***************************************************************************** * www.FindStat.org - The Combinatorial Statistic Finder * * * * Copyright (C) 2019 The FindStatCrew * * * * This information is distributed in the hope that it will be useful, * * but WITHOUT ANY WARRANTY; without even the implied warranty of * * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. * ***************************************************************************** ----------------------------------------------------------------------------- Statistic identifier: St001770 ----------------------------------------------------------------------------- Collection: Signed permutations ----------------------------------------------------------------------------- Description: The number of facets of a certain subword complex associated with the signed permutation. Let $Q=[1,\dots,n,1,\dots,n,\dots,1,\dots,n]$ be the word of length $n^2$, and let $\pi$ be a signed permutation. Then this statistic yields the number of facets of the subword complex $\Delta(Q, \pi)$. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(pi): n = len(list(pi)) S = SignedPermutations(n) Q = S.w0.coxeter_sorting_word(S.coxeter_element()) return len(SubwordComplex(Q, pi).facets()) ----------------------------------------------------------------------------- Statistic values: [1] => 1 [-1] => 1 [1,2] => 1 [1,-2] => 2 [-1,2] => 1 [-1,-2] => 1 [2,1] => 2 [2,-1] => 1 [-2,1] => 3 [-2,-1] => 1 [1,2,3] => 1 [1,2,-3] => 3 [1,-2,3] => 4 [1,-2,-3] => 6 [-1,2,3] => 1 [-1,2,-3] => 2 [-1,-2,3] => 1 [-1,-2,-3] => 1 [1,3,2] => 3 [1,3,-2] => 3 [1,-3,2] => 6 [1,-3,-2] => 4 [-1,3,2] => 2 [-1,3,-2] => 1 [-1,-3,2] => 3 [-1,-3,-2] => 1 [2,1,3] => 3 [2,1,-3] => 9 [2,-1,3] => 1 [2,-1,-3] => 2 [-2,1,3] => 5 [-2,1,-3] => 8 [-2,-1,3] => 1 [-2,-1,-3] => 1 [2,3,1] => 3 [2,3,-1] => 1 [2,-3,1] => 8 [2,-3,-1] => 2 [-2,3,1] => 8 [-2,3,-1] => 2 [-2,-3,1] => 10 [-2,-3,-1] => 2 [3,1,2] => 6 [3,1,-2] => 8 [3,-1,2] => 2 [3,-1,-2] => 1 [-3,1,2] => 10 [-3,1,-2] => 10 [-3,-1,2] => 3 [-3,-1,-2] => 1 [3,2,1] => 8 [3,2,-1] => 3 [3,-2,1] => 6 [3,-2,-1] => 1 [-3,2,1] => 15 [-3,2,-1] => 5 [-3,-2,1] => 7 [-3,-2,-1] => 1 [1,2,3,4] => 1 [1,2,3,-4] => 4 [1,2,-3,4] => 10 [1,2,-3,-4] => 20 [1,-2,3,4] => 6 [1,-2,3,-4] => 16 [1,-2,-3,4] => 15 [1,-2,-3,-4] => 20 [-1,2,3,4] => 1 [-1,2,3,-4] => 3 [-1,2,-3,4] => 4 [-1,2,-3,-4] => 6 [-1,-2,3,4] => 1 [-1,-2,3,-4] => 2 [-1,-2,-3,4] => 1 [-1,-2,-3,-4] => 1 [1,2,4,3] => 4 [1,2,4,-3] => 6 [1,2,-4,3] => 10 [1,2,-4,-3] => 10 [1,-2,4,3] => 16 [1,-2,4,-3] => 13 [1,-2,-4,3] => 29 [1,-2,-4,-3] => 16 [-1,2,4,3] => 3 [-1,2,4,-3] => 3 [-1,2,-4,3] => 6 [-1,2,-4,-3] => 4 [-1,-2,4,3] => 2 [-1,-2,4,-3] => 1 [-1,-2,-4,3] => 3 [-1,-2,-4,-3] => 1 [1,3,2,4] => 4 [1,3,2,-4] => 16 [1,3,-2,4] => 5 [1,3,-2,-4] => 13 [1,-3,2,4] => 15 [1,-3,2,-4] => 33 [1,-3,-2,4] => 11 [1,-3,-2,-4] => 14 [-1,3,2,4] => 3 [-1,3,2,-4] => 9 [-1,3,-2,4] => 1 [-1,3,-2,-4] => 2 [-1,-3,2,4] => 5 [-1,-3,2,-4] => 8 [-1,-3,-2,4] => 1 [-1,-3,-2,-4] => 1 [1,3,4,2] => 6 [1,3,4,-2] => 4 [1,3,-4,2] => 20 [1,3,-4,-2] => 10 [1,-3,4,2] => 