***************************************************************************** * 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: St001402 ----------------------------------------------------------------------------- Collection: Permutations ----------------------------------------------------------------------------- Description: The number of separators in a permutation. Let $\sigma$ be a permutation. Then $\sigma_i$ is a vertical separator if $|\sigma_{i-1} - \sigma_{i+1}| = 1$, and $i$ is a horizontal separator, if it is a vertical separator of $\sigma^{-1}$. The set of separators is the union of the set of the vertical and the set of the horizontal separators. ----------------------------------------------------------------------------- References: [1] Bagno, E., Eisenberg, E., Reches, S., Sigron, M. Separators - a new statistic for permutations [[arXiv:1905.12364]] ----------------------------------------------------------------------------- Code: def statistic(pi): """ sage: oeis([sum(1 for pi in Permutations(n) if not statistic(pi)) for n in range(1,7)]) 0: A137774: Number of ways to place n nonattacking empresses on an n X n board. """ return len(separators(pi)) def vertical_separators(sigma): """ sage: list(vertical_separators(sigma)) [3, 2, 6, 7] """ n = len(sigma) for i in range(n): if 0 < i < n-1 and abs(sigma[i-1]-sigma[i+1]) == 1: yield sigma[i] def horizontal_separators(sigma): """ sage: list(horizontal_separators(sigma)) [2, 3, 5, 8] """ sigma_inv = sigma.inverse() for i in vertical_separators(sigma_inv): yield sigma_inv(i) def separators(sigma): """ sage: separators(sigma) [2, 3, 5, 6, 7, 8] """ return list(set(horizontal_separators(sigma)).union(set(vertical_separators(sigma)))) ----------------------------------------------------------------------------- Statistic values: [1] => 0 [1,2] => 0 [2,1] => 0 [1,2,3] => 0 [1,3,2] => 2 [2,1,3] => 2 [2,3,1] => 1 [3,1,2] => 1 [3,2,1] => 0 [1,2,3,4] => 0 [1,2,4,3] => 2 [1,3,2,4] => 2 [1,3,4,2] => 2 [1,4,2,3] => 2 [1,4,3,2] => 0 [2,1,3,4] => 2 [2,1,4,3] => 0 [2,3,1,4] => 2 [2,3,4,1] => 0 [2,4,1,3] => 4 [2,4,3,1] => 2 [3,1,2,4] => 2 [3,1,4,2] => 4 [3,2,1,4] => 0 [3,2,4,1] => 2 [3,4,1,2] => 0 [3,4,2,1] => 1 [4,1,2,3] => 0 [4,1,3,2] => 2 [4,2,1,3] => 2 [4,2,3,1] => 2 [4,3,1,2] => 1 [4,3,2,1] => 0 [1,2,3,4,5] => 0 [1,2,3,5,4] => 2 [1,2,4,3,5] => 2 [1,2,4,5,3] => 2 [1,2,5,3,4] => 2 [1,2,5,4,3] => 0 [1,3,2,4,5] => 2 [1,3,2,5,4] => 2 [1,3,4,2,5] => 3 [1,3,4,5,2] => 1 [1,3,5,2,4] => 4 [1,3,5,4,2] => 3 [1,4,2,3,5] => 3 [1,4,2,5,3] => 4 [1,4,3,2,5] => 0 [1,4,3,5,2] => 2 [1,4,5,2,3] => 0 [1,4,5,3,2] => 1 [1,5,2,3,4] => 1 [1,5,2,4,3] => 3 [1,5,3,2,4] => 2 [1,5,3,4,2] => 2 [1,5,4,2,3] => 1 [1,5,4,3,2] => 0 [2,1,3,4,5] => 2 [2,1,3,5,4] => 4 [2,1,4,3,5] => 2 [2,1,4,5,3] => 1 [2,1,5,3,4] => 1 [2,1,5,4,3] => 0 [2,3,1,4,5] => 2 [2,3,1,5,4] => 1 [2,3,4,1,5] => 1 [2,3,4,5,1] => 0 [2,3,5,1,4] => 2 [2,3,5,4,1] => 2 [2,4,1,3,5] => 4 [2,4,1,5,3] => 2 [2,4,3,1,5] => 2 [2,4,3,5,1] => 3 [2,4,5,1,3] => 2 [2,4,5,3,1] => 3 [2,5,1,3,4] => 2 [2,5,1,4,3] => 2 [2,5,3,1,4] => 4 [2,5,3,4,1] => 3 [2,5,4,1,3] => 2 [2,5,4,3,1] => 1 [3,1,2,4,5] => 2 [3,1,2,5,4] => 1 [3,1,4,2,5] => 4 [3,1,4,5,2] => 2 [3,1,5,2,4] => 2 [3,1,5,4,2] => 2 [3,2,1,4,5] => 0 [3,2,1,5,4] => 0 [3,2,4,1,5] => 3 [3,2,4,5,1] => 2 [3,2,5,1,4] => 2 [3,2,5,4,1] => 0 [3,4,1,2,5] => 0 [3,4,1,5,2] => 2 [3,4,2,1,5] => 1 [3,4,2,5,1] => 3 [3,4,5,1,2] => 0 [3,4,5,2,1] => 0 [3,5,1,2,4] => 2 [3,5,1,4,2] => 3 [3,5,2,1,4] => 2 [3,5,2,4,1] => 3 [3,5,4,1,2] => 2 [3,5,4,2,1] => 2 [4,1,2,3,5] => 1 [4,1,2,5,3] => 2 [4,1,3,2,5] => 2 [4,1,3,5,2] => 4 [4,1,5,2,3] => 2 [4,1,5,3,2] => 2 [4,2,1,3,5] => 3 [4,2,1,5,3] => 2 [4,2,3,1,5] => 2 [4,2,3,5,1] => 3 [4,2,5,1,3] => 3 [4,2,5,3,1] => 3 [4,3,1,2,5] => 1 [4,3,1,5,2] => 2 [4,3,2,1,5] => 0 [4,3,2,5,1] => 1 [4,3,5,1,2] => 2 [4,3,5,2,1] => 2 [4,5,1,2,3] => 0 [4,5,1,3,2] => 2 [4,5,2,1,3] => 2 [4,5,2,3,1] => 2 [4,5,3,1,2] => 4 [4,5,3,2,1] => 1 [5,1,2,3,4] => 0 [5,1,2,4,3] => 2 [5,1,3,2,4] => 3 [5,1,3,4,2] => 3 [5,1,4,2,3] => 3 [5,1,4,3,2] => 1 [5,2,1,3,4] => 2 [5,2,1,4,3] => 0 [5,2,3,1,4] => 3 [5,2,3,4,1] => 0 [5,2,4,1,3] => 3 [5,2,4,3,1] => 3 [5,3,1,2,4] => 3 [5,3,1,4,2] => 3 [5,3,2,1,4] => 1 [5,3,2,4,1] => 3 [5,3,4,1,2] => 2 [5,3,4,2,1] => 3 [5,4,1,2,3] => 0 [5,4,1,3,2] => 2 [5,4,2,1,3] => 2 [5,4,2,3,1] => 3 [5,4,3,1,2] => 1 [5,4,3,2,1] => 0 [1,2,3,4,5,6] => 0 [1,2,3,4,6,5] => 2 [1,2,3,5,4,6] => 2 [1,2,3,5,6,4] => 2 [1,2,3,6,4,5] => 2 [1,2,3,6,5,4] => 0 [1,2,4,3,5,6] => 2 [1,2,4,3,6,5] => 2 [1,2,4,5,3,6] => 3 [1,2,4,5,6,3] => 1 [1,2,4,6,3,5] => 4 [1,2,4,6,5,3] => 3 [1,2,5,3,4,6] => 3 [1,2,5,3,6,4] => 4 [1,2,5,4,3,6] => 0 [1,2,5,4,6,3] => 2 [1,2,5,6,3,4] => 0 [1,2,5,6,4,3] => 1 [1,2,6,3,4,5] => 1 [1,2,6,3,5,4] => 3 [1,2,6,4,3,5] => 2 [1,2,6,4,5,3] => 2 [1,2,6,5,3,4] => 1 [1,2,6,5,4,3] => 0 [1,3,2,4,5,6] => 2 [1,3,2,4,6,5] => 4 [1,3,2,5,4,6] => 4 [1,3,2,5,6,4] => 3 [1,3,2,6,4,5] => 3 [1,3,2,6,5,4] => 2 [1,3,4,2,5,6] => 3 [1,3,4,2,6,5] => 2 [1,3,4,5,2,6] => 2 [1,3,4,5,6,2] => 1 [1,3,4,6,2,5] => 3 [1,3,4,6,5,2] => 3 [1,3,5,2,4,6] => 4 [1,3,5,2,6,4] => 3 [1,3,5,4,2,6] => 3 [1,3,5,4,6,2] => 3 [1,3,5,6,2,4] => 3 [1,3,5,6,4,2] => 4 [1,3,6,2,4,5] => 3 [1,3,6,2,5,4] => 2 [1,3,6,4,2,5] => 4 [1,3,6,4,5,2] => 4 [1,3,6,5,2,4] => 3 [1,3,6,5,4,2] => 2 [1,4,2,3,5,6] => 3 [1,4,2,3,6,5] => 2 [1,4,2,5,3,6] => 4 [1,4,2,5,6,3] => 3 [1,4,2,6,3,5] => 3 [1,4,2,6,5,3] => 2 [1,4,3,2,5,6] => 0 [1,4,3,2,6,5] => 0 [1,4,3,5,2,6] => 3 [1,4,3,5,6,2] => 2 [1,4,3,6,2,5] => 2 [1,4,3,6,5,2] => 0 [1,4,5,2,3,6] => 0 [1,4,5,2,6,3] => 2 [1,4,5,3,2,6] => 1 [1,4,5,3,6,2] => 3 [1,4,5,6,2,3] => 0 [1,4,5,6,3,2] => 0 [1,4,6,2,3,5] => 2 [1,4,6,2,5,3] => 3 [1,4,6,3,2,5] => 2 [1,4,6,3,5,2] => 3 [1,4,6,5,2,3] => 2 [1,4,6,5,3,2] => 2 [1,5,2,3,4,6] => 2 [1,5,2,3,6,4] => 3 [1,5,2,4,3,6] => 3 [1,5,2,4,6,3] => 4 [1,5,2,6,3,4] => 3 [1,5,2,6,4,3] => 3 [1,5,3,2,4,6] => 3 [1,5,3,2,6,4] => 2 [1,5,3,4,2,6] => 2 [1,5,3,4,6,2] => 3 [1,5,3,6,2,4] => 3 [1,5,3,6,4,2] => 3 [1,5,4,2,3,6] => 1 [1,5,4,2,6,3] => 2 [1,5,4,3,2,6] => 0 [1,5,4,3,6,2] => 1 [1,5,4,6,2,3] => 2 [1,5,4,6,3,2] => 2 [1,5,6,2,3,4] => 0 [1,5,6,2,4,3] => 2 [1,5,6,3,2,4] => 2 [1,5,6,3,4,2] => 2 [1,5,6,4,2,3] => 4 [1,5,6,4,3,2] => 1 [1,6,2,3,4,5] => 1 [1,6,2,3,5,4] => 3 [1,6,2,4,3,5] => 3 [1,6,2,4,5,3] => 4 [1,6,2,5,3,4] => 4 [1,6,2,5,4,3] => 