,167],[127,128,164,167,419], [1,127,128,164,250],[127,128,164,250,502],[127,128,164,416,419],[127,128,164,416,502], [1,127,128,246,247],[127,128,246,247,499],[1,127,128,246,250],[127,128,246,250,502], [127,128,246,498,499],[127,128,246,498,502],[127,128,380,383,419],[127,128,380,413,499], [127,128,380,416,419],[127,128,380,416,502],[127,128,380,498,499],[127,128,380,498,502], [1,127,130,131,167],[127,130,131,167,419],[127,130,131,383,419],[1,127,130,165,167], [127,130,165,167,419],[1,127,130,165,417],[127,130,165,417,419],[127,130,382,383,419], [1,127,130,382,417],[127,130,382,417,419],[1,127,160,161,247],[127,160,161,247,499], [127,160,161,413,499],[1,127,160,241,244],[127,160,241,244,496],[1,127,160,241,247], 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[45,46,298,299,302],[45,46,298,301,302],[45,46,298,301,427],[45,46,298,424,427], [45,48,49,50,302],[45,48,49,175,427],[45,48,49,301,302],[45,48,49,301,427], [45,48,174,175,427],[45,48,174,426,427],[45,48,300,301,302],[45,48,300,301,427], [45,48,300,426,427],[171,172,173,176,428],[171,172,173,425,428],[171,172,175,176,428], [45,171,172,175,427],[171,172,175,427,428],[171,172,424,425,428],[45,171,172,424,427], [171,172,424,427,428],[171,174,175,176,428],[45,171,174,175,427],[171,174,175,427,428], [45,171,174,426,427],[171,174,426,427,428],[171,423,424,425,428],[45,171,423,424,427], [171,423,424,427,428],[45,171,423,426,427],[171,423,426,427,428],[45,297,298,299,302], [297,298,299,302,428],[297,298,299,425,428],[45,297,298,301,302],[297,298,301,302,428], [45,297,298,301,427],[297,298,301,427,428],[297,298,424,425,428],[45,297,298,424,427], [297,298,424,427,428],[45,297,300,301,302],[297,300,301,302,428],[45,297,300,301,427], 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[46,51,177,179,182],[46,51,177,180,182],[46,51,177,180,432],[46,51,177,429,432], [46,51,303,305,308],[46,51,303,306,308],[46,51,303,306,432],[46,51,303,429,432], [46,172,173,176,182],[172,173,176,182,434],[172,173,176,428,434],[46,172,173,179,182], [172,173,179,182,434],[172,173,179,431,434],[172,173,425,428,434],[172,173,425,431,434], [46,172,175,176,182],[172,175,176,182,434],[172,175,176,428,434],[46,172,175,180,182], [172,175,180,182,434],[46,172,175,180,432],[172,175,180,432,434],[172,175,427,428,434], [46,172,175,427,432],[172,175,427,432,434],[46,172,177,179,182],[172,177,179,182,434], [172,177,179,431,434],[46,172,177,180,182],[172,177,180,182,434],[46,172,177,180,432], [172,177,180,432,434],[172,177,429,431,434],[46,172,177,429,432],[172,177,429,432,434], [172,424,425,428,434],[172,424,425,431,434],[172,424,427,428,434],[46,172,424,427,432], [172,424,427,432,434],[172,424,429,431,434],[46,172,424,429,432],[172,424,429,432,434], [46,298,299,302,308],[298,299,302,308,434],[298,299,302,428,434],[46,298,299,305,308], [298,299,305,308,434],[298,299,305,431,434],[298,299,425,428,434],[298,299,425,431,434], [46,298,301,302,308],[298,301,302,308,434],[298,301,302,428,434],[46,298,301,306,308], [298,301,306,308,434],[46,298,301,306,432],[298,301,306,432,434],[298,301,427,428,434], [46,298,301,427,432],[298,301,427,432,434],[46,298,303,305,308],[298,303,305,308,434], [298,303,305,431,434],[46,298,303,306,308],[298,303,306,308,434