33 [1,-3,4,-2] => 17 [1,-3,-4,2] => 50 [1,-3,-4,-2] => 20 [-1,3,4,2] => 3 [-1,3,4,-2] => 1 [-1,3,-4,2] => 8 [-1,3,-4,-2] => 2 [-1,-3,4,2] => 8 [-1,-3,4,-2] => 2 [-1,-3,-4,2] => 10 [-1,-3,-4,-2] => 2 [1,4,2,3] => 10 [1,4,2,-3] => 20 [1,4,-2,3] => 13 [1,4,-2,-3] => 10 [1,-4,2,3] => 20 [1,-4,2,-3] => 30 [1,-4,-2,3] => 23 [1,-4,-2,-3] => 12 [-1,4,2,3] => 6 [-1,4,2,-3] => 8 [-1,4,-2,3] => 2 [-1,4,-2,-3] => 1 [-1,-4,2,3] => 10 [-1,-4,2,-3] => 10 [-1,-4,-2,3] => 3 [-1,-4,-2,-3] => 1 [1,4,3,2] => 20 [1,4,3,-2] => 15 [1,4,-3,2] => 20 [1,4,-3,-2] => 7 [1,-4,3,2] => 45 [1,-4,3,-2] => 30 [1,-4,-3,2] => 27 [1,-4,-3,-2] => 8 [-1,4,3,2] => 8 [-1,4,3,-2] => 3 [-1,4,-3,2] => 6 [-1,4,-3,-2] => 1 [-1,-4,3,2] => 15 [-1,-4,3,-2] => 5 [-1,-4,-3,2] => 7 [-1,-4,-3,-2] => 1 [2,1,3,4] => 4 [2,1,3,-4] => 16 [2,1,-3,4] => 40 [2,1,-3,-4] => 80 [2,-1,3,4] => 1 [2,-1,3,-4] => 3 [2,-1,-3,4] => 4 [2,-1,-3,-4] => 6 [-2,1,3,4] => 7 [-2,1,3,-4] => 19 [-2,1,-3,4] => 19 [-2,1,-3,-4] => 26 [-2,-1,3,4] => 1 [-2,-1,3,-4] => 2 [-2,-1,-3,4] => 1 [-2,-1,-3,-4] => 1 [2,1,4,3] => 16 [2,1,4,-3] => 24 [2,1,-4,3] => 40 [2,1,-4,-3] => 40 [2,-1,4,3] => 3 [2,-1,4,-3] => 3 [2,-1,-4,3] => 6 [2,-1,-4,-3] => 4 [-2,1,4,3] => 19 [-2,1,4,-3] => 16 [-2,1,-4,3] => 35 [-2,1,-4,-3] => 20 [-2,-1,4,3] => 2 [-2,-1,4,-3] => 1 [-2,-1,-4,3] => 3 [-2,-1,-4,-3] => 1 [2,3,1,4] => 6 [2,3,1,-4] => 24 [2,3,-1,4] => 1 [2,3,-1,-4] => 3 [2,-3,1,4] => 39 [2,-3,1,-4] => 83 [2,-3,-1,4] => 4 [2,-3,-1,-4] => 6 [-2,3,1,4] => 19 [-2,3,1,-4] => 51 [-2,3,-1,4] => 2 [-2,3,-1,-4] => 4 [-2,-3,1,4] => 21 [-2,-3,1,-4] => 30 [-2,-3,-1,4] => 2 [-2,-3,-1,-4] => 2 [2,3,4,1] => 4 [2,3,4,-1] => 1 [2,3,-4,1] => 15 [2,3,-4,-1] => 3 [2,-3,4,1] => 33 [2,-3,4,-1] => 7 [2,-3,-4,1] => 60 [2,-3,-4,-1] => 10 [-2,3,4,1] => 16 [-2,3,4,-1] => 3 [-2,3,-4,1] => 39 [-2,3,-4,-1] => 6 [-2,-3,4,1] => 30 [-2,-3,4,-1] => 5 [-2,-3,-4,1] => 35 [-2,-3,-4,-1] => 5 [2,4,1,3] => 20 [2,4,1,-3] => 35 [2,4,-1,3] => 3 [2,4,-1,-3] => 3 [2,-4,1,3] => 45 [2,-4,1,-3] => 57 [2,-4,-1,3] => 6 [2,-4,-1,-3] => 4 [-2,4,1,3] => 35 [-2,4,1,-3] => 39 [-2,4,-1,3] => 4 [-2,4,-1,-3] => 2 [-2,-4,1,3] => 54 [-2,-4,1,-3] => 46 [-2,-4,-1,3] => 6 [-2,-4,-1,-3] => 2 [2,4,3,1] => 15 [2,4,3,-1] => 4 [2,4,-3,1] => 20 [2,4,-3,-1] => 3 [2,-4,3,1] => 36 [2,-4,3,-1] => 9 [2,-4,-3,1] => 31 [2,-4,-3,-1] => 4 [-2,4,3,1] => 39 [-2,4,3,-1] => 8 [-2,4,-3,1] => 26 [-2,4,-3,-1] => 3 [-2,-4,3,1] => 67 [-2,-4,3,-1] => 13 [-2,-4,-3,1] => 29 [-2,-4,-3,-1] => 3 [3,1,2,4] => 10 [3,1,2,-4] => 40 [3,1,-2,4] => 19 [3,1,-2,-4] => 49 [3,-1,2,4] => 3 [3,-1,2,-4] => 9 [3,-1,-2,4] => 1 [3,-1,-2,-4] => 2 [-3,1,2,4] => 21 [-3,1,2,-4] => 49 [-3,1,-2,4] => 26 [-3,1,-2,-4] => 34 [-3,-1,2,4] => 5 [-3,-1,2,-4] => 8 [-3,-1,-2,4] => 1 [-3,-1,-2,-4] => 1 [3,1,4,2] => 20 [3,1,4,-2] => 15 [3,1,-4,2] => 65 [3,1,-4,-2] => 37 [3,-1,4,2] => 3 [3,-1,4,-2] => 1 [3,-1,-4,2] => 8 [3,-1,-4,-2] => 2 [-3,1,4,2] => 49 [-3,1,4,-2] => 30 [-3,1,-4,2] => 79 [-3,1,-4,-2] => 36 [-3,-1,4,2] => 8 [-3,-1,4,-2] => 2 [-3,-1,-4,2] => 10 [-3,-1,-4,-2] => 2 [3,2,1,4] => 20 [3,2,1,-4] => 80 [3,2,-1,4] => 4 [3,2,-1,-4] => 12 [3,-2,1,4] => 