***************************************************************************** * 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: St000795 ----------------------------------------------------------------------------- Collection: Permutations ----------------------------------------------------------------------------- Description: The mad of a permutation. According to [1], this is the sum of twice the number of occurrences of the vincular pattern of \$(2\underline{31})\$ plus the number of occurrences of the vincular patterns \$(\underline{31}2)\$ and \$(\underline{21})\$, where matches of the underlined letters must be adjacent. ----------------------------------------------------------------------------- References: [1] Babson, E., Steingr\'ımsson, E. Generalized permutation patterns and a classification of the Mahonian statistics [[MathSciNet:1758852]] ----------------------------------------------------------------------------- Code: def statistic(pi): patterns = [([2,3,1],[2]), ([2,3,1],[2]), ([3,1,2],[1]), ([2,1],[1])] return sum(vincular_occurrences(pi, p, c) for p, c in patterns) def vincular_occurrences(perm, pat, columns): n = len(pat) R = [(c, i) for c in columns for i in range(n+1)] return mesh_pattern_occurrences(perm, pat, R=R) def G(w): return [ (x+1,y) for (x,y) in enumerate(w) ] def mesh_pattern_occurrences(perm, pat, R=[]): occs = 0 k = len(pat) n = len(perm) pat = G(pat) perm = G(perm) for H in Subsets(perm, k): H = sorted(H) X = dict(G(sorted(i for (i,_) in H))) Y = dict(G(sorted(j for (_,j) in H))) if H == [ (X[i], Y[j]) for (i,j) in pat ]: X[0], X[k+1] = 0, n+1 Y[0], Y[k+1] = 0, n+1 shady = ( X[i] < x < X[i+1] and Y[j] < y < Y[j+1] for (i,j) in R for (x,y) in perm ) if not any(shady): occs = occs + 1 return occs ----------------------------------------------------------------------------- Statistic values: [1,2] => 0 [2,1] => 1 [1,2,3] => 0 [1,3,2] => 1 [2,1,3] => 1 [2,3,1] => 3 [3,1,2] => 2 [3,2,1] => 2 [1,2,3,4] => 0 [1,2,4,3] => 1 [1,3,2,4] => 1 [1,3,4,2] => 3 [1,4,2,3] => 2 [1,4,3,2] => 2 [2,1,3,4] => 1 [2,1,4,3] => 2 [2,3,1,4] => 3 [2,3,4,1] => 5 [2,4,1,3] => 4 [2,4,3,1] => 4 [3,1,2,4] => 2 [3,1,4,2] => 5 [3,2,1,4] => 2 [3,2,4,1] => 6 [3,4,1,2] => 4 [3,4,2,1] => 4 [4,1,2,3] => 3 [4,1,3,2] => 4 [4,2,1,3] => 3 [4,2,3,1] => 5 [4,3,1,2] => 3 [4,3,2,1] => 3 [1,2,3,4,5] => 0 [1,2,3,5,4] => 1 [1,2,4,3,5] => 1 [1,2,4,5,3] => 3 [1,2,5,3,4] => 2 [1,2,5,4,3] => 2 [1,3,2,4,5] => 1 [1,3,2,5,4] => 2 [1,3,4,2,5] => 3 [1,3,4,5,2] => 5 [1,3,5,2,4] => 4 [1,3,5,4,2] => 4 [1,4,2,3,5] => 2 [1,4,2,5,3] => 5 [1,4,3,2,5] => 2 [1,4,3,5,2] => 6 [1,4,5,2,3] => 4 [1,4,5,3,2] => 4 [1,5,2,3,4] => 3 [1,5,2,4,3] => 4 [1,5,3,2,4] => 3 [1,5,3,4,2] => 5 [1,5,4,2,3] => 3 [1,5,4,3,2] => 3 [2,1,3,4,5] => 1 [2,1,3,5,4] => 2 [2,1,4,3,5] => 2 [2,1,4,5,3] => 4 [2,1,5,3,4] => 3 [2,1,5,4,3] => 3 [2,3,1,4,5] => 3 [2,3,1,5,4] => 4 [2,3,4,1,5] => 5 [2,3,4,5,1] => 7 [2,3,5,1,4] => 6 [2,3,5,4,1] => 6 [2,4,1,3,5] => 4 [2,4,1,5,3] => 7 [2,4,3,1,5] => 4 [2,4,3,5,1] => 8 [2,4,5,1,3] => 6 [2,4,5,3,1] => 6 [2,5,1,3,4] => 5 [2,5,1,4,3] => 6 [2,5,3,1,4] => 5 [2,5,3,4,1] => 7 [2,5,4,1,3] => 5 [2,5,4,3,1] => 5 [3,1,2,4,5] => 2 [3,1,2,5,4] => 