],[46,298,303,306,432], [298,303,306,432,434],[298,303,429,431,434],[46,298,303,429,432],[298,303,429,432,434], [298,424,425,428,434],[298,424,425,431,434],[298,424,427,428,434],[46,298,424,427,432], [298,424,427,432,434],[298,424,429,431,434],[46,298,424,429,432],[298,424,429,432,434], [47,50,56,124,250],[47,50,56,124,376],[47,50,56,182,250],[47,50,56,308,376], [47,50,176,182,250],[47,50,302,308,376],[47,53,56,124,250],[47,53,56,124,376], [47,53,56,182,250],[47,53,56,308,376],[47,53,123,124,250],[47,53,123,124,376], [47,53,123,249,250],[47,53,123,249,501],[47,53,123,375,376],[47,53,123,375,501], [47,53,179,182,250],[47,53,179,249,250],[47,53,179,249,501],[47,53,179,431,501], [47,53,305,308,376],[47,53,305,375,376],[47,53,305,375,501],[47,53,305,431,501], [47,173,176,182,250],[173,176,182,250,502],[173,176,182,434,502],[173,176,428,434,502], [47,173,179,182,250],[173,179,182,250,502],[173,179,182,434,502],[47,173,179,249,250], [173,179,249,250,502],[47,173,179,249,501],[173,179,249,501,502],[173,179,431,434,502], [47,173,179,431,501],[173,179,431,501,502],[173,425,428,434,502],[173,425,431,434,502], [47,173,425,431,501],[173,425,431,501,502],[47,299,302,308,376],[299,302,308,376,502], [299,302,308,434,502],[299,302,428,434,502],[47,299,305,308,376],[299,305,308,376,502], [299,305,308,434,502],[47,299,305,375,376],[299,305,375,376,502],[47,299,305,375,501], [299,305,375,501,502],[299,305,431,434,502],[47,299,305,431,501],[299,305,431,501,502], [299,425,428,434,502],[299,425,431,434,502],[47,299,425,431,501],[299,425,431,501,502], [48,49,50,53,305],[48,49,50,302,305],[48,49,52,53,305],[48,49,52,178,430], [48,49,52,304,305],[48,49,52,304,430],[48,49,175,178,430],[48,49,175,427,430], [48,49,301,302,305],[48,49,301,304,305],[48,49,301,304,430],[48,49,301,427,430], [48,51,52,53,305],[48,51,52,178,430],[48,51,52,304,305],[48,51,52,304,430], [48,51,177,178,430],[48,51,177,429,430],[48,51,303,304,305],[48,51,303,304,430], [48,51,303,429,430],[174,175,176,179,431],[174,175,176,428,431],[174,175,178,179,431], [48,174,175,178,430],[174,175,178,430,431],[174,175,427,428,431],[48,174,175,427,430], [174,175,427,430,431],[174,177,178,179,431],[48,174,177,178,430],[174,177,178,430,431], [48,174,177,429,430],[174,177,429,430,431],[174,426,427,428,431],[48,174,426,427,430], [174,426,427,430,431],[48,174,426,429,430],[174,426,429,430,431],[48,300,301,302,305], [300,301,302,305,431],[300,301,302,428,431],[48,300,301,304,305],[300,301,304,305,431], [48,300,301,304,430],[300,301,304,430,431],[300,301,427,428,431],[48,300,301,427,430], [300,301,427,430,431],[48,300,303,304,305],[300,303,304,305,431],[48,300,303,304,430], [300,303,304,430,431],[48,300,303,429,430],[300,303,429,430,431],[300,426,427,428,431], [48,300,426,427,430],[300,426,427,430,431],[48,300,426,429,430],[300,426,429,430,431], [49,50,53,59,185],[50,53,59,185,437],[49,50,53,59,311],[50,53,59,311,437], [49,50,53,179,185],[50,53,179,185,437],[50,53,179,431,437],[49,50,53,305,311], [50,53,305,311,437],[50,53,305,431,437],[49,50,56,59,185],[50,56,59,185,437], [49,50,56,59,311],[50,56,59,311,437],[49,50,56,182,185],[50,56,182,185,437], [50,56,182,434,437],[49,50,56,308,311],[50,56,308,311,437],[50,56,308,434,437], [49