16 [3,-2,1,-4] => 42 [3,-2,-1,4] => 1 [3,-2,-1,-4] => 2 [-3,2,1,4] => 56 [-3,2,1,-4] => 128 [-3,2,-1,4] => 9 [-3,2,-1,-4] => 14 [-3,-2,1,4] => 16 [-3,-2,1,-4] => 22 [-3,-2,-1,4] => 1 [-3,-2,-1,-4] => 1 [3,2,4,1] => 15 [3,2,4,-1] => 4 [3,2,-4,1] => 56 [3,2,-4,-1] => 12 [3,-2,4,1] => 13 [3,-2,4,-1] => 2 [3,-2,-4,1] => 31 [3,-2,-4,-1] => 4 [-3,2,4,1] => 49 [-3,2,4,-1] => 12 [-3,2,-4,1] => 97 [-3,2,-4,-1] => 18 [-3,-2,4,1] => 22 [-3,-2,4,-1] => 3 [-3,-2,-4,1] => 25 [-3,-2,-4,-1] => 3 [3,4,1,2] => 20 [3,4,1,-2] => 20 [3,4,-1,2] => 3 [3,4,-1,-2] => 1 [3,-4,1,2] => 60 [3,-4,1,-2] => 48 [3,-4,-1,2] => 8 [3,-4,-1,-2] => 2 [-3,4,1,2] => 79 [-3,4,1,-2] => 62 [-3,4,-1,2] => 14 [-3,4,-1,-2] => 3 [-3,-4,1,2] => 105 [-3,-4,1,-2] => 70 [-3,-4,-1,2] => 17 [-3,-4,-1,-2] => 3 [3,4,2,1] => 20 [3,4,2,-1] => 6 [3,4,-2,1] => 10 [3,4,-2,-1] => 1 [3,-4,2,1] => 64 [3,-4,2,-1] => 17 [3,-4,-2,1] => 23 [3,-4,-2,-1] => 2 [-3,4,2,1] => 97 [-3,4,2,-1] => 27 [-3,4,-2,1] => 34 [-3,4,-2,-1] => 3 [-3,-4,2,1] => 140 [-3,-4,2,-1] => 35 [-3,-4,-2,1] => 37 [-3,-4,-2,-1] => 3 [4,1,2,3] => 20 [4,1,2,-3] => 45 [4,1,-2,3] => 39 [4,1,-2,-3] => 36 [4,-1,2,3] => 6 [4,-1,2,-3] => 8 [4,-1,-2,3] => 2 [4,-1,-2,-3] => 1 [-4,1,2,3] => 35 [-4,1,2,-3] => 63 [-4,1,-2,3] => 63 [-4,1,-2,-3] => 42 [-4,-1,2,3] => 10 [-4,-1,2,-3] => 10 [-4,-1,-2,3] => 3 [-4,-1,-2,-3] => 1 [4,1,3,2] => 45 [4,1,3,-2] => 36 [4,1,-3,2] => 60 [4,1,-3,-2] => 25 [4,-1,3,2] => 8 [4,-1,3,-2] => 3 [4,-1,-3,2] => 6 [4,-1,-3,-2] => 1 [-4,1,3,2] => 84 [-4,1,3,-2] => 63 [-4,1,-3,2] => 77 [-4,1,-3,-2] => 28 [-4,-1,3,2] => 15 [-4,-1,3,-2] => 5 [-4,-1,-3,2] => 7 [-4,-1,-3,-2] => 1 [4,2,1,3] => 45 [4,2,1,-3] => 96 [4,2,-1,3] => 9 [4,2,-1,-3] => 11 [4,-2,1,3] => 29 [4,-2,1,-3] => 31 [4,-2,-1,3] => 2 [4,-2,-1,-3] => 1 [-4,2,1,3] => 84 [-4,2,1,-3] => 140 [-4,2,-1,3] => 16 [-4,2,-1,-3] => 14 [-4,-2,1,3] => 44 [-4,-2,1,-3] => 36 [-4,-2,-1,3] => 3 [-4,-2,-1,-3] => 1 [4,2,3,1] => 36 [4,2,3,-1] => 10 [4,2,-3,1] => 64 [4,2,-3,-1] => 11 [4,-2,3,1] => 31 [4,-2,3,-1] => 5 [4,-2,-3,1] => 20 [4,-2,-3,-1] => 2 [-4,2,3,1] => 70 [-4,2,3,-1] => 19 [-4,2,-3,1] => 91 [-4,2,-3,-1] => 14 [-4,-2,3,1] => 52 [-4,-2,3,-1] => 8 [-4,-2,-3,1] => 22 [-4,-2,-3,-1] => 2 [4,3,1,2] => 60 [4,3,1,-2] => 64 [4,3,-1,2] => 11 [4,3,-1,-2] => 4 [4,-3,1,2] => 50 [4,-3,1,-2] => 31 [4,-3,-1,2] => 6 [4,-3,-1,-2] => 1 [-4,3,1,2] => 126 [-4,3,1,-2] => 121 [-4,3,-1,2] => 23 [-4,3,-1,-2] => 7 [-4,-3,1,2] => 61 [-4,-3,1,-2] => 34 [-4,-3,-1,2] => 7 [-4,-3,-1,-2] => 1 [4,3,2,1] => 64 [4,3,2,-1] => 20 [4,3,-2,1] => 36 [4,3,-2,-1] => 4 [4,-3,2,1] => 60 [4,-3,2,-1] => 14 [4,-3,-2,1] => 14 [4,-3,-2,-1] => 1 [-4,3,2,1] => 140 [-4,3,2,-1] => 42 [-4,3,-2,1] => 68 [-4,3,-2,-1] => 7 [-4,-3,2,1] => 78 [-4,-3,2,-1] => 17 [-4,-3,-2,1] => 15 [-4,-3,-2,-1] => 1 [1,2,3,4,5] => 1 [1,2,3,4,-5] => 5 [1,2,3,-4,5] => 20 [1,2,3,-4,-5] => 50 [1,2,-3,4,5] => 21 [1,2,-3,4,-5] => 70 [1,2,-3,-4,5] => 105 [1,2,-3,-4,-5] => 175 [1,-2,3,4,5] => 8 [1,-2,3,4,-5] => 30 [1,-2,3,-4,5] => 64 [1,-2,3,-4,-5] => 120 [1,-2,-3,4,5] => 28 [1,-2,-3,4,-5] => 70 [1,-2,-3,-4,5] => 56 [1,-2,-3,-4,-5] => 70 [-1,2,3,4,5] => 