#################################################################################### #################################################################################### #################################################################################### ### ### ### ### ### LIBRARY OF TRIANGULATIONS ### ### by Bruno Benedetti and Frank H. Lutz ### ### http://page.math.tu-berlin.de/~lutz/stellar/library_of_triangulations.html ### ### ### ### ### ### name of example: ### ### ### ### S_3_50_1033 ### ### ### ### ### ### description: ### ### ### ### random triangulation of the 3-sphere with 50 vertices ### ### obtained via random bistellar flips ### ### ### ### ### ### properties: ### ### ### ### f=(50,1083,2066,1033), ### ### H_*=(Z,0,0,Z), ### ### perfect discrete Morse vector: (1,0,0,1) ### ### ### ### ### ### references: ### ### ### ### A. Björner and F. H. Lutz. ### ### Simplicial manifolds, bistellar flips and a 16-vertex ### ### triangulation of the Poincaré homology 3-sphere. ### ### Exp. Math. 9, 275-289 (2000). ### ### ### ### B. Benedetti and F. H. Lutz. ### ### Random discrete Morse theory and a new library of triangulations. ### ### Exp. Math. 23, 66-94 (2014). ### ### ### ### ### #################################################################################### #################################################################################### #################################################################################### facets:=[ [ 1, 2, 3, 10 ], [ 1, 2, 3, 48 ], [ 1, 2, 5, 6 ], [ 1, 2, 5, 48 ], [ 1, 2, 6, 47 ], [ 1, 2, 10, 11 ], [ 1, 2, 11, 12 ], [ 1, 2, 12, 13 ], [ 1, 2, 13, 14 ], [ 1, 2, 14, 15 ], [ 1, 2, 15, 16 ], [ 1, 2, 16, 50 ], [ 1, 2, 19, 20 ], [ 1, 2, 19, 50 ], [ 1, 2, 20, 21 ], [ 1, 2, 21, 22 ], [ 1, 2, 22, 23 ], [ 1, 2, 23, 24 ], [ 1, 2, 24, 25 ], [ 1, 2, 25, 26 ], [ 1, 2, 26, 27 ], [ 1, 2, 27, 28 ], [ 1, 2, 28, 29 ], [ 1, 2, 29, 30 ], [ 1, 2, 30, 31 ], [ 1, 2, 31, 32 ], [ 1, 2, 32, 33 ], [ 1, 2, 33, 34 ], [ 1, 2, 34, 35 ], [ 1, 2, 35, 36 ], [ 1, 2, 36, 37 ], [ 1, 2, 37, 38 ], [ 1, 2, 38, 49 ], [ 1, 2, 40, 41 ], [ 1, 2, 40, 42 ], [ 1, 2, 41, 49 ], [ 1, 2, 42, 43 ], [ 1, 2, 43, 44 ], [ 1, 2, 44, 45 ], [ 1, 2, 45, 47 ], [ 1, 3, 4, 10 ], [ 1, 3, 4, 50 ], [ 1, 3, 48, 50 ], [ 1, 4, 7, 9 ], [ 1, 4, 7, 50 ], [ 1, 4, 9, 10 ], [ 1, 5, 6, 47 ], [ 1, 5, 47, 48 ], [ 1, 7, 9, 50 ], [ 1, 9, 10, 50 ], [ 1, 10, 11, 50 ], [ 1, 11, 12, 50 ], [ 1, 12, 13, 50 ], [ 1, 13, 14, 50 ], [ 1, 14, 15, 50 ], [ 1, 15, 16, 50 ], [ 1, 19, 20, 50 ], [ 1, 20, 21, 50 ], [ 1, 21, 22, 50 ], [ 1, 22, 23, 50 ], [ 1, 23, 24, 50 ], [ 1, 24, 25, 50 ], [ 1, 25, 26, 50 ], [ 1, 26, 27, 50 ], [ 1, 27, 28, 29 ], [ 1, 27, 29, 50 ], [ 1, 29, 