***************************************************************************** * 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: St001848 ----------------------------------------------------------------------------- Collection: Signed permutations ----------------------------------------------------------------------------- Description: The atomic length of a signed permutation. The atomic length of an element $w$ of a Weyl group is the sum of the heights of the inversions of $w$. ----------------------------------------------------------------------------- References: [1] not yet indexed [[arXiv 2211.12359]] ----------------------------------------------------------------------------- Code: def atomic_length(pi): """ EXAMPLES:: sage: l = [atomic_length(SignedPermutations(n).long_element()) for n in range(1,8)] sage: l sage: fricas.guess(l)[0].sage().factor() 1/6*(4*n + 3)*(n + 2)*(n + 1) """ W = WeylGroup(pi.parent().coxeter_type()) w = W.from_reduced_word(pi.reduced_word()) return sum(a.height() for a in w.inversions(inversion_type="roots")) ----------------------------------------------------------------------------- Statistic values: [1] => 0 [-1] => 1 [1,2] => 0 [1,-2] => 1 [-1,2] => 6 [-1,-2] => 7 [2,1] => 1 [2,-1] => 3 [-2,1] => 4 [-2,-1] => 6 [1,2,3] => 0 [1,2,-3] => 1 [1,-2,3] => 6 [1,-2,-3] => 7 [-1,2,3] => 15 [-1,2,-3] => 16 [-1,-2,3] => 21 [-1,-2,-3] => 22 [1,3,2] => 1 [1,3,-2] => 3 [1,-3,2] => 4 [1,-3,-2] => 6 [-1,3,2] => 16 [-1,3,-2] => 18 [-1,-3,2] => 19 [-1,-3,-2] => 21 [2,1,3] => 1 [2,1,-3] => 2 [2,-1,3] => 10 [2,-1,-3] => 11 [-2,1,3] => 11 [-2,1,-3] => 12 [-2,-1,3] => 20 [-2,-1,-3] => 21 [2,3,1] => 3 [2,3,-1] => 6 [2,-3,1] => 6 [2,-3,-1] => 9 [-2,3,1] => 13 [-2,3,-1] => 16 [-2,-3,1] => 16 [-2,-3,-1] => 19 [3,1,2] => 3 [3,1,-2] => 5 [3,-1,2] => 12 [3,-1,-2] => 14 [-3,1,2] => 8 [-3,1,-2] => 10 [-3,-1,2] => 17 [-3,-1,-2] => 19 [3,2,1] => 4 [3,2,-1] => 7 [3,-2,1] => 10 [3,-2,-1] => 13 [-3,2,1] => 9 [-3,2,-1] => 12 [-3,-2,1] => 15 [-3,-2,-1] => 18 [1,2,3,4] => 0 [1,2,3,-4] => 1 [1,2,-3,4] => 6 [1,2,-3,-4] => 7 [1,-2,3,4] => 15 [1,-2,3,-4] => 16 [1,-2,-3,4] => 21 [1,-2,-3,-4] => 22 [-1,2,3,4] => 28 [-1,2,3,-4] => 29 [-1,2,-3,4] => 34 [-1,2,-3,-4] => 35 [-1,-2,3,4] => 43 [-1,-2,3,-4] => 44 [-1,-2,-3,4] => 49 [-1,-2,-3,-4] => 50 [1,2,4,3] => 1 [1,2,4,-3] => 3 [1,2,-4,3] => 4 [1,2,-4,-3] => 6 [1,-2,4,3] => 16 [1,-2,4,-3] => 18 [1,-2,-4,3] => 19 [1,-2,-4,-3] => 21 [-1,2,4,3] => 29 [-1,2,4,-3] => 31 [-1,2,-4,3] => 32 [-1,2,-4,-3] => 34 [-1,-2,4,3] => 44 [-1,-2,4,-3] => 46 [-1,-2,-4,3] => 47 [-1,-2,-4,-3] => 49 [1,3,2,4] => 1 [1,3,2,-4] => 2 [1,3,-2,4] => 10 [1,3,-2,-4] => 11 [1,-3,2,4] => 11 [1,-3,2,-4] => 12 [1,-3,-2,4] => 20 [1,-3,-2,-4] => 21 [-1,3,2,4] => 29 [-1,3,2,-4] => 30 [-1,3,-2,4] => 38 [-1,3,-2,-4] => 39 [-1,-3,2,4] => 39 [-1,-3,2,-4] => 40 [-1,-3,-2,4] => 48 [-1,-3,-2,-4] => 49 [1,3,4,2] => 3 [1,3,4,-2] => 6 [1,3,-4,2] => 6 [1,3,-4,-2] => 9 [1,-3,4,2] => 13 [1,-3,4,-2] => 16 [1,-3,-4,2] => 16 [1,-3,-4,-2] => 19 [-1,3,4,2] => 31 [-1,3,4,-2] => 34 [-1,3,-4,2] => 34 [-1,3,-4,-2] => 37 [-1,-3,4,2] => 41 [-1,-3,4,-2] => 44 [-1,-3,-4,2] => 44 [-1,-3,-4,-2] => 47 [1,4,2,3] => 3 [1,4,2,-3] => 5 [1,4,-2,3] => 12 [1,4,-2,-3] => 14 [1,-4,2,3] => 8 [1,-4,2,-3] => 10 [1,-4,-2,3] => 17 [1,-4,-2,-3] => 19 [-1,4,2,3] => 31 [-1,4,2,-3] => 33 [-1,4,-2,3] => 40 [-1,4,-2,-3] => 42 [-1,-4,2,3] => 36 [-1,-4,2,-3] => 38 [-1,-4,-2,3] => 45 [-1,-4,-2,-3] => 47 [1,4,3,2] => 4 [1,4,3,-2] => 7 [1,4,-3,2] => 10 [1,4,-3,-2] => 13 [1,-4,3,2] => 9 [1,-4,3,-2] => 12 [1,-4,-3,2] => 15 [1,-4,-3,-2] => 18 [-1,4,3,2] => 32 [-1,4,3,-2] => 35 [-1,4,-3,2] => 38 [-1,4,-3,-2] => 41 [-1,-4,3,2] => 37 [-1,-4,3,-2] => 40 [-1,-4,-3,2] => 43 [-1,-4,-3,-2] => 46 [2,1,3,4] => 1 [2,1,3,-4] => 2 [2,1,-3,4] => 7 [2,1,-3,-4] => 8 [2,-1,3,4] => 21 [2,-1,3,-4] => 22 [2,-1,-3,4] => 27 [2,-1,-3,-4] => 28 [-2,1,3,4] => 22 [-2,1,3,-4] => 23 [-2,1,-3,4] => 28 [-2,1,-3,-4] => 29 [-2,-1,3,4] => 42 [-2,-1,3,-4] => 43 [-2,-1,-3,4] => 48 [-2,-1,-3,-4] => 49 [2,1,4,3] => 2 [2,1,4,-3] => 4 [2,1,-4,3] => 5 [2,1,-4,-3] => 7 [2,-1,4,3] => 22 [2,-1,4,-3] => 24 [2,-1,-4,3] => 25 [2,-1,-4,-3] => 27 [-2,1,4,3] => 23 [-2,1,4,-3] => 25 [-2,1,-4,3] => 26 [-2,1,-4,-3] => 28 [-2,-1,4,3] => 43 [-2,-1,4,-3] => 45 [-2,-1,-4,3] => 46 [-2,-1,-4,-3] => 48 [2,3,1,4] => 3 [2,3,1,-4] => 4 [2,3,-1,4] => 15 [2,3,-1,-4] => 16 [2,-3,1,4] => 13 [2,-3,1,-4] => 14 [2,-3,-1,4] => 25 [2,-3,-1,-4] => 26 [-2,3,1,4] => 24 [-2,3,1,-4] => 25 [-2,3,-1,4] => 36 [-2,3,-1,-4] => 37 [-2,-3,1,4] => 34 [-2,-3,1,-4] => 35 [-2,-3,-1,4] => 46 [-2,-3,-1,-4] => 47 [2,3,4,1] => 6 [2,3,4,-1] => 10 [2,3,-4,1] => 9 [2,3,-4,-1] => 13 [2,-3,4,1] => 16 [2,-3,4,-1] => 20 [2,-3,-4,1] => 19 [2,-3,-4,-1] => 23 [-2,3,4,1] => 27 [-2,3,4,-1] => 31 [-2,3,-4,1] => 30 [-2,3,-4,-1] => 34 [-2,-3,4,1] => 37 [-2,-3,4,-1] => 41 [-2,-3,-4,1] => 40 [-2,-3,-4,-1] => 44 [2,4,1,3] => 5 [2,4,1,-3] => 7 [2,4,-1,3] => 17 [2,4,-1,-3] => 19 [2,-4,1,3] => 10 [2,-4,1,-3] => 12 [2,-4,-1,3] => 22 [2,-4,-1,-3] => 24 [-2,4,1,3] => 26 [-2,4,1,-3] => 28 [-2,4,-1,3] => 38 [-2,4,-1,-3] => 40 [-2,-4,1,3] => 31 [-2,-4,1,-3] => 33 [-2,-4,-1,3] => 43 [-2,-4,-1,-3] => 45 [2,4,3,1] => 7 [2,4,3,-1] => 11 [2,4,-3,1] => 13 [2,4,-3,-1] => 17 [2,-4,3,1] => 12 [2,-4,3,-1] => 16 [2,-4,-3,1] => 18 [2,-4,-3,-1] => 22 [-2,4,3,1] => 28 [-2,4,3,-1] => 32 [-2,4,-3,1] => 34 [-2,4,-3,-1] => 38 [-2,-4,3,1] => 33 [-2,-4,3,-1] => 37 [-2,-4,-3,1] => 39 [-2,-4,-3,-1] => 43 [3,1,2,4] => 3 [3,1,2,-4] => 4 [3,1,-2,4] => 12 [3,1,-2,-4] => 13 [3,-1,2,4] => 23 [3,-1,2,-4] => 24 [3,-1,-2,4] => 32 [3,-1,-2,-4] => 33 [-3,1,2,4] => 17 [-3,1,2,-4] => 18 [-3,1,-2,4] => 26 [-3,1,-2,-4] => 27 [-3,-1,2,4] => 37 [-3,-1,2,-4] => 38 [-3,-1,-2,4] => 46 [-3,-1,-2,-4] => 47 [3,1,4,2] => 5 [3,1,4,-2] => 8 [3,1,-4,2] => 8 [3,1,-4,-2] => 11 [3,-1,4,2] => 25 [3,-1,4,-2] => 28 [3,-1,-4,2] => 28 [3,-1,-4,-2] => 31 [-3,1,4,2] => 19 [-3,1,4,-2] => 22 [-3,1,-4,2] => 22 [-3,1,-4,-2] => 25 [-3,-1,4,2] => 39 [-3,-1,4,-2] => 42 [-3,-1,-4,2] => 42 [-3,-1,-4,-2] => 45 [3,2,1,4] => 4 [3,2,1,-4] => 5 [3,2,-1,4] => 16 [3,2,-1,-4] => 17 [3,-2,1,4] => 19 [3,-2,1,-4] => 20 [3,-2,-1,4] => 31 [3,-2,-1,-4] => 32 [-3,2,1,4] => 18 [-3,2,1,-4] => 19 [-3,2,-1,4] => 30 [-3,2,-1,-4] => 31 [-3,-2,1,4] => 33 [-3,-2,1,-4] => 34 [-3,-2,-1,4] => 45 [-3,-2,-1,-4] => 46 [3,2,4,1] => 7 [3,2,4,-1] => 11 [3,2,-4,1] => 10 [3,2,-4,-1] => 14 [3,-2,4,1] => 22 [3,-2,4,-1] => 26 [3,-2,-4,1] => 25 [3,-2,-4,-1] => 29 [-3,2,4,1] => 21 [-3,2,4,-1] => 25 [-3,2,-4,1] => 24 [-3,2,-4,-1] => 28 [-3,-2,4,1] => 36 [-3,-2,4,-1] => 40 [-3,-2,-4,1] => 39 [-3,-2,-4,-1] => 43 [3,4,1,2] => 8 [3,4,1,-2] => 11 [3,4,-1,2] => 20 [3,4,-1,-2] => 23 [3,-4,1,2] => 13 [3,-4,1,-2] => 16 [3,-4,-1,2] => 25 [3,-4,-1,-2] => 28 [-3,4,1,2] => 22 [-3,4,1,-2] => 25 [-3,4,-1,2] => 34 [-3,4,-1,-2] => 37 [-3,-4,1,2] => 27 [-3,-4,1,-2] => 30 [-3,-4,-1,2] => 39 [-3,-4,-1,-2] => 42 [3,4,2,1] => 9 [3,4,2,-1] => 13 [3,4,-2,1] => 18 [3,4,-2,-1] => 22 [3,-4,2,1] => 14 [3,-4,2,-1] => 18 [3,-4,-2,1] => 23 [3,-4,-2,-1] => 27 [-3,4,2,1] => 23 [-3,4,2,-1] => 27 [-3,4,-2,1] => 32 [-3,4,-2,-1] => 36 [-3,-4,2,1] => 28 [-3,-4,2,-1] => 32 [-3,-4,-2,1] => 37 [-3,-4,-2,-1] => 41 [4,1,2,3] => 6 [4,1,2,-3] => 8 [4,1,-2,3] => 15 [4,1,-2,-3] => 17 [4,-1,2,3] => 26 [4,-1,2,-3] => 28 [4,-1,-2,3] => 35 [4,-1,-2,-3] => 37 [-4,1,2,3] => 13 [-4,1,2,-3] => 15 [-4,1,-2,3] => 22 [-4,1,-2,-3] => 24 [-4,-1,2,3] => 33 [-4,-1,2,-3] => 35 [-4,-1,-2,3] => 42 [-4,-1,-2,-3] => 44 [4,1,3,2] => 7 [4,1,3,-2] => 10 [4,1,-3,2] => 13 [4,1,-3,-2] => 16 [4,-1,3,2] => 27 [4,-1,3,-2] => 30 [4,-1,-3,2] => 33 [4,-1,-3,-2] => 36 [-4,1,3,2] => 14 [-4,1,3,-2] => 17 [-4,1,-3,2] => 20 [-4,1,-3,-2] => 23 [-4,-1,3,2] => 34 [-4,-1,3,-2] => 37 [-4,-1,-3,2] => 40 [-4,-1,-3,-2] => 43 [4,2,1,3] => 7 [4,2,1,-3] => 9 [4,2,-1,3] => 19 [4,2,-1,-3] => 21 [4,-2,1,3] => 22 [4,-2,1,-3] => 24 [4,-2,-1,3] => 34 [4,-2,-1,-3] => 36 [-4,2,1,3] => 14 [-4,2,1,-3] => 16 [-4,2,-1,3] => 26 [-4,2,-1,-3] => 28 [-4,-2,1,3] => 29 [-4,-2,1,-3] => 31 [-4,-2,-1,3] => 41 [-4,-2,-1,-3] => 43 [4,2,3,1] => 9 [4,2,3,-1] => 13 [4,2,-3,1] => 15 [4,2,-3,-1] => 19 [4,-2,3,1] => 24 [4,-2,3,-1] => 28 [4,-2,-3,1] => 30 [4,-2,-3,-1] => 34 [-4,2,3,1] => 16 [-4,2,3,-1] => 20 [-4,2,-3,1] => 22 [-4,2,-3,-1] => 26 [-4,-2,3,1] => 31 [-4,-2,3,-1] => 35 [-4,-2,-3,1] => 37 [-4,-2,-3,-1] => 41 [4,3,1,2] => 9 [4,3,1,-2] => 12 [4,3,-1,2] => 21 [4,3,-1,-2] => 24 [4,-3,1,2] => 19 [4,-3,1,-2] => 22 [4,-3,-1,2] => 31 [4,-3,-1,-2] => 34 [-4,3,1,2] => 16 [-4,3,1,-2] => 19 [-4,3,-1,2] => 28 [-4,3,-1,-2] => 31 [-4,-3,1,2] => 26 [-4,-3,1,-2] => 29 [-4,-3,-1,2] => 38 [-4,-3,-1,-2] => 41 [4,3,2,1] => 10 [4,3,2,-1] => 14 [4,3,-2,1] => 19 [4,3,-2,-1] => 23 [4,-3,2,1] => 20 [4,-3,2,-1] => 24 [4,-3,-2,1] => 29 [4,-3,-2,-1] => 33 [-4,3,2,1] => 17 [-4,3,2,-1] => 21 [-4,3,-2,1] => 26 [-4,3,-2,-1] => 30 [-4,-3,2,1] => 27 [-4,-3,2,-1] => 31 [-4,-3,-2,1] => 36 [-4,-3,-2,-1] => 40 [1,2,3,4,5] => 0 [1,2,3,4,-5] => 1 [1,2,3,-4,5] => 6 [1,2,3,-4,-5] => 7 [1,2,-3,4,5] => 15 [1,2,-3,4,-5] => 16 [1,2,-3,-4,5] => 21 [1,2,-3,-4,-5] => 22 [1,-2,3,4,5] => 28 [1,-2,3,4,-5] => 29 [1,-2,3,-4,5] => 34 [1,-2,3,-4,-5] => 35 [1,-2,-3,4,5] => 43 [1,-2,-3,4,-5] => 44 [1,-2,-3,-4,5] => 49 [1,-2,-3,-4,-5] => 50 [-1,2,3,4,5] => 45 [-1,2,3,4,-5] => 46 [-1,2,3,-4,5] => 51 [-1,2,3,-4,-5] => 52 [-1,2,-3,4,5] => 60 [-1,2,-3,4,-5] => 61 [-1,2,-3,-4,5] => 66 [-1,2,-3,-4,-5] => 67 [-1,-2,3,4,5] => 73 [-1,-2,3,4,-5] => 74 [-1,-2,3,-4,5] => 79 [-1,-2,3,-4,-5] => 80 [-1,-2,-3,4,5] => 88 [-1,-2,-3,4,-5] => 89 [-1,-2,-3,-4,5] => 94 [-1,-2,-3,-4,-5] => 95 [1,2,3,5,4] => 1 [1,2,3,5,-4] => 3 [1,2,3,-5,4] => 4 [1,2,3,-5,-4] => 6 [1,2,-3,5,4] => 16 [1,2,-3,5,-4] => 18 [1,2,-3,-5,4] => 19 [1,2,-3,-5,-4] => 21 [1,-2,3,5,4] => 29 [1,-2,3,5,-4] => 31 [1,-2,3,-5,4] => 32 [1,-2,3,-5,-4] => 34 [1,-2,-3,5,4] => 44 [1,-2,-3,5,-4] => 46 [1,-2,-3,-5,4] => 47 [1,-2,-3,-5,-4] => 49 [-1,2,3,5,4] => 46 [-1,2,3,5,-4] => 48 [-1,2,3,-5,4] => 49 [-1,2,3,-5,-4] => 51 [-1,2,-3,5,4] => 61 [-1,2,-3,5,-4] => 63 [-1,2,-3,-5,4] => 64 [-1,2,-3,-5,-4] => 66 [-1,-2,3,5,4] => 74 [-1,-2,3,5,-4] => 76 [-1,-2,3,-5,4] => 77 [-1,-2,3,-5,-4] => 79 [-1,-2,-3,5,4] => 89 [-1,-2,-3,5,-4] => 91 [-1,-2,-3,-5,4] => 92 [-1,-2,-3,-5,-4] => 94 [1,2,4,3,5] => 1 [1,2,4,3,-5] => 2 [1,2,4,-3,5] => 10 [1,2,4,-3,-5] => 11 [1,2,-4,3,5] => 11 [1,2,-4,3,-5] => 12 [1,2,-4,-3,5] => 20 [1,2,-4,-3,-5] => 21 [1,-2,4,3,5] => 29 [1,-2,4,3,-5] => 30 [1,-2,4,-3,5] => 38 [1,-2,4,-3,-5] => 39 [1,-2,-4,3,5] => 39 [1,-2,-4,3,-5] => 40 [1,-2,-4,-3,5] => 48 [1,-2,-4,-3,-5] => 49 [-1,2,4,3,5] => 46 [-1,2,4,3,-5] => 47 [-1,2,4,-3,5] => 55 [-1,2,4,-3,-5] => 56 [-1,2,-4,3,5] => 56 [-1,2,-4,3,-5] => 57 [-1,2,-4,-3,5] => 65 [-1,2,-4,-3,-5] => 66 [-1,-2,4,3,5] => 74 [-1,-2,4,3,-5] => 75 [-1,-2,4,-3,5] => 83 [-1,-2,4,-3,-5] => 84 [-1,-2,-4,3,5] => 84 [-1,-2,-4,3,-5] => 85 [-1,-2,-4,-3,5] => 93 [-1,-2,-4,-3,-5] => 94 [1,2,4,5,3] => 3 [1,2,4,5,-3] => 6 [1,2,4,-5,3] => 6 [1,2,4,-5,-3] => 9 [1,2,-4,5,3] => 13 [1,2,-4,5,-3] => 16 [1,2,-4,-5,3] => 16 [1,2,-4,-5,-3] => 19 [1,-2,4,5,3] => 31 [1,-2,4,5,-3] => 34 [1,-2,4,-5,3] => 34 [1,-2,4,-5,-3] => 37 [1,-2,-4,5,3] => 41 [1,-2,-4,5,-3] => 44 [1,-2,-4,-5,3] => 44 [1,-2,-4,-5,-3] => 47 [-1,2,4,5,3] => 48 [-1,2,4,5,-3] => 51 [-1,2,4,-5,3] => 51 [-1,2,4,-5,-3] => 54 [-1,2,-4,5,3] => 58 [-1,2,-4,5,-3] => 61 [-1,2,-4,-5,3] => 61 [-1,2,-4,-5,-3] => 64 [-1,-2,4,5,3] => 76 [-1,-2,4,5,-3] => 79 [-1,-2,4,-5,3] => 79 [-1,-2,4,-5,-3] => 82 [-1,-2,-4,5,3] => 86 [-1,-2,-4,5,-3] => 89 [-1,-2,-4,-5,3] => 89 [-1,-2,-4,-5,-3] => 92 [1,2,5,3,4] => 3 [1,2,5,3,-4] => 5 [1,2,5,-3,4] => 12 [1,2,5,-3,-4] => 14 [1,2,-5,3,4] => 8 [1,2,-5,3,-4] => 10 [1,2,-5,-3,4] => 17 [1,2,-5,-3,-4] => 19 [1,-2,5,3,4] => 31 [1,-2,5,3,-4] => 33 [1,-2,5,-3,4] => 40 [1,-2,5,-3,-4] => 42 [1,-2,-5,3,4] => 36 [1,-2,-5,3,-4] => 38 [1,-2,-5,-3,4] => 45 [1,-2,-5,-3,-4] => 47 [-1,2,5,3,4] => 48 [-1,2,5,3,-4] => 50 [-1,2,5,-3,4] => 57 [-1,2,5,-3,-4] => 59 [-1,2,-5,3,4] => 53 [-1,2,-5,3,-4] => 55 [-1,2,-5,-3,4] => 62 [-1,2,-5,-3,-4] => 64 [-1,-2,5,3,4] => 76 [-1,-2,5,3,-4] => 78 [-1,-2,5,-3,4] => 85 [-1,-2,5,-3,-4] => 87 [-1,-2,-5,3,4] => 81 [-1,-2,-5,3,-4] => 83 [-1,-2,-5,-3,4] => 90 [-1,-2,-5,-3,-4] => 92 [1,2,5,4,3] => 4 [1,2,5,4,-3] => 7 [1,2,5,-4,3] => 10 [1,2,5,-4,-3] => 13 [1,2,-5,4,3] => 9 [1,2,-5,4,-3] => 12 [1,2,-5,-4,3] => 15 [1,2,-5,-4,-3] => 