,50,176,179,185],[50,176,179,185,437],[50,176,179,431,437],[49,50,176,182,185], [50,176,182,185,437],[50,176,182,434,437],[50,176,428,431,437],[50,176,428,434,437], [49,50,302,305,311],[50,302,305,311,437],[50,302,305,431,437],[49,50,302,308,311], [50,302,308,311,437],[50,302,308,434,437],[50,302,428,431,437],[50,302,428,434,437], [49,52,53,59,185],[49,52,53,59,311],[49,52,53,179,185],[49,52,53,305,311], [49,52,57,59,185],[49,52,57,59,311],[49,52,57,183,185],[49,52,57,183,435], [49,52,57,309,311],[49,52,57,309,435],[49,52,178,179,185],[49,52,178,183,185], [49,52,178,183,435],[49,52,178,430,435],[49,52,304,305,311],[49,52,304,309,311], [49,52,304,309,435],[49,52,304,430,435],[49,54,56,59,185],[49,54,56,59,311], [49,54,56,182,185],[49,54,56,308,311],[49,54,57,59,185],[49,54,57,59,311], [49,54,57,183,185],[49,54,57,183,435],[49,54,57,309,311],[49,54,57,309,435], [49,54,180,182,185],[49,54,180,183,185],[49,54,180,183,435],[49,54,180,432,435], [49,54,306,308,311],[49,54,306,309,311],[49,54,306,309,435],[49,54,306,432,435], [49,175,176,179,185],[175,176,179,185,437],[175,176,179,431,437],[49,175,176,182,185], [175,176,182,185,437],[175,176,182,434,437],[175,176,428,431,437],[175,176,428,434,437], [49,175,178,179,185],[175,178,179,185,437],[175,178,179,431,437],[49,175,178,183,185], [175,178,183,185,437],[49,175,178,183,435],[175,178,183,435,437],[175,178,430,431,437], [49,175,178,430,435],[175,178,430,435,437],[49,175,180,182,185],[175,180,182,185,437], [175,180,182,434,437],[49,175,180,183,185],[175,180,183,185,437],[49,175,180,183,435], [175,180,183,435,437],[175,180,432,434,437],[49,175,180,432,435],[175,180,432,435,437], [175,427,428,431,437],[175,427,428,434,437],[175,427,430,431,437],[49,175,427,430,435], [175,427,430,435,437],[175,427,432,434,437],[49,175,427,432,435],[175,427,432,435,437], [49,301,302,305,311],[301,302,305,311,437],[301,302,305,431,437],[49,301,302,308,311], [301,302,308,311,437],[301,302,308,434,437],[301,302,428,431,437],[301,302,428,434,437], [49,301,304,305,311],[301,304,305,311,437],[301,304,305,431,437],[49,301,304,309,311], [301,304,309,311,437],[49,301,304,309,435],[301,304,309,435,437],[301,304,430,431,437], [49,301,304,430,435],[301,304,430,435,437],[49,301,306,308,311],[301,306,308,311,437], [301,306,308,434,437],[49,301,306,309,311],[301,306,309,311,437],[49,301,306,309,435], [301,306,309,435,437],[301,306,432,434,437],[49,301,306,432,435],[301,306,432,435,437], [301,427,428,431,437],[301,427,428,434,437],[301,427,430,431,437],[49,301,427,430,435], [301,427,430,435,437],[301,427,432,434,437],[49,301,427,432,435],[301,427,432,435,437], [50,56,122,124,250],[50,56,122,124,376],[50,56,122,248,250],[50,56,122,248,500], [50,56,122,374,376],[50,56,122,374,500],[50,56,182,248,250],[50,56,182,248,500], [50,56,182,434,500],[50,56,308,374,376],[50,56,308,374,500],[50,56,308,434,500], [50,176,182,248,250],[176,182,248,250,502],[50,176,182,248,500],[176,182,248,500,502], [50,176,182,434,500],[176,182,434,500,502],[50,176,428,434,500],[176,428,434,500,502], [50,302,308,374,376],[302,308,374,376,502],[50,302,308,374,500],[302,308,374,500,502], [50,302,308,434,500],[302,308,434,500,502],[50,302,428,434,500],[302,428,434,500,502], [51,52,53