30, 50 ], [ 1, 30, 31, 50 ], [ 1, 31, 32, 50 ], [ 1, 32, 33, 50 ], [ 1, 33, 34, 50 ], [ 1, 34, 35, 50 ], [ 1, 35, 36, 50 ], [ 1, 36, 37, 49 ], [ 1, 36, 49, 50 ], [ 1, 37, 38, 49 ], [ 1, 39, 44, 45 ], [ 1, 39, 44, 50 ], [ 1, 39, 45, 47 ], [ 1, 39, 47, 48 ], [ 1, 39, 48, 50 ], [ 1, 40, 41, 49 ], [ 1, 40, 42, 50 ], [ 1, 40, 49, 50 ], [ 1, 42, 43, 50 ], [ 1, 43, 44, 50 ], [ 2, 3, 4, 23 ], [ 2, 3, 4, 24 ], [ 2, 3, 5, 46 ], [ 2, 3, 5, 48 ], [ 2, 3, 8, 30 ], [ 2, 3, 8, 31 ], [ 2, 3, 10, 11 ], [ 2, 3, 11, 12 ], [ 2, 3, 12, 13 ], [ 2, 3, 13, 14 ], [ 2, 3, 14, 15 ], [ 2, 3, 15, 16 ], [ 2, 3, 16, 17 ], [ 2, 3, 17, 18 ], [ 2, 3, 18, 19 ], [ 2, 3, 19, 20 ], [ 2, 3, 20, 21 ], [ 2, 3, 21, 23 ], [ 2, 3, 24, 25 ], [ 2, 3, 25, 26 ], [ 2, 3, 26, 27 ], [ 2, 3, 27, 28 ], [ 2, 3, 28, 29 ], [ 2, 3, 29, 30 ], [ 2, 3, 31, 32 ], [ 2, 3, 32, 33 ], [ 2, 3, 33, 34 ], [ 2, 3, 34, 35 ], [ 2, 3, 35, 36 ], [ 2, 3, 36, 37 ], [ 2, 3, 37, 38 ], [ 2, 3, 38, 39 ], [ 2, 3, 39, 49 ], [ 2, 3, 42, 43 ], [ 2, 3, 42, 49 ], [ 2, 3, 43, 44 ], [ 2, 3, 44, 45 ], [ 2, 3, 45, 47 ], [ 2, 3, 46, 47 ], [ 2, 4, 23, 24 ], [ 2, 5, 6, 46 ], [ 2, 6, 7, 46 ], [ 2, 6, 7, 47 ], [ 2, 7, 46, 47 ], [ 2, 8, 30, 31 ], [ 2, 16, 17, 50 ], [ 2, 17, 18, 50 ], [ 2, 18, 19, 50 ], [ 2, 21, 22, 23 ], [ 2, 38, 39, 49 ], [ 2, 40, 41, 42 ], [ 2, 41, 42, 49 ], [ 3, 4, 5, 45 ], [ 3, 4, 5, 50 ], [ 3, 4, 6, 8 ], [ 3, 4, 6, 31 ], [ 3, 4, 8, 30 ], [ 3, 4, 9, 10 ], [ 3, 4, 9, 11 ], [ 3, 4, 11, 12 ], [ 3, 4, 12, 13 ], [ 3, 4, 13, 14 ], [ 3, 4, 14, 16 ], [ 3, 4, 16, 17 ], [ 3, 4, 17, 18 ], [ 3, 4, 18, 19 ], [ 3, 4, 19, 20 ], [ 3, 4, 20, 21 ], [ 3, 4, 21, 23 ], [ 3, 4, 24, 25 ], [ 3, 4, 25, 26 ], [ 3, 4, 26, 27 ], [ 3, 4, 27, 28 ], [ 3, 4, 28, 29 ], [ 3, 4, 29, 30 ], [ 3, 4, 31, 32 ], [ 3, 4, 32, 33 ], [ 3, 4, 33, 35 ], [ 3, 4, 35, 36 ], [ 3, 4, 36, 37 ], [ 3, 4, 37, 38 ], [ 3, 4, 38, 39 ], [ 3, 4, 39, 40 ], [ 3, 4, 40, 41 ], [ 3, 4, 41, 42 ], [ 3, 4, 42, 43 ], [ 3, 4, 43, 44 ], [ 3, 4, 44, 45 ], [ 3, 5, 45, 46 ], [ 3, 5, 48, 50 ], [ 3, 6, 8, 31 ], [ 3, 9, 10, 11 ], [ 3, 14, 15, 16 ], [ 3, 33, 34, 35 ], [ 3, 39, 40, 49 ], [ 3, 40, 41, 49 ], [ 3, 41, 42, 49 ], [ 3, 45, 46, 47 ], [ 4, 5, 7, 11 ], [ 4, 5, 7, 50 ], [ 4, 5, 11, 12 ], [ 4, 5, 12, 13 ], [ 4, 5, 13, 14 ], [ 4, 5, 14, 16 ], [ 4, 5, 16, 17 ], [ 4, 5, 17, 18 ], [ 4, 5, 18, 19 ], [ 4, 5, 19, 20 ], [ 4, 5, 20, 21 ], [ 4, 5, 21, 22 ], [ 4, 5, 22, 23 ], [ 4, 5, 23, 24 ], [ 4, 5, 24, 25 ], [ 4, 5, 25, 26 ], [ 4, 5, 26, 27 ], [ 4, 5, 27, 28 ], [ 4, 5, 28, 29 ], [ 4, 5, 29, 34 ], [ 4, 5, 34, 35 ], [ 4, 5, 35, 36 ], [ 4, 5, 36, 37 ], [ 4, 5, 37, 38 ], [ 4, 5, 38, 39 ], [ 4, 5, 39, 40 ], [ 4, 5, 40, 41 ], [ 4, 5, 41, 42 ], [ 4, 5, 42, 43 ], [ 4, 5, 43, 44 ], [ 