***************************************************************************** * 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: St001726 ----------------------------------------------------------------------------- Collection: Permutations ----------------------------------------------------------------------------- Description: The number of visible inversions of a permutation. A visible inversion of a permutation $\pi$ is a pair $i < j$ such that $\pi(j) \leq \min(i, \pi(i))$. ----------------------------------------------------------------------------- References: [1] Hamaker, Z., Marberg, E., Pawlowski, B. Schur $P$-positivity and involution Stanley symmetric functions [[MathSciNet:4023763]] ----------------------------------------------------------------------------- Code: def statistic(pi): return sum(1 for i in range(len(pi)) for j in range(i+1, len(pi)) if pi[j] <= min(i+1, pi[i])) ----------------------------------------------------------------------------- Statistic values: [1] => 0 [1,2] => 0 [2,1] => 1 [1,2,3] => 0 [1,3,2] => 1 [2,1,3] => 1 [2,3,1] => 2 [3,1,2] => 1 [3,2,1] => 2 [1,2,3,4] => 0 [1,2,4,3] => 1 [1,3,2,4] => 1 [1,3,4,2] => 2 [1,4,2,3] => 1 [1,4,3,2] => 2 [2,1,3,4] => 1 [2,1,4,3] => 2 [2,3,1,4] => 2 [2,3,4,1] => 3 [2,4,1,3] => 2 [2,4,3,1] => 3 [3,1,2,4] => 1 [3,1,4,2] => 2 [3,2,1,4] => 2 [3,2,4,1] => 3 [3,4,1,2] => 3 [3,4,2,1] => 4 [4,1,2,3] => 1 [4,1,3,2] => 2 [4,2,1,3] => 2 [4,2,3,1] => 3 [4,3,1,2] => 3 [4,3,2,1] => 4 [1,2,3,4,5] => 0 [1,2,3,5,4] => 1 [1,2,4,3,5] => 1 [1,2,4,5,3] => 2 [1,2,5,3,4] => 1 [1,2,5,4,3] => 2 [1,3,2,4,5] => 1 [1,3,2,5,4] => 2 [1,3,4,2,5] => 2 [1,3,4,5,2] => 3 [1,3,5,2,4] => 2 [1,3,5,4,2] => 3 [1,4,2,3,5] => 1 [1,4,2,5,3] => 2 [1,4,3,2,5] => 2 [1,4,3,5,2] => 3 [1,4,5,2,3] => 3 [1,4,5,3,2] => 4 [1,5,2,3,4] => 1 [1,5,2,4,3] => 2 [1,5,3,2,4] => 2 [1,5,3,4,2] => 3 [1,5,4,2,3] => 3 [1,5,4,3,2] => 4 [2,1,3,4,5] => 1 [2,1,3,5,4] => 2 [2,1,4,3,5] => 2 [2,1,4,5,3] => 3 [2,1,5,3,4] => 