***************************************************************************** * 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: St000308 ----------------------------------------------------------------------------- Collection: Permutations ----------------------------------------------------------------------------- Description: The height of the tree associated to a permutation. A permutation can be mapped to a rooted tree with vertices \$\{0,1,2,\ldots,n\}\$ and root \$0\$ in the following way. Entries of the permutations are inserted one after the other, each child is larger than its parent and the children are in strict order from left to right. Details of the construction are found in [1]. The statistic is given by the height of this tree. See also [[St000325]] for the width of this tree. ----------------------------------------------------------------------------- References: [1] Permutation trees of power n and height k. [[OEIS:A179454]] [2] [[http://oeis.org/wiki/User:Peter_Luschny/PermutationTrees]] ----------------------------------------------------------------------------- Code: def statistic(pi): if pi == []: return 0 root, i, h = 0, 0, 0 branch, next = [root], pi[0] while true: while next < branch[len(branch)-1]: del(branch[len(branch)-1]) current = root while next > current: i += 1 branch.append(next) h = max(h, len(branch)) if i >= len(pi): return h-1 current, next = next, pi[i] ----------------------------------------------------------------------------- Statistic values: [1] => 1 [1,2] => 2 [2,1] => 1 [1,2,3] => 3 [1,3,2] => 2 [2,1,3] => 2 [2,3,1] => 2 [3,1,2] => 2 [3,2,1] => 1 [1,2,3,4] => 4 [1,2,4,3] => 3 [1,3,2,4] => 3 [1,3,4,2] => 3 [1,4,2,3] => 3 [1,4,3,2] => 2 [2,1,3,4] => 3 [2,1,4,3] => 2 [2,3,1,4] => 2 [2,3,4,1] => 3 [2,4,1,3] => 2 [2,4,3,1] => 2 [3,1,2,4] => 3 [3,1,4,2] => 2 [3,2,1,4] => 2 [3,2,4,1] => 2 [3,4,1,2] => 2 [3,4,2,1] => 2 [4,1,2,3] => 3 [4,1,3,2] => 2 [4,2,1,3] => 2 [4,2,3,1] => 2 [4,3,1,2] => 2 [4,3,2,1] => 1 [1,2,3,4,5] => 5 [1,2,3,5,4] => 4 [1,2,4,3,5] => 4 [1,2,4,5,3] => 4 [1,2,5,3,4] => 4 [1,2,5,4,3] => 3 [1,3,2,4,5] => 4 [1,3,2,5,4] => 3 [1,3,4,2,5] => 3 [1,3,4,5,2] => 4 [1,3,5,2,4] => 3 [1,3,5,4,2] => 3 [1,4,2,3,5] => 4 [1,4,2,5,3] => 3 [1,4,3,2,5] => 3 [1,4,3,5,2] => 3 [1,4,5,2,3] => 3 [1,4,5,3,2] => 3 [1,5,2,3,4] => 4 [1,5,2,4,3] => 3 [1,5,3,2,4] => 3 [1,5,3,4,2] => 3 [1,5,4,2,3] => 3 [1,5,4,3,2] => 2 [2,1,3,4,5] => 4 [2,1,3,5,4] => 3 [2,1,4,3,5] => 3 [2,1,4,5,3] => 3 [2,1,5,3,4] => 3 [2,1,5,4,3] => 2 [2,3,1,4,5] => 3 [2,3,1,5,4] => 2 [2,3,4,1,5] => 3 [2,3,4,5,1] => 4 [2,3,5,1,4] => 3 [2,3,5,4,1] => 3 [2,4,1,3,5] => 3 [2,4,1,5,3] => 2 [2,4,3,1,5] => 2 [2,4,3,5,1] => 3 [2,4,5,1,3] => 3 [2,4,5,3,1] => 3 [2,5,1,3,4] => 3 [2,5,1,4,3] => 2 [2,5,3,1,4] => 2 [2,5,3,4,1] => 3 [2,5,4,1,3] => 2 [2,5,4,3,1] => 2 [3,1,2,4,5] => 4 [3,1,2,5,4] => 3 [3,1,4,2,5] => 3 [3,1,4,5,2] => 3 [3,1,5,2,4] => 3 [3,1,5,4,2] => 2 [3,2,1,4,5] => 3 [3,2,1,5,4] => 2 [3,2,4,1,5] => 2 [3,2,4,5,1] => 3 [3,2,5,1,4] => 2 [3,2,5,4,1] => 2 [3,4,1,2,5] => 3 [3,4,1,5,2] => 2 [3,4,2,1,5] => 2 [3,4,2,5,1] => 2 [3,4,5,1,2] => 3 [3,4,5,2,1] => 3 [3,5,1,2,4] => 3 [3,5,1,4,2] => 2 [3,5,2,1,4] => 2 [3,5,2,4,1] => 2 [3,5,4,1,2] => 2 [3,5,4,2,1] => 2 [4,1,2,3,5] => 4 [4,1,2,5,3] => 3 [4,1,3,2,5] => 3 [4,1,3,5,2] => 3 [4,1,5,2,3] => 3 [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] => 2 [4,2,5,3,1] => 2 [4,3,1,2,5] => 3 [4,3,1,5,2] => 2 [4,3,2,1,5] => 2 [4,3,2,5,1] => 2 [4,3,5,1,2] => 2 [4,3,5,2,1] => 2 [4,5,1,2,3] => 3 [4,5,1,3,2] => 2 [4,5,2,1,3] => 2 [4,5,2,3,1] => 2 [4,5,3,1,2] => 2 [4,5,3,2,1] => 2 [5,1,2,3,4] => 4 [5,1,2,4,3] => 3 [5,1,3,2,4] => 3 [5,1,3,4,2] => 3 [5,1,4,2,3] => 3 [5,1,4,3,2] => 2 [5,2,1,3,4] => 3 [5,2,1,4,3] => 2 [5,2,3,1,4] => 2 [5,2,3,4,1] => 3 [5,2,4,1,3] => 2 [5,2,4,3,1] => 2 [5,3,1,2,4] => 3 [5,3,1,4,2] => 2 [5,3,2,1,4] => 2 [5,3,2,4,1] => 2 [5,3,4,1,2] => 2 [5,3,4,2,1] => 2 [5,4,1,2,3] => 3 [5,4,1,3,2] => 2 [5,4,2,1,3] => 2 [5,4,2,3,1] => 2 [5,4,3,1,2] => 2 [5,4,3,2,1] => 1 [1,2,3,4,5,6] => 6 [1,2,3,4,6,5] => 5 [1,2,3,5,4,6] => 5 [1,2,3,5,6,4] => 5 [1,2,3,6,4,5] => 5 [1,2,3,6,5,4] => 4 [1,2,4,3,5,6] => 5 [1,2,4,3,6,5] => 4 [1,2,4,5,3,6] => 4 [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] => 5 [1,2,5,3,6,4] => 4 [1,2,5,4,3,6] => 4 [1,2,5,4,6,3] => 4 [1,2,5,6,3,4] => 4 [1,2,5,6,4,3] => 4 [1,2,6,3,4,5] => 5 [1,2,6,3,5,4] => 4 [1,2,6,4,3,5] => 4 [1,2,6,4,5,3] => 4 [1,2,6,5,3,4] => 4 [1,2,6,5,4,3] => 3 [1,3,2,4,5,6] => 5 [1,3,2,4,6,5] => 4 [1,3,2,5,4,6] => 4 [1,3,2,5,6,4] => 4 [1,3,2,6,4,5] => 4 [1,3,2,6,5,4] => 3 [1,3,4,2,5,6] => 4 [1,3,4,2,6,5] => 3 [1,3,4,5,2,6] => 4 [1,3,4,5,6,2] => 5 [1,3,4,6,2,5] => 4 [1,3,4,6,5,2] => 4 [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] => 4 [1,3,5,6,2,4] => 4 [1,3,5,6,4,2] => 4 [1,3,6,2,4,5] => 4 [1,3,6,2,5,4] => 3 [1,3,6,4,2,5] => 3 [1,3,6,4,5,2] => 4 [1,3,6,5,2,4] => 3 [1,3,6,5,4,2] => 3 [1,4,2,3,5,6] => 5 [1,4,2,3,6,5] => 4 [1,4,2,5,3,6] => 4 [1,4,2,5,6,3] => 4 [1,4,2,6,3,5] => 4 [1,4,2,6,5,3] => 3 [1,4,3,2,5,6] => 4 [1,4,3,2,6,5] => 3 [1,4,3,5,2,6] => 3 [1,4,3,5,6,2] => 4 [1,4,3,6,2,5] => 3 [1,4,3,6,5,2] => 3 [1,4,5,2,3,6] => 4 [1,4,5,2,6,3] => 3 [1,4,5,3,2,6] => 3 [1,4,5,3,6,2] => 3 [1,4,5,6,2,3] => 4 [1,4,5,6,3,2] => 4 [1,4,6,2,3,5] => 4 [1,4,6,2,5,3] => 3 [1,4,6,3,2,5] => 3 [1,4,6,3,5,2] => 3 [1,4,6,5,2,3] => 3 [1,4,6,5,3,2] => 3 [1,5,2,3,4,6] => 5 [1,5,2,3,6,4] => 4 [1,5,2,4,3,6] => 4 [1,5,2,4,6,3] => 4 [1,5,2,6,3,4] => 4 [1,5,2,6,4,3] => 3 [1,5,3,2,4,6] => 4 [1,5,3,2,6,4] => 3 [1,5,3,4,2,6] => 3 [1,5,3,4,6,2] => 4 [1,5,3,6,2,4] => 3 [1,5,3,6,4,2] => 3 [1,5,4,2,3,6] => 4 [1,5,4,2,6,3] => 3 [1,5,4,3,2,6] => 3 [1,5,4,3,6,2] => 3 [1,5,4,6,2,3] => 3 [1,5,4,6,3,2] => 3 [1,5,6,2,3,4] => 4 [1,5,6,2,4,3] => 3 [1,5,6,3,2,4] => 3 [1,5,6,3,4,2] => 3 [1,5,6,4,2,3] => 3 [1,5,6,4,3,2] => 3 [1,6,2,3,4,5] => 5 [1,6,2,3,5,4] => 4 [1,6,2,4,3,5] => 4 [1,6,2,4,5,3] => 4 [1,6,2,5,3,4] => 4 [1,6,2,5,4,3] => 3 [1,6,3,2,4,5] => 4 [1,6,3,2,5,4] => 3 [1,6,3,4,2,5] => 3 [1,6,3,4,5,2] => 4 [1,6,3,5,2,4] => 3 [1,6,3,5,4,2] => 3 [1,6,4,2,3,5] => 4 [1,6,4,2,5,3] => 3 [1,6,4,3,2,5] => 3 [1,6,4,3,5,2] => 3 [1,6,4,5,2,3] => 3 [1,6,4,5,3,2] => 3 [1,6,5,2,3,4] => 4 [1,6,5,2,4,3] => 3 [1,6,5,3,2,4] => 3 [1,6,5,3,4,2] => 3 [1,6,5,4,2,3] => 3 [1,6,5,4,3,2] => 2 [2,1,3,4,5,6] => 5 [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] => 3 [2,1,4,3,5,6] => 4 [2,1,4,3,6,5] => 3 [2,1,4,5,3,6] => 3 [2,1,4,5,6,3] => 4 [2,1,4,6,3,5] => 3 [2,1,4,6,5,3] => 3 [2,1,5,3,4,6] => 4 [2,1,5,3,6,4] => 3 [2,1,5,4,3,6] => 3 [2,1,5,4,6,3] => 3 [2,1,5,6,3,4] => 3 [2,1,5,6,4,3] => 3 [2,1,6,3,4,5] => 4 [2,1,6,3,5,4] => 3 [2,1,6,4,3,5] => 3 [2,1,6,4,5,3] => 3 [2,1,6,5,3,4] => 3 [2,1,6,5,4,3] => 2 [2,3,1,4,5,6] => 4 [2,3,1,4,6,5] => 3 [2,3,1,5,4,6] => 3 [2,3,1,5,6,4] => 3 [2,3,1,6,4,5] => 3 [2,3,1,6,5,4] => 2 [2,3,4,1,5,6] => 3 [2,3,4,1,6,5] => 3 [2,3,4,5,1,6] => 4 [2,3,4,5,6,1] => 5 [2,3,4,6,1,5] => 4 [2,3,4,6,5,1] => 4 [2,3,5,1,4,6] => 3 [2,3,5,1,6,4] => 3 [2,3,5,4,1,6] => 3 [2,3,5,4,6,1] => 4 [2,3,5,6,1,4] => 4 [2,3,5,6,4,1] => 4 [2,3,6,1,4,5] => 3 [2,3,6,1,5,4] => 3 [2,3,6,4,1,5] => 3 [2,3,6,4,5,1] => 4 [2,3,6,5,1,4] => 3 [2,3,6,5,4,1] => 3 [2,4,1,3,5,6] => 4 [2,4,1,3,6,5] => 3 [2,4,1,5,3,6] => 3 [2,4,1,5,6,3] => 3 [2,4,1,6,3,5] => 3 [2,4,1,6,5,3] => 2 [2,4,3,1,5,6] => 3 [2,4,3,1,6,5] => 2 [2,4,3,5,1,6] => 3 [2,4,3,5,6,1] => 4 [2,4,3,6,1,5] => 3 [2,4,3,6,5,1] => 3 [2,4,5,1,3,6] => 3 [2,4,5,1,6,3] => 3 [2,4,5,3,1,6] => 3 [2,4,5,3,6,1] => 3 [2,4,5,6,1,3] => 4 [2,4,5,6,3,1] => 4 [2,4,6,1,3,5] => 3 [2,4,6,1,5,3] => 3 [2,4,6,3,1,5] => 3 [2,4,6,3,5,1] => 3 [2,4,6,5,1,3] => 3 [2,4,6,5,3,1] => 3 [2,5,1,3,4,6] => 4 [2,5,1,3,6,4] => 3 [2,5,1,4,3,6] => 3 [2,5,1,4,6,3] => 3 [2,5,1,6,3,4] => 3 [2,5,1,6,4,3] => 2 [2,5,3,1,4,6] => 3 [2,5,3,1,6,4] => 2 [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] => 3 [2,5,4,1,3,6] => 3 [2,5,4,1,6,3] => 2 [2,5,4,3,1,6] => 2 [2,5,4,3,6,1] => 3 [2,5,4,6,1,3] => 3 [2,5,4,6,3,1] => 3 [2,5,6,1,3,4] => 3 [2,5,6,1,4,3] => 3 [2,5,6,3,1,4] => 3 [2,5,6,3,4,1] => 3 [2,5,6,4,1,3] => 3 [2,5,6,4,3,1] => 3 [2,6,1,3,4,5] => 4 [2,6,1,3,5,4] => 3 [2,6,1,4,3,5] => 3 [2,6,1,4,5,3] => 3 [2,6,1,5,3,4] => 3 [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] => 3 [2,6,3,4,5,1] => 4 [2,6,3,5,1,4] => 3 [2,6,3,5,4,1] => 3 [2,6,4,1,3,5] => 3 [2,6,4,1,5,3] => 2 [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] => 3 [2,6,5,1,3,4] => 3 [2,6,5,1,4,3] => 2 [2,6,5,3,1,4] => 2 [2,6,5,3,4,1] => 3 [2,6,5,4,1,3] => 2 [2,6,5,4,3,1] => 2 [3,1,2,4,5,6] => 5 [3,1,2,4,6,5] => 4 [3,1,2,5,4,6] => 4 [3,1,2,5,6,4] => 4 [3,1,2,6,4,5] => 4 [3,1,2,6,5,4] => 3 [3,1,4,2,5,6] => 4 [3,1,4,2,6,5] => 3 [3,1,4,5,2,6] => 3 [3,1,4,5,6,2] => 4 [3,1,4,6,2,5] => 3 [3,1,4,6,5,2] => 3 [3,1,5,2,4,6] => 4 [3,1,5,2,6,4] => 3 [3,1,5,4,2,6] => 3 [3,1,5,4,6,2] => 3 [3,1,5,6,2,4] => 3 [3,1,5,6,4,2] => 3 [3,1,6,2,4,5] => 4 [3,1,6,2,5,4] => 3 [3,1,6,4,2,5] => 3 [3,1,6,4,5,2] => 3 [3,1,6,5,2,4] => 3 [3,1,6,5,4,2] => 2 [3,2,1,4,5,6] => 4 [3,2,1,4,6,5] => 3 [3,2,1,5,4,6] => 3 [3,2,1,5,6,4] => 3 [3,2,1,6,4,5] => 3 [3,2,1,6,5,4] => 2 [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] => 4 [3,2,4,6,1,5] => 3 [3,2,4,6,5,1] => 3 [3,2,5,1,4,6] => 3 [3,2,5,1,6,4] => 2 [3,2,5,4,1,6] => 2 [3,2,5,4,6,1] => 3 [3,2,5,6,1,4] => 3 [3,2,5,6,4,1] => 3 [3,2,6,1,4,5] => 3 [3,2,6,1,5,4] => 2 [3,2,6,4,1,5] => 2 [3,2,6,4,5,1] => 3 [3,2,6,5,1,4] => 2 [3,2,6,5,4,1] => 2 [3,4,1,2,5,6] => 4 [3,4,1,2,6,5] => 3 [3,4,1,5,2,6] => 3 [3,4,1,5,6,2] => 3 [3,4,1,6,2,5] => 3 [3,4,1,6,5,2] => 2 [3,4,2,1,5,6] => 3 [3,4,2,1,6,5] => 2 [3,4,2,5,1,6] => 2 [3,4,2,5,6,1] => 3 [3,4,2,6,1,5] => 2 [3,4,2,6,5,1] => 2 [3,4,5,1,2,6] => 3 [3,4,5,1,6,2] => 3 [3,4,5,2,1,6] => 3 [3,4,5,2,6,1] => 3 [3,4,5,6,1,2] => 4 [3,4,5,6,2,1] => 4 [3,4,6,1,2,5] => 3 [3,4,6,1,5,2] => 3 [3,4,6,2,1,5] => 3 [3,4,6,2,5,1] => 3 [3,4,6,5,1,2] => 3 [3,4,6,5,2,1] => 3 [3,5,1,2,4,6] => 4 [3,5,1,2,6,4] => 3 [3,5,1,4,2,6] => 3 [3,5,1,4,6,2] => 3 [3,5,1,6,2,4] => 3 [3,5,1,6,4,2] => 2 [3,5,2,1,4,6] => 3 [3,5,2,1,6,4] => 2 [3,5,2,4,1,6] => 2 [3,5,2,4,6,1] => 3 [3,5,2,6,1,4] => 2 [3,5,2,6,4,1] => 2 [3,5,4,1,2,6] => 3 [3,5,4,1,6,2] => 2 [3,5,4,2,1,6] => 2 [3,5,4,2,6,1] => 2 [3,5,4,6,1,2] => 3 [3,5,4,6,2,1] => 3 [3,5,6,1,2,4] => 3 [3,5,6,1,4,2] => 3 [3,5,6,2,1,4] => 3 [3,5,6,2,4,1] => 3 [3,5,6,4,1,2] => 3 [3,5,6,4,2,1] => 3 [3,6,1,2,4,5] => 4 [3,6,1,2,5,4] => 3 [3,6,1,4,2,5] => 3 [3,6,1,4,5,2] => 3 [3,6,1,5,2,4] => 3 [3,6,1,5,4,2] => 2 [3,6,2,1,4,5] => 3 [3,6,2,1,5,4] => 2 [3,6,2,4,1,5] => 2 [3,6,2,4,5,1] => 3 [3,6,2,5,1,4] => 2 [3,6,2,5,4,1] => 2 [3,6,4,1,2,5] => 3 [3,6,4,1,5,2] => 2 [3,6,4,2,1,5] => 2 [3,6,4,2,5,1] => 2 [3,6,4,5,1,2] => 3 [3,6,4,5,2,1] => 3 [3,6,5,1,2,4] => 3 [3,6,5,1,4,2] => 2 [3,6,5,2,1,4] => 2 [3,6,5,2,4,1] => 2 [3,6,5,4,1,2] => 2 [3,6,5,4,2,1] => 2 [4,1,2,3,5,6] => 5 [4,1,2,3,6,5] => 4 [4,1,2,5,3,6] => 4 [4,1,2,5,6,3] => 4 [4,1,2,6,3,5] => 4 [4,1,2,6,5,3] => 3 [4,1,3,2,5,6] => 4 [4,1,3,2,6,5] => 3 [4,1,3,5,2,6] => 3 [4,1,3,5,6,2] => 4 [4,1,3,6,2,5] => 3 [4,1,3,6,5,2] => 3 [4,1,5,2,3,6] => 4 [4,1,5,2,6,3] => 3 [4,1,5,3,2,6] => 3 [4,1,5,3,6,2] => 3 [4,1,5,6,2,3] => 3 [4,1,5,6,3,2] => 3 [4,1,6,2,3,5] => 4 [4,1,6,2,5,3] => 3 [4,1,6,3,2,5] => 3 [4,1,6,3,5,2] => 3 [4,1,6,5,2,3] => 3 [4,1,6,5,3,2] => 2 [4,2,1,3,5,6] => 4 [4,2,1,3,6,5] => 3 [4,2,1,5,3,6] => 3 [4,2,1,5,6,3] => 3 [4,2,1,6,3,5] => 3 [4,2,1,6,5,3] => 2 [4,2,3,1,5,6] => 3 [4,2,3,1,6,5] => 2 [4,2,3,5,1,6] => 3 [4,2,3,5,6,1] => 4 [4,2,3,6,1,5] => 3 [4,2,3,6,5,1] => 3 [4,2,5,1,3,6] => 3 [4,2,5,1,6,3] => 2 [4,2,5,3,1,6] => 2 [4,2,5,3,6,1] => 3 [4,2,5,6,1,3] => 3 [4,2,5,6,3,1] => 3 [4,2,6,1,3,5] => 3 [4,2,6,1,5,3] => 2 [4,2,6,3,1,5] => 2 [4,2,6,3,5,1] => 3 [4,2,6,5,1,3] => 2 [4,2,6,5,3,1] => 2 [4,3,1,2,5,6] => 4 [4,3,1,2,6,5] => 3 [4,3,1,5,2,6] => 3 [4,3,1,5,6,2] => 3 [4,3,1,6,2,5] => 3 [4,3,1,6,5,2] => 2 [4,3,2,1,5,6] => 3 [4,3,2,1,6,5] => 2 [4,3,2,5,1,6] => 2 [4,3,2,5,6,1] => 3 [4,3,2,6,1,5] => 2 [4,3,2,6,5,1] => 2 [4,3,5,1,2,6] => 3 [4,3,5,1,6,2] => 2 [4,3,5,2,1,6] => 2 [4,3,5,2,6,1] => 2 [4,3,5,6,1,2] => 3 [4,3,5,6,2,1] => 3 [4,3,6,1,2,5] => 3 [4,3,6,1,5,2] => 2 [4,3,6,2,1,5] => 2 [4,3,6,2,5,1] => 2 [4,3,6,5,1,2] => 2 [4,3,6,5,2,1] => 2 [4,5,1,2,3,6] => 4 [4,5,1,2,6,3] => 3 [4,5,1,3,2,6] => 3 [4,5,1,3,6,2] => 3 [4,5,1,6,2,3] => 3 [4,5,1,6,3,2] => 2 [4,5,2,1,3,6] => 3 [4,5,2,1,6,3] => 2 [4,5,2,3,1,6] => 2 [4,5,2,3,6,1] => 3 [4,5,2,6,1,3] => 2 [4,5,2,6,3,1] => 2 [4,5,3,1,2,6] => 3 [4,5,3,1,6,2] => 2 [4,5,3,2,1,6] => 2 [4,5,3,2,6,1] => 2 [4,5,3,6,1,2] => 2 [4,5,3,6,2,1] => 2 [4,5,6,1,2,3] => 3 [4,5,6,1,3,2] => 3 [4,5,6,2,1,3] => 3 [4,5,6,2,3,1] => 3 [4,5,6,3,1,2] => 3 [4,5,6,3,2,1] => 3 [4,6,1,2,3,5] => 4 [4,6,1,2,5,3] => 3 [4,6,1,3,2,5] => 3 [4,6,1,3,5,2] => 3 [4,6,1,5,2,3] => 3 [4,6,1,5,3,2] => 2 [4,6,2,1,3,5] => 3 [4,6,2,1,5,3] => 2 [4,6,2,3,1,5] => 2 [4,6,2,3,5,1] => 3 [4,6,2,5,1,3] => 2 [4,6,2,5,3,1] => 2 [4,6,3,1,2,5] => 3 [4,6,3,1,5,2] => 2 [4,6,3,2,1,5] => 2 [4,6,3,2,5,1] => 2 [4,6,3,5,1,2] => 2 [4,6,3,5,2,1] => 2 [4,6,5,1,2,3] => 3 [4,6,5,1,3,2] => 2 [4,6,5,2,1,3] => 2 [4,6,5,2,3,1] => 2 [4,6,5,3,1,2] => 2 [4,6,5,3,2,1] => 2 [5,1,2,3,4,6] => 5 [5,1,2,3,6,4] => 4 [5,1,2,4,3,6] => 4 [5,1,2,4,6,3] => 4 [5,1,2,6,3,4] => 4 [5,1,2,6,4,3] => 3 [5,1,3,2,4,6] => 4 [5,1,3,2,6,4] => 3 [5,1,3,4,2,6] => 3 [5,1,3,4,6,2] => 4 [5,1,3,6,2,4] => 3 [5,1,3,6,4,2] => 3 [5,1,4,2,3,6] => 4 [5,1,4,2,6,3] => 3 [5,1,4,3,2,6] => 3 [5,1,4,3,6,2] => 3 [5,1,4,6,2,3] => 3 [5,1,4,6,3,2] => 3 [5,1,6,2,3,4] => 4 [5,1,6,2,4,3] => 3 [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] => 4 [5,2,1,3,6,4] => 3 [5,2,1,4,3,6] => 3 [5,2,1,4,6,3] => 3 [5,2,1,6,3,4] => 3 [5,2,1,6,4,3] => 2 [5,2,3,1,4,6] => 3 [5,2,3,1,6,4] => 2 [5,2,3,4,1,6] => 3 [5,2,3,4,6,1] => 4 [5,2,3,6,1,4] => 3 [5,2,3,6,4,1] => 3 [5,2,4,1,3,6] => 3 [5,2,4,1,6,3] => 2 [5,2,4,3,1,6] => 2 [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] => 3 [5,2,6,1,4,3] => 2 [5,2,6,3,1,4] => 2 [5,2,6,3,4,1] => 3 [5,2,6,4,1,3] => 2 [5,2,6,4,3,1] => 2 [5,3,1,2,4,6] => 4 [5,3,1,2,6,4] => 3 [5,3,1,4,2,6] => 3 [5,3,1,4,6,2] => 3 [5,3,1,6,2,4] => 3 [5,3,1,6,4,2] => 2 [5,3,2,1,4,6] => 3 [5,3,2,1,6,4] => 2 [5,3,2,4,1,6] => 2 [5,3,2,4,6,1] => 3 [5,3,2,6,1,4] => 2 [5,3,2,6,4,1] => 2 [5,3,4,1,2,6] => 3 [5,3,4,1,6,2] => 2 [5,3,4,2,1,6] => 2 [5,3,4,2,6,1] => 2 [5,3,4,6,1,2] => 3 [5,3,4,6,2,1] => 3 [5,3,6,1,2,4] => 3 [5,3,6,1,4,2] => 2 [5,3,6,2,1,4] => 2 [5,3,6,2,4,1] => 2 [5,3,6,4,1,2] => 2 [5,3,6,4,2,1] => 2 [5,4,1,2,3,6] => 4 [5,4,1,2,6,3] => 3 [5,4,1,3,2,6] => 3 [5,4,1,3,6,2] => 3 [5,4,1,6,2,3] => 3 [5,4,1,6,3,2] => 2 [5,4,2,1,3,6] => 3 [5,4,2,1,6,3] => 2 [5,4,2,3,1,6] => 2 [5,4,2,3,6,1] => 3 [5,4,2,6,1,3] => 2 [5,4,2,6,3,1] => 2 [5,4,3,1,2,6] => 3 [5,4,3,1,6,2] => 2 [5,4,3,2,1,6] => 2 [5,4,3,2,6,1] => 2 [5,4,3,6,1,2] => 2 [5,4,3,6,2,1] => 2 [5,4,6,1,2,3] => 3 [5,4,6,1,3,2] => 2 [5,4,6,2,1,3] => 2 [5,4,6,2,3,1] => 2 [5,4,6,3,1,2] => 2 [5,4,6,3,2,1] => 2 [5,6,1,2,3,4] => 4 [5,6,1,2,4,3] => 3 [5,6,1,3,2,4] => 3 [5,6,1,3,4,2] => 3 [5,6,1,4,2,3] => 3 [5,6,1,4,3,2] => 2 [5,6,2,1,3,4] => 3 [5,6,2,1,4,3] => 2 [5,6,2,3,1,4] => 2 [5,6,2,3,4,1] => 3 [5,6,2,4,1,3] => 2 [5,6,2,4,3,1] => 2 [5,6,3,1,2,4] => 3 [5,6,3,1,4,2] => 2 [5,6,3,2,1,4] => 2 [5,6,3,2,4,1] => 2 [5,6,3,4,1,2] => 2 [5,6,3,4,2,1] => 2 [5,6,4,1,2,3] => 3 [5,6,4,1,3,2] => 2 [5,6,4,2,1,3] => 2 [5,6,4,2,3,1] => 2 [5,6,4,3,1,2] => 2 [5,6,4,3,2,1] => 2 [6,1,2,3,4,5] => 5 [6,1,2,3,5,4] => 4 [6,1,2,4,3,5] => 4 [6,1,2,4,5,3] => 4 [6,1,2,5,3,4] => 4 [6,1,2,5,4,3] => 3 [6,1,3,2,4,5] => 4 [6,1,3,2,5,4] => 3 [6,1,3,4,2,5] => 3 [6,1,3,4,5,2] => 4 [6,1,3,5,2,4] => 3 [6,1,3,5,4,2] => 3 [6,1,4,2,3,5] => 4 [6,1,4,2,5,3] => 3 [6,1,4,3,2,5] => 3 [6,1,4,3,5,2] => 3 [6,1,4,5,2,3] => 3 [6,1,4,5,3,2] => 3 [6,1,5,2,3,4] => 4 [6,1,5,2,4,3] => 3 [6,1,5,3,2,4] => 3 [6,1,5,3,4,2] => 3 [6,1,5,4,2,3] => 3 [6,1,5,4,3,2] => 2 [6,2,1,3,4,5] => 4 [6,2,1,3,5,4] => 3 [6,2,1,4,3,5] => 3 [6,2,1,4,5,3] => 3 [6,2,1,5,3,4] => 3 [6,2,1,5,4,3] => 2 [6,2,3,1,4,5] => 3 [6,2,3,1,5,4] => 2 [6,2,3,4,1,5] => 3 [6,2,3,4,5,1] => 4 [6,2,3,5,1,4] => 3 [6,2,3,5,4,1] => 3 [6,2,4,1,3,5] => 3 [6,2,4,1,5,3] => 2 [6,2,4,3,1,5] => 2 [6,2,4,3,5,1] => 3 [6,2,4,5,1,3] => 3 [6,2,4,5,3,1] => 3 [6,2,5,1,3,4] => 3 [6,2,5,1,4,3] => 2 [6,2,5,3,1,4] => 2 [6,2,5,3,4,1] => 3 [6,2,5,4,1,3] => 2 [6,2,5,4,3,1] => 2 [6,3,1,2,4,5] => 4 [6,3,1,2,5,4] => 3 [6,3,1,4,2,5] => 3 [6,3,1,4,5,2] => 3 [6,3,1,5,2,4] => 3 [6,3,1,5,4,2] => 2 [6,3,2,1,4,5] => 3 [6,3,2,1,5,4] => 2 [6,3,2,4,1,5] => 2 [6,3,2,4,5,1] => 3 [6,3,2,5,1,4] => 2 [6,3,2,5,4,1] => 2 [6,3,4,1,2,5] => 3 [6,3,4,1,5,2] => 2 [6,3,4,2,1,5] => 2 [6,3,4,2,5,1] => 2 [6,3,4,5,1,2] => 3 [6,3,4,5,2,1] => 3 [6,3,5,1,2,4] => 3 [6,3,5,1,4,2] => 2 [6,3,5,2,1,4] => 2 [6,3,5,2,4,1] => 2 [6,3,5,4,1,2] => 2 [6,3,5,4,2,1] => 2 [6,4,1,2,3,5] => 4 [6,4,1,2,5,3] => 3 [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] => 2 [6,4,2,1,3,5] => 3 [6,4,2,1,5,3] => 2 [6,4,2,3,1,5] => 2 [6,4,2,3,5,1] => 3 [6,4,2,5,1,3] => 2 [6,4,2,5,3,1] => 2 [6,4,3,1,2,5] => 3 [6,4,3,1,5,2] => 2 [6,4,3,2,1,5] => 2 [6,4,3,2,5,1] => 2 [6,4,3,5,1,2] => 2 [6,4,3,5,2,1] => 2 [6,4,5,1,2,3] => 3 [6,4,5,1,3,2] => 2 [6,4,5,2,1,3] => 2 [6,4,5,2,3,1] => 2 [6,4,5,3,1,2] => 2 [6,4,5,3,2,1] => 2 [6,5,1,2,3,4] => 4 [6,5,1,2,4,3] => 3 [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] => 2 [6,5,2,1,3,4] => 3 [6,5,2,1,4,3] => 2 [6,5,2,3,1,4] => 2 [6,5,2,3,4,1] => 3 [6,5,2,4,1,3] => 2 [6,5,2,4,3,1] => 2 [6,5,3,1,2,4] => 3 [6,5,3,1,4,2] => 2 [6,5,3,2,1,4] => 2 [6,5,3,2,4,1] => 2 [6,5,3,4,1,2] => 2 [6,5,3,4,2,1] => 2 [6,5,4,1,2,3] => 3 [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] => 2 [6,5,4,3,2,1] => 1 [1,2,3,4,5,6,7] => 7 [2,1,3,4,5,6,7] => 6 [2,3,1,4,5,6,7] => 5 [2,3,4,1,5,6,7] => 4 [2,3,4,5,1,6,7] => 4 [2,3,4,5,6,1,7] => 5 [2,3,4,5,6,7,1] => 6 [3,1,2,4,5,6,7] => 6 [3,1,4,2,5,6,7] => 5 [3,1,4,5,2,6,7] => 4 [3,1,4,5,6,2,7] => 4 [3,1,4,5,6,7,2] => 5 [3,2,1,4,5,6,7] => 5 [3,2,4,1,5,6,7] => 4 [3,2,4,5,1,6,7] => 3 [3,2,4,5,6,1,7] => 4 [3,2,4,5,6,7,1] => 5 [3,4,2,1,5,6,7] => 4 [3,4,2,5,1,6,7] => 3 [3,4,2,5,6,1,7] => 3 [3,4,2,5,6,7,1] => 4 [3,4,5,2,1,6,7] => 3 [3,4,5,2,6,1,7] => 3 [3,4,5,2,6,7,1] => 3 [3,4,5,6,2,1,7] => 4 [3,4,5,6,2,7,1] => 4 [3,4,5,6,7,2,1] => 5 [4,1,2,3,5,6,7] => 6 [4,1,2,5,3,6,7] => 