4, 5, 44, 45 ], [ 4, 6, 8, 30 ], [ 4, 6, 30, 34 ], [ 4, 6, 31, 32 ], [ 4, 6, 32, 33 ], [ 4, 6, 33, 34 ], [ 4, 7, 9, 11 ], [ 4, 21, 22, 23 ], [ 4, 29, 30, 34 ], [ 4, 33, 34, 35 ], [ 5, 6, 7, 14 ], [ 5, 6, 7, 50 ], [ 5, 6, 8, 29 ], [ 5, 6, 8, 30 ], [ 5, 6, 14, 16 ], [ 5, 6, 16, 17 ], [ 5, 6, 17, 19 ], [ 5, 6, 19, 20 ], [ 5, 6, 20, 21 ], [ 5, 6, 21, 22 ], [ 5, 6, 22, 23 ], [ 5, 6, 23, 24 ], [ 5, 6, 24, 25 ], [ 5, 6, 25, 26 ], [ 5, 6, 26, 27 ], [ 5, 6, 27, 28 ], [ 5, 6, 28, 29 ], [ 5, 6, 30, 34 ], [ 5, 6, 34, 35 ], [ 5, 6, 35, 36 ], [ 5, 6, 36, 37 ], [ 5, 6, 37, 38 ], [ 5, 6, 38, 39 ], [ 5, 6, 39, 40 ], [ 5, 6, 40, 41 ], [ 5, 6, 41, 42 ], [ 5, 6, 42, 43 ], [ 5, 6, 43, 45 ], [ 5, 6, 45, 46 ], [ 5, 6, 47, 48 ], [ 5, 6, 48, 50 ], [ 5, 7, 11, 13 ], [ 5, 7, 13, 14 ], [ 5, 8, 29, 33 ], [ 5, 8, 30, 31 ], [ 5, 8, 31, 32 ], [ 5, 8, 32, 33 ], [ 5, 9, 10, 30 ], [ 5, 9, 10, 33 ], [ 5, 9, 29, 30 ], [ 5, 9, 29, 33 ], [ 5, 10, 30, 31 ], [ 5, 10, 31, 32 ], [ 5, 10, 32, 33 ], [ 5, 11, 12, 13 ], [ 5, 17, 18, 19 ], [ 5, 29, 30, 34 ], [ 5, 43, 44, 45 ], [ 6, 7, 8, 25 ], [ 6, 7, 8, 31 ], [ 6, 7, 14, 16 ], [ 6, 7, 16, 17 ], [ 6, 7, 17, 18 ], [ 6, 7, 18, 19 ], [ 6, 7, 19, 20 ], [ 6, 7, 20, 21 ], [ 6, 7, 21, 22 ], [ 6, 7, 22, 23 ], [ 6, 7, 23, 24 ], [ 6, 7, 24, 25 ], [ 6, 7, 31, 33 ], [ 6, 7, 33, 34 ], [ 6, 7, 34, 35 ], [ 6, 7, 35, 36 ], [ 6, 7, 36, 37 ], [ 6, 7, 37, 38 ], [ 6, 7, 38, 39 ], [ 6, 7, 39, 40 ], [ 6, 7, 40, 41 ], [ 6, 7, 41, 42 ], [ 6, 7, 42, 43 ], [ 6, 7, 43, 46 ], [ 6, 7, 47, 48 ], [ 6, 7, 48, 50 ], [ 6, 8, 9, 26 ], [ 6, 8, 9, 29 ], [ 6, 8, 25, 26 ], [ 6, 9, 10, 28 ], [ 6, 9, 10, 29 ], [ 6, 9, 26, 27 ], [ 6, 9, 27, 28 ], [ 6, 10, 11, 28 ], [ 6, 10, 11, 29 ], [ 6, 11, 12, 15 ], [ 6, 11, 12, 28 ], [ 6, 11, 15, 29 ], [ 6, 12, 15, 29 ], [ 6, 12, 28, 29 ], [ 6, 17, 18, 19 ], [ 6, 31, 32, 33 ], [ 6, 43, 45, 46 ], [ 7, 8, 9, 11 ], [ 7, 8, 9, 50 ], [ 7, 8, 10, 22 ], [ 7, 8, 10, 23 ], [ 7, 8, 11, 13 ], [ 7, 8, 13, 16 ], [ 7, 8, 16, 17 ], [ 7, 8, 17, 18 ], [ 7, 8, 18, 19 ], [ 7, 8, 19, 20 ], [ 7, 8, 20, 21 ], [ 7, 8, 21, 22 ], [ 7, 8, 23, 24 ], [ 7, 8, 24, 25 ], [ 7, 8, 31, 32 ], [ 7, 8, 32, 33 ], [ 7, 8, 33, 34 ], [ 7, 8, 34, 35 ], [ 7, 8, 35, 36 ], [ 7, 8, 36, 37 ], [ 7, 8, 37, 38 ], [ 7, 8, 38, 39 ], [ 7, 8, 39, 40 ], [ 7, 8, 40, 41 ], [ 7, 8, 41, 42 ], [ 7, 8, 42, 43 ], [ 7, 8, 43, 46 ], [ 7, 8, 46, 47 ], [ 7, 8, 47, 48 ], [ 7, 8, 48, 49 ], [ 7, 8, 49, 50 ], [ 7, 10, 22, 23 ], [ 7, 13, 14, 16 ], [ 7, 31, 32, 33 ], [ 7, 48, 49, 50 ], [ 8, 9, 10, 22 ], [ 8, 9, 10, 26 ], [ 8, 9, 11, 13 ], [ 8, 9, 13, 14 ], [ 8, 9, 14, 16 ], [ 8, 9, 16, 17 ], [ 8, 9, 17, 18 ], [ 8, 9, 18, 19 ], [ 8, 9, 19, 20 ], [ 8, 9, 20, 21 ], [ 8, 9, 21, 22 ], [ 8, 9, 29, 33 ], [ 8, 9, 33, 34 ], [ 8, 9, 34, 35 ], [ 8, 9, 35, 36 ], [ 8, 9, 36, 37 ], [ 8, 9, 37, 38 ], [ 8, 9, 38, 39 ], [ 8, 9, 39, 40 ], [ 8, 9, 40, 41 ], [ 8, 9, 41, 42 ], [ 8, 9, 42, 44 ], [ 8, 9, 43, 44 ], [ 8, 9, 43, 47 ], [ 8, 9, 47, 48 ], [ 8, 9, 48, 49 ], [ 8, 9, 49, 50 ], [ 8, 10, 12, 24 ], [ 8, 10, 12, 26 ], [ 8, 10, 23, 24 ], [ 8, 12, 24, 25 ], [ 8, 12, 25, 26 ], [ 8, 13, 14, 16 ], [ 8, 42, 43, 44 ], [ 8, 43, 46, 47 ], [ 9, 10, 11, 13 ], [ 9, 10, 13, 14 ], [ 9, 10, 14, 16 ], [ 9, 10, 15, 29 ], [ 9, 10, 15, 30 ], [ 9, 10, 16, 17 ], [ 9, 10, 17, 18 ], [ 9, 10, 18, 19 ], [ 9, 10, 19, 20 ], [ 9, 10, 20, 21 ], [ 9, 10, 21, 22 ], [ 9, 10, 26, 27 ], [ 9, 10, 27, 28 ], [ 9, 10, 33, 34 ], [ 9, 10, 34, 35 ], [ 9, 10, 35, 36 ], [ 9, 10, 36, 37 ], [ 9, 10, 37, 38 ], [ 9, 10, 38, 39 ], [ 9, 10, 39, 40 ], [ 9, 10, 40, 41 ], [ 9, 10, 41, 42 ], [ 9, 10, 42, 44 ], [ 9, 10, 43, 44 ], [ 9, 10, 43, 45 ], [ 9, 10, 45, 46 ], [ 9, 10, 46, 47 ], [ 9, 10, 47, 48 ], [ 9, 10, 48, 49 ], [ 9, 10, 49, 50 ], [ 9, 15, 29, 30 ], [ 9, 43, 45, 46 ], [ 9, 43, 46, 47 ], [ 10, 11, 12, 23 ], [ 10, 11, 12, 27 ], [ 10, 11, 13, 17 ], [ 10, 11, 15, 29 ], [ 10, 11, 15, 31 ], [ 10, 11, 17, 20 ], [ 10, 11, 20, 21 ], [ 10, 11, 21, 22 ], [ 10, 11, 22, 23 ], [ 10, 11, 27, 28 ], [ 10, 11, 31, 32 ], [ 10, 11, 32, 33 ], [ 10, 11, 33, 34 ], [ 10, 11, 34, 35 ], [ 10, 11, 35, 36 ], [ 10, 11, 36, 37 ], [ 10, 11, 37, 38 ], [ 10, 11, 38, 39 ], [ 10, 11, 39, 40 ], [ 10, 11, 40, 41 ], [ 10, 11, 41, 42 ], [ 10, 11, 42, 44 ], [ 10, 11, 43, 44 ], [ 10, 11, 43, 45 ], [ 10, 11, 45, 46 ], [ 10, 11, 46, 47 ], [ 10, 11, 47, 48 ], [ 10, 11, 48, 49 ], [ 10, 11, 49, 50 ], [ 10, 12, 23, 24 ], [ 10, 12, 26, 27 ], [ 10, 13, 14, 17 ], [ 10, 14, 16, 17 ], [ 10, 15, 30, 31 ], [ 10, 17, 18, 20 ], [ 10, 18, 19, 20 ], [ 11, 12, 13, 20 ], [ 11, 12, 14, 34 ], [ 11, 12, 14, 35 ], [ 11, 12, 15, 31 ], [ 11, 12, 16, 31 ], [ 11, 12, 16, 33 ], [ 11, 12, 20, 21 ], [ 11, 12, 21, 22 ], [ 11, 12, 22, 23 ], [ 11, 12, 27, 28 ], [ 11, 12, 33, 34 ], [ 11, 12, 35, 36 ], [ 11, 12, 36, 37 ], [ 11, 12, 37, 38 ], [ 11, 12, 38, 39 ], [ 11, 12, 39, 40 ], [ 11, 12, 40, 41 ], [ 11, 12, 41, 42 ], [ 11, 12, 42, 44 ], [ 11, 12, 43, 44 ], [ 11, 12, 43, 45 ], [ 11, 12, 45, 46 ], [ 11, 12, 46, 47 ], [ 11, 12, 47, 48 ], [ 11, 12, 48, 49 ], [ 11, 12, 49, 50 ], [ 11, 13, 17, 20 ], [ 11, 14, 34, 35 ], [ 11, 16, 31, 32 ], [ 11, 16, 32, 33 ], [ 12, 13, 14, 34 ], [ 12, 13, 14, 42 ], [ 12, 13, 15, 27 ], [ 12, 13, 15, 32 ], [ 12, 13, 20, 21 ], [ 12, 13, 21, 22 ], [ 12, 13, 22, 23 ], [ 12, 13, 23, 24 ], [ 12, 13, 24, 26 ], [ 12, 13, 26, 27 ], [ 12, 13, 32, 33 ], [ 12, 13, 33, 34 ], [ 12, 13, 42, 44 ], [ 12, 13, 44, 45 ], [ 12, 13, 45, 46 ], [ 12, 13, 46, 47 ], [ 12, 13, 47, 48 ], [ 12, 13, 48, 49 ], [ 12, 13, 49, 50 ], [ 12, 14, 35, 36 ], [ 12, 14, 36, 37 ], [ 12, 14, 37, 38 ], [ 12, 14, 38, 39 ], [ 12, 14, 39, 40 ], [ 12, 14, 40, 41 ], [ 12, 14, 41, 42 ], [ 12, 15, 16, 30 ], [ 12, 15, 16, 32 ], [ 12, 15, 27, 28 ], [ 12, 15, 28, 29 ], [ 12, 15, 30, 31 ], [ 12, 16, 17, 30 ], [ 12, 16, 17, 31 ], [ 12, 16, 32, 33 ], [ 12, 17, 30, 31 ], [ 12, 24, 25, 26 ], [ 12, 43, 44, 45 ], [ 13, 14, 15, 26 ], [ 13, 14, 15, 33 ], [ 13, 14, 17, 20 ], [ 13, 14, 19, 33 ], [ 13, 14, 19, 34 ], [ 13, 14, 20, 21 ], [ 13, 14, 21, 22 ], [ 13, 14, 22, 23 ], [ 13, 14, 23, 24 ], [ 13, 14, 24, 26 ], [ 13, 14, 42, 44 ], [ 13, 14, 44, 45 ], [ 13, 14, 45, 46 ], [ 13, 14, 46, 47 ], [ 13, 14, 47, 48 ], [ 13, 14, 48, 49 ], [ 13, 14, 49, 50 ], [ 13, 15, 26, 27 ], [ 13, 15, 32, 33 ], [ 13, 19, 33, 34 ], [ 14, 15, 16, 23 ], [ 14, 15, 23, 24 ], [ 14, 15, 24, 26 ], [ 14, 15, 32, 33 ], [ 14, 15, 32, 34 ], [ 14, 15, 34, 35 ], [ 14, 15, 35, 36 ], [ 14, 15, 36, 37 ], [ 14, 15, 37, 38 ], [ 14, 15, 38, 39 ], [ 14, 15, 39, 40 ], [ 14, 15, 40, 41 ], [ 14, 15, 41, 42 ], [ 14, 15, 42, 44 ], [ 14, 15, 44, 45 ], [ 14, 15, 45, 46 ], [ 14, 15, 46, 47 ], [ 14, 15, 47, 48 ], [ 14, 15, 48, 49 ], [ 14, 15, 49, 50 ], [ 14, 16, 17, 23 ], [ 14, 17, 18, 20 ], [ 14, 17, 18, 21 ], [ 14, 17, 21, 22 ], [ 14, 17, 22, 23 ], [ 14, 18, 20, 21 ], [ 14, 19, 32, 33 ], [ 14, 19, 32, 34 ], [ 15, 16, 17, 23 ], [ 15, 16, 17, 25 ], [ 15, 16, 20, 36 ], [ 15, 16, 20, 38 ], [ 15, 16, 24, 25 ], [ 15, 16, 24, 26 ], [ 15, 16, 26, 27 ], [ 15, 16, 27, 28 ], [ 15, 16, 28, 29 ], [ 15, 16, 29, 30 ], [ 15, 16, 32, 36 ], [ 15, 16, 38, 39 ], [ 15, 16, 39, 40 ], [ 15, 16, 40, 41 ], [ 15, 16, 41, 42 ], [ 15, 16, 42, 45 ], [ 15, 16, 45, 46 ], [ 15, 16, 46, 47 ], [ 15, 16, 47, 48 ], [ 15, 16, 48, 49 ], [ 15, 16, 49, 50 ], [ 15, 17, 23, 24 ], [ 15, 17, 24, 25 ], [ 15, 19, 20, 36 ], [ 15, 19, 20, 37 ], [ 15, 19, 36, 37 ], [ 15, 20, 21, 37 ], [ 15, 20, 21, 38 ], [ 15, 21, 37, 38 ], [ 15, 32, 34, 35 ], [ 15, 32, 35, 36 ], [ 15, 42, 44, 45 ], [ 16, 17, 25, 26 ], [ 16, 17, 26, 27 ], [ 16, 17, 27, 28 ], [ 16, 17, 28, 29 ], [ 16, 17, 29, 30 ], [ 16, 17, 31, 32 ], [ 16, 17, 32, 35 ], [ 16, 17, 35, 36 ], [ 16, 17, 36, 39 ], [ 16, 17, 39, 40 ], [ 16, 17, 40, 41 ], [ 16, 17, 41, 42 ], [ 16, 17, 42, 44 ], [ 16, 17, 44, 45 ], [ 16, 17, 45, 46 ], [ 16, 17, 46, 47 ], [ 16, 17, 47, 48 ], [ 16, 17, 48, 49 ], [ 16, 17, 49, 50 ], [ 16, 18, 19, 36 ], [ 16, 18, 19, 38 ], [ 16, 18, 36, 39 ], [ 16, 18, 38, 39 ], [ 16, 19, 20, 36 ], [ 16, 19, 20, 38 ], [ 16, 24, 25, 26 ], [ 16, 32, 35, 36 ], [ 16, 42, 44, 45 ], [ 17, 18, 21, 22 ], [ 17, 18, 22, 23 ], [ 17, 18, 23, 24 ], [ 17, 18, 