3 [3,1,4,2,5] => 5 [3,1,4,5,2] => 7 [3,1,5,2,4] => 6 [3,1,5,4,2] => 6 [3,2,1,4,5] => 2 [3,2,1,5,4] => 3 [3,2,4,1,5] => 6 [3,2,4,5,1] => 8 [3,2,5,1,4] => 7 [3,2,5,4,1] => 7 [3,4,1,2,5] => 4 [3,4,1,5,2] => 9 [3,4,2,1,5] => 4 [3,4,2,5,1] => 10 [3,4,5,1,2] => 6 [3,4,5,2,1] => 6 [3,5,1,2,4] => 5 [3,5,1,4,2] => 8 [3,5,2,1,4] => 5 [3,5,2,4,1] => 9 [3,5,4,1,2] => 5 [3,5,4,2,1] => 5 [4,1,2,3,5] => 3 [4,1,2,5,3] => 6 [4,1,3,2,5] => 4 [4,1,3,5,2] => 8 [4,1,5,2,3] => 7 [4,1,5,3,2] => 7 [4,2,1,3,5] => 3 [4,2,1,5,3] => 6 [4,2,3,1,5] => 5 [4,2,3,5,1] => 9 [4,2,5,1,3] => 8 [4,2,5,3,1] => 8 [4,3,1,2,5] => 3 [4,3,1,5,2] => 8 [4,3,2,1,5] => 3 [4,3,2,5,1] => 9 [4,3,5,1,2] => 7 [4,3,5,2,1] => 7 [4,5,1,2,3] => 5 [4,5,1,3,2] => 6 [4,5,2,1,3] => 5 [4,5,2,3,1] => 7 [4,5,3,1,2] => 5 [4,5,3,2,1] => 5 [5,1,2,3,4] => 4 [5,1,2,4,3] => 5 [5,1,3,2,4] => 5 [5,1,3,4,2] => 7 [5,1,4,2,3] => 6 [5,1,4,3,2] => 6 [5,2,1,3,4] => 4 [5,2,1,4,3] => 5 [5,2,3,1,4] => 6 [5,2,3,4,1] => 8 [5,2,4,1,3] => 7 [5,2,4,3,1] => 7 [5,3,1,2,4] => 4 [5,3,1,4,2] => 7 [5,3,2,1,4] => 4 [5,3,2,4,1] => 8 [5,3,4,1,2] => 6 [5,3,4,2,1] => 6 [5,4,1,2,3] => 4 [5,4,1,3,2] => 5 [5,4,2,1,3] => 4 [5,4,2,3,1] => 6 [5,4,3,1,2] => 4 [5,4,3,2,1] => 4 [1,2,3,4,5,6] => 0 [1,2,3,4,6,5] => 1 [1,2,3,5,4,6] => 1 [1,2,3,5,6,4] => 3 [1,2,3,6,4,5] => 2 [1,2,3,6,5,4] => 2 [1,2,4,3,5,6] => 1 [1,2,4,3,6,5] => 2 [1,2,4,5,3,6] => 3 [1,2,4,5,6,3] => 5 [1,2,4,6,3,5] => 4 [1,2,4,6,5,3] => 4 [1,2,5,3,4,6] => 2 [1,2,5,3,6,4] => 5 [1,2,5,4,3,6] => 2 [1,2,5,4,6,3] => 6 [1,2,5,6,3,4] => 4 [1,2,5,6,4,3] => 4 [1,2,6,3,4,5] => 3 [1,2,6,3,5,4] => 4 [1,2,6,4,3,5] => 3 [1,2,6,4,5,3] => 5 [1,2,6,5,3,4] => 3 [1,2,6,5,4,3] => 3 [1,3,2,4,5,6] => 1 [1,3,2,4,6,5] => 2 [1,3,2,5,4,6] => 2 [1,3,2,5,6,4] => 4 [1,3,2,6,4,5] => 3 [1,3,2,6,5,4] => 3 [1,3,4,2,5,6] => 3 [1,3,4,2,6,5] => 4 [1,3,4,5,2,6] => 5 [1,3,4,5,6,2] => 7 [1,3,4,6,2,5] => 6 [1,3,4,6,5,2] => 6 [1,3,5,2,4,6] => 4 [1,3,5,2,6,4] => 7 [1,3,5,4,2,6] => 4 [1,3,5,4,6,2] => 8 [1,3,5,6,2,4] => 6 [1,3,5,6,4,2] => 6 [1,3,6,2,4,5] => 5 [1,3,6,2,5,4] => 6 [1,3,6,4,2,5] => 5 [1,3,6,4,5,2] => 7 [1,3,6,5,2,4] => 5 [1,3,6,5,4,2] => 5 [1,4,2,3,5,6] => 2 [1,4,2,3,6,5] => 3 [1,4,2,5,3,6] => 5 [1,4,2,5,6,3] => 7 [1,4,2,6,3,5] => 6 [1,4,2,6,5,3] => 6 [1,4,3,2,5,6] => 2 [1,4,3,2,6,5] => 3 [1,4,3,5,2,6] => 6 [1,4,3,5,6,2] => 8 [1,4,3,6,2,5] => 7 [1,4,3,6,5,2] => 7 [1,4,5,2,3,6] => 4 [1,4,5,2,6,3] => 9 [1,4,5,3,2,6] => 4 [1,4,5,3,6,2] => 10 [1,4,5,6,2,3] => 6 [1,4,5,6,3,2] => 6 [1,4,6,2,3,5] => 5 [1,4,6,2,5,3] => 8 [1,4,6,3,2,5] => 5 [1,4,6,3,5,2] => 9 [1,4,6,5,2,3] => 5 [1,4,6,5,3,2] => 5 [1,5,2,3,4,6] => 3 [1,5,2,3,6,4] => 6 [1,5,2,4,3,6] => 4 [1,5,2,4,6,3] => 8 [1,5,2,6,3,4] => 7 [1,5,2,6,4,3] => 7 [1,5,3,2,4,6] => 3 [1,5,3,2,6,4] => 6 [1,5,3,4,2,6] => 5 [1,5,3,4,6,2] => 9 [1,5,3,6,2,4] => 8 [1,5,3,6,4,2] => 8 [1,5,4,2,3,6] => 3 [1,5,4,2,6,3] => 8 [1,5,4,3,2,6] => 3 [1,5,4,3,6,2] => 9 [1,5,4,6,2,3] => 7 [1,5,4,6,3,2] => 7 [1,5,6,2,3,4] => 5 [1,5,6,2,4,3] => 6 [1,5,6,3,2,4] => 5 [1,5,6,3,4,2] => 7 [1,5,6,4,2,3] => 5 [1,5,6,4,3,2] => 5 [1,6,2,3,4,5] => 4 [1,6,2,3,5,4] => 5 [1,6,2,4,3,5] => 5 [1,6,2,4,5,3] => 7 [1,6,2,5,3,4] => 6 [1,6,2,5,4,3] => 6 [1,6,3,2,4,5] => 4 [1,6,3,2,5,4] => 