2 [2,1,5,4,3] => 3 [2,3,1,4,5] => 2 [2,3,1,5,4] => 3 [2,3,4,1,5] => 3 [2,3,4,5,1] => 4 [2,3,5,1,4] => 3 [2,3,5,4,1] => 4 [2,4,1,3,5] => 2 [2,4,1,5,3] => 3 [2,4,3,1,5] => 3 [2,4,3,5,1] => 4 [2,4,5,1,3] => 4 [2,4,5,3,1] => 5 [2,5,1,3,4] => 2 [2,5,1,4,3] => 3 [2,5,3,1,4] => 3 [2,5,3,4,1] => 4 [2,5,4,1,3] => 4 [2,5,4,3,1] => 5 [3,1,2,4,5] => 1 [3,1,2,5,4] => 2 [3,1,4,2,5] => 2 [3,1,4,5,2] => 3 [3,1,5,2,4] => 2 [3,1,5,4,2] => 3 [3,2,1,4,5] => 2 [3,2,1,5,4] => 3 [3,2,4,1,5] => 3 [3,2,4,5,1] => 4 [3,2,5,1,4] => 3 [3,2,5,4,1] => 4 [3,4,1,2,5] => 3 [3,4,1,5,2] => 4 [3,4,2,1,5] => 4 [3,4,2,5,1] => 5 [3,4,5,1,2] => 5 [3,4,5,2,1] => 6 [3,5,1,2,4] => 3 [3,5,1,4,2] => 4 [3,5,2,1,4] => 4 [3,5,2,4,1] => 5 [3,5,4,1,2] => 5 [3,5,4,2,1] => 6 [4,1,2,3,5] => 1 [4,1,2,5,3] => 2 [4,1,3,2,5] => 2 [4,1,3,5,2] => 3 [4,1,5,2,3] => 3 [4,1,5,3,2] => 4 [4,2,1,3,5] => 2 [4,2,1,5,3] => 3 [4,2,3,1,5] => 3 [4,2,3,5,1] => 4 [4,2,5,1,3] => 4 [4,2,5,3,1] => 5 [4,3,1,2,5] => 3 [4,3,1,5,2] => 4 [4,3,2,1,5] => 4 [4,3,2,5,1] => 5 [4,3,5,1,2] => 5 [4,3,5,2,1] => 6 [4,5,1,2,3] => 3 [4,5,1,3,2] => 4 [4,5,2,1,3] => 4 [4,5,2,3,1] => 5 [4,5,3,1,2] => 5 [4,5,3,2,1] => 6 [5,1,2,3,4] => 1 [5,1,2,4,3] => 2 [5,1,3,2,4] => 2 [5,1,3,4,2] => 3 [5,1,4,2,3] => 3 [5,1,4,3,2] => 4 [5,2,1,3,4] => 2 [5,2,1,4,3] => 3 [5,2,3,1,4] => 3 [5,2,3,4,1] => 4 [5,2,4,1,3] => 4 [5,2,4,3,1] => 5 [5,3,1,2,4] => 3 [5,3,1,4,2] => 4 [5,3,2,1,4] => 4 [5,3,2,4,1] => 5 [5,3,4,1,2] => 5 [5,3,4,2,1] => 6 [5,4,1,2,3] => 3 [5,4,1,3,2] => 4 [5,4,2,1,3] => 4 [5,4,2,3,1] => 5 [5,4,3,1,2] => 5 [5,4,3,2,1] => 6 [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] => 2 [1,2,3,6,4,5] => 1 [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] => 2 [1,2,4,5,6,3] => 3 [1,2,4,6,3,5] => 2 [1,2,4,6,5,3] => 3 [1,2,5,3,4,6] => 1 [1,2,5,3,6,4] => 2 [1,2,5,4,3,6] => 2 [1,2,5,4,6,3] => 3 [1,2,5,6,3,4] => 3 [1,2,5,6,4,3] => 4 [1,2,6,3,4,5] => 1 [1,2,6,3,5,4] => 2 [1,2,6,4,3,5] => 2 [1,2,6,4,5,3] => 3 [1,2,6,5,3,4] => 3 [1,2,6,5,4,3] => 4 [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] => 3 [1,3,2,6,4,5] => 2 [1,3,2,6,5,4] => 3 [1,3,4,2,5,6] => 2 [1,3,4,2,6,5] => 3 [1,3,4,5,2,6] => 3 [1,3,4,5,6,2] => 4 [1,3,4,6,2,5] => 3 [1,3,4,6,5,2] => 4 [1,3,5,2,4,6] => 2 [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] => 5 [1,3,6,2,4,5] => 2 [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] => 4 [1,3,6,5,4,2] => 5 [1,4,2,3,5,6] => 1 [1,4,2,3,6,5] => 2 [1,4,2,5,3,6] => 2 [1,4,2,5,6,3] => 3 [1,4,2,6,3,5] => 2 [1,4,2,6,5,3] => 3 [1,4,3,2,5,6] => 2 [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] => 4 [1,4,5,2,3,6] => 3 [1,4,5,2,6,3] => 4 [1,4,5,3,2,6] => 4 [1,4,5,3,6,2] => 5 [1,4,5,6,2,3] => 5 [1,4,5,6,3,2] => 6 [1,4,6,2,3,5] => 3 [1,4,6,2,5,3] => 4 [1,4,6,3,2,5] => 4 [1,4,6,3,5,2] => 5 [1,4,6,5,2,3] => 5 [1,4,6,5,3,2] => 6 [1,5,2,3,4,6] => 1 [1,5,2,3,6,4] => 2 [1,5,2,4,3,6] => 2 [1,5,2,4,6,3] => 3 [1,5,2,6,3,4] => 3 [1,5,2,6,4,3] => 4 [1,5,3,2,4,6] => 2 [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] => 4 [1,5,3,6,4,2] => 5 [1,5,4,2,3,6] => 3 [1,5,4,2,6,3] => 4 [1,5,4,3,2,6] => 4 [1,5,4,3,6,2] => 5 [1,5,4,6,2,3] => 5 [1,5,4,6,3,2] => 6 [1,5,6,2,3,4] => 3 [1,5,6,2,4,3] => 4 [1,5,6,3,2,4] => 4 [1,5,6,3,4,2] => 5 [1,5,6,4,2,3] => 5 [1,5,6,4,3,2] => 6 [1,6,2,3,4,5] => 1 [1,6,2,3,5,4] => 2 [1,6,2,4,3,5] => 2 [1,6,2,4,5,3] => 3 [1,6,2,5,3,4] => 3 [1,6,2,5,4,3] => 4 [1,6,3,2,4,5] => 2 [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] => 4 [1,6,3,5,4,2] => 5 [1,6,4,2,3,5] => 3 [1,6,4,2,5,3] => 4 [1,6,4,3,2,5] => 4 [1,6,4,3,5,2] => 5 [1,6,4,5,2,3] => 5 [1,6,4,5,3,2] => 6 [1,6,5,2,3,4] => 3 [1,6,5,2,4,3] => 4 [1,6,5,3,2,4] => 4 [1,6,5,3,4,2] => 5 [1,6,5,4,2,3] => 5 [1,6,5,4,3,2] => 6 [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] => 3 [2,1,3,6,4,5] => 2 [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] => 3 [2,1,4,5,6,3] => 4 [2,1,4,6,3,5] => 3 [2,1,4,6,5,3] => 4 [2,1,5,3,4,6] => 2 [2,1,5,3,6,4] => 3 [2,1,5,4,3,6] => 