2 [1,6,3,2,4,5] => 2 [1,6,3,2,5,4] => 0 [1,6,3,4,2,5] => 3 [1,6,3,4,5,2] => 0 [1,6,3,5,2,4] => 3 [1,6,3,5,4,2] => 3 [1,6,4,2,3,5] => 3 [1,6,4,2,5,3] => 3 [1,6,4,3,2,5] => 1 [1,6,4,3,5,2] => 3 [1,6,4,5,2,3] => 2 [1,6,4,5,3,2] => 3 [1,6,5,2,3,4] => 0 [1,6,5,2,4,3] => 2 [1,6,5,3,2,4] => 2 [1,6,5,3,4,2] => 3 [1,6,5,4,2,3] => 1 [1,6,5,4,3,2] => 0 [2,1,3,4,5,6] => 2 [2,1,3,4,6,5] => 4 [2,1,3,5,4,6] => 4 [2,1,3,5,6,4] => 4 [2,1,3,6,4,5] => 4 [2,1,3,6,5,4] => 2 [2,1,4,3,5,6] => 2 [2,1,4,3,6,5] => 0 [2,1,4,5,3,6] => 2 [2,1,4,5,6,3] => 0 [2,1,4,6,3,5] => 4 [2,1,4,6,5,3] => 2 [2,1,5,3,4,6] => 2 [2,1,5,3,6,4] => 4 [2,1,5,4,3,6] => 0 [2,1,5,4,6,3] => 2 [2,1,5,6,3,4] => 0 [2,1,5,6,4,3] => 1 [2,1,6,3,4,5] => 0 [2,1,6,3,5,4] => 2 [2,1,6,4,3,5] => 2 [2,1,6,4,5,3] => 2 [2,1,6,5,3,4] => 1 [2,1,6,5,4,3] => 0 [2,3,1,4,5,6] => 2 [2,3,1,4,6,5] => 4 [2,3,1,5,4,6] => 3 [2,3,1,5,6,4] => 2 [2,3,1,6,4,5] => 2 [2,3,1,6,5,4] => 1 [2,3,4,1,5,6] => 1 [2,3,4,1,6,5] => 0 [2,3,4,5,1,6] => 1 [2,3,4,5,6,1] => 0 [2,3,4,6,1,5] => 2 [2,3,4,6,5,1] => 2 [2,3,5,1,4,6] => 3 [2,3,5,1,6,4] => 3 [2,3,5,4,1,6] => 2 [2,3,5,4,6,1] => 3 [2,3,5,6,1,4] => 1 [2,3,5,6,4,1] => 3 [2,3,6,1,4,5] => 0 [2,3,6,1,5,4] => 1 [2,3,6,4,1,5] => 3 [2,3,6,4,5,1] => 3 [2,3,6,5,1,4] => 1 [2,3,6,5,4,1] => 0 [2,4,1,3,5,6] => 4 [2,4,1,3,6,5] => 4 [2,4,1,5,3,6] => 3 [2,4,1,5,6,3] => 3 [2,4,1,6,3,5] => 4 [2,4,1,6,5,3] => 2 [2,4,3,1,5,6] => 2 [2,4,3,1,6,5] => 2 [2,4,3,5,1,6] => 3 [2,4,3,5,6,1] => 3 [2,4,3,6,1,5] => 3 [2,4,3,6,5,1] => 2 [2,4,5,1,3,6] => 2 [2,4,5,1,6,3] => 2 [2,4,5,3,1,6] => 3 [2,4,5,3,6,1] => 4 [2,4,5,6,1,3] => 2 [2,4,5,6,3,1] => 2 [2,4,6,1,3,5] => 4 [2,4,6,1,5,3] => 3 [2,4,6,3,1,5] => 4 [2,4,6,3,5,1] => 5 [2,4,6,5,1,3] => 4 [2,4,6,5,3,1] => 4 [2,5,1,3,4,6] => 3 [2,5,1,3,6,4] => 4 [2,5,1,4,3,6] => 2 [2,5,1,4,6,3] => 3 [2,5,1,6,3,4] => 2 [2,5,1,6,4,3] => 2 [2,5,3,1,4,6] => 4 [2,5,3,1,6,4] => 3 [2,5,3,4,1,6] => 3 [2,5,3,4,6,1] => 4 [2,5,3,6,1,4] => 3 [2,5,3,6,4,1] => 5 [2,5,4,1,3,6] => 2 [2,5,4,1,6,3] => 0 [2,5,4,3,1,6] => 1 [2,5,4,3,6,1] => 0 [2,5,4,6,1,3] => 3 [2,5,4,6,3,1] => 3 [2,5,6,1,3,4] => 1 [2,5,6,1,4,3] => 0 [2,5,6,3,1,4] => 2 [2,5,6,3,4,1] => 0 [2,5,6,4,1,3] => 3 [2,5,6,4,3,1] => 2 [2,6,1,3,4,5] => 2 [2,6,1,3,5,4] => 4 [2,6,1,4,3,5] => 3 [2,6,1,4,5,3] => 3 [2,6,1,5,3,4] => 4 [2,6,1,5,4,3] => 2 [2,6,3,1,4,5] => 3 [2,6,3,1,5,4] => 2 [2,6,3,4,1,5] => 2 [2,6,3,4,5,1] => 1 [2,6,3,5,1,4] => 4 [2,6,3,5,4,1] => 4 [2,6,4,1,3,5] => 4 [2,6,4,1,5,3] => 3 [2,6,4,3,1,5] => 2 [2,6,4,3,5,1] => 3 [2,6,4,5,1,3] => 3 [2,6,4,5,3,1] => 4 [2,6,5,1,3,4] => 1 [2,6,5,1,4,3] => 1 [2,6,5,3,1,4] => 3 [2,6,5,3,4,1] => 1 [2,6,5,4,1,3] => 2 [2,6,5,4,3,1] => 1 [3,1,2,4,5,6] => 2 [3,1,2,4,6,5] => 4 [3,1,2,5,4,6] => 3 [3,1,2,5,6,4] => 2 [3,1,2,6,4,5] => 2 [3,1,2,6,5,4] => 1 [3,1,4,2,5,6] => 4 [3,1,4,2,6,5] => 4 [3,1,4,5,2,6] => 3 [3,1,4,5,6,2] => 2 [3,1,4,6,2,5] => 4 [3,1,4,6,5,2] => 4 [3,1,5,2,4,6] => 3 [3,1,5,2,6,4] => 4 [3,1,5,4,2,6] => 2 [3,1,5,4,6,2] => 3 [3,1,5,6,2,4] => 2 [3,1,5,6,4,2] => 4 [3,1,6,2,4,5] => 3 [3,1,6,2,5,4] => 2 [3,1,6,4,2,5] => 3 [3,1,6,4,5,2] => 3 [3,1,6,5,2,4] => 2 [3,1,6,5,4,2] => 2 [3,2,1,4,5,6] => 0 [3,2,1,4,6,5] => 2 [3,2,1,5,4,6] => 