5 [1,6,3,4,2,5] => 6 [1,6,3,4,5,2] => 8 [1,6,3,5,2,4] => 7 [1,6,3,5,4,2] => 7 [1,6,4,2,3,5] => 4 [1,6,4,2,5,3] => 7 [1,6,4,3,2,5] => 4 [1,6,4,3,5,2] => 8 [1,6,4,5,2,3] => 6 [1,6,4,5,3,2] => 6 [1,6,5,2,3,4] => 4 [1,6,5,2,4,3] => 5 [1,6,5,3,2,4] => 4 [1,6,5,3,4,2] => 6 [1,6,5,4,2,3] => 4 [1,6,5,4,3,2] => 4 [2,1,3,4,5,6] => 1 [2,1,3,4,6,5] => 2 [2,1,3,5,4,6] => 2 [2,1,3,5,6,4] => 4 [2,1,3,6,4,5] => 3 [2,1,3,6,5,4] => 3 [2,1,4,3,5,6] => 2 [2,1,4,3,6,5] => 3 [2,1,4,5,3,6] => 4 [2,1,4,5,6,3] => 6 [2,1,4,6,3,5] => 5 [2,1,4,6,5,3] => 5 [2,1,5,3,4,6] => 3 [2,1,5,3,6,4] => 6 [2,1,5,4,3,6] => 3 [2,1,5,4,6,3] => 7 [2,1,5,6,3,4] => 5 [2,1,5,6,4,3] => 5 [2,1,6,3,4,5] => 4 [2,1,6,3,5,4] => 5 [2,1,6,4,3,5] => 4 [2,1,6,4,5,3] => 6 [2,1,6,5,3,4] => 4 [2,1,6,5,4,3] => 4 [2,3,1,4,5,6] => 3 [2,3,1,4,6,5] => 4 [2,3,1,5,4,6] => 4 [2,3,1,5,6,4] => 6 [2,3,1,6,4,5] => 5 [2,3,1,6,5,4] => 5 [2,3,4,1,5,6] => 5 [2,3,4,1,6,5] => 6 [2,3,4,5,1,6] => 7 [2,3,4,5,6,1] => 9 [2,3,4,6,1,5] => 8 [2,3,4,6,5,1] => 8 [2,3,5,1,4,6] => 6 [2,3,5,1,6,4] => 9 [2,3,5,4,1,6] => 6 [2,3,5,4,6,1] => 10 [2,3,5,6,1,4] => 8 [2,3,5,6,4,1] => 8 [2,3,6,1,4,5] => 7 [2,3,6,1,5,4] => 8 [2,3,6,4,1,5] => 7 [2,3,6,4,5,1] => 9 [2,3,6,5,1,4] => 7 [2,3,6,5,4,1] => 7 [2,4,1,3,5,6] => 4 [2,4,1,3,6,5] => 5 [2,4,1,5,3,6] => 7 [2,4,1,5,6,3] => 9 [2,4,1,6,3,5] => 8 [2,4,1,6,5,3] => 8 [2,4,3,1,5,6] => 4 [2,4,3,1,6,5] => 5 [2,4,3,5,1,6] => 8 [2,4,3,5,6,1] => 10 [2,4,3,6,1,5] => 9 [2,4,3,6,5,1] => 9 [2,4,5,1,3,6] => 6 [2,4,5,1,6,3] => 11 [2,4,5,3,1,6] => 6 [2,4,5,3,6,1] => 12 [2,4,5,6,1,3] => 8 [2,4,5,6,3,1] => 8 [2,4,6,1,3,5] => 7 [2,4,6,1,5,3] => 10 [2,4,6,3,1,5] => 7 [2,4,6,3,5,1] => 11 [2,4,6,5,1,3] => 7 [2,4,6,5,3,1] => 7 [2,5,1,3,4,6] => 5 [2,5,1,3,6,4] => 8 [2,5,1,4,3,6] => 6 [2,5,1,4,6,3] => 10 [2,5,1,6,3,4] => 9 [2,5,1,6,4,3] => 9 [2,5,3,1,4,6] => 5 [2,5,3,1,6,4] => 8 [2,5,3,4,1,6] => 7 [2,5,3,4,6,1] => 11 [2,5,3,6,1,4] => 10 [2,5,3,6,4,1] => 10 [2,5,4,1,3,6] => 5 [2,5,4,1,6,3] => 10 [2,5,4,3,1,6] => 5 [2,5,4,3,6,1] => 11 [2,5,4,6,1,3] => 9 [2,5,4,6,3,1] => 9 [2,5,6,1,3,4] => 7 [2,5,6,1,4,3] => 8 [2,5,6,3,1,4] => 7 [2,5,6,3,4,1] => 9 [2,5,6,4,1,3] => 7 [2,5,6,4,3,1] => 7 [2,6,1,3,4,5] => 6 [2,6,1,3,5,4] => 7 [2,6,1,4,3,5] => 7 [2,6,1,4,5,3] => 9 [2,6,1,5,3,4] => 8 [2,6,1,5,4,3] => 8 [2,6,3,1,4,5] => 6 [2,6,3,1,5,4] => 7 [2,6,3,4,1,5] => 8 [2,6,3,4,5,1] => 10 [2,6,3,5,1,4] => 9 [2,6,3,5,4,1] => 9 [2,6,4,1,3,5] => 6 [2,6,4,1,5,3] => 9 [2,6,4,3,1,5] => 6 [2,6,4,3,5,1] => 10 [2,6,4,5,1,3] => 8 [2,6,4,5,3,1] => 8 [2,6,5,1,3,4] => 6 [2,6,5,1,4,3] => 7 [2,6,5,3,1,4] => 6 [2,6,5,3,4,1] => 8 [2,6,5,4,1,3] => 6 [2,6,5,4,3,1] => 6 [3,1,2,4,5,6] => 2 [3,1,2,4,6,5] => 3 [3,1,2,5,4,6] => 3 [3,1,2,5,6,4] => 5 [3,1,2,6,4,5] => 4 [3,1,2,6,5,4] => 4 [3,1,4,2,5,6] => 5 [3,1,4,2,6,5] => 6 [3,1,4,5,2,6] => 7 [3,1,4,5,6,2] => 9 [3,1,4,6,2,5] => 8 [3,1,4,6,5,2] => 8 [3,1,5,2,4,6] => 6 [3,1,5,2,6,4] => 9 [3,1,5,4,2,6] => 6 [3,1,5,4,6,2] => 10 [3,1,5,6,2,4] => 8 [3,1,5,6,4,2] => 8 [3,1,6,2,4,5] => 7 [3,1,6,2,5,4] => 8 [3,1,6,4,2,5] => 7 [3,1,6,4,5,2] => 9 [3,1,6,5,2,4] => 7 [3,1,6,5,4,2] => 7 [3,2,1,4,5,6] => 2 [3,2,1,4,6,5] => 3 [3,2,1,5,4,6] => 3 [3,2,1,5,6,4] => 5 [3,2,1,6,4,5] => 4 [3,2,1,6,5,4] => 