24, 25 ], [ 17, 18, 25, 26 ], [ 17, 18, 26, 27 ], [ 17, 18, 27, 28 ], [ 17, 18, 28, 29 ], [ 17, 18, 29, 30 ], [ 17, 18, 30, 31 ], [ 17, 18, 31, 32 ], [ 17, 18, 32, 34 ], [ 17, 18, 34, 35 ], [ 17, 18, 35, 37 ], [ 17, 18, 36, 37 ], [ 17, 18, 36, 39 ], [ 17, 18, 39, 40 ], [ 17, 18, 40, 41 ], [ 17, 18, 41, 42 ], [ 17, 18, 42, 44 ], [ 17, 18, 44, 45 ], [ 17, 18, 45, 46 ], [ 17, 18, 46, 47 ], [ 17, 18, 47, 48 ], [ 17, 18, 48, 49 ], [ 17, 18, 49, 50 ], [ 17, 32, 34, 35 ], [ 17, 35, 36, 37 ], [ 18, 19, 20, 21 ], [ 18, 19, 21, 25 ], [ 18, 19, 25, 27 ], [ 18, 19, 27, 28 ], [ 18, 19, 28, 29 ], [ 18, 19, 29, 30 ], [ 18, 19, 30, 31 ], [ 18, 19, 31, 32 ], [ 18, 19, 32, 34 ], [ 18, 19, 34, 37 ], [ 18, 19, 36, 37 ], [ 18, 19, 38, 39 ], [ 18, 19, 39, 40 ], [ 18, 19, 40, 41 ], [ 18, 19, 41, 42 ], [ 18, 19, 42, 43 ], [ 18, 19, 43, 44 ], [ 18, 19, 44, 45 ], [ 18, 19, 45, 46 ], [ 18, 19, 46, 47 ], [ 18, 19, 47, 48 ], [ 18, 19, 48, 49 ], [ 18, 19, 49, 50 ], [ 18, 21, 22, 24 ], [ 18, 21, 24, 25 ], [ 18, 22, 23, 24 ], [ 18, 25, 26, 27 ], [ 18, 34, 35, 37 ], [ 18, 42, 43, 44 ], [ 19, 20, 21, 25 ], [ 19, 20, 22, 29 ], [ 19, 20, 22, 32 ], [ 19, 20, 24, 33 ], [ 19, 20, 24, 34 ], [ 19, 20, 25, 27 ], [ 19, 20, 27, 28 ], [ 19, 20, 28, 29 ], [ 19, 20, 32, 33 ], [ 19, 20, 34, 37 ], [ 19, 20, 38, 39 ], [ 19, 20, 39, 40 ], [ 19, 20, 40, 41 ], [ 19, 20, 41, 42 ], [ 19, 20, 42, 43 ], [ 19, 20, 43, 44 ], [ 19, 20, 44, 45 ], [ 19, 20, 45, 46 ], [ 19, 20, 46, 47 ], [ 19, 20, 47, 50 ], [ 19, 22, 29, 30 ], [ 19, 22, 30, 31 ], [ 19, 22, 31, 32 ], [ 19, 24, 33, 34 ], [ 19, 47, 48, 49 ], [ 19, 47, 49, 50 ], [ 20, 21, 22, 29 ], [ 20, 21, 22, 37 ], [ 20, 21, 25, 27 ], [ 20, 21, 27, 28 ], [ 20, 21, 28, 29 ], [ 20, 21, 38, 39 ], [ 20, 21, 39, 40 ], [ 20, 21, 40, 41 ], [ 20, 21, 41, 42 ], [ 20, 21, 42, 43 ], [ 20, 21, 43, 44 ], [ 20, 21, 44, 45 ], [ 20, 21, 45, 46 ], [ 20, 21, 46, 47 ], [ 20, 21, 47, 49 ], [ 20, 21, 49, 50 ], [ 20, 22, 23, 32 ], [ 20, 22, 23, 34 ], [ 20, 22, 34, 35 ], [ 20, 22, 35, 37 ], [ 20, 23, 24, 32 ], [ 20, 23, 24, 34 ], [ 20, 24, 32, 33 ], [ 20, 34, 35, 37 ], [ 20, 47, 49, 50 ], [ 21, 22, 24, 27 ], [ 21, 22, 26, 45 ], [ 21, 22, 26, 46 ], [ 21, 22, 27, 28 ], [ 21, 22, 28, 29 ], [ 21, 22, 37, 38 ], [ 21, 22, 38, 39 ], [ 21, 22, 39, 40 ], [ 21, 22, 40, 41 ], [ 21, 22, 41, 42 ], [ 21, 22, 42, 43 ], [ 21, 22, 43, 44 ], [ 21, 22, 44, 45 ], [ 21, 22, 46, 47 ], [ 21, 22, 47, 49 ], [ 21, 22, 49, 50 ], [ 21, 24, 25, 32 ], [ 21, 24, 27, 32 ], [ 21, 25, 27, 31 ], [ 21, 25, 31, 32 ], [ 21, 26, 45, 46 ], [ 21, 27, 31, 32 ], [ 22, 23, 24, 29 ], [ 22, 23, 26, 45 ], [ 22, 23, 26, 48 ], [ 22, 23, 29, 30 ], [ 22, 23, 30, 31 ], [ 22, 23, 31, 32 ], [ 22, 23, 34, 35 ], [ 22, 23, 35, 36 ], [ 22, 23, 36, 37 ], [ 22, 23, 37, 38 ], [ 22, 23, 38, 39 ], [ 22, 23, 39, 40 ], [ 22, 23, 40, 41 ], [ 22, 23, 41, 42 ], [ 22, 23, 42, 43 ], [ 22, 23, 43, 44 ], [ 22, 23, 44, 45 ], [ 22, 23, 48, 49 ], [ 22, 23, 49, 50 ], [ 22, 24, 27, 28 ], [ 22, 24, 28, 29 ], [ 22, 26, 46, 47 ], [ 22, 26, 47, 48 ], [ 22, 35, 36, 37 ], [ 22, 47, 48, 49 ], [ 23, 24, 25, 43 ], [ 23, 24, 25, 48 ], [ 23, 24, 29, 30 ], [ 23, 24, 30, 31 ], [ 23, 24, 31, 32 ], [ 23, 24, 34, 35 ], [ 23, 24, 35, 36 ], [ 23, 24, 36, 37 ], [ 23, 24, 37, 38 ], [ 23, 24, 38, 39 ], [ 23, 24, 39, 40 ], [ 23, 24, 40, 41 ], [ 23, 24, 41, 42 ], [ 23, 24, 42, 43 ], [ 23, 24, 48, 49 ], [ 23, 24, 49, 50 ], [ 23, 25, 26, 43 ], [ 23, 25, 26, 48 ], [ 23, 26, 27, 43 ], [ 23, 26, 27, 45 ], [ 23, 27, 43, 44 ], [ 23, 27, 44, 45 ], [ 24, 25, 32, 33 ], [ 24, 25, 33, 34 ], [ 24, 25, 34, 35 ], [ 24, 25, 35, 36 ], [ 24, 25, 36, 37 ], [ 24, 25, 37, 38 ], [ 24, 25, 38, 39 ], [ 24, 25, 39, 40 ], [ 24, 25, 40, 41 ], [ 24, 25, 41, 42 ], [ 24, 25, 42, 43 ], [ 24, 25, 48, 49 ], [ 24, 25, 49, 50 ], [ 24, 27, 28, 30 ], [ 24, 27, 30, 31 ], [ 24, 27, 31, 32 ], [ 24, 28, 29, 30 ], [ 25, 26, 27, 31 ], [ 25, 26, 28, 34 ], [ 25, 26, 28, 37 ], [ 25, 26, 29, 47 ], [ 25, 26, 29, 49 ], [ 25, 26, 31, 32 ], [ 25, 26, 32, 33 ], [ 25, 26, 33, 34 ], [ 25, 26, 37, 38 ], [ 25, 26, 38, 39 ], [ 25, 26, 39, 40 ], [ 25, 26, 40, 41 ], [ 25, 26, 41, 42 ], [ 25, 26, 42, 43 ], [ 25, 26, 47, 48 ], [ 25, 26, 49, 50 ], [ 25, 28, 34, 36 ], [ 25, 28, 36, 37 ], [ 25, 29, 30, 47 ], [ 25, 29, 30, 49 ], [ 25, 30, 47, 48 ], [ 25, 30, 48, 49 ], [ 25, 34, 35, 36 ], [ 26, 27, 28, 33 ], [ 26, 27, 28, 37 ], [ 26, 27, 29, 46 ], [ 26, 27, 29, 49 ], [ 26, 27, 30, 31 ], [ 26, 27, 30, 33 ], [ 26, 27, 37, 38 ], [ 26, 27, 38, 39 ], [ 26, 27, 39, 40 ], [ 26, 27, 40, 41 ], [ 26, 27, 41, 42 ], [ 26, 27, 42, 43 ], [ 26, 27, 45, 46 ], [ 26, 27, 49, 50 ], [ 26, 28, 33, 36 ], [ 26, 28, 34, 36 ], [ 26, 29, 46, 47 ], [ 26, 30, 31, 32 ], [ 26, 30, 32, 33 ], [ 26, 33, 34, 36 ], [ 27, 28, 29, 45 ], [ 27, 28, 30, 33 ], [ 27, 28, 37, 38 ], [ 27, 28, 38, 39 ], [ 27, 28, 39, 40 ], [ 27, 28, 40, 41 ], [ 27, 28, 41, 42 ], [ 27, 28, 42, 43 ], [ 27, 28, 43, 44 ], [ 27, 28, 44, 45 ], [ 27, 29, 45, 46 ], [ 27, 29, 49, 50 ], [ 28, 29, 30, 37 ], [ 28, 29, 37, 38 ], [ 28, 29, 38, 39 ], [ 28, 29, 39, 40 ], [ 28, 29, 40, 41 ], [ 28, 29, 41, 42 ], [ 28, 29, 42, 43 ], [ 28, 29, 43, 44 ], [ 28, 29, 44, 45 ], [ 28, 30, 33, 36 ], [ 28, 30, 36, 37 ], [ 29, 30, 31, 35 ], [ 29, 30, 31, 43 ], [ 29, 30, 35, 48 ], [ 29, 30, 37, 38 ], [ 29, 30, 38, 39 ], [ 29, 30, 39, 40 ], [ 29, 30, 40, 41 ], [ 29, 30, 41, 42 ], [ 29, 30, 42, 43 ], [ 29, 30, 47, 48 ], [ 29, 30, 