5 [4,1,2,5,6,3,7] => 4 [4,1,2,5,6,7,3] => 5 [4,2,1,3,5,6,7] => 5 [4,2,1,5,3,6,7] => 4 [4,2,1,5,6,3,7] => 3 [4,2,1,5,6,7,3] => 4 [4,2,3,1,5,6,7] => 4 [4,2,3,5,1,6,7] => 3 [4,2,3,5,6,1,7] => 4 [4,2,3,5,6,7,1] => 5 [4,2,5,3,1,6,7] => 3 [4,2,5,3,6,1,7] => 3 [4,2,5,3,6,7,1] => 4 [4,2,5,6,3,1,7] => 3 [4,2,5,6,3,7,1] => 3 [4,2,5,6,7,3,1] => 4 [4,3,1,2,5,6,7] => 5 [4,3,1,5,2,6,7] => 4 [4,3,1,5,6,2,7] => 3 [4,3,1,5,6,7,2] => 4 [4,3,2,1,5,6,7] => 4 [4,3,2,5,1,6,7] => 3 [4,3,2,5,6,1,7] => 3 [4,3,2,5,6,7,1] => 4 [4,3,5,2,1,6,7] => 3 [4,3,5,2,6,7,1] => 3 [4,3,5,6,2,1,7] => 3 [4,3,5,6,2,7,1] => 3 [4,3,5,6,7,2,1] => 4 [4,5,1,3,2,6,7] => 4 [4,5,1,3,6,2,7] => 3 [4,5,1,3,6,7,2] => 4 [4,5,1,6,3,2,7] => 3 [4,5,1,6,3,7,2] => 3 [4,5,1,6,7,3,2] => 3 [4,5,3,2,1,6,7] => 3 [4,5,3,2,6,7,1] => 3 [4,5,3,6,7,2,1] => 3 [4,5,6,3,2,1,7] => 3 [4,5,6,3,2,7,1] => 3 [4,5,6,3,7,2,1] => 3 [4,5,6,7,3,2,1] => 4 [5,1,2,3,4,6,7] => 6 [5,1,2,3,6,4,7] => 5 [5,1,2,3,6,7,4] => 5 [5,2,1,3,4,6,7] => 5 [5,2,1,3,6,4,7] => 4 [5,2,1,3,6,7,4] => 4 [5,2,3,1,4,6,7] => 4 [5,2,3,1,6,4,7] => 3 [5,2,3,1,6,7,4] => 3 [5,2,3,4,1,6,7] => 3 [5,2,3,4,6,1,7] => 4 [5,2,3,4,6,7,1] => 5 [5,2,3,6,4,1,7] => 3 [5,2,3,6,4,7,1] => 4 [5,2,3,6,7,4,1] => 4 [5,3,1,2,4,6,7] => 5 [5,3,1,2,6,4,7] => 4 [5,3,1,2,6,7,4] => 4 [5,3,1,4,2,6,7] => 4 [5,3,1,4,6,2,7] => 3 [5,3,1,4,6,7,2] => 4 [5,3,1,6,4,2,7] => 3 [5,3,1,6,4,7,2] => 3 [5,3,1,6,7,4,2] => 3 [5,3,2,1,4,6,7] => 4 [5,3,2,1,6,4,7] => 3 [5,3,2,1,6,7,4] => 3 [5,3,2,4,1,6,7] => 3 [5,3,2,4,6,1,7] => 3 [5,3,2,4,6,7,1] => 4 [5,3,2,6,4,7,1] => 3 [5,3,2,6,7,4,1] => 3 [5,3,4,2,1,6,7] => 3 [5,3,4,2,6,7,1] => 3 [5,3,4,6,2,1,7] => 3 [5,3,4,6,2,7,1] => 3 [5,3,4,6,7,2,1] => 4 [5,3,6,4,7,2,1] => 3 [5,3,6,7,4,2,1] => 3 [5,4,1,2,3,6,7] => 5 [5,4,1,2,6,3,7] => 4 [5,4,1,2,6,7,3] => 4 [5,4,2,1,3,6,7] => 4 [5,4,2,1,6,3,7] => 3 [5,4,2,1,6,7,3] => 3 [5,4,2,3,1,6,7] => 3 [5,4,2,3,6,1,7] => 3 [5,4,2,3,6,7,1] => 4 [5,4,2,6,3,7,1] => 3 [5,4,2,6,7,3,1] => 3 [5,4,3,1,2,6,7] => 4 [5,4,3,1,6,2,7] => 3 [5,4,3,1,6,7,2] => 3 [5,4,3,2,1,6,7] => 3 [5,4,3,2,6,7,1] => 3 [5,4,3,6,7,2,1] => 3 [5,4,6,1,3,2,7] => 3 [5,4,6,1,3,7,2] => 3 [5,4,6,7,3,2,1] => 3 [5,6,1,2,4,3,7] => 4 [5,6,1,2,4,7,3] => 4 [5,6,1,2,7,4,3] => 3 [5,6,2,1,4,3,7] => 3 [5,6,2,1,4,7,3] => 3 [5,6,2,4,3,7,1] => 3 [5,6,2,4,7,3,1] => 3 [5,6,4,1,3,2,7] => 3 [5,6,4,1,3,7,2] => 3 [5,6,7,1,4,3,2] => 3 [5,6,7,4,3,2,1] => 3 [6,1,2,3,4,5,7] => 6 [6,1,2,3,4,7,5] => 5 [6,2,1,3,4,5,7] => 5 [6,2,1,3,4,7,5] => 4 [6,2,3,1,4,5,7] => 4 [6,2,3,1,4,7,5] => 3 [6,2,3,4,1,5,7] => 3 [6,2,3,4,1,7,5] => 3 [6,2,3,4,5,1,7] => 4 [6,2,3,4,5,7,1] => 5 [6,2,3,4,7,5,1] => 4 [6,3,1,2,4,5,7] => 5 [6,3,1,2,4,7,5] => 4 [6,3,1,4,2,5,7] => 4 [6,3,1,4,2,7,5] => 3 [6,3,1,4,5,2,7] => 3 [6,3,1,4,5,7,2] => 4 [6,3,1,4,7,5,2] => 3 [6,3,2,1,4,5,7] => 4 [6,3,2,1,4,7,5] => 3 [6,3,2,4,1,5,7] => 3 [6,3,2,4,5,1,7] => 3 [6,3,2,4,5,7,1] => 4 [6,3,2,4,7,5,1] => 3 [6,3,4,2,1,5,7] => 3 [6,3,4,2,5,7,1] => 3 [6,3,4,5,2,1,7] => 3 [6,3,4,5,2,7,1] => 3 [6,3,4,5,7,2,1] => 4 [6,3,4,7,5,2,1] => 3 [6,4,1,2,3,5,7] => 5 [6,4,1,2,3,7,5] => 4 [6,4,1,2,5,3,7] => 4 [6,4,1,2,5,7,3] => 4 [6,4,1,2,7,5,3] => 3 [6,4,2,1,3,5,7] => 4 [6,4,2,1,3,7,5] => 3 [6,4,2,1,5,3,7] => 3 [6,4,2,1,5,7,3] => 3 [6,4,2,3,1,5,7] => 3 [6,4,2,3,5,1,7] => 3 [6,4,2,3,5,7,1] => 4 [6,4,2,3,7,5,1] => 3 [6,4,2,5,3,7,1] => 3 [6,4,2,5,7,3,1] => 3 [6,4,3,1,2,5,7] => 4 [6,4,3,1,2,7,5] => 3 [6,4,3,1,5,2,7] => 3 [6,4,3,1,5,7,2] => 3 [6,4,3,2,1,5,7] => 3 [6,4,3,2,5,7,1] => 3 [6,4,3,5,7,2,1] => 3 [6,4,5,1,3,2,7] => 3 [6,4,5,1,3,7,2] => 3 [6,4,5,7,3,2,1] => 3 [6,5,1,2,3,4,7] => 5 [6,5,1,2,3,7,4] => 4 [6,5,2,1,3,4,7] => 4 [6,5,2,1,3,7,4] => 3 [6,5,2,3,1,4,7] => 3 [6,5,2,3,4,1,7] => 3 [6,5,2,3,4,7,1] => 4 [6,5,2,3,7,4,1] => 3 [6,5,3,1,2,4,7] => 4 [6,5,3,1,2,7,4] => 3 [6,5,3,1,4,2,7] => 3 [6,5,3,1,4,7,2] => 3 [6,5,3,2,1,4,7] => 3 [6,5,3,2,4,7,1] => 3 [6,5,3,4,7,2,1] => 3 [6,5,4,1,2,3,7] => 4 [6,5,4,1,2,7,3] => 3 [6,5,4,2,1,3,7] => 3 [6,5,4,2,3,7,1] => 3 [6,5,4,3,1,2,7] => 3 [6,5,7,1,2,4,3] => 3 [6,7,1,2,3,5,4] => 4 [6,7,2,1,3,5,4] => 3 [6,7,2,3,5,4,1] => 3 [6,7,3,1,2,5,4] => 3 [6,7,5,1,2,4,3] => 3 [7,1,2,3,4,5,6] => 6 [7,2,1,3,4,5,6] => 5 [7,2,3,1,4,5,6] => 4 [7,2,3,4,1,5,6] => 3 [7,2,3,4,5,1,6] => 4 [7,2,3,4,5,6,1] => 5 [7,3,1,2,4,5,6] => 5 [7,3,1,4,2,5,6] => 4 [7,3,1,4,5,2,6] => 3 [7,3,1,4,5,6,2] => 4 [7,3,2,1,4,5,6] => 4 [7,3,2,4,1,5,6] => 3 [7,3,2,4,5,1,6] => 3 [7,3,2,4,5,6,1] => 4 [7,3,4,2,1,5,6] => 3 [7,3,4,2,5,6,1] => 3 [7,3,4,5,2,1,6] => 3 [7,3,4,5,2,6,1] => 3 [7,3,4,5,6,2,1] => 4 [7,4,1,2,3,5,6] => 5 [7,4,1,2,5,3,6] => 4 [7,4,1,2,5,6,3] => 4 [7,4,2,1,3,5,6] => 4 [7,4,2,1,5,3,6] => 3 [7,4,2,1,5,6,3] => 3 [7,4,2,3,1,5,6] => 3 [7,4,2,3,5,1,6] => 3 [7,4,2,3,5,6,1] => 4 [7,4,2,5,3,6,1] => 3 [7,4,2,5,6,3,1] => 3 [7,4,3,1,2,5,6] => 4 [7,4,3,1,5,2,6] => 3 [7,4,3,1,5,6,2] => 3 [7,4,3,2,1,5,6] => 3 [7,4,3,2,5,6,1] => 3 [7,4,3,5,6,2,1] => 3 [7,4,5,1,3,2,6] => 3 [7,4,5,1,3,6,2] => 3 [7,4,5,6,3,2,1] => 3 [7,5,1,2,3,4,6] => 5 [7,5,1,2,3,6,4] => 4 [7,5,2,1,3,4,6] => 4 [7,5,2,1,3,6,4] => 3 [7,5,2,3,1,4,6] => 3 [7,5,2,3,4,1,6] => 3 [7,5,2,3,4,6,1] => 4 [7,5,2,3,6,4,1] => 3 [7,5,3,1,2,4,6] => 4 [7,5,3,1,2,6,4] => 3 [7,5,3,1,4,2,6] => 3 [7,5,3,1,4,6,2] => 3 [7,5,3,2,1,4,6] => 3 [7,5,3,2,4,6,1] => 3 [7,5,3,4,6,2,1] => 3 [7,5,4,1,2,3,6] => 4 [7,5,4,1,2,6,3] => 3 [7,5,4,2,1,3,6] => 3 [7,5,4,2,3,6,1] => 3 [7,5,4,3,1,2,6] => 3 [7,5,6,1,2,4,3] => 3 [7,6,1,2,3,4,5] => 5 [7,6,2,1,3,4,5] => 4 [7,6,2,3,1,4,5] => 3 [7,6,2,3,4,1,5] => 3 [7,6,2,3,4,5,1] => 4 [7,6,3,1,2,4,5] => 4 [7,6,3,1,4,2,5] => 3 [7,6,3,1,4,5,2] => 3 [7,6,3,2,1,4,5] => 3 [7,6,3,2,4,5,1] => 3 [7,6,3,4,5,2,1] => 3 [7,6,4,1,2,3,5] => 4 [7,6,4,1,2,5,3] => 3 [7,6,4,2,1,3,5] => 3 [7,6,4,2,3,5,1] => 3 [7,6,4,3,1,2,5] => 3 [7,6,5,1,2,3,4] => 4 [7,6,5,2,1,3,4] => 3 [7,6,5,2,3,4,1] => 3 [7,6,5,3,1,2,4] => 3 [7,6,5,4,1,2,3] => 3 ----------------------------------------------------------------------------- Created: Dec 08, 2015 at 08:43 by Peter Luschny ----------------------------------------------------------------------------- Last Updated: Feb 25, 2022 at 16:58 by Nadia Lafreniere