2 [3,2,1,5,6,4] => 1 [3,2,1,6,4,5] => 1 [3,2,1,6,5,4] => 0 [3,2,4,1,5,6] => 3 [3,2,4,1,6,5] => 2 [3,2,4,5,1,6] => 3 [3,2,4,5,6,1] => 2 [3,2,4,6,1,5] => 4 [3,2,4,6,5,1] => 3 [3,2,5,1,4,6] => 2 [3,2,5,1,6,4] => 2 [3,2,5,4,1,6] => 0 [3,2,5,4,6,1] => 2 [3,2,5,6,1,4] => 0 [3,2,5,6,4,1] => 2 [3,2,6,1,4,5] => 1 [3,2,6,1,5,4] => 2 [3,2,6,4,1,5] => 2 [3,2,6,4,5,1] => 2 [3,2,6,5,1,4] => 1 [3,2,6,5,4,1] => 0 [3,4,1,2,5,6] => 0 [3,4,1,2,6,5] => 0 [3,4,1,5,2,6] => 3 [3,4,1,5,6,2] => 1 [3,4,1,6,2,5] => 2 [3,4,1,6,5,2] => 0 [3,4,2,1,5,6] => 1 [3,4,2,1,6,5] => 1 [3,4,2,5,1,6] => 4 [3,4,2,5,6,1] => 3 [3,4,2,6,1,5] => 4 [3,4,2,6,5,1] => 2 [3,4,5,1,2,6] => 0 [3,4,5,1,6,2] => 2 [3,4,5,2,1,6] => 0 [3,4,5,2,6,1] => 2 [3,4,5,6,1,2] => 0 [3,4,5,6,2,1] => 0 [3,4,6,1,2,5] => 1 [3,4,6,1,5,2] => 2 [3,4,6,2,1,5] => 1 [3,4,6,2,5,1] => 2 [3,4,6,5,1,2] => 2 [3,4,6,5,2,1] => 2 [3,5,1,2,4,6] => 3 [3,5,1,2,6,4] => 2 [3,5,1,4,2,6] => 3 [3,5,1,4,6,2] => 3 [3,5,1,6,2,4] => 4 [3,5,1,6,4,2] => 4 [3,5,2,1,4,6] => 3 [3,5,2,1,6,4] => 2 [3,5,2,4,1,6] => 3 [3,5,2,4,6,1] => 5 [3,5,2,6,1,4] => 4 [3,5,2,6,4,1] => 3 [3,5,4,1,2,6] => 2 [3,5,4,1,6,2] => 3 [3,5,4,2,1,6] => 2 [3,5,4,2,6,1] => 3 [3,5,4,6,1,2] => 4 [3,5,4,6,2,1] => 3 [3,5,6,1,2,4] => 2 [3,5,6,1,4,2] => 2 [3,5,6,2,1,4] => 1 [3,5,6,2,4,1] => 3 [3,5,6,4,1,2] => 2 [3,5,6,4,2,1] => 3 [3,6,1,2,4,5] => 1 [3,6,1,2,5,4] => 0 [3,6,1,4,2,5] => 3 [3,6,1,4,5,2] => 0 [3,6,1,5,2,4] => 4 [3,6,1,5,4,2] => 2 [3,6,2,1,4,5] => 1 [3,6,2,1,5,4] => 1 [3,6,2,4,1,5] => 4 [3,6,2,4,5,1] => 1 [3,6,2,5,1,4] => 4 [3,6,2,5,4,1] => 2 [3,6,4,1,2,5] => 2 [3,6,4,1,5,2] => 3 [3,6,4,2,1,5] => 3 [3,6,4,2,5,1] => 3 [3,6,4,5,1,2] => 3 [3,6,4,5,2,1] => 3 [3,6,5,1,2,4] => 1 [3,6,5,1,4,2] => 2 [3,6,5,2,1,4] => 0 [3,6,5,2,4,1] => 3 [3,6,5,4,1,2] => 0 [3,6,5,4,2,1] => 1 [4,1,2,3,5,6] => 1 [4,1,2,3,6,5] => 0 [4,1,2,5,3,6] => 3 [4,1,2,5,6,3] => 0 [4,1,2,6,3,5] => 3 [4,1,2,6,5,3] => 1 [4,1,3,2,5,6] => 2 [4,1,3,2,6,5] => 2 [4,1,3,5,2,6] => 4 [4,1,3,5,6,2] => 3 [4,1,3,6,2,5] => 3 [4,1,3,6,5,2] => 2 [4,1,5,2,3,6] => 2 [4,1,5,2,6,3] => 4 [4,1,5,3,2,6] => 2 [4,1,5,3,6,2] => 4 [4,1,5,6,2,3] => 1 [4,1,5,6,3,2] => 1 [4,1,6,2,3,5] => 2 [4,1,6,2,5,3] => 3 [4,1,6,3,2,5] => 0 [4,1,6,3,5,2] => 3 [4,1,6,5,2,3] => 0 [4,1,6,5,3,2] => 1 [4,2,1,3,5,6] => 3 [4,2,1,3,6,5] => 2 [4,2,1,5,3,6] => 2 [4,2,1,5,6,3] => 1 [4,2,1,6,3,5] => 2 [4,2,1,6,5,3] => 2 [4,2,3,1,5,6] => 2 [4,2,3,1,6,5] => 2 [4,2,3,5,1,6] => 4 [4,2,3,5,6,1] => 3 [4,2,3,6,1,5] => 3 [4,2,3,6,5,1] => 2 [4,2,5,1,3,6] => 3 [4,2,5,1,6,3] => 3 [4,2,5,3,1,6] => 3 [4,2,5,3,6,1] => 5 [4,2,5,6,1,3] => 2 [4,2,5,6,3,1] => 2 [4,2,6,1,3,5] => 3 [4,2,6,1,5,3] => 4 [4,2,6,3,1,5] => 3 [4,2,6,3,5,1] => 3 [4,2,6,5,1,3] => 2 [4,2,6,5,3,1] => 3 [4,3,1,2,5,6] => 1 [4,3,1,2,6,5] => 1 [4,3,1,5,2,6] => 3 [4,3,1,5,6,2] => 1 [4,3,1,6,2,5] => 2 [4,3,1,6,5,2] => 1 [4,3,2,1,5,6] => 0 [4,3,2,1,6,5] => 0 [4,3,2,5,1,6] => 2 [4,3,2,5,6,1] => 0 [4,3,2,6,1,5] => 2 [4,3,2,6,5,1] => 0 [4,3,5,1,2,6] => 2 [4,3,5,1,6,2] => 4 [4,3,5,2,1,6] => 2 [4,3,5,2,6,1] => 4 [4,3,5,6,1,2] => 2 [4,3,5,6,2,1] => 2 [4,3,6,1,2,5] => 0 [4,3,6,1,5,2] => 2 [4,3,6,2,1,5] => 1 [4,3,6,2,5,1] => 3 [4,3,6,5,1,2] => 0 [4,3,6,5,2,1] => 