49, 50 ], [ 29, 31, 32, 44 ], [ 29, 31, 32, 46 ], [ 29, 31, 35, 47 ], [ 29, 31, 43, 44 ], [ 29, 31, 46, 47 ], [ 29, 32, 44, 45 ], [ 29, 32, 45, 46 ], [ 29, 35, 36, 47 ], [ 29, 35, 36, 48 ], [ 29, 36, 47, 48 ], [ 30, 31, 32, 37 ], [ 30, 31, 35, 48 ], [ 30, 31, 37, 38 ], [ 30, 31, 38, 39 ], [ 30, 31, 39, 41 ], [ 30, 31, 41, 42 ], [ 30, 31, 42, 43 ], [ 30, 31, 48, 49 ], [ 30, 31, 49, 50 ], [ 30, 32, 33, 37 ], [ 30, 33, 36, 37 ], [ 30, 39, 40, 41 ], [ 31, 32, 37, 38 ], [ 31, 32, 38, 39 ], [ 31, 32, 39, 41 ], [ 31, 32, 41, 42 ], [ 31, 32, 42, 43 ], [ 31, 32, 43, 44 ], [ 31, 32, 46, 48 ], [ 31, 32, 48, 49 ], [ 31, 32, 49, 50 ], [ 31, 34, 35, 45 ], [ 31, 34, 35, 48 ], [ 31, 34, 45, 46 ], [ 31, 34, 46, 48 ], [ 31, 35, 36, 45 ], [ 31, 35, 36, 46 ], [ 31, 35, 46, 47 ], [ 31, 36, 45, 46 ], [ 32, 33, 37, 38 ], [ 32, 33, 38, 41 ], [ 32, 33, 41, 42 ], [ 32, 33, 42, 43 ], [ 32, 33, 43, 44 ], [ 32, 33, 44, 45 ], [ 32, 33, 45, 46 ], [ 32, 33, 46, 50 ], [ 32, 38, 39, 41 ], [ 32, 46, 48, 49 ], [ 32, 46, 49, 50 ], [ 33, 34, 36, 38 ], [ 33, 34, 38, 39 ], [ 33, 34, 39, 41 ], [ 33, 34, 41, 42 ], [ 33, 34, 42, 43 ], [ 33, 34, 43, 44 ], [ 33, 34, 44, 45 ], [ 33, 34, 45, 46 ], [ 33, 34, 46, 48 ], [ 33, 34, 48, 49 ], [ 33, 34, 49, 50 ], [ 33, 36, 37, 38 ], [ 33, 38, 39, 41 ], [ 33, 46, 48, 49 ], [ 33, 46, 49, 50 ], [ 34, 35, 36, 38 ], [ 34, 35, 38, 43 ], [ 34, 35, 43, 44 ], [ 34, 35, 44, 45 ], [ 34, 35, 48, 49 ], [ 34, 35, 49, 50 ], [ 34, 38, 39, 42 ], [ 34, 38, 42, 43 ], [ 34, 39, 41, 42 ], [ 35, 36, 38, 43 ], [ 35, 36, 43, 44 ], [ 35, 36, 44, 45 ], [ 35, 36, 46, 47 ], [ 35, 36, 48, 49 ], [ 35, 36, 49, 50 ], [ 36, 37, 38, 42 ], [ 36, 37, 41, 46 ], [ 36, 37, 41, 48 ], [ 36, 37, 42, 43 ], [ 36, 37, 43, 44 ], [ 36, 37, 44, 46 ], [ 36, 37, 48, 49 ], [ 36, 38, 42, 43 ], [ 36, 41, 46, 47 ], [ 36, 41, 47, 48 ], [ 36, 44, 45, 46 ], [ 37, 38, 39, 42 ], [ 37, 38, 39, 50 ], [ 37, 38, 40, 47 ], [ 37, 38, 40, 48 ], [ 37, 38, 44, 46 ], [ 37, 38, 44, 50 ], [ 37, 38, 46, 47 ], [ 37, 38, 48, 49 ], [ 37, 39, 42, 43 ], [ 37, 39, 43, 50 ], [ 37, 40, 41, 45 ], [ 37, 40, 41, 48 ], [ 37, 40, 45, 47 ], [ 37, 41, 45, 47 ], [ 37, 41, 46, 47 ], [ 37, 43, 44, 50 ], [ 38, 39, 44, 49 ], [ 38, 39, 44, 50 ], [ 38, 40, 44, 46 ], [ 38, 40, 44, 49 ], [ 38, 40, 46, 47 ], [ 38, 40, 48, 49 ], [ 39, 40, 41, 44 ], [ 39, 40, 44, 49 ], [ 39, 41, 42, 47 ], [ 39, 41, 44, 47 ], [ 39, 42, 43, 48 ], [ 39, 42, 47, 48 ], [ 39, 43, 48, 50 ], [ 39, 44, 45, 47 ], [ 40, 41, 42, 43 ], [ 40, 41, 43, 48 ], [ 40, 41, 44, 45 ], [ 40, 42, 43, 50 ], [ 40, 43, 48, 49 ], [ 40, 43, 49, 50 ], [ 40, 44, 45, 46 ], [ 40, 45, 46, 47 ], [ 41, 42, 43, 48 ], [ 41, 42, 47, 48 ], [ 41, 44, 45, 47 ], [ 43, 48, 49, 50 ] ];