1 [-1,2,3,4,-5] => 4 [-1,2,3,-4,5] => 10 [-1,2,3,-4,-5] => 20 [-1,2,-3,4,5] => 6 [-1,2,-3,4,-5] => 16 [-1,2,-3,-4,5] => 15 [-1,2,-3,-4,-5] => 20 [-1,-2,3,4,5] => 1 [-1,-2,3,4,-5] => 3 [-1,-2,3,-4,5] => 4 [-1,-2,3,-4,-5] => 6 [-1,-2,-3,4,5] => 1 [-1,-2,-3,4,-5] => 2 [-1,-2,-3,-4,5] => 1 [-1,-2,-3,-4,-5] => 1 [1,2,3,5,4] => 5 [1,2,3,5,-4] => 10 [1,2,3,-5,4] => 15 [1,2,3,-5,-4] => 20 [1,2,-3,5,4] => 70 [1,2,-3,5,-4] => 79 [1,2,-3,-5,4] => 149 [1,2,-3,-5,-4] => 115 [1,-2,3,5,4] => 30 [1,-2,3,5,-4] => 41 [1,-2,3,-5,4] => 71 [1,-2,3,-5,-4] => 65 [1,-2,-3,5,4] => 70 [1,-2,-3,5,-4] => 51 [1,-2,-3,-5,4] => 121 [1,-2,-3,-5,-4] => 60 [-1,2,3,5,4] => 4 [-1,2,3,5,-4] => 6 [-1,2,3,-5,4] => 10 [-1,2,3,-5,-4] => 10 [-1,2,-3,5,4] => 16 [-1,2,-3,5,-4] => 13 [-1,2,-3,-5,4] => 29 [-1,2,-3,-5,-4] => 16 [-1,-2,3,5,4] => 3 [-1,-2,3,5,-4] => 3 [-1,-2,3,-5,4] => 6 [-1,-2,3,-5,-4] => 4 [-1,-2,-3,5,4] => 2 [-1,-2,-3,5,-4] => 1 [-1,-2,-3,-5,4] => 3 [-1,-2,-3,-5,-4] => 1 [1,2,4,3,5] => 5 [1,2,4,3,-5] => 25 [1,2,4,-3,5] => 15 [1,2,4,-3,-5] => 48 [1,2,-4,3,5] => 35 [1,2,-4,3,-5] => 98 [1,2,-4,-3,5] => 61 [1,2,-4,-3,-5] => 95 [1,-2,4,3,5] => 30 [1,-2,4,3,-5] => 112 [1,-2,4,-3,5] => 26 [1,-2,4,-3,-5] => 64 [1,-2,-4,3,5] => 90 [1,-2,-4,3,-5] => 184 [1,-2,-4,-3,5] => 48 [1,-2,-4,-3,-5] => 58 [-1,2,4,3,5] => 4 [-1,2,4,3,-5] => 16 [-1,2,4,-3,5] => 5 [-1,2,4,-3,-5] => 13 [-1,2,-4,3,5] => 15 [-1,2,-4,3,-5] => 33 [-1,2,-4,-3,5] => 11 [-1,2,-4,-3,-5] => 14 [-1,-2,4,3,5] => 3 [-1,-2,4,3,-5] => 9 [-1,-2,4,-3,5] => 1 [-1,-2,4,-3,-5] => 2 [-1,-2,-4,3,5] => 5 [-1,-2,-4,3,-5] => 8 [-1,-2,-4,-3,5] => 1 [-1,-2,-4,-3,-5] => 1 [1,2,4,5,3] => 10 [1,2,4,5,-3] => 10 [1,2,4,-5,3] => 40 [1,2,4,-5,-3] => 30 [1,2,-4,5,3] => 98 [1,2,-4,5,-3] => 77 [1,2,-4,-5,3] => 175 [1,2,-4,-5,-3] => 105 [1,-2,4,5,3] => 41 [1,-2,4,5,-3] => 23 [1,-2,4,-5,3] => 129 [1,-2,4,-5,-3] => 55 [1,-2,-4,5,3] => 184 [1,-2,-4,5,-3] => 81 [1,-2,-4,-5,3] => 265 [1,-2,-4,-5,-3] => 92 [-1,2,4,5,3] => 6 [-1,2,4,5,-3] => 4 [-1,2,4,-5,3] => 20 [-1,2,4,-5,-3] => 10 [-1,2,-4,5,3] => 33 [-1,2,-4,5,-3] => 17 [-1,2,-4,-5,3] => 50 [-1,2,-4,-5,-3] => 20 [-1,-2,4,5,3] => 3 [-1,-2,4,5,-3] => 1 [-1,-2,4,-5,3] => 8 [-1,-2,4,-5,-3] => 2 [-1,-2,-4,5,3] => 8 [-1,-2,-4,5,-3] => 2 [-1,-2,-4,-5,3] => 10 [-1,-2,-4,-5,-3] => 2 [1,2,5,3,4] => 15 [1,2,5,3,-4] => 40 [1,2,5,-3,4] => 48 [1,2,5,-3,-4] => 50 [1,2,-5,3,4] => 35 [1,2,-5,3,-4] => 70 [1,2,-5,-3,4] => 98 [1,2,-5,-3,-4] => 70 [1,-2,5,3,4] => 71 [1,-2,5,3,-4] => 129 [1,-2,5,-3,4] => 64 [1,-2,5,-3,-4] => 45 [1,-2,-5,3,4] => 135 [1,-2,-5,3,-4] => 185 [1,-2,-5,-3,4] => 109 [1,-2,-5,-3,-4] => 52 [-1,2,5,3,4] => 10 [-1,2,5,3,-4] => 20 [-1,2,5,-3,4] => 13 [-1,2,5,-3,-4] => 10 [-1,2,-5,3,4] => 20 [-1,2,-5,3,-4] => 30 [-1,2,-5,-3,4] => 23 [-1,2,-5,-3,-4] => 12 [-1,-2,5,3,4] => 6 [-1,-2,5,3,-4] => 8 [-1,-2,5,-3,4] => 2 [-1,-2,5,-3,-4] => 1 [-1,-2,-5,3,4] => 10 [-1,-2,-5,3,-4] => 10 [-1,-2,-5,-3,4] => 3 [-1,-2,-5,-3,-4] => 1 [1,2,5,4,3] => 40 [1,2,5,4,-3] => 45 [1,2,5,-4,3] => 50 [1,2,5,-4,-3] => 27 [1,2,-5,4,3] => 105 [1,2,-5,4,-3] => 105 [1,2,-5,-4,3] => 77 [1,2,-5,-4,-3] => 35 [1,-2,5,4,3] => 129 [1,-2,5,4,-3] => 81 [1,-2,5,-4,3] => 120 [1,-2,5,-4,-3] => 36 [1,-2,-5,4,3] => 275 [1,-2,-5,4,-3] => 155 [1,-2,-5,-4,3] => 156 [1,-2,-5,-4,-3] => 40 [-1,2,5,4,3] => 20 [-1,2,5,4,-3] => 15 [-1,2,5,-4,3] => 20 [-1,2,5,-4,-3] => 7 [-1,2,-5,4,3] => 45 [-1,2,-5,4,-3] => 30 [-1,2,-5,-4,3] => 27 [-1,2,-5,-4,-3] => 8 [-1,-2,5,4,3] => 8 [-1,-2,5,4,-3] => 3 [-1,-2,5,-4,3] => 6 [-1,-2,5,-4,-3] => 1 [-1,-2,-5,4,3] => 15 [-1,-2,-5,4,-3] => 5 [-1,-2,-5,-4,3] => 7 [-1,-2,-5,-4,-3] => 1 [1,3,2,4,5] => 5 [1,3,2,4,-5] => 25 [1,3,2,-4,5] => 100 [1,3,2,-4,-5] => 250 [1,3,-2,4,5] => 7 [1,3,-2,4,-5] => 26 [1,3,-2,-4,5] => 54 [1,3,-2,-4,-5] => 100 [1,-3,2,4,5] => 28 [1,-3,2,4,-5] => 96 [1,-3,2,-4,5] => 159 [1,-3,2,-4,-5] => 275 [1,-3,-2,4,5] => 22 [1,-3,-2,4,-5] => 54 [1,-3,-2,-4,5] => 41 [1,-3,-2,-4,-5] => 50 [-1,3,2,4,5] => 4 [-1,3,2,4,-5] => 16 [-1,3,2,-4,5] => 40 [-1,3,2,-4,-5] => 80 [-1,3,-2,4,5] => 1 [-1,3,-2,4,-5] => 3 [-1,3,-2,-4,5] => 4 [-1,3,-2,-4,-5] => 6 [-1,-3,2,4,5] => 7 [-1,-3,2,4,-5] => 19 [-1,-3,2,-4,5] => 19 [-1,-3,2,-4,-5] => 26 [-1,-3,-2,4,5] => 1 [-1,-3,-2,4,-5] => 2 [-1,-3,-2,-4,5] => 1 [-1,-3,-2,-4,-5] => 1 [1,3,2,5,4] => 25 [1,3,2,5,-4] => 50 [1,3,2,-5,4] => 75 [1,3,2,-5,-4] => 100 [1,3,-2,5,4] => 26 [1,3,-2,5,-4] => 35 [1,3,-2,-5,4] => 61 [1,3,-2,-5,-4] => 55 [1,-3,2,5,4] => 96 [1,-3,2,5,-4] => 114 [1,-3,2,-5,4] => 210 [1,-3,2,-5,-4] => 170 [1,-3,-2,5,4] => 54 [1,-3,-2,5,-4] => 38 [1,-3,-2,-5,4] => 92 [1,-3,-2,-5,-4] => 44 [-1,3,2,5,4] => 16 [-1,3,2,5,-4] => 24 [-1,3,2,-5,4] => 40 [-1,3,2,-5,-4] => 40 [-1,3,-2,5,4] => 3 [-1,3,-2,5,-4] => 3 [-1,3,-2,-5,4] => 6 [-1,3,-2,-5,-4] => 4 [-1,-3,2,5,4] => 19 [-1,-3,2,5,-4] => 16 [-1,-3,2,-5,4] => 35 [-1,-3,2,-5,-4] => 20 [-1,-3,-2,5,4] => 2 [-1,-3,-2,5,-4] => 1 [-1,-3,-2,-5,4] => 3 [-1,-3,-2,-5,-4] => 1 [1,3,4,2,5] => 10 [1,3,4,2,-5] => 50 [1,3,4,-2,5] => 6 [1,3,4,-2,-5] => 22 [1,3,-4,2,5] => 119 [1,3,-4,2,-5] => 322 [1,3,-4,-2,5] => 44 [1,3,-4,-2,-5] => 80 [1,-3,4,2,5] => 96 [1,-3,4,2,-5] => 324 [1,-3,4,-2,5] => 37 [1,-3,4,-2,-5] => 89 [1,-3,-4,2,5] => 196 [1,-3,-4,2,-5] => 364 [1,-3,-4,-2,5] => 63 [1,-3,-4,-2,-5] => 74 [-1,3,4,2,5] => 6 [-1,3,4,2,-5] => 24 [-1,3,4,-2,5] => 1 [-1,3,4,-2,-5] => 3 [-1,3,-4,2,5] => 39 [-1,3,-4,2,-5] => 83 [-1,3,-4,-2,5] => 4 [-1,3,-4,-2,-5] => 6 [-1,-3,4,2,5] => 19 [-1,-3,4,2,-5] => 51 [-1,-3,4,-2,5] => 2 [-1,-3,4,-2,-5] => 4 [-1,-3,-4,2,5] => 21 [-1,-3,-4,2,-5] => 30 [-1,-3,-4,-2,5] => 2 [-1,-3,-4,-2,-5] => 2 [1,3,4,5,2] => 10 [1,3,4,5,-2] => 5 [1,3,4,-5,2] => 45 [1,3,4,-5,-2] => 18 [1,3,-4,5,2] => 147 [1,3,-4,5,-2] => 63 [1,3,-4,-5,2] => 315 [1,3,-4,-5,-2] => 105 [1,-3,4,5,2] => 114 [1,-3,4,5,-2] => 45 [1,-3,4,-5,2] => 329 [1,-3,4,-5,-2] => 105 [1,-3,-4,5,2] => 364 [1,-3,-4,5,-2] => 126 [1,-3,-4,-5,2] => 490 [1,-3,-4,-5,-2] => 140 [-1,3,4,5,2] => 4 [-1,3,4,5,-2] => 1 [-1,3,4,-5,2] => 15 [-1,3,4,-5,-2] => 3 [-1,3,-4,5,2] => 33 [-1,3,-4,5,-2] => 7 [-1,3,-4,-5,2] => 60 [-1,3,-4,-5,-2] => 10 [-1,-3,4,5,2] => 16 [-1,-3,4,5,-2] => 3 [-1,-3,4,-5,2] => 39 [-1,-3,4,-5,-2] => 6 [-1,-3,-4,5,2] => 30 [-1,-3,-4,5,-2] => 5 [-1,-3,-4,-5,2] => 35 [-1,-3,-4,-5,-2] => 5 [1,3,5,2,4] => 40 [1,3,5,2,-4] => 95 [1,3,5,-2,4] => 22 [1,3,5,-2,-4] => 29 [1,3,-5,2,4] => 105 [1,3,-5,2,-4] => 182 [1,3,-5,-2,4] => 51 [1,3,-5,-2,-4] => 45 [1,-3,5,2,4] => 210 [1,-3,5,2,-4] => 329 [1,-3,5,-2,4] => 89 [1,-3,5,-2,-4] => 60 [1,-3,-5,2,4] => 369 [1,-3,-5,2,-4] => 445 [1,-3,-5,-2,4] => 149 [1,-3,-5,-2,-4] => 68 [-1,3,5,2,4] => 20 [-1,3,5,2,-4] => 35 [-1,3,5,-2,4] => 3 [-1,3,5,-2,-4] => 3 [-1,3,-5,2,4] => 45 [-1,3,-5,2,-4] => 57 [-1,3,-5,-2,4] => 6 [-1,3,-5,-2,-4] => 4 [-1,-3,5,2,4] => 35 [-1,-3,5,2,-4] => 39 [-1,-3,5,-2,4] => 4 [-1,-3,5,-2,-4] => 2 [-1,-3,-5,2,4] => 54 [-1,-3,-5,2,-4] => 46 [-1,-3,-5,-2,4] => 6 [-1,-3,-5,-2,-4] => 2 [1,3,5,4,2] => 45 [1,3,5,4,-2] => 24 [1,3,5,-4,2] => 75 [1,3,5,-4,-2] => 23 [1,3,-5,4,2] => 126 [1,3,-5,4,-2] => 63 [1,3,-5,-4,2] => 133 [1,3,-5,-4,-2] => 35 [1,-3,5,4,2] => 329 [1,-3,5,4,-2] => 142 [1,-3,5,-4,2] => 275 [1,-3,5,-4,-2] => 66 [1,-3,-5,4,2] => 641 [1,-3,-5,4,-2] => 260 [1,-3,-5,-4,2] => 341 [1,-3,-5,-4,-2] => 72 [-1,3,5,4,2] => 15 [-1,3,5,4,-2] => 4 [-1,3,5,-4,2] => 20 [-1,3,5,-4,-2] => 3 [-1,3,-5,4,2] => 36 [-1,3,-5,4,-2] => 9 [-1,3,-5,-4,2] => 31 [-1,3,-5,-4,-2] => 4 [-1,-3,5,4,2] => 39 [-1,-3,5,4,-2] => 8 [-1,-3,5,-4,2] => 26 [-1,-3,5,-4,-2] => 3 [-1,-3,-5,4,2] => 67 [-1,-3,-5,4,-2] => 13 [-1,-3,-5,-4,2] => 29 [-1,-3,-5,-4,-2] => 3 [1,4,2,3,5] => 15 [1,4,2,3,-5] => 75 [1,4,2,-3,5] => 69 [1,4,2,-3,-5] => 218 [1,4,-2,3,5] => 26 [1,4,-2,3,-5] => 96 [1,4,-2,-3,5] => 21 [1,4,-2,-3,-5] => 51 [1,-4,2,3,5] => 56 [1,-4,2,3,-5] => 168 [1,-4,2,-3,5] => 166 [1,-4,2,-3,-5] => 270 [1,-4,-2,3,5] => 75 [1,-4,-2,3,-5] => 151 [1,-4,-2,-3,5] => 37 [1,-4,-2,-3,-5] => 44 [-1,4,2,3,5] => 10 [-1,4,2,3,-5] => 40 [-1,4,2,-3,5] => 19 [-1,4,2,-3,-5] => 49 [-1,4,-2,3,5] => 3 [-1,4,-2,3,-5] => 9 [-1,4,-2,-3,5] => 1 [-1,4,-2,-3,-5] => 2 [-1,-4,2,3,5] => 21 [-1,-4,2,3,-5] => 49 [-1,-4,2,-3,5] => 26 [-1,-4,2,-3,-5] => 34 [-1,-4,-2,3,5] => 5 [-1,-4,-2,3,-5] => 8 [-1,-4,-2,-3,5] => 1 [-1,-4,-2,-3,-5] => 1 [1,4,2,5,3] => 40 [1,4,2,5,-3] => 45 [1,4,2,-5,3] => 155 [1,4,2,-5,-3] => 132 [1,4,-2,5,3] => 35 [1,4,-2,5,-3] => 19 [1,4,-2,-5,3] => 109 [1,4,-2,-5,-3] => 45 [1,-4,2,5,3] => 168 [1,-4,2,5,-3] => 156 [1,-4,2,-5,3] => 324 [1,-4,2,-5,-3] => 220 [1,-4,-2,5,3] => 151 [1,-4,-2,5,-3] => 64 [1,-4,-2,-5,3] => 215 [1,-4,-2,-5,-3] => 72 [-1,4,2,5,3] => 20 [-1,4,2,5,-3] => 15 [-1,4,2,-5,3] => 65 [-1,4,2,-5,-3] => 37 [-1,4,-2,5,3] => 3 [-1,4,-2,5,-3] => 1 [-1,4,-2,-5,3] => 8 [-1,4,-2,-5,-3] => 2 [-1,-4,2,5,3] => 49 [-1,-4,2,5,-3] => 30 [-1,-4,2,-5,3] => 79 [-1,-4,2,-5,-3] => 36 [-1,-4,-2,5,3] => 8 [-1,-4,-2,5,-3] => 2 [-1,-4,-2,-5,3] => 10 [-1,-4,-2,-5,-3] => 2 [1,4,3,2,5] => 40 [1,4,3,2,-5] => 200 [1,4,3,-2,5] => 29 [1,4,3,-2,-5] => 106 [1,4,-3,2,5] => 70 [1,4,-3,2,-5] => 228 [1,4,-3,-2,5] => 16 [1,4,-3,-2,-5] => 38 [1,-4,3,2,5] => 196 [1,-4,3,2,-5] => 576 [1,-4,3,-2,5] => 114 [1,-4,3,-2,-5] => 218 [1,-4,-3,2,5] => 121 [1,-4,-3,2,-5] => 213 [1,-4,-3,-2,5] => 26 [1,-4,-3,-2,-5] => 30 [-1,4,3,2,5] => 20 [-1,4,3,2,-5] => 80 [-1,4,3,-2,5] => 4 [-1,4,3,-2,-5] => 12 [-1,4,-3,2,5] => 16 [-1,4,-3,2,-5] => 