18 [1,-2,5,4,3] => 32 [1,-2,5,4,-3] => 35 [1,-2,5,-4,3] => 38 [1,-2,5,-4,-3] => 41 [1,-2,-5,4,3] => 37 [1,-2,-5,4,-3] => 40 [1,-2,-5,-4,3] => 43 [1,-2,-5,-4,-3] => 46 [-1,2,5,4,3] => 49 [-1,2,5,4,-3] => 52 [-1,2,5,-4,3] => 55 [-1,2,5,-4,-3] => 58 [-1,2,-5,4,3] => 54 [-1,2,-5,4,-3] => 57 [-1,2,-5,-4,3] => 60 [-1,2,-5,-4,-3] => 63 [-1,-2,5,4,3] => 77 [-1,-2,5,4,-3] => 80 [-1,-2,5,-4,3] => 83 [-1,-2,5,-4,-3] => 86 [-1,-2,-5,4,3] => 82 [-1,-2,-5,4,-3] => 85 [-1,-2,-5,-4,3] => 88 [-1,-2,-5,-4,-3] => 91 [1,3,2,4,5] => 1 [1,3,2,4,-5] => 2 [1,3,2,-4,5] => 7 [1,3,2,-4,-5] => 8 [1,3,-2,4,5] => 21 [1,3,-2,4,-5] => 22 [1,3,-2,-4,5] => 27 [1,3,-2,-4,-5] => 28 [1,-3,2,4,5] => 22 [1,-3,2,4,-5] => 23 [1,-3,2,-4,5] => 28 [1,-3,2,-4,-5] => 29 [1,-3,-2,4,5] => 42 [1,-3,-2,4,-5] => 43 [1,-3,-2,-4,5] => 48 [1,-3,-2,-4,-5] => 49 [-1,3,2,4,5] => 46 [-1,3,2,4,-5] => 47 [-1,3,2,-4,5] => 52 [-1,3,2,-4,-5] => 53 [-1,3,-2,4,5] => 66 [-1,3,-2,4,-5] => 67 [-1,3,-2,-4,5] => 72 [-1,3,-2,-4,-5] => 73 [-1,-3,2,4,5] => 67 [-1,-3,2,4,-5] => 68 [-1,-3,2,-4,5] => 73 [-1,-3,2,-4,-5] => 74 [-1,-3,-2,4,5] => 87 [-1,-3,-2,4,-5] => 88 [-1,-3,-2,-4,5] => 93 [-1,-3,-2,-4,-5] => 94 [1,3,2,5,4] => 2 [1,3,2,5,-4] => 4 [1,3,2,-5,4] => 5 [1,3,2,-5,-4] => 7 [1,3,-2,5,4] => 22 [1,3,-2,5,-4] => 24 [1,3,-2,-5,4] => 25 [1,3,-2,-5,-4] => 27 [1,-3,2,5,4] => 23 [1,-3,2,5,-4] => 25 [1,-3,2,-5,4] => 26 [1,-3,2,-5,-4] => 28 [1,-3,-2,5,4] => 43 [1,-3,-2,5,-4] => 45 [1,-3,-2,-5,4] => 46 [1,-3,-2,-5,-4] => 48 [-1,3,2,5,4] => 47 [-1,3,2,5,-4] => 49 [-1,3,2,-5,4] => 50 [-1,3,2,-5,-4] => 52 [-1,3,-2,5,4] => 67 [-1,3,-2,5,-4] => 69 [-1,3,-2,-5,4] => 70 [-1,3,-2,-5,-4] => 72 [-1,-3,2,5,4] => 68 [-1,-3,2,5,-4] => 70 [-1,-3,2,-5,4] => 71 [-1,-3,2,-5,-4] => 73 [-1,-3,-2,5,4] => 88 [-1,-3,-2,5,-4] => 90 [-1,-3,-2,-5,4] => 91 [-1,-3,-2,-5,-4] => 93 [1,3,4,2,5] => 3 [1,3,4,2,-5] => 4 [1,3,4,-2,5] => 15 [1,3,4,-2,-5] => 16 [1,3,-4,2,5] => 13 [1,3,-4,2,-5] => 14 [1,3,-4,-2,5] => 25 [1,3,-4,-2,-5] => 26 [1,-3,4,2,5] => 24 [1,-3,4,2,-5] => 25 [1,-3,4,-2,5] => 36 [1,-3,4,-2,-5] => 37 [1,-3,-4,2,5] => 34 [1,-3,-4,2,-5] => 35 [1,-3,-4,-2,5] => 46 [1,-3,-4,-2,-5] => 47 [-1,3,4,2,5] => 48 [-1,3,4,2,-5] => 49 [-1,3,4,-2,5] => 60 [-1,3,4,-2,-5] => 61 [-1,3,-4,2,5] => 58 [-1,3,-4,2,-5] => 59 [-1,3,-4,-2,5] => 70 [-1,3,-4,-2,-5] => 71 [-1,-3,4,2,5] => 69 [-1,-3,4,2,-5] => 70 [-1,-3,4,-2,5] => 81 [-1,-3,4,-2,-5] => 82 [-1,-3,-4,2,5] => 79 [-1,-3,-4,2,-5] => 80 [-1,-3,-4,-2,5] => 91 [-1,-3,-4,-2,-5] => 92 [1,3,4,5,2] => 6 [1,3,4,5,-2] => 10 [1,3,4,-5,2] => 9 [1,3,4,-5,-2] => 13 [1,3,-4,5,2] => 16 [1,3,-4,5,-2] => 20 [1,3,-4,-5,2] => 19 [1,3,-4,-5,-2] => 23 [1,-3,4,5,2] => 27 [1,-3,4,5,-2] => 31 [1,-3,4,-5,2] => 30 [1,-3,4,-5,-2] => 34 [1,-3,-4,5,2] => 37 [1,-3,-4,5,-2] => 41 [1,-3,-4,-5,2] => 40 [1,-3,-4,-5,-2] => 44 [-1,3,4,5,2] => 51 [-1,3,4,5,-2] => 55 [-1,3,4,-5,2] => 54 [-1,3,4,-5,-2] => 58 [-1,3,-4,5,2] => 61 [-1,3,-4,5,-2] => 65 [-1,3,-4,-5,2] => 64 [-1,3,-4,-5,-2] => 68 [-1,-3,4,5,2] => 72 [-1,-3,4,5,-2] => 76 [-1,-3,4,-5,2] => 75 [-1,-3,4,-5,-2] => 79 [-1,-3,-4,5,2] => 82 [-1,-3,-4,5,-2] => 