0 [4,5,1,2,3,6] => 0 [4,5,1,2,6,3] => 1 [4,5,1,3,2,6] => 2 [4,5,1,3,6,2] => 2 [4,5,1,6,2,3] => 2 [4,5,1,6,3,2] => 1 [4,5,2,1,3,6] => 2 [4,5,2,1,6,3] => 0 [4,5,2,3,1,6] => 2 [4,5,2,3,6,1] => 0 [4,5,2,6,1,3] => 2 [4,5,2,6,3,1] => 3 [4,5,3,1,2,6] => 4 [4,5,3,1,6,2] => 3 [4,5,3,2,1,6] => 1 [4,5,3,2,6,1] => 2 [4,5,3,6,1,2] => 2 [4,5,3,6,2,1] => 3 [4,5,6,1,2,3] => 0 [4,5,6,1,3,2] => 1 [4,5,6,2,1,3] => 1 [4,5,6,2,3,1] => 2 [4,5,6,3,1,2] => 2 [4,5,6,3,2,1] => 0 [4,6,1,2,3,5] => 2 [4,6,1,2,5,3] => 2 [4,6,1,3,2,5] => 3 [4,6,1,3,5,2] => 3 [4,6,1,5,2,3] => 2 [4,6,1,5,3,2] => 2 [4,6,2,1,3,5] => 4 [4,6,2,1,5,3] => 2 [4,6,2,3,1,5] => 3 [4,6,2,3,5,1] => 2 [4,6,2,5,1,3] => 4 [4,6,2,5,3,1] => 4 [4,6,3,1,2,5] => 3 [4,6,3,1,5,2] => 3 [4,6,3,2,1,5] => 2 [4,6,3,2,5,1] => 2 [4,6,3,5,1,2] => 4 [4,6,3,5,2,1] => 4 [4,6,5,1,2,3] => 1 [4,6,5,1,3,2] => 4 [4,6,5,2,1,3] => 2 [4,6,5,2,3,1] => 4 [4,6,5,3,1,2] => 5 [4,6,5,3,2,1] => 2 [5,1,2,3,4,6] => 1 [5,1,2,3,6,4] => 2 [5,1,2,4,3,6] => 2 [5,1,2,4,6,3] => 3 [5,1,2,6,3,4] => 1 [5,1,2,6,4,3] => 1 [5,1,3,2,4,6] => 3 [5,1,3,2,6,4] => 3 [5,1,3,4,2,6] => 3 [5,1,3,4,6,2] => 2 [5,1,3,6,2,4] => 3 [5,1,3,6,4,2] => 4 [5,1,4,2,3,6] => 3 [5,1,4,2,6,3] => 4 [5,1,4,3,2,6] => 1 [5,1,4,3,6,2] => 2 [5,1,4,6,2,3] => 2 [5,1,4,6,3,2] => 3 [5,1,6,2,3,4] => 2 [5,1,6,2,4,3] => 4 [5,1,6,3,2,4] => 3 [5,1,6,3,4,2] => 3 [5,1,6,4,2,3] => 3 [5,1,6,4,3,2] => 2 [5,2,1,3,4,6] => 3 [5,2,1,3,6,4] => 4 [5,2,1,4,3,6] => 0 [5,2,1,4,6,3] => 2 [5,2,1,6,3,4] => 0 [5,2,1,6,4,3] => 1 [5,2,3,1,4,6] => 4 [5,2,3,1,6,4] => 3 [5,2,3,4,1,6] => 0 [5,2,3,4,6,1] => 1 [5,2,3,6,1,4] => 0 [5,2,3,6,4,1] => 1 [5,2,4,1,3,6] => 3 [5,2,4,1,6,3] => 3 [5,2,4,3,1,6] => 3 [5,2,4,3,6,1] => 3 [5,2,4,6,1,3] => 3 [5,2,4,6,3,1] => 3 [5,2,6,1,3,4] => 2 [5,2,6,1,4,3] => 2 [5,2,6,3,1,4] => 3 [5,2,6,3,4,1] => 2 [5,2,6,4,1,3] => 3 [5,2,6,4,3,1] => 2 [5,3,1,2,4,6] => 4 [5,3,1,2,6,4] => 4 [5,3,1,4,2,6] => 3 [5,3,1,4,6,2] => 4 [5,3,1,6,2,4] => 4 [5,3,1,6,4,2] => 4 [5,3,2,1,4,6] => 2 [5,3,2,1,6,4] => 2 [5,3,2,4,1,6] => 3 [5,3,2,4,6,1] => 4 [5,3,2,6,1,4] => 2 [5,3,2,6,4,1] => 2 [5,3,4,1,2,6] => 2 [5,3,4,1,6,2] => 3 [5,3,4,2,1,6] => 3 [5,3,4,2,6,1] => 4 [5,3,4,6,1,2] => 3 [5,3,4,6,2,1] => 3 [5,3,6,1,2,4] => 2 [5,3,6,1,4,2] => 4 [5,3,6,2,1,4] => 2 [5,3,6,2,4,1] => 4 [5,3,6,4,1,2] => 4 [5,3,6,4,2,1] => 4 [5,4,1,2,3,6] => 0 [5,4,1,2,6,3] => 1 [5,4,1,3,2,6] => 2 [5,4,1,3,6,2] => 3 [5,4,1,6,2,3] => 1 [5,4,1,6,3,2] => 0 [5,4,2,1,3,6] => 2 [5,4,2,1,6,3] => 1 [5,4,2,3,1,6] => 3 [5,4,2,3,6,1] => 1 [5,4,2,6,1,3] => 2 [5,4,2,6,3,1] => 3 [5,4,3,1,2,6] => 1 [5,4,3,1,6,2] => 2 [5,4,3,2,1,6] => 0 [5,4,3,2,6,1] => 1 [5,4,3,6,1,2] => 0 [5,4,3,6,2,1] => 1 [5,4,6,1,2,3] => 1 [5,4,6,1,3,2] => 2 [5,4,6,2,1,3] => 4 [5,4,6,2,3,1] => 4 [5,4,6,3,1,2] => 5 [5,4,6,3,2,1] => 2 [5,6,1,2,3,4] => 0 [5,6,1,2,4,3] => 2 [5,6,1,3,2,4] => 4 [5,6,1,3,4,2] => 3 [5,6,1,4,2,3] => 2 [5,6,1,4,3,2] => 0 [5,6,2,1,3,4] => 2 [5,6,2,1,4,3] => 0 [5,6,2,3,1,4] => 3 [5,6,2,3,4,1] => 0 [5,6,2,4,1,3] => 4 [5,6,2,4,3,1] => 3 [5,6,3,1,2,4] => 2 [5,6,3,1,4,2] => 4 [5,6,3,2,1,4] => 0 [5,6,3,2,4,1] => 3 [5,6,3,4,1,2] => 0 [5,6,3,4,2,1] => 2 [5,6,4,1,2,3] => 2 [5,6,4,1,3,2] => 5 [5,6,4,2,1,3] => 