4 [3,2,4,1,5,6] => 6 [3,2,4,1,6,5] => 7 [3,2,4,5,1,6] => 8 [3,2,4,5,6,1] => 10 [3,2,4,6,1,5] => 9 [3,2,4,6,5,1] => 9 [3,2,5,1,4,6] => 7 [3,2,5,1,6,4] => 10 [3,2,5,4,1,6] => 7 [3,2,5,4,6,1] => 11 [3,2,5,6,1,4] => 9 [3,2,5,6,4,1] => 9 [3,2,6,1,4,5] => 8 [3,2,6,1,5,4] => 9 [3,2,6,4,1,5] => 8 [3,2,6,4,5,1] => 10 [3,2,6,5,1,4] => 8 [3,2,6,5,4,1] => 8 [3,4,1,2,5,6] => 4 [3,4,1,2,6,5] => 5 [3,4,1,5,2,6] => 9 [3,4,1,5,6,2] => 11 [3,4,1,6,2,5] => 10 [3,4,1,6,5,2] => 10 [3,4,2,1,5,6] => 4 [3,4,2,1,6,5] => 5 [3,4,2,5,1,6] => 10 [3,4,2,5,6,1] => 12 [3,4,2,6,1,5] => 11 [3,4,2,6,5,1] => 11 [3,4,5,1,2,6] => 6 [3,4,5,1,6,2] => 13 [3,4,5,2,1,6] => 6 [3,4,5,2,6,1] => 14 [3,4,5,6,1,2] => 8 [3,4,5,6,2,1] => 8 [3,4,6,1,2,5] => 7 [3,4,6,1,5,2] => 12 [3,4,6,2,1,5] => 7 [3,4,6,2,5,1] => 13 [3,4,6,5,1,2] => 7 [3,4,6,5,2,1] => 7 [3,5,1,2,4,6] => 5 [3,5,1,2,6,4] => 8 [3,5,1,4,2,6] => 8 [3,5,1,4,6,2] => 12 [3,5,1,6,2,4] => 11 [3,5,1,6,4,2] => 11 [3,5,2,1,4,6] => 5 [3,5,2,1,6,4] => 8 [3,5,2,4,1,6] => 9 [3,5,2,4,6,1] => 13 [3,5,2,6,1,4] => 12 [3,5,2,6,4,1] => 12 [3,5,4,1,2,6] => 5 [3,5,4,1,6,2] => 12 [3,5,4,2,1,6] => 5 [3,5,4,2,6,1] => 13 [3,5,4,6,1,2] => 9 [3,5,4,6,2,1] => 9 [3,5,6,1,2,4] => 7 [3,5,6,1,4,2] => 10 [3,5,6,2,1,4] => 7 [3,5,6,2,4,1] => 11 [3,5,6,4,1,2] => 7 [3,5,6,4,2,1] => 7 [3,6,1,2,4,5] => 6 [3,6,1,2,5,4] => 7 [3,6,1,4,2,5] => 9 [3,6,1,4,5,2] => 11 [3,6,1,5,2,4] => 10 [3,6,1,5,4,2] => 10 [3,6,2,1,4,5] => 6 [3,6,2,1,5,4] => 7 [3,6,2,4,1,5] => 10 [3,6,2,4,5,1] => 12 [3,6,2,5,1,4] => 11 [3,6,2,5,4,1] => 11 [3,6,4,1,2,5] => 6 [3,6,4,1,5,2] => 11 [3,6,4,2,1,5] => 6 [3,6,4,2,5,1] => 12 [3,6,4,5,1,2] => 8 [3,6,4,5,2,1] => 8 [3,6,5,1,2,4] => 6 [3,6,5,1,4,2] => 9 [3,6,5,2,1,4] => 6 [3,6,5,2,4,1] => 10 [3,6,5,4,1,2] => 6 [3,6,5,4,2,1] => 6 [4,1,2,3,5,6] => 3 [4,1,2,3,6,5] => 4 [4,1,2,5,3,6] => 6 [4,1,2,5,6,3] => 8 [4,1,2,6,3,5] => 7 [4,1,2,6,5,3] => 7 [4,1,3,2,5,6] => 4 [4,1,3,2,6,5] => 5 [4,1,3,5,2,6] => 8 [4,1,3,5,6,2] => 10 [4,1,3,6,2,5] => 9 [4,1,3,6,5,2] => 9 [4,1,5,2,3,6] => 7 [4,1,5,2,6,3] => 12 [4,1,5,3,2,6] => 7 [4,1,5,3,6,2] => 13 [4,1,5,6,2,3] => 9 [4,1,5,6,3,2] => 9 [4,1,6,2,3,5] => 8 [4,1,6,2,5,3] => 11 [4,1,6,3,2,5] => 8 [4,1,6,3,5,2] => 12 [4,1,6,5,2,3] => 8 [4,1,6,5,3,2] => 8 [4,2,1,3,5,6] => 3 [4,2,1,3,6,5] => 4 [4,2,1,5,3,6] => 6 [4,2,1,5,6,3] => 8 [4,2,1,6,3,5] => 7 [4,2,1,6,5,3] => 7 [4,2,3,1,5,6] => 5 [4,2,3,1,6,5] => 6 [4,2,3,5,1,6] => 9 [4,2,3,5,6,1] => 11 [4,2,3,6,1,5] => 10 [4,2,3,6,5,1] => 10 [4,2,5,1,3,6] => 8 [4,2,5,1,6,3] => 13 [4,2,5,3,1,6] => 8 [4,2,5,3,6,1] => 14 [4,2,5,6,1,3] => 10 [4,2,5,6,3,1] => 10 [4,2,6,1,3,5] => 9 [4,2,6,1,5,3] => 12 [4,2,6,3,1,5] => 9 [4,2,6,3,5,1] => 13 [4,2,6,5,1,3] => 9 [4,2,6,5,3,1] => 9 [4,3,1,2,5,6] => 3 [4,3,1,2,6,5] => 4 [4,3,1,5,2,6] => 8 [4,3,1,5,6,2] => 10 [4,3,1,6,2,5] => 9 [4,3,1,6,5,2] => 9 [4,3,2,1,5,6] => 3 [4,3,2,1,6,5] => 4 [4,3,2,5,1,6] => 9 [4,3,2,5,6,1] => 11 [4,3,2,6,1,5] => 10 [4,3,2,6,5,1] => 10 [4,3,5,1,2,6] => 7 [4,3,5,1,6,2] => 14 [4,3,5,2,1,6] => 7 [4,3,5,2,6,1] => 15 [4,3,5,6,1,2] => 9 [4,3,5,6,2,1] => 9 [4,3,6,1,2,5] => 8 [4,3,6,1,5,2] => 13 [4,3,6,2,1,5] => 8 [4,3,6,2,5,1] => 14 [4,3,6,5,1,2] => 8 [4,3,6,5,2,1] => 8 [4,5,1,2,3,6] => 5 [4,5,1,2,6,3] => 10 [4,5,1,3,2,6] => 6 [4,5,1,3,6,2] => 12 [4,5,1,6,2,3] => 11 [4,5,1,6,3,2] => 11 [4,5,2,1,3,6] => 5 [4,5,2,1,6,3] => 10 [4,5,2,3,1,6] => 7 [4,5,2,3,6,1] => 13 [4,5,2,6,1,3] => 12 [4,5,2,6,3,1] => 12 [4,5,3,1,2,6] => 5 [4,5,3,1,6,2] => 12 [4,5,3,2,1,6] => 5 [4,5,3,2,6,1] => 13 [4,5,3,6,1,2] => 11 [4,5,3,6,2,1] => 11 [4,5,6,1,2,3] => 7 [4,5,6,1,3,2] => 8 [4,5,6,2,1,3] => 7 [4,5,6,2,3,1] => 9 [4,5,6,3,1,2] => 7 [4,5,6,3,2,1] => 7 [4,6,1,2,3,5] => 6 [4,6,1,2,5,3] => 9 [4,6,1,3,2,5] => 7 [4,6,1,3,5,2] => 11 [4,6,1,5,2,3] => 10 [4,6,1,5,3,2] => 10 [4,6,2,1,3,5] => 6 [4,6,2,1,5,3] => 9 [4,6,2,3,1,5] => 8 [4,6,2,3,5,1] => 12 [4,6,2,5,1,3] => 11 [4,6,2,5,3,1] => 11 [4,6,3,1,2,5] => 6 [4,6,3,1,5,2] => 11 [4,6,3,2,1,5] => 6 [4,6,3,2,5,1] => 12 [4,6,3,5,1,2] => 10 [4,6,3,5,2,1] => 10 [4,6,5,1,2,3] => 6 [4,6,5,1,3,2] => 7 [4,6,5,2,1,3] => 6 [4,6,5,2,3,1] => 8 [4,6,5,3,1,2] => 6 [4,6,5,3,2,1] => 6 [5,1,2,3,4,6] => 4 [5,1,2,3,6,4] => 7 [5,1,2,4,3,6] => 5 [5,1,2,4,6,3] => 9 [5,1,2,6,3,4] => 8 [5,1,2,6,4,3] => 8 [5,1,3,2,4,6] => 5 [5,1,3,2,6,4] => 8 [5,1,3,4,2,6] => 7 [5,1,3,4,6,2] => 11 [5,1,3,6,2,4] => 10 [5,1,3,6,4,2] => 10 [5,1,4,2,3,6] => 6 [5,1,4,2,6,3] => 11 [5,1,4,3,2,6] => 6 [5,1,4,3,6,2] => 12 [5,1,4,6,2,3] => 10 [5,1,4,6,3,2] => 10 [5,1,6,2,3,4] => 9 [5,1,6,2,4,3] => 10 [5,1,6,3,2,4] => 9 [5,1,6,3,4,2] => 11 [5,1,6,4,2,3] => 9 [5,1,6,4,3,2] => 9 [5,2,1,3,4,6] => 4 [5,2,1,3,6,4] => 7 [5,2,1,4,3,6] => 5 [5,2,1,4,6,3] => 9 [5,2,1,6,3,4] => 8 [5,2,1,6,4,3] => 8 [5,2,3,1,4,6] => 6 [5,2,3,1,6,4] => 9 [5,2,3,4,1,6] => 8 [5,2,3,4,6,1] => 12 [5,2,3,6,1,4] => 11 [5,2,3,6,4,1] => 11 [5,2,4,1,3,6] => 7 [5,2,4,1,6,3] => 12 [5,2,4,3,1,6] => 7 [5,2,4,3,6,1] => 13 [5,2,4,6,1,3] => 11 [5,2,4,6,3,1] => 11 [5,2,6,1,3,4] => 10 [5,2,6,1,4,3] => 11 [5,2,6,3,1,4] => 10 [5,2,6,3,4,1] => 12 [5,2,6,4,1,3] => 10 [5,2,6,4,3,1] => 10 [5,3,1,2,4,6] => 4 [5,3,1,2,6,4] => 7 [5,3,1,4,2,6] => 7 [5,3,1,4,6,2] => 11 [5,3,1,6,2,4] => 10 [5,3,1,6,4,2] => 10 [5,3,2,1,4,6] => 4 [5,3,2,1,6,4] => 7 [5,3,2,4,1,6] => 8 [5,3,2,4,6,1] => 12 [5,3,2,6,1,4] => 11 [5,3,2,6,4,1] => 11 [5,3,4,1,2,6] => 6 [5,3,4,1,6,2] => 13 [5,3,4,2,1,6] => 6 [5,3,4,2,6,1] => 14 [5,3,4,6,1,2] => 10 [5,3,4,6,2,1] => 10 [5,3,6,1,2,4] => 9 [5,3,6,1,4,2] => 12 [5,3,6,2,1,4] => 9 [5,3,6,2,4,1] => 13 [5,3,6,4,1,2] => 9 [5,3,6,4,2,1] => 9 [5,4,1,2,3,6] => 4 [5,4,1,2,6,3] => 9 [5,4,1,3,2,6] => 5 [5,4,1,3,6,2] => 11 [5,4,1,6,2,3] => 10 [5,4,1,6,3,2] => 10 [5,4,2,1,3,6] => 4 [5,4,2,1,6,3] => 9 [5,4,2,3,1,6] => 6 [5,4,2,3,6,1] => 12 [5,4,2,6,1,3] => 11 [5,4,2,6,3,1] => 11 [5,4,3,1,2,6] => 4 [5,4,3,1,6,2] => 11 [5,4,3,2,1,6] => 4 [5,4,3,2,6,1] => 12 [5,4,3,6,1,2] => 10 [5,4,3,6,2,1] => 10 [5,4,6,1,2,3] => 8 [5,4,6,1,3,2] => 9 [5,4,6,2,1,3] => 8 [5,4,6,2,3,1] => 10 [5,4,6,3,1,2] => 8 [5,4,6,3,2,1] => 8 [5,6,1,2,3,4] => 6 [5,6,1,2,4,3] => 7 [5,6,1,3,2,4] => 7 [5,6,1,3,4,2] => 9 [5,6,1,4,2,3] => 8 [5,6,1,4,3,2] => 8 [5,6,2,1,3,4] => 6 [5,6,2,1,4,3] => 7 [5,6,2,3,1,4] => 8 [5,6,2,3,4,1] => 10 [5,6,2,4,1,3] => 9 [5,6,2,4,3,1] => 9 [5,6,3,1,2,4] => 6 [5,6,3,1,4,2] => 9 [5,6,3,2,1,4] => 6 [5,6,3,2,4,1] => 10 [5,6,3,4,1,2] => 8 [5,6,3,4,2,1] => 8 [5,6,4,1,2,3] => 6 [5,6,4,1,3,2] => 7 [5,6,4,2,1,3] => 6 [5,6,4,2,3,1] => 8 [5,6,4,3,1,2] => 6 [5,6,4,3,2,1] => 6 [6,1,2,3,4,5] => 5 [6,1,2,3,5,4] => 6 [6,1,2,4,3,5] => 6 [6,1,2,4,5,3] => 8 [6,1,2,5,3,4] => 7 [6,1,2,5,4,3] => 7 [6,1,3,2,4,5] => 6 [6,1,3,2,5,4] => 7 [6,1,3,4,2,5] => 8 [6,1,3,4,5,2] => 10 [6,1,3,5,2,4] => 9 [6,1,3,5,4,2] => 9 [6,1,4,2,3,5] => 7 [6,1,4,2,5,3] => 10 [6,1,4,3,2,5] => 7 [6,1,4,3,5,2] => 11 [6,1,4,5,2,3] => 9 [6,1,4,5,3,2] => 9 [6,1,5,2,3,4] => 8 [6,1,5,2,4,3] => 9 [6,1,5,3,2,4] => 8 [6,1,5,3,4,2] => 10 [6,1,5,4,2,3] => 8 [6,1,5,4,3,2] => 8 [6,2,1,3,4,5] => 5 [6,2,1,3,5,4] => 6 [6,2,1,4,3,5] => 6 [6,2,1,4,5,3] => 8 [6,2,1,5,3,4] => 7 [6,2,1,5,4,3] => 7 [6,2,3,1,4,5] => 7 [6,2,3,1,5,4] => 8 [6,2,3,4,1,5] => 9 [6,2,3,4,5,1] => 11 [6,2,3,5,1,4] => 10 [6,2,3,5,4,1] => 10 [6,2,4,1,3,5] => 8 [6,2,4,1,5,3] => 11 [6,2,4,3,1,5] => 8 [6,2,4,3,5,1] => 12 [6,2,4,5,1,3] => 10 [6,2,4,5,3,1] => 10 [6,2,5,1,3,4] => 9 [6,2,5,1,4,3] => 10 [6,2,5,3,1,4] => 9 [6,2,5,3,4,1] => 11 [6,2,5,4,1,3] => 9 [6,2,5,4,3,1] => 9 [6,3,1,2,4,5] => 5 [6,3,1,2,5,4] => 6 [6,3,1,4,2,5] => 8 [6,3,1,4,5,2] => 10 [6,3,1,5,2,4] => 9 [6,3,1,5,4,2] => 9 [6,3,2,1,4,5] => 5 [6,3,2,1,5,4] => 6 [6,3,2,4,1,5] => 9 [6,3,2,4,5,1] => 11 [6,3,2,5,1,4] => 10 [6,3,2,5,4,1] => 10 [6,3,4,1,2,5] => 7 [6,3,4,1,5,2] => 12 [6,3,4,2,1,5] => 7 [6,3,4,2,5,1] => 13 [6,3,4,5,1,2] => 9 [6,3,4,5,2,1] => 9 [6,3,5,1,2,4] => 8 [6,3,5,1,4,2] => 11 [6,3,5,2,1,4] => 8 [6,3,5,2,4,1] => 12 [6,3,5,4,1,2] => 8 [6,3,5,4,2,1] => 8 [6,4,1,2,3,5] => 5 [6,4,1,2,5,3] => 8 [6,4,1,3,2,5] => 6 [6,4,1,3,5,2] => 10 [6,4,1,5,2,3] => 9 [6,4,1,5,3,2] => 9 [6,4,2,1,3,5] => 5 [6,4,2,1,5,3] => 8 [6,4,2,3,1,5] => 7 [6,4,2,3,5,1] => 11 [6,4,2,5,1,3] => 10 [6,4,2,5,3,1] => 10 [6,4,3,1,2,5] => 5 [6,4,3,1,5,2] => 10 [6,4,3,2,1,5] => 5 [6,4,3,2,5,1] => 11 [6,4,3,5,1,2] => 9 [6,4,3,5,2,1] => 9 [6,4,5,1,2,3] => 7 [6,4,5,1,3,2] => 8 [6,4,5,2,1,3] => 7 [6,4,5,2,3,1] => 9 [6,4,5,3,1,2] => 7 [6,4,5,3,2,1] => 7 [6,5,1,2,3,4] => 5 [6,5,1,2,4,3] => 6 [6,5,1,3,2,4] => 6 [6,5,1,3,4,2] => 8 [6,5,1,4,2,3] => 7 [6,5,1,4,3,2] => 7 [6,5,2,1,3,4] => 5 [6,5,2,1,4,3] => 6 [6,5,2,3,1,4] => 7 [6,5,2,3,4,1] => 9 [6,5,2,4,1,3] => 8 [6,5,2,4,3,1] => 8 [6,5,3,1,2,4] => 5 [6,5,3,1,4,2] => 8 [6,5,3,2,1,4] => 5 [6,5,3,2,4,1] => 9 [6,5,3,4,1,2] => 7 [6,5,3,4,2,1] => 7 [6,5,4,1,2,3] => 5 [6,5,4,1,3,2] => 6 [6,5,4,2,1,3] => 5 [6,5,4,2,3,1] => 7 [6,5,4,3,1,2] => 5 [6,5,4,3,2,1] => 5 [1,2,3,4,5,6,7] => 0 [1,2,3,4,5,7,6] => 1 [1,2,3,4,6,5,7] => 1 [1,2,3,4,6,7,5] => 3 [1,2,3,4,7,5,6] => 2 [1,2,3,4,7,6,5] => 2 [1,2,3,5,4,6,7] => 1 [1,2,3,5,4,7,6] => 2 [1,2,3,5,6,4,7] => 3 [1,2,3,5,6,7,4] => 5 [1,2,3,5,7,4,6] => 4 [1,2,3,5,7,6,4] => 4 [1,2,3,6,4,5,7] => 2 [1,2,3,6,4,7,5] => 5 [1,2,3,6,5,4,7] => 2 [1,2,3,6,5,7,4] => 6 [1,2,3,6,7,4,5] => 4 [1,2,3,6,7,5,4] => 4 [1,2,3,7,4,5,6] => 3 [1,2,3,7,4,6,5] => 4 [1,2,3,7,5,4,6] => 3 [1,2,3,7,5,6,4] => 5 [1,2,3,7,6,4,5] => 3 [1,2,3,7,6,5,4] => 3 [1,2,4,3,5,6,7] => 1 [1,2,4,3,5,7,6] => 2 [1,2,4,3,6,5,7] => 2 [1,2,4,3,6,7,5] => 4 [1,2,4,3,7,5,6] => 3 [1,2,4,3,7,6,5] => 3 [1,2,4,5,3,6,7] => 3 [1,2,4,5,3,7,6] => 4 [1,2,4,5,6,3,7] => 5 [1,2,4,5,6,7,3] => 7 [1,2,4,5,7,3,6] => 6 [1,2,4,5,7,6,3] => 6 [1,2,4,6,3,5,7] => 4 [1,2,4,6,3,7,5] => 