,56,308],[51,52,53,305,308],[51,52,55,56,308],[51,52,55,181,433], [51,52,55,307,308],[51,52,55,307,433],[51,52,178,181,433],[51,52,178,430,433], [51,52,304,305,308],[51,52,304,307,308],[51,52,304,307,433],[51,52,304,430,433], [51,54,55,56,308],[51,54,55,181,433],[51,54,55,307,308],[51,54,55,307,433], [51,54,180,181,433],[51,54,180,432,433],[51,54,306,307,308],[51,54,306,307,433], [51,54,306,432,433],[177,178,179,182,434],[177,178,179,431,434],[177,178,181,182,434], [51,177,178,181,433],[177,178,181,433,434],[177,178,430,431,434],[51,177,178,430,433], [177,178,430,433,434],[177,180,181,182,434],[51,177,180,181,433],[177,180,181,433,434], [51,177,180,432,433],[177,180,432,433,434],[177,429,430,431,434],[51,177,429,430,433], [177,429,430,433,434],[51,177,429,432,433],[177,429,432,433,434],[51,303,304,305,308], [303,304,305,308,434],[303,304,305,431,434],[51,303,304,307,308],[303,304,307,308,434], [51,303,304,307,433],[303,304,307,433,434],[303,304,430,431,434],[51,303,304,430,433], [303,304,430,433,434],[51,303,306,307,308],[303,306,307,308,434],[51,303,306,307,433], [303,306,307,433,434],[51,303,306,432,433],[303,306,432,433,434],[303,429,430,431,434], [51,303,429,430,433],[303,429,430,433,434],[51,303,429,432,433],[303,429,432,433,434], [52,53,56,62,188],[52,53,56,62,314],[52,53,56,182,188],[52,53,56,308,314], [52,53,59,62,188],[52,53,59,62,314],[52,53,59,185,188],[52,53,59,311,314], [52,53,179,182,188],[52,53,179,185,188],[52,53,305,308,314],[52,53,305,311,314], [52,55,56,62,188],[52,55,56,62,314],[52,55,56,182,188],[52,55,56,308,314], [52,55,60,62,188],[52,55,60,62,314],[52,55,60,186,188],[52,55,60,186,438], [52,55,60,312,314],[52,55,60,312,438],[52,55,181,182,188],[52,55,181,186,188], [52,55,181,186,438],[52,55,181,433,438],[52,55,307,308,314],[52,55,307,312,314], [52,55,307,312,438],[52,55,307,433,438],[52,57,59,62,188],[52,57,59,62,314], [52,57,59,185,188],[52,57,59,311,314],[52,57,60,62,188],[52,57,60,62,314], [52,57,60,186,188],[52,57,60,186,438],[52,57,60,312,314],[52,57,60,312,438], [52,57,183,185,188],[52,57,183,186,188],[52,57,183,186,438],[52,57,183,435,438], [52,57,309,311,314],[52,57,309,312,314],[52,57,309,312,438],[52,57,309,435,438], [52,178,179,182,188],[178,179,182,188,440],[178,179,182,434,440],[52,178,179,185,188], [178,179,185,188,440],[178,179,185,437,440],[178,179,431,434,440],[178,179,431,437,440], [52,178,181,182,188],[178,181,182,188,440],[178,181,182,434,440],[52,178,181,186,188], [178,181,186,188,440],[52,178,181,186,438],[178,181,186,438,440],[178,181,433,434,440], [52,178,181,433,438],[178,181,433,438,440],[52,178,183,185,188],[178,183,185,188,440], [178,183,185,437,440],[52,178,183,186,188],[178,183,186,188,440],[52,178,183,186,438], [178,183,186,438,440],[178,183,435,437,440],[52,178,183,435,438],[178,183,435,438,440], [178,430,431,434,440],[178,430,431,437,440],[178,430,433,434,440],[52,178,430,433,438], [178,430,433,438,440],[178,430,435,437,440],[52,178,430,435,438],[178,430,435,438,440], [52,304,305,308,314],[304,305,308,314,440],[304,305,308,434,440],[52,304,305,311,314], [304,305,311,314,440],[304,305,311,437,440],[304,305,431,434,440],[304,305,431,437,440], [52,304,307,308,314],[304,307,308,314,440],[304,307,308,434,