86 [-1,-3,-4,-5,2] => 85 [-1,-3,-4,-5,-2] => 89 [1,3,5,2,4] => 5 [1,3,5,2,-4] => 7 [1,3,5,-2,4] => 17 [1,3,5,-2,-4] => 19 [1,3,-5,2,4] => 10 [1,3,-5,2,-4] => 12 [1,3,-5,-2,4] => 22 [1,3,-5,-2,-4] => 24 [1,-3,5,2,4] => 26 [1,-3,5,2,-4] => 28 [1,-3,5,-2,4] => 38 [1,-3,5,-2,-4] => 40 [1,-3,-5,2,4] => 31 [1,-3,-5,2,-4] => 33 [1,-3,-5,-2,4] => 43 [1,-3,-5,-2,-4] => 45 [-1,3,5,2,4] => 50 [-1,3,5,2,-4] => 52 [-1,3,5,-2,4] => 62 [-1,3,5,-2,-4] => 64 [-1,3,-5,2,4] => 55 [-1,3,-5,2,-4] => 57 [-1,3,-5,-2,4] => 67 [-1,3,-5,-2,-4] => 69 [-1,-3,5,2,4] => 71 [-1,-3,5,2,-4] => 73 [-1,-3,5,-2,4] => 83 [-1,-3,5,-2,-4] => 85 [-1,-3,-5,2,4] => 76 [-1,-3,-5,2,-4] => 78 [-1,-3,-5,-2,4] => 88 [-1,-3,-5,-2,-4] => 90 [1,3,5,4,2] => 7 [1,3,5,4,-2] => 11 [1,3,5,-4,2] => 13 [1,3,5,-4,-2] => 17 [1,3,-5,4,2] => 12 [1,3,-5,4,-2] => 16 [1,3,-5,-4,2] => 18 [1,3,-5,-4,-2] => 22 [1,-3,5,4,2] => 28 [1,-3,5,4,-2] => 32 [1,-3,5,-4,2] => 34 [1,-3,5,-4,-2] => 38 [1,-3,-5,4,2] => 33 [1,-3,-5,4,-2] => 37 [1,-3,-5,-4,2] => 39 [1,-3,-5,-4,-2] => 43 [-1,3,5,4,2] => 52 [-1,3,5,4,-2] => 56 [-1,3,5,-4,2] => 58 [-1,3,5,-4,-2] => 62 [-1,3,-5,4,2] => 57 [-1,3,-5,4,-2] => 61 [-1,3,-5,-4,2] => 63 [-1,3,-5,-4,-2] => 67 [-1,-3,5,4,2] => 73 [-1,-3,5,4,-2] => 77 [-1,-3,5,-4,2] => 79 [-1,-3,5,-4,-2] => 83 [-1,-3,-5,4,2] => 78 [-1,-3,-5,4,-2] => 82 [-1,-3,-5,-4,2] => 84 [-1,-3,-5,-4,-2] => 88 [1,4,2,3,5] => 3 [1,4,2,3,-5] => 4 [1,4,2,-3,5] => 12 [1,4,2,-3,-5] => 13 [1,4,-2,3,5] => 23 [1,4,-2,3,-5] => 24 [1,4,-2,-3,5] => 32 [1,4,-2,-3,-5] => 33 [1,-4,2,3,5] => 17 [1,-4,2,3,-5] => 18 [1,-4,2,-3,5] => 26 [1,-4,2,-3,-5] => 27 [1,-4,-2,3,5] => 37 [1,-4,-2,3,-5] => 38 [1,-4,-2,-3,5] => 46 [1,-4,-2,-3,-5] => 47 [-1,4,2,3,5] => 48 [-1,4,2,3,-5] => 49 [-1,4,2,-3,5] => 57 [-1,4,2,-3,-5] => 58 [-1,4,-2,3,5] => 68 [-1,4,-2,3,-5] => 69 [-1,4,-2,-3,5] => 77 [-1,4,-2,-3,-5] => 78 [-1,-4,2,3,5] => 62 [-1,-4,2,3,-5] => 63 [-1,-4,2,-3,5] => 71 [-1,-4,2,-3,-5] => 72 [-1,-4,-2,3,5] => 82 [-1,-4,-2,3,-5] => 83 [-1,-4,-2,-3,5] => 91 [-1,-4,-2,-3,-5] => 92 [1,4,2,5,3] => 5 [1,4,2,5,-3] => 8 [1,4,2,-5,3] => 8 [1,4,2,-5,-3] => 11 [1,4,-2,5,3] => 25 [1,4,-2,5,-3] => 28 [1,4,-2,-5,3] => 28 [1,4,-2,-5,-3] => 31 [1,-4,2,5,3] => 19 [1,-4,2,5,-3] => 22 [1,-4,2,-5,3] => 22 [1,-4,2,-5,-3] => 25 [1,-4,-2,5,3] => 39 [1,-4,-2,5,-3] => 42 [1,-4,-2,-5,3] => 42 [1,-4,-2,-5,-3] => 45 [-1,4,2,5,3] => 50 [-1,4,2,5,-3] => 53 [-1,4,2,-5,3] => 53 [-1,4,2,-5,-3] => 56 [-1,4,-2,5,3] => 70 [-1,4,-2,5,-3] => 73 [-1,4,-2,-5,3] => 73 [-1,4,-2,-5,-3] => 76 [-1,-4,2,5,3] => 64 [-1,-4,2,5,-3] => 67 [-1,-4,2,-5,3] => 67 [-1,-4,2,-5,-3] => 70 [-1,-4,-2,5,3] => 84 [-1,-4,-2,5,-3] => 87 [-1,-4,-2,-5,3] => 87 [-1,-4,-2,-5,-3] => 90 [1,4,3,2,5] => 4 [1,4,3,2,-5] => 5 [1,4,3,-2,5] => 16 [1,4,3,-2,-5] => 17 [1,4,-3,2,5] => 19 [1,4,-3,2,-5] => 20 [1,4,-3,-2,5] => 31 [1,4,-3,-2,-5] => 32 [1,-4,3,2,5] => 18 [1,-4,3,2,-5] => 19 [1,-4,3,-2,5] => 30 [1,-4,3,-2,-5] => 31 [1,-4,-3,2,5] => 33 [1,-4,-3,2,-5] => 34 [1,-4,-3,-2,5] => 45 [1,-4,-3,-2,-5] => 46 [-1,4,3,2,5] => 49 [-1,4,3,2,-5] => 50 [-1,4,3,-2,5] => 61 [-1,4,3,-2,-5] => 62 [-1,4,-3,2,5] => 64 [-1,4,-3,2,-5] => 65 [-1,4,-3,-2,5] => 76 [-1,4,-3,-2,-5] => 77 [-1,-4,3,2,5] => 63 [-1,-4,3,2,-5] => 64 [-1,-4,3,-2,5] => 75 [-1,-4,3,-2,-5] => 76 [-1,-4,-3,2,5] => 78 [-1,-4,-3,2,-5] => 79 [-1,-4,-3,-2,5] => 90 [-1,-4,-3,-2,-5] => 91 [1,4,3,5,2] => 7 [1,4,3,5,-2] => 11 [1,4,3,-5,2] => 10 [1,4,3,-5,-2] => 14 [1,4,-3,5,2] => 22 [1,4,-3,5,-2] => 26 [1,4,-3,-5,2] => 25 [1,4,-3,-5,-2] => 29 [1,-4,3,5,2] => 21 [1,-4,3,5,-2] => 25 [1,-4,3,-5,2] => 24 [1,-4,3,-5,-2] => 28 [1,-4,-3,5,2] => 36 [1,-4,-3,5,-2] => 40 [1,-4,-3,-5,2] => 39 [1,-4,-3,-5,-2] => 43 [-1,4,3,5,2] => 52 [-1,4,3,5,-2] => 56 [-1,4,3,-5,2] => 55 [-1,4,3,-5,-2] => 59 [-1,4,-3,5,2] => 67 [-1,4,-3,5,-2] => 71 [-1,4,-3,-5,2] => 70 [-1,4,-3,-5,-2] => 74 [-1,-4,3,5,2] => 66 [-1,-4,3,5,-2] => 70 [-1,-4,3,-5,2] => 69 [-1,-4,3,-5,-2] => 73 [-1,-4,-3,5,2] => 81 [-1,-4,-3,5,-2] => 85 [-1,-4,-3,-5,2] => 84 [-1,-4,-3,-5,-2] => 88 [1,4,5,2,3] => 8 [1,4,5,2,-3] => 11 [1,4,5,-2,3] => 20 [1,4,5,-2,-3] => 23 [1,4,-5,2,3] => 13 [1,4,-5,2,-3] => 16 [1,4,-5,-2,3] => 25 [1,4,-5,-2,-3] => 28 [1,-4,5,2,3] => 22 [1,-4,5,2,-3] => 25 [1,-4,5,-2,3] => 34 [1,-4,5,-2,-3] => 37 [1,-4,-5,2,3] => 27 [1,-4,-5,2,-3] => 30 [1,-4,-5,-2,3] => 39 [1,-4,-5,-2,-3] => 42 [-1,4,5,2,3] => 53 [-1,4,5,2,-3] => 56 [-1,4,5,-2,3] => 65 [-1,4,5,-2,-3] => 68 [-1,4,-5,2,3] => 58 [-1,4,-5,2,-3] => 61 [-1,4,-5,-2,3] => 70 [-1,4,-5,-2,-3] => 73 [-1,-4,5,2,3] => 67 [-1,-4,5,2,-3] => 70 [-1,-4,5,-2,3] => 79 [-1,-4,5,-2,-3] => 82 [-1,-4,-5,2,3] => 72 [-1,-4,-5,2,-3] => 75 [-1,-4,-5,-2,3] => 84 [-1,-4,-5,-2,-3] => 87 [1,4,5,3,2] => 9 [1,4,5,3,-2] => 13 [1,4,5,-3,2] => 18 [1,4,5,-3,-2] => 22 [1,4,-5,3,2] => 14 [1,4,-5,3,-2] => 18 [1,4,-5,-3,2] => 23 [1,4,-5,-3,-2] => 27 [1,-4,5,3,2] => 23 [1,-4,5,3,-2] => 27 [1,-4,5,-3,2] => 32 [1,-4,5,-3,-2] => 36 [1,-4,-5,3,2] => 28 [1,-4,-5,3,-2] => 32 [1,-4,-5,-3,2] => 37 [1,-4,-5,-3,-2] => 41 [-1,4,5,3,2] => 54 [-1,4,5,3,-2] => 58 [-1,4,5,-3,2] => 63 [-1,4,5,-3,-2] => 67 [-1,4,-5,3,2] => 59 [-1,4,-5,3,-2] => 63 [-1,4,-5,-3,2] => 68 [-1,4,-5,-3,-2] => 72 [-1,-4,5,3,2] => 68 [-1,-4,5,3,-2] => 72 [-1,-4,5,-3,2] => 77 [-1,-4,5,-3,-2] => 81 [-1,-4,-5,3,2] => 73 [-1,-4,-5,3,-2] => 77 [-1,-4,-5,-3,2] => 82 [-1,-4,-5,-3,-2] => 86 [1,5,2,3,4] => 6 [1,5,2,3,-4] => 8 [1,5,2,-3,4] => 15 [1,5,2,-3,-4] => 17 [1,5,-2,3,4] => 26 [1,5,-2,3,-4] => 28 [1,5,-2,-3,4] => 35 [1,5,-2,-3,-4] => 37 [1,-5,2,3,4] => 13 [1,-5,2,3,-4] => 15 [1,-5,2,-3,4] => 22 [1,-5,2,-3,-4] => 24 [1,-5,-2,3,4] => 33 [1,-5,-2,3,-4] => 35 [1,-5,-2,-3,4] => 42 [1,-5,-2,-3,-4] => 44 [-1,5,2,3,4] => 51 [-1,5,2,3,-4] => 53 [-1,5,2,-3,4] => 60 [-1,5,2,-3,-4] => 62 [-1,5,-2,3,4] => 71 [-1,5,-2,3,-4] => 73 [-1,5,-2,-3,4] => 80 [-1,5,-2,-3,-4] => 82 [-1,-5,2,3,4] => 58 [-1,-5,2,3,-4] => 60 [-1,-5,2,-3,4] => 67 [-1,-5,2,-3,-4] => 69 [-1,-5,-2,3,4] => 78 [-1,-5,-2,3,-4] => 80 [-1,-5,-2,-3,4] => 87 [-1,-5,-2,-3,-4] => 89 [1,5,2,4,3] => 7 [1,5,2,4,-3] => 10 [1,5,2,-4,3] => 13 [1,5,2,-4,-3] => 16 [1,5,-2,4,3] => 27 [1,5,-2,4,-3] => 30 [1,5,-2,-4,3] => 33 [1,5,-2,-4,-3] => 36 [1,-5,2,4,3] => 14 [1,-5,2,4,-3] => 