5 [5,6,4,2,3,1] => 4 [5,6,4,3,1,2] => 4 [5,6,4,3,2,1] => 1 [6,1,2,3,4,5] => 0 [6,1,2,3,5,4] => 2 [6,1,2,4,3,5] => 3 [6,1,2,4,5,3] => 3 [6,1,2,5,3,4] => 3 [6,1,2,5,4,3] => 0 [6,1,3,2,4,5] => 3 [6,1,3,2,5,4] => 2 [6,1,3,4,2,5] => 4 [6,1,3,4,5,2] => 1 [6,1,3,5,2,4] => 5 [6,1,3,5,4,2] => 4 [6,1,4,2,3,5] => 4 [6,1,4,2,5,3] => 5 [6,1,4,3,2,5] => 0 [6,1,4,3,5,2] => 3 [6,1,4,5,2,3] => 0 [6,1,4,5,3,2] => 1 [6,1,5,2,3,4] => 2 [6,1,5,2,4,3] => 4 [6,1,5,3,2,4] => 3 [6,1,5,3,4,2] => 4 [6,1,5,4,2,3] => 2 [6,1,5,4,3,2] => 1 [6,2,1,3,4,5] => 2 [6,2,1,3,5,4] => 3 [6,2,1,4,3,5] => 2 [6,2,1,4,5,3] => 2 [6,2,1,5,3,4] => 2 [6,2,1,5,4,3] => 0 [6,2,3,1,4,5] => 3 [6,2,3,1,5,4] => 2 [6,2,3,4,1,5] => 1 [6,2,3,4,5,1] => 0 [6,2,3,5,1,4] => 1 [6,2,3,5,4,1] => 2 [6,2,4,1,3,5] => 5 [6,2,4,1,5,3] => 3 [6,2,4,3,1,5] => 3 [6,2,4,3,5,1] => 2 [6,2,4,5,1,3] => 2 [6,2,4,5,3,1] => 3 [6,2,5,1,3,4] => 2 [6,2,5,1,4,3] => 3 [6,2,5,3,1,4] => 3 [6,2,5,3,4,1] => 3 [6,2,5,4,1,3] => 2 [6,2,5,4,3,1] => 1 [6,3,1,2,4,5] => 3 [6,3,1,2,5,4] => 2 [6,3,1,4,2,5] => 5 [6,3,1,4,5,2] => 1 [6,3,1,5,2,4] => 3 [6,3,1,5,4,2] => 2 [6,3,2,1,4,5] => 0 [6,3,2,1,5,4] => 0 [6,3,2,4,1,5] => 4 [6,3,2,4,5,1] => 2 [6,3,2,5,1,4] => 2 [6,3,2,5,4,1] => 0 [6,3,4,1,2,5] => 0 [6,3,4,1,5,2] => 2 [6,3,4,2,1,5] => 1 [6,3,4,2,5,1] => 3 [6,3,4,5,1,2] => 0 [6,3,4,5,2,1] => 0 [6,3,5,1,2,4] => 3 [6,3,5,1,4,2] => 4 [6,3,5,2,1,4] => 3 [6,3,5,2,4,1] => 4 [6,3,5,4,1,2] => 3 [6,3,5,4,2,1] => 3 [6,4,1,2,3,5] => 2 [6,4,1,2,5,3] => 2 [6,4,1,3,2,5] => 3 [6,4,1,3,5,2] => 3 [6,4,1,5,2,3] => 3 [6,4,1,5,3,2] => 3 [6,4,2,1,3,5] => 4 [6,4,2,1,5,3] => 3 [6,4,2,3,1,5] => 4 [6,4,2,3,5,1] => 3 [6,4,2,5,1,3] => 4 [6,4,2,5,3,1] => 4 [6,4,3,1,2,5] => 2 [6,4,3,1,5,2] => 2 [6,4,3,2,1,5] => 1 [6,4,3,2,5,1] => 1 [6,4,3,5,1,2] => 3 [6,4,3,5,2,1] => 3 [6,4,5,1,2,3] => 2 [6,4,5,1,3,2] => 4 [6,4,5,2,1,3] => 4 [6,4,5,2,3,1] => 4 [6,4,5,3,1,2] => 4 [6,4,5,3,2,1] => 2 [6,5,1,2,3,4] => 0 [6,5,1,2,4,3] => 2 [6,5,1,3,2,4] => 3 [6,5,1,3,4,2] => 3 [6,5,1,4,2,3] => 3 [6,5,1,4,3,2] => 1 [6,5,2,1,3,4] => 2 [6,5,2,1,4,3] => 0 [6,5,2,3,1,4] => 3 [6,5,2,3,4,1] => 0 [6,5,2,4,1,3] => 4 [6,5,2,4,3,1] => 3 [6,5,3,1,2,4] => 3 [6,5,3,1,4,2] => 4 [6,5,3,2,1,4] => 1 [6,5,3,2,4,1] => 3 [6,5,3,4,1,2] => 2 [6,5,3,4,2,1] => 2 [6,5,4,1,2,3] => 0 [6,5,4,1,3,2] => 2 [6,5,4,2,1,3] => 2 [6,5,4,2,3,1] => 2 [6,5,4,3,1,2] => 1 [6,5,4,3,2,1] => 0 [1,2,3,4,5,6,7] => 0 [1,2,3,4,5,7,6] => 2 [1,2,3,4,6,5,7] => 2 [1,2,3,4,6,7,5] => 2 [1,2,3,4,7,5,6] => 2 [1,2,3,4,7,6,5] => 0 [1,2,3,5,4,6,7] => 2 [1,2,3,5,4,7,6] => 2 [1,2,3,5,6,4,7] => 3 [1,2,3,5,6,7,4] => 1 [1,2,3,5,7,4,6] => 4 [1,2,3,5,7,6,4] => 3 [1,2,3,6,4,5,7] => 3 [1,2,3,6,4,7,5] => 4 [1,2,3,6,5,4,7] => 0 [1,2,3,6,5,7,4] => 2 [1,2,3,6,7,4,5] => 0 [1,2,3,6,7,5,4] => 1 [1,2,3,7,4,5,6] => 1 [1,2,3,7,4,6,5] => 3 [1,2,3,7,5,4,6] => 2 [1,2,3,7,5,6,4] => 2 [1,2,3,7,6,4,5] => 1 [1,2,3,7,6,5,4] => 0 [1,2,4,3,5,6,7] => 2 [1,2,4,3,5,7,6] => 4 [1,2,4,3,6,5,7] => 4 [1,2,4,3,6,7,5] => 3 [1,2,4,3,7,5,6] => 3 [1,2,4,3,7,6,5] => 2 [1,2,4,5,3,6,7] => 3 [1,2,4,5,3,7,6] => 2 [1,2,4,5,6,3,7] => 2 [1,2,4,5,6,7,3] => 1 [1,2,4,5,7,3,6] => 3 [1,2,4,5,7,6,3] => 3 [1,2,4,6,3,5,7] => 4 [1,2,4,6,3,7,5] => 