440],[52,304,307,312,314], [304,307,312,314,440],[52,304,307,312,438],[304,307,312,438,440],[304,307,433,434,440], [52,304,307,433,438],[304,307,433,438,440],[52,304,309,311,314],[304,309,311,314,440], [304,309,311,437,440],[52,304,309,312,314],[304,309,312,314,440],[52,304,309,312,438], [304,309,312,438,440],[304,309,435,437,440],[52,304,309,435,438],[304,309,435,438,440], [304,430,431,434,440],[304,430,431,437,440],[304,430,433,434,440],[52,304,430,433,438], [304,430,433,438,440],[304,430,435,437,440],[52,304,430,435,438],[304,430,435,438,440], [53,56,62,124,250],[53,56,62,124,376],[53,56,62,188,250],[53,56,62,314,376], [53,56,182,188,250],[53,56,308,314,376],[53,59,62,124,250],[53,59,62,124,376], [53,59,62,188,250],[53,59,62,314,376],[53,59,123,124,250],[53,59,123,124,376], [53,59,123,249,250],[53,59,123,249,501],[53,59,123,375,376],[53,59,123,375,501], [53,59,185,188,250],[53,59,185,249,250],[53,59,185,249,501],[53,59,185,437,501], [53,59,311,314,376],[53,59,311,375,376],[53,59,311,375,501],[53,59,311,437,501], [53,179,182,188,250],[179,182,188,250,502],[179,182,188,440,502],[179,182,434,440,502], [53,179,185,188,250],[179,185,188,250,502],[179,185,188,440,502],[53,179,185,249,250], [179,185,249,250,502],[53,179,185,249,501],[179,185,249,501,502],[179,185,437,440,502], [53,179,185,437,501],[179,185,437,501,502],[179,431,434,440,502],[179,431,437,440,502], [53,179,431,437,501],[179,431,437,501,502],[53,305,308,314,376],[305,308,314,376,502], [305,308,314,440,502],[305,308,434,440,502],[53,305,311,314,376],[305,311,314,376,502], [305,311,314,440,502],[53,305,311,375,376],[305,311,375,376,502],[53,305,311,375,501], [305,311,375,501,502],[305,311,437,440,502],[53,305,311,437,501],[305,311,437,501,502], [305,431,434,440,502],[305,431,437,440,502],[53,305,431,437,501],[305,431,437,501,502], [54,55,56,59,311],[54,55,56,308,311],[54,55,58,59,311],[54,55,58,184,436], [54,55,58,310,311],[54,55,58,310,436],[54,55,181,184,436],[54,55,181,433,436], [54,55,307,308,311],[54,55,307,310,311],[54,55,307,310,436],[54,55,307,433,436], [54,57,58,59,311],[54,57,58,184,436],[54,57,58,310,311],[54,57,58,310,436], [54,57,183,184,436],[54,57,183,435,436],[54,57,309,310,311],[54,57,309,310,436], [54,57,309,435,436],[180,181,182,185,437],[180,181,182,434,437],[180,181,184,185,437], [54,180,181,184,436],[180,181,184,436,437],[180,181,433,434,437],[54,180,181,433,436], [180,181,433,436,437],[180,183,184,185,437],[54,180,183,184,436],[180,183,184,436,437], [54,180,183,435,436],[180,183,435,436,437],[180,432,433,434,437],[54,180,432,433,436], [180,432,433,436,437],[54,180,432,435,436],[180,432,435,436,437],[54,306,307,308,311], [306,307,308,311,437],[306,307,308,434,437],[54,306,307,310,311],[306,307,310,311,437], [54,306,307,310,436],[306,307,310,436,437],[306,307,433,434,437],[54,306,307,433,436], [306,307,433,436,437],[54,306,309,310,311],[306,309,310,311,437],[54,306,309,310,436], [306,309,310,436,437],[54,306,309,435,436],[306,309,435,436,437],[306,432,433,434,437], [54,306,432,433,436],[306,432,433,436,437],[54,306,432,435,436],[306,432,435,436,437], [55,56,59,65,191],[56,59,65,191,443],[55,56,59,65,317],[56,59,65,317,443], 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