17 [1,-5,2,-4,3] => 20 [1,-5,2,-4,-3] => 23 [1,-5,-2,4,3] => 34 [1,-5,-2,4,-3] => 37 [1,-5,-2,-4,3] => 40 [1,-5,-2,-4,-3] => 43 [-1,5,2,4,3] => 52 [-1,5,2,4,-3] => 55 [-1,5,2,-4,3] => 58 [-1,5,2,-4,-3] => 61 [-1,5,-2,4,3] => 72 [-1,5,-2,4,-3] => 75 [-1,5,-2,-4,3] => 78 [-1,5,-2,-4,-3] => 81 [-1,-5,2,4,3] => 59 [-1,-5,2,4,-3] => 62 [-1,-5,2,-4,3] => 65 [-1,-5,2,-4,-3] => 68 [-1,-5,-2,4,3] => 79 [-1,-5,-2,4,-3] => 82 [-1,-5,-2,-4,3] => 85 [-1,-5,-2,-4,-3] => 88 [1,5,3,2,4] => 7 [1,5,3,2,-4] => 9 [1,5,3,-2,4] => 19 [1,5,3,-2,-4] => 21 [1,5,-3,2,4] => 22 [1,5,-3,2,-4] => 24 [1,5,-3,-2,4] => 34 [1,5,-3,-2,-4] => 36 [1,-5,3,2,4] => 14 [1,-5,3,2,-4] => 16 [1,-5,3,-2,4] => 26 [1,-5,3,-2,-4] => 28 [1,-5,-3,2,4] => 29 [1,-5,-3,2,-4] => 31 [1,-5,-3,-2,4] => 41 [1,-5,-3,-2,-4] => 43 [-1,5,3,2,4] => 52 [-1,5,3,2,-4] => 54 [-1,5,3,-2,4] => 64 [-1,5,3,-2,-4] => 66 [-1,5,-3,2,4] => 67 [-1,5,-3,2,-4] => 69 [-1,5,-3,-2,4] => 79 [-1,5,-3,-2,-4] => 81 [-1,-5,3,2,4] => 59 [-1,-5,3,2,-4] => 61 [-1,-5,3,-2,4] => 71 [-1,-5,3,-2,-4] => 73 [-1,-5,-3,2,4] => 74 [-1,-5,-3,2,-4] => 76 [-1,-5,-3,-2,4] => 86 [-1,-5,-3,-2,-4] => 88 [1,5,3,4,2] => 9 [1,5,3,4,-2] => 13 [1,5,3,-4,2] => 15 [1,5,3,-4,-2] => 19 [1,5,-3,4,2] => 24 [1,5,-3,4,-2] => 28 [1,5,-3,-4,2] => 30 [1,5,-3,-4,-2] => 34 [1,-5,3,4,2] => 16 [1,-5,3,4,-2] => 20 [1,-5,3,-4,2] => 22 [1,-5,3,-4,-2] => 26 [1,-5,-3,4,2] => 31 [1,-5,-3,4,-2] => 35 [1,-5,-3,-4,2] => 37 [1,-5,-3,-4,-2] => 41 [-1,5,3,4,2] => 54 [-1,5,3,4,-2] => 58 [-1,5,3,-4,2] => 60 [-1,5,3,-4,-2] => 64 [-1,5,-3,4,2] => 69 [-1,5,-3,4,-2] => 73 [-1,5,-3,-4,2] => 75 [-1,5,-3,-4,-2] => 79 [-1,-5,3,4,2] => 61 [-1,-5,3,4,-2] => 65 [-1,-5,3,-4,2] => 67 [-1,-5,3,-4,-2] => 71 [-1,-5,-3,4,2] => 76 [-1,-5,-3,4,-2] => 80 [-1,-5,-3,-4,2] => 82 [-1,-5,-3,-4,-2] => 86 [1,5,4,2,3] => 9 [1,5,4,2,-3] => 12 [1,5,4,-2,3] => 21 [1,5,4,-2,-3] => 24 [1,5,-4,2,3] => 19 [1,5,-4,2,-3] => 22 [1,5,-4,-2,3] => 31 [1,5,-4,-2,-3] => 34 [1,-5,4,2,3] => 16 [1,-5,4,2,-3] => 19 [1,-5,4,-2,3] => 28 [1,-5,4,-2,-3] => 31 [1,-5,-4,2,3] => 26 [1,-5,-4,2,-3] => 29 [1,-5,-4,-2,3] => 38 [1,-5,-4,-2,-3] => 41 [-1,5,4,2,3] => 54 [-1,5,4,2,-3] => 57 [-1,5,4,-2,3] => 66 [-1,5,4,-2,-3] => 69 [-1,5,-4,2,3] => 64 [-1,5,-4,2,-3] => 67 [-1,5,-4,-2,3] => 76 [-1,5,-4,-2,-3] => 79 [-1,-5,4,2,3] => 61 [-1,-5,4,2,-3] => 64 [-1,-5,4,-2,3] => 73 [-1,-5,4,-2,-3] => 76 [-1,-5,-4,2,3] => 71 [-1,-5,-4,2,-3] => 74 [-1,-5,-4,-2,3] => 83 [-1,-5,-4,-2,-3] => 86 [1,5,4,3,2] => 10 [1,5,4,3,-2] => 14 [1,5,4,-3,2] => 19 [1,5,4,-3,-2] => 23 [1,5,-4,3,2] => 20 [1,5,-4,3,-2] => 24 [1,5,-4,-3,2] => 29 [1,5,-4,-3,-2] => 33 [1,-5,4,3,2] => 17 [1,-5,4,3,-2] => 21 [1,-5,4,-3,2] => 26 [1,-5,4,-3,-2] => 30 [1,-5,-4,3,2] => 27 [1,-5,-4,3,-2] => 31 [1,-5,-4,-3,2] => 36 [1,-5,-4,-3,-2] => 40 [-1,5,4,3,2] => 55 [-1,5,4,3,-2] => 59 [-1,5,4,-3,2] => 64 [-1,5,4,-3,-2] => 68 [-1,5,-4,3,2] => 65 [-1,5,-4,3,-2] => 69 ----------------------------------------------------------------------------- Created: Nov 23, 2022 at 10:16 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Nov 23, 2022 at 10:16 by Martin Rubey