42 [-1,4,-3,-2,5] => 1 [-1,4,-3,-2,-5] => 2 [-1,-4,3,2,5] => 56 [-1,-4,3,2,-5] => 128 [-1,-4,3,-2,5] => 9 [-1,-4,3,-2,-5] => 14 [-1,-4,-3,2,5] => 16 [-1,-4,-3,2,-5] => 22 [-1,-4,-3,-2,5] => 1 [-1,-4,-3,-2,-5] => 1 [1,4,3,5,2] => 45 [1,4,3,5,-2] => 24 [1,4,3,-5,2] => 201 [1,4,3,-5,-2] => 86 [1,4,-3,5,2] => 79 [1,4,-3,5,-2] => 26 [1,4,-3,-5,2] => 220 [1,4,-3,-5,-2] => 60 [1,-4,3,5,2] => 252 [1,-4,3,5,-2] => 124 [1,-4,3,-5,2] => 596 [1,-4,3,-5,-2] => 220 [1,-4,-3,5,2] => 213 [1,-4,-3,5,-2] => 62 [1,-4,-3,-5,2] => 275 [1,-4,-3,-5,-2] => 68 [-1,4,3,5,2] => 15 [-1,4,3,5,-2] => 4 [-1,4,3,-5,2] => 56 [-1,4,3,-5,-2] => 12 [-1,4,-3,5,2] => 13 [-1,4,-3,5,-2] => 2 [-1,4,-3,-5,2] => 31 [-1,4,-3,-5,-2] => 4 [-1,-4,3,5,2] => 49 [-1,-4,3,5,-2] => 12 [-1,-4,3,-5,2] => 97 [-1,-4,3,-5,-2] => 18 [-1,-4,-3,5,2] => 22 [-1,-4,-3,5,-2] => 3 [-1,-4,-3,-5,2] => 25 [-1,-4,-3,-5,-2] => 3 [1,4,5,2,3] => 50 [1,4,5,2,-3] => 75 [1,4,5,-2,3] => 29 [1,4,5,-2,-3] => 15 [1,4,-5,2,3] => 175 [1,4,-5,2,-3] => 210 [1,4,-5,-2,3] => 89 [1,4,-5,-2,-3] => 35 [1,-4,5,2,3] => 324 [1,-4,5,2,-3] => 386 [1,-4,5,-2,3] => 218 [1,-4,5,-2,-3] => 76 [1,-4,-5,2,3] => 490 [1,-4,-5,2,-3] => 490 [1,-4,-5,-2,3] => 294 [1,-4,-5,-2,-3] => 84 [-1,4,5,2,3] => 20 [-1,4,5,2,-3] => 20 [-1,4,5,-2,3] => 3 [-1,4,5,-2,-3] => 1 [-1,4,-5,2,3] => 60 [-1,4,-5,2,-3] => 48 [-1,4,-5,-2,3] => 8 [-1,4,-5,-2,-3] => 2 [-1,-4,5,2,3] => 79 [-1,-4,5,2,-3] => 62 [-1,-4,5,-2,3] => 14 [-1,-4,5,-2,-3] => 3 [-1,-4,-5,2,3] => 105 [-1,-4,-5,2,-3] => 70 [-1,-4,-5,-2,3] => 17 [-1,-4,-5,-2,-3] => 3 [1,4,5,3,2] => 75 [1,4,5,3,-2] => 45 [1,4,5,-3,2] => 50 [1,4,5,-3,-2] => 11 [1,4,-5,3,2] => 280 [1,4,-5,3,-2] => 149 [1,4,-5,-3,2] => 131 [1,4,-5,-3,-2] => 25 [1,-4,5,3,2] => 596 [1,-4,5,3,-2] => 334 [1,-4,5,-3,2] => 270 [1,-4,5,-3,-2] => 52 [1,-4,-5,3,2] => 980 [1,-4,-5,3,-2] => 490 [1,-4,-5,-3,2] => 322 [1,-4,-5,-3,-2] => 56 [-1,4,5,3,2] => 20 [-1,4,5,3,-2] => 6 [-1,4,5,-3,2] => 10 [-1,4,5,-3,-2] => 1 [-1,4,-5,3,2] => 64 [-1,4,-5,3,-2] => 17 [-1,4,-5,-3,2] => 23 [-1,4,-5,-3,-2] => 2 [-1,-4,5,3,2] => 97 [-1,-4,5,3,-2] => 27 [-1,-4,5,-3,2] => 34 [-1,-4,5,-3,-2] => 3 [-1,-4,-5,3,2] => 140 [-1,-4,-5,3,-2] => 35 [-1,-4,-5,-3,2] => 37 [-1,-4,-5,-3,-2] => 3 [1,5,2,3,4] => 35 [1,5,2,3,-4] => 105 [1,5,2,-3,4] => 168 [1,5,2,-3,-4] => 210 [1,5,-2,3,4] => 61 [1,5,-2,3,-4] => 109 [1,5,-2,-3,4] => 51 [1,5,-2,-3,-4] => 35 [1,-5,2,3,4] => 70 [1,-5,2,3,-4] => 168 [1,-5,2,-3,4] => 308 [1,-5,2,-3,-4] => 280 [1,-5,-2,3,4] => 115 [1,-5,-2,3,-4] => 155 [1,-5,-2,-3,4] => 86 [1,-5,-2,-3,-4] => 40 [-1,5,2,3,4] => 20 [-1,5,2,3,-4] => 45 [-1,5,2,-3,4] => 39 [-1,5,2,-3,-4] => 36 [-1,5,-2,3,4] => 6 [-1,5,-2,3,-4] => 8 [-1,5,-2,-3,4] => 2 [-1,5,-2,-3,-4] => 1 [-1,-5,2,3,4] => 35 [-1,-5,2,3,-4] => 63 [-1,-5,2,-3,4] => 63 [-1,-5,2,-3,-4] => 42 [-1,-5,-2,3,4] => 10 [-1,-5,-2,3,-4] => 10 [-1,-5,-2,-3,4] => 3 [-1,-5,-2,-3,-4] => 1 [1,5,2,4,3] => 105 [1,5,2,4,-3] => 126 [1,5,2,-4,3] => 175 [1,5,2,-4,-3] => 112 [1,5,-2,4,3] => 109 [1,5,-2,4,-3] => 66 [1,5,-2,-4,3] => 100 [1,5,-2,-4,-3] => 29 [1,-5,2,4,3] => 224 [1,-5,2,4,-3] => 252 [1,-5,2,-4,3] => 252 [1,-5,2,-4,-3] => 140 [1,-5,-2,4,3] => 230 [1,-5,-2,4,-3] => 125 [1,-5,-2,-4,3] => 129 [1,-5,-2,-4,-3] => 32 [-1,5,2,4,3] => 45 [-1,5,2,4,-3] => 36 [-1,5,2,-4,3] => 60 [-1,5,2,-4,-3] => 25 [-1,5,-2,4,3] => 8 [-1,5,-2,4,-3] => 3 [-1,5,-2,-4,3] => 6 [-1,5,-2,-4,-3] => 1 [-1,-5,2,4,3] => 84 [-1,-5,2,4,-3] => 63 [-1,-5,2,-4,3] => 77 [-1,-5,2,-4,-3] => 28 [-1,-5,-2,4,3] => 15 [-1,-5,-2,4,-3] => 5 [-1,-5,-2,-4,3] => 7 [-1,-5,-2,-4,-3] => 1 [1,5,3,2,4] => 105 [1,5,3,2,-4] => 301 [1,5,3,-2,4] => 77 [1,5,3,-2,-4] => 124 [1,5,-3,2,4] => 149 [1,5,-3,2,-4] => 220 [1,5,-3,-2,4] => 38 [1,5,-3,-2,-4] => 25 [1,-5,3,2,4] => 224 [1,-5,3,2,-4] => 504 [1,-5,3,-2,4] => 156 [1,-5,3,-2,-4] => 180 [1,-5,-3,2,4] => 254 [1,-5,-3,2,-4] => 290 [1,-5,-3,-2,4] => 63 [1,-5,-3,-2,-4] => 28 [-1,5,3,2,4] => 45 [-1,5,3,2,-4] => 96 [-1,5,3,-2,4] => 9 [-1,5,3,-2,-4] => 11 [-1,5,-3,2,4] => 29 [-1,5,-3,2,-4] => 31 [-1,5,-3,-2,4] => 2 [-1,5,-3,-2,-4] => 1 [-1,-5,3,2,4] => 84 [-1,-5,3,2,-4] => 140 [-1,-5,3,-2,4] => 16 [-1,-5,3,-2,-4] => 14 [-1,-5,-3,2,4] => 44 [-1,-5,-3,2,-4] => 36 [-1,-5,-3,-2,4] => 3 [-1,-5,-3,-2,-4] => 1 [1,5,3,4,2] => 126 [1,5,3,4,-2] => 70 [1,5,3,-4,2] => 280 [1,5,3,-4,-2] => 98 [1,5,-3,4,2] => 220 [1,5,-3,4,-2] => 76 [1,5,-3,-4,2] => 175 [1,5,-3,-4,-2] => 37 [1,-5,3,4,2] => 280 [1,-5,3,4,-2] => 152 [1,-5,3,-4,2] => 448 [1,-5,3,-4,-2] => 140 [1,-5,-3,4,2] => 411 [1,-5,-3,4,-2] => 135 [1,-5,-3,-4,2] => 212 [1,-5,-3,-4,-2] => 40 [-1,5,3,4,2] => 36 [-1,5,3,4,-2] => 10 [-1,5,3,-4,2] => 64 [-1,5,3,-4,-2] => 11 [-1,5,-3,4,2] => 31 [-1,5,-3,4,-2] => 5 [-1,5,-3,-4,2] => 20 [-1,5,-3,-4,-2] => 2 [-1,-5,3,4,2] => 70 [-1,-5,3,4,-2] => 19 [-1,-5,3,-4,2] => 91 [-1,-5,3,-4,-2] => 14 [-1,-5,-3,4,2] => 52 [-1,-5,-3,4,-2] => 8 [-1,-5,-3,-4,2] => 22 [-1,-5,-3,-4,-2] => 2 [1,5,4,2,3] => 175 [1,5,4,2,-3] => 280 [1,5,4,-2,3] => 124 [1,5,4,-2,-3] => 70 [1,5,-4,2,3] => 175 [1,5,-4,2,-3] => 166 [1,5,-4,-2,3] => 80 [1,5,-4,-2,-3] => 22 [1,-5,4,2,3] => 420 [1,-5,4,2,-3] => 604 [1,-5,4,-2,3] => 294 [1,-5,4,-2,-3] => 140 [1,-5,-4,2,3] => 236 [1,-5,-4,2,-3] => 200 [1,-5,-4,-2,3] => 102 [1,-5,-4,-2,-3] => 24 [-1,5,4,2,3] => 60 [-1,5,4,2,-3] => 64 [-1,5,4,-2,3] => 11 [-1,5,4,-2,-3] => 4 [-1,5,-4,2,3] => 50 [-1,5,-4,2,-3] => 31 [-1,5,-4,-2,3] => 6 [-1,5,-4,-2,-3] => 1 [-1,-5,4,2,3] => 126 [-1,-5,4,2,-3] => 121 [-1,-5,4,-2,3] => 23 [-1,-5,4,-2,-3] => 7 [-1,-5,-4,2,3] => 61 [-1,-5,-4,2,-3] => 34 [-1,-5,-4,-2,3] => 7 [-1,-5,-4,-2,-3] => 1 [1,5,4,3,2] => 280 [1,5,4,3,-2] => 175 [1,5,4,-3,2] => 210 [1,5,4,-3,-2] => 51 [1,5,-4,3,2] => 315 [1,5,-4,3,-2] => 149 [1,5,-4,-3,2] => 95 [1,5,-4,-3,-2] => 15 [1,-5,4,3,2] => 700 [1,-5,4,3,-2] => 420 [1,-5,4,-3,2] => 446 [1,-5,4,-3,-2] => 100 [1,-5,-4,3,2] => 454 [1,-5,-4,3,-2] => 200 [1,-5,-4,-3,2] => 110 [1,-5,-4,-3,-2] => 16 [-1,5,4,3,2] => 64 [-1,5,4,3,-2] => 20 [-1,5,4,-3,2] => 36 [-1,5,4,-3,-2] => 4 [-1,5,-4,3,2] => 60 [-1,5,-4,3,-2] => 14 ----------------------------------------------------------------------------- Created: Feb 05, 2022 at 17:47 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Feb 05, 2022 at 17:47 by Martin Rubey