7 [1,2,4,6,5,3,7] => 4 [1,2,4,6,5,7,3] => 8 [1,2,4,6,7,3,5] => 6 [1,2,4,6,7,5,3] => 6 [1,2,4,7,3,5,6] => 5 [1,2,4,7,3,6,5] => 6 [1,2,4,7,5,3,6] => 5 [1,2,4,7,5,6,3] => 7 [1,2,4,7,6,3,5] => 5 [1,2,4,7,6,5,3] => 5 [1,2,5,3,4,6,7] => 2 [1,2,5,3,4,7,6] => 3 [1,2,5,3,6,4,7] => 5 [1,2,5,3,6,7,4] => 7 [1,2,5,3,7,4,6] => 6 [1,2,5,3,7,6,4] => 6 [1,2,5,4,3,6,7] => 2 [1,2,5,4,3,7,6] => 3 [1,2,5,4,6,3,7] => 6 [1,2,5,4,6,7,3] => 8 [1,2,5,4,7,3,6] => 7 [1,2,5,4,7,6,3] => 7 [1,2,5,6,3,4,7] => 4 [1,2,5,6,3,7,4] => 9 [1,2,5,6,4,3,7] => 4 [1,2,5,6,4,7,3] => 10 [1,2,5,6,7,3,4] => 6 [1,2,5,6,7,4,3] => 6 [1,2,5,7,3,4,6] => 5 [1,2,5,7,3,6,4] => 8 [1,2,5,7,4,3,6] => 5 [1,2,5,7,4,6,3] => 9 [1,2,5,7,6,3,4] => 5 [1,2,5,7,6,4,3] => 5 [1,2,6,3,4,5,7] => 3 [1,2,6,3,4,7,5] => 6 [1,2,6,3,5,4,7] => 4 [1,2,6,3,5,7,4] => 8 [1,2,6,3,7,4,5] => 7 [1,2,6,3,7,5,4] => 7 [1,2,6,4,3,5,7] => 3 [1,2,6,4,3,7,5] => 6 [1,2,6,4,5,3,7] => 5 [1,2,6,4,5,7,3] => 9 [1,2,6,4,7,3,5] => 8 [1,2,6,4,7,5,3] => 8 [1,2,6,5,3,4,7] => 3 [1,2,6,5,3,7,4] => 8 [1,2,6,5,4,3,7] => 3 [1,2,6,5,4,7,3] => 9 [1,2,6,5,7,3,4] => 7 [1,2,6,5,7,4,3] => 7 [1,2,6,7,3,4,5] => 5 [1,2,6,7,3,5,4] => 6 [1,2,6,7,4,3,5] => 5 [1,2,6,7,4,5,3] => 7 [1,2,6,7,5,3,4] => 5 [1,2,6,7,5,4,3] => 5 [1,2,7,3,4,5,6] => 4 [1,2,7,3,4,6,5] => 5 [1,2,7,3,5,4,6] => 5 [1,2,7,3,5,6,4] => 7 [1,2,7,3,6,4,5] => 6 [1,2,7,3,6,5,4] => 6 [1,2,7,4,3,5,6] => 4 [1,2,7,4,3,6,5] => 5 [1,2,7,4,5,3,6] => 6 [1,2,7,4,5,6,3] => 8 [1,2,7,4,6,3,5] => 7 [1,2,7,4,6,5,3] => 7 [1,2,7,5,3,4,6] => 4 [1,2,7,5,3,6,4] => 7 [1,2,7,5,4,3,6] => 4 [1,2,7,5,4,6,3] => 8 [1,2,7,5,6,3,4] => 6 [1,2,7,5,6,4,3] => 6 [1,2,7,6,3,4,5] => 4 [1,2,7,6,3,5,4] => 5 [1,2,7,6,4,3,5] => 4 [1,2,7,6,4,5,3] => 6 [1,2,7,6,5,3,4] => 4 [1,2,7,6,5,4,3] => 4 [1,3,2,4,5,6,7] => 1 [1,3,2,4,5,7,6] => 2 [1,3,2,4,6,5,7] => 2 [1,3,2,4,6,7,5] => 4 [1,3,2,4,7,5,6] => 3 [1,3,2,4,7,6,5] => 3 [1,3,2,5,4,6,7] => 2 [1,3,2,5,4,7,6] => 3 [1,3,2,5,6,4,7] => 4 [1,3,2,5,6,7,4] => 6 [1,3,2,5,7,4,6] => 5 [1,3,2,5,7,6,4] => 5 [1,3,2,6,4,5,7] => 3 [1,3,2,6,4,7,5] => 6 [1,3,2,6,5,4,7] => 3 [1,3,2,6,5,7,4] => 7 [1,3,2,6,7,4,5] => 5 [1,3,2,6,7,5,4] => 5 [1,3,2,7,4,5,6] => 4 [1,3,2,7,4,6,5] => 5 [1,3,2,7,5,4,6] => 4 [1,3,2,7,5,6,4] => 6 [1,3,2,7,6,4,5] => 4 [1,3,2,7,6,5,4] => 4 [1,3,4,2,5,6,7] => 3 [1,3,4,2,5,7,6] => 4 [1,3,4,2,6,5,7] => 4 [1,3,4,2,6,7,5] => 6 [1,3,4,2,7,5,6] => 5 [1,3,4,2,7,6,5] => 5 [1,3,4,5,2,6,7] => 5 [1,3,4,5,2,7,6] => 6 [1,3,4,5,6,2,7] => 7 [1,3,4,5,6,7,2] => 9 [1,3,4,5,7,2,6] => 8 [1,3,4,5,7,6,2] => 8 [1,3,4,6,2,5,7] => 6 [1,3,4,6,2,7,5] => 9 [1,3,4,6,5,2,7] => 6 [1,3,4,6,5,7,2] => 10 [1,3,4,6,7,2,5] => 8 [1,3,4,6,7,5,2] => 8 [1,3,4,7,2,5,6] => 7 [1,3,4,7,2,6,5] => 8 [1,3,4,7,5,2,6] => 7 [1,3,4,7,5,6,2] => 9 [1,3,4,7,6,2,5] => 7 [1,3,4,7,6,5,2] => 7 [1,3,5,2,4,6,7] => 4 [1,3,5,2,4,7,6] => 5 [1,3,5,2,6,4,7] => 7 [1,3,5,2,6,7,4] => 9 [1,3,5,2,7,4,6] => 8 [1,3,5,2,7,6,4] => 8 [1,3,5,4,2,6,7] => 4 [1,3,5,4,2,7,6] => 5 [1,3,5,4,6,2,7] => 8 [1,3,5,4,6,7,2] => 10 [1,3,5,4,7,2,6] => 9 [1,3,5,4,7,6,2] => 9 [1,3,5,6,2,4,7] => 6 [1,3,5,6,2,7,4] => 11 [1,3,5,6,4,2,7] => 6 [1,3,5,6,4,7,2] => 12 [1,3,5,6,7,2,4] => 8 [1,3,5,6,7,4,2] => 8 [1,3,5,7,2,4,6] => 7 [1,3,5,7,2,6,4] => 10 [1,3,5,7,4,2,6] => 7 [1,3,5,7,4,6,2] => 11 [1,3,5,7,6,2,4] => 7 [1,3,5,7,6,4,2] => 7 [1,3,6,2,4,5,7] => 5 [1,3,6,2,4,7,5] => 8 [1,3,6,2,5,4,7] => 6 [1,3,6,2,5,7,4] => 10 [1,3,6,2,7,4,5] => 9 [1,3,6,2,7,5,4] => 9 [1,3,6,4,2,5,7] => 5 [1,3,6,4,2,7,5] => 8 [1,3,6,4,5,2,7] => 7 [1,3,6,4,5,7,2] => 11 [1,3,6,4,7,2,5] => 10 [1,3,6,4,7,5,2] => 10 [1,3,6,5,2,4,7] => 5 [1,3,6,5,2,7,4] => 10 [1,3,6,5,4,2,7] => 5 [1,3,6,5,4,7,2] => 11 [1,3,6,5,7,2,4] => 9 [1,3,6,5,7,4,2] => 9 [1,3,6,7,2,4,5] => 7 [1,3,6,7,2,5,4] => 8 [1,3,6,7,4,2,5] => 7 [1,3,6,7,4,5,2] => 9 [1,3,6,7,5,2,4] => 7 [1,3,6,7,5,4,2] => 7 [1,3,7,2,4,5,6] => 6 [1,3,7,2,4,6,5] => 7 [1,3,7,2,5,4,6] => 7 [1,3,7,2,5,6,4] => 9 [1,3,7,2,6,4,5] => 8 [1,3,7,2,6,5,4] => 8 [1,3,7,4,2,5,6] => 6 [1,3,7,4,2,6,5] => 7 [1,3,7,4,5,2,6] => 8 [1,3,7,4,5,6,2] => 10 [1,3,7,4,6,2,5] => 9 [1,3,7,4,6,5,2] => 9 [1,3,7,5,2,4,6] => 6 [1,3,7,5,2,6,4] => 9 [1,3,7,5,4,2,6] => 6 [1,3,7,5,4,6,2] => 10 [1,3,7,5,6,2,4] => 8 [1,3,7,5,6,4,2] => 8 [1,3,7,6,2,4,5] => 6 [1,3,7,6,2,5,4] => 7 [1,3,7,6,4,2,5] => 6 [1,3,7,6,4,5,2] => 8 [1,3,7,6,5,2,4] => 6 [1,3,7,6,5,4,2] => 6 [1,4,2,3,5,6,7] => 2 [1,4,2,3,5,7,6] => 3 [1,4,2,3,6,5,7] => 3 [1,4,2,3,6,7,5] => 5 [1,4,2,3,7,5,6] => 4 [1,4,2,3,7,6,5] => 4 [1,4,2,5,3,6,7] => 5 [1,4,2,5,3,7,6] => 6 [1,4,2,5,6,3,7] => 7 [1,4,2,5,6,7,3] => 9 [1,4,2,5,7,3,6] => 8 [1,4,2,5,7,6,3] => 8 [1,4,2,6,3,5,7] => 6 [1,4,2,6,3,7,5] => 9 [1,4,2,6,5,3,7] => 6 [1,4,2,6,5,7,3] => 10 [1,4,2,6,7,3,5] => 8 [1,4,2,6,7,5,3] => 8 [1,4,2,7,3,5,6] => 7 [1,4,2,7,3,6,5] => 8 [1,4,2,7,5,3,6] => 7 [1,4,2,7,5,6,3] => 9 [1,4,2,7,6,3,5] => 7 [1,4,2,7,6,5,3] => 7 [1,4,3,2,5,6,7] => 2 [1,4,3,2,5,7,6] => 3 [1,4,3,2,6,5,7] => 3 [1,4,3,2,6,7,5] => 5 [1,4,3,2,7,5,6] => 4 [1,4,3,2,7,6,5] => 4 [1,4,3,5,2,6,7] => 6 [1,4,3,5,2,7,6] => 7 [1,4,3,5,6,2,7] => 8 [1,4,3,5,6,7,2] => 10 [1,4,3,5,7,2,6] => 9 [1,4,3,5,7,6,2] => 9 [1,4,3,6,2,5,7] => 7 [1,4,3,6,2,7,5] => 10 [1,4,3,6,5,2,7] => 7 [1,4,3,6,5,7,2] => 11 [1,4,3,6,7,2,5] => 9 [1,4,3,6,7,5,2] => 9 [1,4,3,7,2,5,6] => 8 [1,4,3,7,2,6,5] => 9 [1,4,3,7,5,2,6] => 8 [1,4,3,7,5,6,2] => 10 [1,4,3,7,6,2,5] => 8 [1,4,3,7,6,5,2] => 8 [1,4,5,2,3,6,7] => 4 [1,4,5,2,3,7,6] => 5 [1,4,5,2,6,3,7] => 9 [1,4,5,2,6,7,3] => 11 [1,4,5,2,7,3,6] => 10 [1,4,5,2,7,6,3] => 10 [1,4,5,3,2,6,7] => 4 [1,4,5,3,2,7,6] => 5 [1,4,5,3,6,2,7] => 10 [1,4,5,3,6,7,2] => 12 [1,4,5,3,7,2,6] => 11 [1,4,5,3,7,6,2] => 11 [1,4,5,6,2,3,7] => 6 [1,4,5,6,2,7,3] => 13 [1,4,5,6,3,2,7] => 6 [1,4,5,6,3,7,2] => 14 [1,4,5,6,7,2,3] => 8 [1,4,5,6,7,3,2] => 8 [1,4,5,7,2,3,6] => 7 [1,4,5,7,2,6,3] => 12 [1,4,5,7,3,2,6] => 7 [1,4,5,7,3,6,2] => 13 [1,4,5,7,6,2,3] => 7 [1,4,5,7,6,3,2] => 7 [1,4,6,2,3,5,7] => 5 [1,4,6,2,3,7,5] => 8 [1,4,6,2,5,3,7] => 8 [1,4,6,2,5,7,3] => 12 [1,4,6,2,7,3,5] => 11 [1,4,6,2,7,5,3] => 11 [1,4,6,3,2,5,7] => 5 [1,4,6,3,2,7,5] => 8 [1,4,6,3,5,2,7] => 9 [1,4,6,3,5,7,2] => 13 [1,4,6,3,7,2,5] => 12 [1,4,6,3,7,5,2] => 12 [1,4,6,5,2,3,7] => 5 [1,4,6,5,2,7,3] => 12 [1,4,6,5,3,2,7] => 5 [1,4,6,5,3,7,2] => 13 ----------------------------------------------------------------------------- Created: May 16, 2017 at 16:42 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Jan 11, 2018 at 08:01 by Martin Rubey