3 [1,2,4,6,5,3,7] => 3 [1,2,4,6,5,7,3] => 3 [1,2,4,6,7,3,5] => 3 [1,2,4,6,7,5,3] => 4 [1,2,4,7,3,5,6] => 3 [1,2,4,7,3,6,5] => 2 [1,2,4,7,5,3,6] => 4 [1,2,4,7,5,6,3] => 4 [1,2,4,7,6,3,5] => 3 [1,2,4,7,6,5,3] => 2 [1,2,5,3,4,6,7] => 3 [1,2,5,3,4,7,6] => 2 [1,2,5,3,6,4,7] => 4 [1,2,5,3,6,7,4] => 3 [1,2,5,3,7,4,6] => 3 [1,2,5,3,7,6,4] => 2 [1,2,5,4,3,6,7] => 0 [1,2,5,4,3,7,6] => 0 [1,2,5,4,6,3,7] => 3 [1,2,5,4,6,7,3] => 2 [1,2,5,4,7,3,6] => 2 [1,2,5,4,7,6,3] => 0 [1,2,5,6,3,4,7] => 0 [1,2,5,6,3,7,4] => 2 [1,2,5,6,4,3,7] => 1 [1,2,5,6,4,7,3] => 3 [1,2,5,6,7,3,4] => 0 [1,2,5,6,7,4,3] => 0 [1,2,5,7,3,4,6] => 2 [1,2,5,7,3,6,4] => 3 [1,2,5,7,4,3,6] => 2 [1,2,5,7,4,6,3] => 3 [1,2,5,7,6,3,4] => 2 [1,2,5,7,6,4,3] => 2 [1,2,6,3,4,5,7] => 2 [1,2,6,3,4,7,5] => 3 [1,2,6,3,5,4,7] => 3 [1,2,6,3,5,7,4] => 4 [1,2,6,3,7,4,5] => 3 [1,2,6,3,7,5,4] => 3 [1,2,6,4,3,5,7] => 3 [1,2,6,4,3,7,5] => 2 [1,2,6,4,5,3,7] => 2 [1,2,6,4,5,7,3] => 3 [1,2,6,4,7,3,5] => 3 [1,2,6,4,7,5,3] => 3 [1,2,6,5,3,4,7] => 1 [1,2,6,5,3,7,4] => 2 [1,2,6,5,4,3,7] => 0 [1,2,6,5,4,7,3] => 1 [1,2,6,5,7,3,4] => 2 [1,2,6,5,7,4,3] => 2 [1,2,6,7,3,4,5] => 0 [1,2,6,7,3,5,4] => 2 [1,2,6,7,4,3,5] => 2 [1,2,6,7,4,5,3] => 2 [1,2,6,7,5,3,4] => 4 [1,2,6,7,5,4,3] => 1 [1,2,7,3,4,5,6] => 1 [1,2,7,3,4,6,5] => 3 [1,2,7,3,5,4,6] => 3 [1,2,7,3,5,6,4] => 4 [1,2,7,3,6,4,5] => 4 [1,2,7,3,6,5,4] => 2 [1,2,7,4,3,5,6] => 2 [1,2,7,4,3,6,5] => 0 [1,2,7,4,5,3,6] => 3 [1,2,7,4,5,6,3] => 0 [1,2,7,4,6,3,5] => 3 [1,2,7,4,6,5,3] => 3 [1,2,7,5,3,4,6] => 3 [1,2,7,5,3,6,4] => 3 [1,2,7,5,4,3,6] => 1 [1,2,7,5,4,6,3] => 3 [1,2,7,5,6,3,4] => 2 [1,2,7,5,6,4,3] => 3 [1,2,7,6,3,4,5] => 0 [1,2,7,6,3,5,4] => 2 [1,2,7,6,4,3,5] => 2 [1,2,7,6,4,5,3] => 3 [1,2,7,6,5,3,4] => 1 [1,2,7,6,5,4,3] => 0 [1,3,2,4,5,6,7] => 2 [1,3,2,4,5,7,6] => 4 [1,3,2,4,6,5,7] => 4 [1,3,2,4,6,7,5] => 4 [1,3,2,4,7,5,6] => 4 [1,3,2,4,7,6,5] => 2 [1,3,2,5,4,6,7] => 4 [1,3,2,5,4,7,6] => 2 [1,3,2,5,6,4,7] => 4 [1,3,2,5,6,7,4] => 2 [1,3,2,5,7,4,6] => 6 [1,3,2,5,7,6,4] => 4 [1,3,2,6,4,5,7] => 4 [1,3,2,6,4,7,5] => 6 [1,3,2,6,5,4,7] => 2 [1,3,2,6,5,7,4] => 4 [1,3,2,6,7,4,5] => 2 [1,3,2,6,7,5,4] => 3 [1,3,2,7,4,5,6] => 2 [1,3,2,7,4,6,5] => 4 [1,3,2,7,5,4,6] => 4 [1,3,2,7,5,6,4] => 4 [1,3,2,7,6,4,5] => 3 [1,3,2,7,6,5,4] => 2 [1,3,4,2,5,6,7] => 3 [1,3,4,2,5,7,6] => 5 [1,3,4,2,6,5,7] => 4 [1,3,4,2,6,7,5] => 3 [1,3,4,2,7,5,6] => 3 [1,3,4,2,7,6,5] => 2 [1,3,4,5,2,6,7] => 2 [1,3,4,5,2,7,6] => 1 [1,3,4,5,6,2,7] => 2 [1,3,4,5,6,7,2] => 1 [1,3,4,5,7,2,6] => 3 [1,3,4,5,7,6,2] => 3 [1,3,4,6,2,5,7] => 4 [1,3,4,6,2,7,5] => 4 [1,3,4,6,5,2,7] => 3 [1,3,4,6,5,7,2] => 3 [1,3,4,6,7,2,5] => 2 [1,3,4,6,7,5,2] => 4 [1,3,4,7,2,5,6] => 1 [1,3,4,7,2,6,5] => 2 [1,3,4,7,5,2,6] => 3 [1,3,4,7,5,6,2] => 4 [1,3,4,7,6,2,5] => 2 [1,3,4,7,6,5,2] => 1 [1,3,5,2,4,6,7] => 4 [1,3,5,2,4,7,6] => 4 [1,3,5,2,6,4,7] => 4 [1,3,5,2,6,7,4] => 4 [1,3,5,2,7,4,6] => 5 [1,3,5,2,7,6,4] => 3 [1,3,5,4,2,6,7] => 3 [1,3,5,4,2,7,6] => 3 [1,3,5,4,6,2,7] => 3 [1,3,5,4,6,7,2] => 4 [1,3,5,4,7,2,6] => 4 [1,3,5,4,7,6,2] => 2 [1,3,5,6,2,4,7] => 3 [1,3,5,6,2,7,4] => 3 [1,3,5,6,4,2,7] => 4 [1,3,5,6,4,7,2] => 4 [1,3,5,6,7,2,4] => 3 [1,3,5,6,7,4,2] => 3 [1,3,5,7,2,4,6] => 5 [1,3,5,7,2,6,4] => 4 [1,3,5,7,4,2,6] => 4 [1,3,5,7,4,6,2] => 5 [1,3,5,7,6,2,4] => 5 [1,3,5,7,6,4,2] => 5 [1,3,6,2,4,5,7] => 4 [1,3,6,2,4,7,5] => 5 [1,3,6,2,5,4,7] => 2 [1,3,6,2,5,7,4] => 3 [1,3,6,2,7,4,5] => 2 [1,3,6,2,7,5,4] => 3 [1,3,6,4,2,5,7] => 4 [1,3,6,4,2,7,5] => 4 [1,3,6,4,5,2,7] => 4 [1,3,6,4,5,7,2] => 4 [1,3,6,4,7,2,5] => 4 [1,3,6,4,7,5,2] => 6 [1,3,6,5,2,4,7] => 3 [1,3,6,5,2,7,4] => 1 [1,3,6,5,4,2,7] => 2 [1,3,6,5,4,7,2] => 1 [1,3,6,5,7,2,4] => 4 [1,3,6,5,7,4,2] => 3 [1,3,6,7,2,4,5] => 2 [1,3,6,7,2,5,4] => 1 [1,3,6,7,4,2,5] => 3 [1,3,6,7,4,5,2] => 1 [1,3,6,7,5,2,4] => 4 [1,3,6,7,5,4,2] => 3 [1,3,7,2,4,5,6] => 3 [1,3,7,2,4,6,5] => 5 [1,3,7,2,5,4,6] => 4 [1,3,7,2,5,6,4] => 3 [1,3,7,2,6,4,5] => 5 [1,3,7,2,6,5,4] => 2 [1,3,7,4,2,5,6] => 4 [1,3,7,4,2,6,5] => 2 [1,3,7,4,5,2,6] => 2 [1,3,7,4,5,6,2] => 2 [1,3,7,4,6,2,5] => 5 [1,3,7,4,6,5,2] => 5 [1,3,7,5,2,4,6] => 5 [1,3,7,5,2,6,4] => 4 [1,3,7,5,4,2,6] => 3 [1,3,7,5,4,6,2] => 4 [1,3,7,5,6,2,4] => 3 [1,3,7,5,6,4,2] => 5 [1,3,7,6,2,4,5] => 2 [1,3,7,6,2,5,4] => 2 [1,3,7,6,4,2,5] => 4 [1,3,7,6,4,5,2] => 2 [1,3,7,6,5,2,4] => 3 [1,3,7,6,5,4,2] => 2 [1,4,2,3,5,6,7] => 3 [1,4,2,3,5,7,6] => 5 [1,4,2,3,6,5,7] => 4 [1,4,2,3,6,7,5] => 3 [1,4,2,3,7,5,6] => 3 [1,4,2,3,7,6,5] => 2 [1,4,2,5,3,6,7] => 4 [1,4,2,5,3,7,6] => 4 [1,4,2,5,6,3,7] => 4 [1,4,2,5,6,7,3] => 3 [1,4,2,5,7,3,6] => 5 [1,4,2,5,7,6,3] => 5 [1,4,2,6,3,5,7] => 4 [1,4,2,6,3,7,5] => 5 [1,4,2,6,5,3,7] => 2 [1,4,2,6,5,7,3] => 4 [1,4,2,6,7,3,5] => 2 [1,4,2,6,7,5,3] => 5 [1,4,2,7,3,5,6] => 4 [1,4,2,7,3,6,5] => 3 [1,4,2,7,5,3,6] => 3 [1,4,2,7,5,6,3] => 3 [1,4,2,7,6,3,5] => 3 [1,4,2,7,6,5,3] => 2 [1,4,3,2,5,6,7] => 0 [1,4,3,2,5,7,6] => 2 [1,4,3,2,6,5,7] => 2 [1,4,3,2,6,7,5] => 1 [1,4,3,2,7,5,6] => 1 [1,4,3,2,7,6,5] => 0 [1,4,3,5,2,6,7] => 3 [1,4,3,5,2,7,6] => 2 [1,4,3,5,6,2,7] => 3 [1,4,3,5,6,7,2] => 2 [1,4,3,5,7,2,6] => 4 [1,4,3,5,7,6,2] => 3 [1,4,3,6,2,5,7] => 2 [1,4,3,6,2,7,5] => 2 [1,4,3,6,5,2,7] => 0 [1,4,3,6,5,7,2] => 2 [1,4,3,6,7,2,5] => 0 [1,4,3,6,7,5,2] => 2 [1,4,3,7,2,5,6] => 1 [1,4,3,7,2,6,5] => 2 [1,4,3,7,5,2,6] => 2 [1,4,3,7,5,6,2] => 2 [1,4,3,7,6,2,5] => 1 [1,4,3,7,6,5,2] => 0 [1,4,5,2,3,6,7] => 0 [1,4,5,2,3,7,6] => 0 [1,4,5,2,6,3,7] => 3 [1,4,5,2,6,7,3] => 1 [1,4,5,2,7,3,6] => 2 [1,4,5,2,7,6,3] => 0 [1,4,5,3,2,6,7] => 1 [1,4,5,3,2,7,6] => 1 [1,4,5,3,6,2,7] => 4 [1,4,5,3,6,7,2] => 3 [1,4,5,3,7,2,6] => 4 [1,4,5,3,7,6,2] => 2 [1,4,5,6,2,3,7] => 0 [1,4,5,6,2,7,3] => 2 [1,4,5,6,3,2,7] => 0 [1,4,5,6,3,7,2] => 2 [1,4,5,6,7,2,3] => 0 [1,4,5,6,7,3,2] => 0 [1,4,5,7,2,3,6] => 1 [1,4,5,7,2,6,3] => 2 [1,4,5,7,3,2,6] => 1 [1,4,5,7,3,6,2] => 2 [1,4,5,7,6,2,3] => 2 [1,4,5,7,6,3,2] => 2 [1,4,6,2,3,5,7] => 3 [1,4,6,2,3,7,5] => 2 [1,4,6,2,5,3,7] => 3 [1,4,6,2,5,7,3] => 3 [1,4,6,2,7,3,5] => 4 [1,4,6,2,7,5,3] => 4 [1,4,6,3,2,5,7] => 3 [1,4,6,3,2,7,5] => 2 [1,4,6,3,5,2,7] => 3 [1,4,6,3,5,7,2] => 5 [1,4,6,3,7,2,5] => 4 [1,4,6,3,7,5,2] => 3 [1,4,6,5,2,3,7] => 2 [1,4,6,5,2,7,3] => 3 [1,4,6,5,3,2,7] => 2 ----------------------------------------------------------------------------- Created: May 30, 2019 at 14:29 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: May 30, 2019 at 14:29 by Martin Rubey