3 [2,1,5,4,6,3] => 4 [2,1,5,6,3,4] => 4 [2,1,5,6,4,3] => 5 [2,1,6,3,4,5] => 2 [2,1,6,3,5,4] => 3 [2,1,6,4,3,5] => 3 [2,1,6,4,5,3] => 4 [2,1,6,5,3,4] => 4 [2,1,6,5,4,3] => 5 [2,3,1,4,5,6] => 2 [2,3,1,4,6,5] => 3 [2,3,1,5,4,6] => 3 [2,3,1,5,6,4] => 4 [2,3,1,6,4,5] => 3 [2,3,1,6,5,4] => 4 [2,3,4,1,5,6] => 3 [2,3,4,1,6,5] => 4 [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] => 5 [2,3,5,1,4,6] => 3 [2,3,5,1,6,4] => 4 [2,3,5,4,1,6] => 4 [2,3,5,4,6,1] => 5 [2,3,5,6,1,4] => 5 [2,3,5,6,4,1] => 6 [2,3,6,1,4,5] => 3 [2,3,6,1,5,4] => 4 [2,3,6,4,1,5] => 4 [2,3,6,4,5,1] => 5 [2,3,6,5,1,4] => 5 [2,3,6,5,4,1] => 6 [2,4,1,3,5,6] => 2 [2,4,1,3,6,5] => 3 [2,4,1,5,3,6] => 3 [2,4,1,5,6,3] => 4 [2,4,1,6,3,5] => 3 [2,4,1,6,5,3] => 4 [2,4,3,1,5,6] => 3 [2,4,3,1,6,5] => 4 [2,4,3,5,1,6] => 4 [2,4,3,5,6,1] => 5 [2,4,3,6,1,5] => 4 [2,4,3,6,5,1] => 5 [2,4,5,1,3,6] => 4 [2,4,5,1,6,3] => 5 [2,4,5,3,1,6] => 5 [2,4,5,3,6,1] => 6 [2,4,5,6,1,3] => 6 [2,4,5,6,3,1] => 7 [2,4,6,1,3,5] => 4 [2,4,6,1,5,3] => 5 [2,4,6,3,1,5] => 5 [2,4,6,3,5,1] => 6 [2,4,6,5,1,3] => 6 [2,4,6,5,3,1] => 7 [2,5,1,3,4,6] => 2 [2,5,1,3,6,4] => 3 [2,5,1,4,3,6] => 3 [2,5,1,4,6,3] => 4 [2,5,1,6,3,4] => 4 [2,5,1,6,4,3] => 5 [2,5,3,1,4,6] => 3 [2,5,3,1,6,4] => 4 [2,5,3,4,1,6] => 4 [2,5,3,4,6,1] => 5 [2,5,3,6,1,4] => 5 [2,5,3,6,4,1] => 6 [2,5,4,1,3,6] => 4 [2,5,4,1,6,3] => 5 [2,5,4,3,1,6] => 5 [2,5,4,3,6,1] => 6 [2,5,4,6,1,3] => 6 [2,5,4,6,3,1] => 7 [2,5,6,1,3,4] => 4 [2,5,6,1,4,3] => 5 [2,5,6,3,1,4] => 5 [2,5,6,3,4,1] => 6 [2,5,6,4,1,3] => 6 [2,5,6,4,3,1] => 7 [2,6,1,3,4,5] => 2 [2,6,1,3,5,4] => 3 [2,6,1,4,3,5] => 3 [2,6,1,4,5,3] => 4 [2,6,1,5,3,4] => 4 [2,6,1,5,4,3] => 5 [2,6,3,1,4,5] => 3 [2,6,3,1,5,4] => 4 [2,6,3,4,1,5] => 4 [2,6,3,4,5,1] => 5 [2,6,3,5,1,4] => 5 [2,6,3,5,4,1] => 6 [2,6,4,1,3,5] => 4 [2,6,4,1,5,3] => 5 [2,6,4,3,1,5] => 5 [2,6,4,3,5,1] => 6 [2,6,4,5,1,3] => 6 [2,6,4,5,3,1] => 7 [2,6,5,1,3,4] => 4 [2,6,5,1,4,3] => 5 [2,6,5,3,1,4] => 5 [2,6,5,3,4,1] => 6 [2,6,5,4,1,3] => 6 [2,6,5,4,3,1] => 7 [3,1,2,4,5,6] => 1 [3,1,2,4,6,5] => 2 [3,1,2,5,4,6] => 2 [3,1,2,5,6,4] => 3 [3,1,2,6,4,5] => 2 [3,1,2,6,5,4] => 3 [3,1,4,2,5,6] => 2 [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] => 4 [3,1,5,2,4,6] => 2 [3,1,5,2,6,4] => 3 [3,1,5,4,2,6] => 3 [3,1,5,4,6,2] => 4 [3,1,5,6,2,4] => 4 [3,1,5,6,4,2] => 5 [3,1,6,2,4,5] => 2 [3,1,6,2,5,4] => 3 [3,1,6,4,2,5] => 3 [3,1,6,4,5,2] => 4 [3,1,6,5,2,4] => 4 [3,1,6,5,4,2] => 5 [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] => 4 [3,2,1,6,4,5] => 3 [3,2,1,6,5,4] => 4 [3,2,4,1,5,6] => 3 [3,2,4,1,6,5] => 4 [3,2,4,5,1,6] => 4 [3,2,4,5,6,1] => 5 [3,2,4,6,1,5] => 4 [3,2,4,6,5,1] => 5 [3,2,5,1,4,6] => 3 [3,2,5,1,6,4] => 4 [3,2,5,4,1,6] => 4 [3,2,5,4,6,1] => 5 [3,2,5,6,1,4] => 5 [3,2,5,6,4,1] => 6 [3,2,6,1,4,5] => 3 [3,2,6,1,5,4] => 4 [3,2,6,4,1,5] => 4 [3,2,6,4,5,1] => 5 [3,2,6,5,1,4] => 5 [3,2,6,5,4,1] => 6 [3,4,1,2,5,6] => 3 [3,4,1,2,6,5] => 4 [3,4,1,5,2,6] => 4 [3,4,1,5,6,2] => 5 [3,4,1,6,2,5] => 4 [3,4,1,6,5,2] => 5 [3,4,2,1,5,6] => 4 [3,4,2,1,6,5] => 5 [3,4,2,5,1,6] => 5 [3,4,2,5,6,1] => 6 [3,4,2,6,1,5] => 5 [3,4,2,6,5,1] => 6 [3,4,5,1,2,6] => 5 [3,4,5,1,6,2] => 6 [3,4,5,2,1,6] => 6 [3,4,5,2,6,1] => 7 [3,4,5,6,1,2] => 7 [3,4,5,6,2,1] => 8 [3,4,6,1,2,5] => 5 [3,4,6,1,5,2] => 6 [3,4,6,2,1,5] => 6 [3,4,6,2,5,1] => 7 [3,4,6,5,1,2] => 7 [3,4,6,5,2,1] => 8 [3,5,1,2,4,6] => 3 [3,5,1,2,6,4] => 4 [3,5,1,4,2,6] => 4 [3,5,1,4,6,2] => 5 [3,5,1,6,2,4] => 5 [3,5,1,6,4,2] => 6 [3,5,2,1,4,6] => 4 [3,5,2,1,6,4] => 5 [3,5,2,4,1,6] => 5 [3,5,2,4,6,1] => 6 [3,5,2,6,1,4] => 6 [3,5,2,6,4,1] => 7 [3,5,4,1,2,6] => 5 [3,5,4,1,6,2] => 6 [3,5,4,2,1,6] => 6 [3,5,4,2,6,1] => 7 [3,5,4,6,1,2] => 7 [3,5,4,6,2,1] => 8 [3,5,6,1,2,4] => 5 [3,5,6,1,4,2] => 6 [3,5,6,2,1,4] => 6 [3,5,6,2,4,1] => 7 [3,5,6,4,1,2] => 7 [3,5,6,4,2,1] => 8 [3,6,1,2,4,5] => 3 [3,6,1,2,5,4] => 4 [3,6,1,4,2,5] => 4 [3,6,1,4,5,2] => 5 [3,6,1,5,2,4] => 5 [3,6,1,5,4,2] => 6 [3,6,2,1,4,5] => 4 [3,6,2,1,5,4] => 5 [3,6,2,4,1,5] => 5 [3,6,2,4,5,1] => 6 [3,6,2,5,1,4] => 6 [3,6,2,5,4,1] => 7 [3,6,4,1,2,5] => 5 [3,6,4,1,5,2] => 6 [3,6,4,2,1,5] => 6 [3,6,4,2,5,1] => 7 [3,6,4,5,1,2] => 7 [3,6,4,5,2,1] => 8 [3,6,5,1,2,4] => 5 [3,6,5,1,4,2] => 6 [3,6,5,2,1,4] => 6 [3,6,5,2,4,1] => 7 [3,6,5,4,1,2] => 7 [3,6,5,4,2,1] => 8 [4,1,2,3,5,6] => 1 [4,1,2,3,6,5] => 2 [4,1,2,5,3,6] => 2 [4,1,2,5,6,3] => 3 [4,1,2,6,3,5] => 2 [4,1,2,6,5,3] => 3 [4,1,3,2,5,6] => 2 [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] => 4 [4,1,5,2,3,6] => 3 [4,1,5,2,6,3] => 4 [4,1,5,3,2,6] => 4 [4,1,5,3,6,2] => 5 [4,1,5,6,2,3] => 5 [4,1,5,6,3,2] => 6 [4,1,6,2,3,5] => 3 [4,1,6,2,5,3] => 4 [4,1,6,3,2,5] => 4 [4,1,6,3,5,2] => 5 [4,1,6,5,2,3] => 5 [4,1,6,5,3,2] => 6 [4,2,1,3,5,6] => 2 [4,2,1,3,6,5] => 3 [4,2,1,5,3,6] => 3 [4,2,1,5,6,3] => 4 [4,2,1,6,3,5] => 3 [4,2,1,6,5,3] => 4 [4,2,3,1,5,6] => 3 [4,2,3,1,6,5] => 4 [4,2,3,5,1,6] => 4 [4,2,3,5,6,1] => 5 [4,2,3,6,1,5] => 4 [4,2,3,6,5,1] => 5 [4,2,5,1,3,6] => 4 [4,2,5,1,6,3] => 5 [4,2,5,3,1,6] => 5 [4,2,5,3,6,1] => 6 [4,2,5,6,1,3] => 6 [4,2,5,6,3,1] => 7 [4,2,6,1,3,5] => 4 [4,2,6,1,5,3] => 5 [4,2,6,3,1,5] => 5 [4,2,6,3,5,1] => 6 [4,2,6,5,1,3] => 6 [4,2,6,5,3,1] => 7 [4,3,1,2,5,6] => 3 [4,3,1,2,6,5] => 4 [4,3,1,5,2,6] => 4 [4,3,1,5,6,2] => 5 [4,3,1,6,2,5] => 4 [4,3,1,6,5,2] => 5 [4,3,2,1,5,6] => 4 [4,3,2,1,6,5] => 5 [4,3,2,5,1,6] => 5 [4,3,2,5,6,1] => 6 [4,3,2,6,1,5] => 5 [4,3,2,6,5,1] => 6 [4,3,5,1,2,6] => 5 [4,3,5,1,6,2] => 6 [4,3,5,2,1,6] => 6 [4,3,5,2,6,1] => 7 [4,3,5,6,1,2] => 7 [4,3,5,6,2,1] => 8 [4,3,6,1,2,5] => 5 [4,3,6,1,5,2] => 6 [4,3,6,2,1,5] => 6 [4,3,6,2,5,1] => 7 [4,3,6,5,1,2] => 7 [4,3,6,5,2,1] => 8 [4,5,1,2,3,6] => 3 [4,5,1,2,6,3] => 4 [4,5,1,3,2,6] => 4 [4,5,1,3,6,2] => 5 [4,5,1,6,2,3] => 5 [4,5,1,6,3,2] => 6 [4,5,2,1,3,6] => 4 [4,5,2,1,6,3] => 5 [4,5,2,3,1,6] => 5 [4,5,2,3,6,1] => 6 [4,5,2,6,1,3] => 6 [4,5,2,6,3,1] => 7 [4,5,3,1,2,6] => 5 [4,5,3,1,6,2] => 6 [4,5,3,2,1,6] => 6 [4,5,3,2,6,1] => 7 [4,5,3,6,1,2] => 7 [4,5,3,6,2,1] => 8 [4,5,6,1,2,3] => 6 [4,5,6,1,3,2] => 7 [4,5,6,2,1,3] => 7 [4,5,6,2,3,1] => 8 [4,5,6,3,1,2] => 8 [4,5,6,3,2,1] => 9 [4,6,1,2,3,5] => 3 [4,6,1,2,5,3] => 4 [4,6,1,3,2,5] => 4 [4,6,1,3,5,2] => 5 [4,6,1,5,2,3] => 5 [4,6,1,5,3,2] => 6 [4,6,2,1,3,5] => 4 [4,6,2,1,5,3] => 5 [4,6,2,3,1,5] => 5 [4,6,2,3,5,1] => 6 [4,6,2,5,1,3] => 6 [4,6,2,5,3,1] => 7 [4,6,3,1,2,5] => 5 [4,6,3,1,5,2] => 6 [4,6,3,2,1,5] => 6 [4,6,3,2,5,1] => 7 [4,6,3,5,1,2] => 7 [4,6,3,5,2,1] => 8 [4,6,5,1,2,3] => 6 [4,6,5,1,3,2] => 7 [4,6,5,2,1,3] => 7 [4,6,5,2,3,1] => 8 [4,6,5,3,1,2] => 8 [4,6,5,3,2,1] => 9 [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] => 3 [5,1,2,6,4,3] => 4 [5,1,3,2,4,6] => 2 [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] => 4 [5,1,3,6,4,2] => 5 [5,1,4,2,3,6] => 3 [5,1,4,2,6,3] => 4 [5,1,4,3,2,6] => 4 [5,1,4,3,6,2] => 5 [5,1,4,6,2,3] => 5 [5,1,4,6,3,2] => 6 [5,1,6,2,3,4] => 3 [5,1,6,2,4,3] => 4 [5,1,6,3,2,4] => 4 [5,1,6,3,4,2] => 5 [5,1,6,4,2,3] => 5 [5,1,6,4,3,2] => 6 [5,2,1,3,4,6] => 2 [5,2,1,3,6,4] => 3 [5,2,1,4,3,6] => 3 [5,2,1,4,6,3] => 4 [5,2,1,6,3,4] => 4 [5,2,1,6,4,3] => 5 [5,2,3,1,4,6] => 3 [5,2,3,1,6,4] => 4 [5,2,3,4,1,6] => 4 [5,2,3,4,6,1] => 5 [5,2,3,6,1,4] => 5 [5,2,3,6,4,1] => 6 [5,2,4,1,3,6] => 4 [5,2,4,1,6,3] => 5 [5,2,4,3,1,6] => 5 [5,2,4,3,6,1] => 6 [5,2,4,6,1,3] => 6 [5,2,4,6,3,1] => 7 [5,2,6,1,3,4] => 4 [5,2,6,1,4,3] => 5 [5,2,6,3,1,4] => 5 [5,2,6,3,4,1] => 6 [5,2,6,4,1,3] => 6 [5,2,6,4,3,1] => 7 [5,3,1,2,4,6] => 3 [5,3,1,2,6,4] => 4 [5,3,1,4,2,6] => 4 [5,3,1,4,6,2] => 5 [5,3,1,6,2,4] => 5 [5,3,1,6,4,2] => 6 [5,3,2,1,4,6] => 4 [5,3,2,1,6,4] => 5 [5,3,2,4,1,6] => 5 [5,3,2,4,6,1] => 6 [5,3,2,6,1,4] => 6 [5,3,2,6,4,1] => 7 [5,3,4,1,2,6] => 5 [5,3,4,1,6,2] => 6 [5,3,4,2,1,6] => 6 [5,3,4,2,6,1] => 7 [5,3,4,6,1,2] => 7 [5,3,4,6,2,1] => 8 [5,3,6,1,2,4] => 5 [5,3,6,1,4,2] => 6 [5,3,6,2,1,4] => 6 [5,3,6,2,4,1] => 7 [5,3,6,4,1,2] => 7 [5,3,6,4,2,1] => 8 [5,4,1,2,3,6] => 3 [5,4,1,2,6,3] => 4 [5,4,1,3,2,6] => 4 [5,4,1,3,6,2] => 5 [5,4,1,6,2,3] => 5 [5,4,1,6,3,2] => 6 [5,4,2,1,3,6] => 4 [5,4,2,1,6,3] => 5 [5,4,2,3,1,6] => 5 [5,4,2,3,6,1] => 6 [5,4,2,6,1,3] => 6 [5,4,2,6,3,1] => 7 [5,4,3,1,2,6] => 5 [5,4,3,1,6,2] => 6 [5,4,3,2,1,6] => 6 [5,4,3,2,6,1] => 7 [5,4,3,6,1,2] => 7 [5,4,3,6,2,1] => 8 [5,4,6,1,2,3] => 6 [5,4,6,1,3,2] => 7 [5,4,6,2,1,3] => 7 [5,4,6,2,3,1] => 8 [5,4,6,3,1,2] => 8 [5,4,6,3,2,1] => 9 [5,6,1,2,3,4] => 3 [5,6,1,2,4,3] => 4 [5,6,1,3,2,4] => 4 [5,6,1,3,4,2] => 5 [5,6,1,4,2,3] => 5 [5,6,1,4,3,2] => 6 [5,6,2,1,3,4] => 4 [5,6,2,1,4,3] => 5 [5,6,2,3,1,4] => 5 [5,6,2,3,4,1] => 6 [5,6,2,4,1,3] => 6 [5,6,2,4,3,1] => 7 [5,6,3,1,2,4] => 5 [5,6,3,1,4,2] => 6 [5,6,3,2,1,4] => 6 [5,6,3,2,4,1] => 7 [5,6,3,4,1,2] => 7 [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] => 7 [5,6,4,2,3,1] => 8 [5,6,4,3,1,2] => 8 [5,6,4,3,2,1] => 9 [6,1,2,3,4,5] => 1 [6,1,2,3,5,4] => 2 [6,1,2,4,3,5] => 2 [6,1,2,4,5,3] => 3 [6,1,2,5,3,4] => 3 [6,1,2,5,4,3] => 4 [6,1,3,2,4,5] => 2 [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] => 4 [6,1,3,5,4,2] => 5 [6,1,4,2,3,5] => 3 [6,1,4,2,5,3] => 4 [6,1,4,3,2,5] => 4 [6,1,4,3,5,2] => 5 [6,1,4,5,2,3] => 5 [6,1,4,5,3,2] => 6 [6,1,5,2,3,4] => 3 [6,1,5,2,4,3] => 4 [6,1,5,3,2,4] => 4 [6,1,5,3,4,2] => 5 [6,1,5,4,2,3] => 5 [6,1,5,4,3,2] => 6 [6,2,1,3,4,5] => 2 [6,2,1,3,5,4] => 3 [6,2,1,4,3,5] => 3 [6,2,1,4,5,3] => 4 [6,2,1,5,3,4] => 4 [6,2,1,5,4,3] => 5 [6,2,3,1,4,5] => 3 [6,2,3,1,5,4] => 4 [6,2,3,4,1,5] => 4 [6,2,3,4,5,1] => 5 [6,2,3,5,1,4] => 5 [6,2,3,5,4,1] => 6 [6,2,4,1,3,5] => 4 [6,2,4,1,5,3] => 5 [6,2,4,3,1,5] => 5 [6,2,4,3,5,1] => 6 [6,2,4,5,1,3] => 6 [6,2,4,5,3,1] => 7 [6,2,5,1,3,4] => 4 [6,2,5,1,4,3] => 5 [6,2,5,3,1,4] => 5 [6,2,5,3,4,1] => 6 [6,2,5,4,1,3] => 6 [6,2,5,4,3,1] => 7 [6,3,1,2,4,5] => 3 [6,3,1,2,5,4] => 4 [6,3,1,4,2,5] => 4 [6,3,1,4,5,2] => 5 [6,3,1,5,2,4] => 5 [6,3,1,5,4,2] => 6 [6,3,2,1,4,5] => 4 [6,3,2,1,5,4] => 5 [6,3,2,4,1,5] => 5 [6,3,2,4,5,1] => 6 [6,3,2,5,1,4] => 6 [6,3,2,5,4,1] => 7 [6,3,4,1,2,5] => 5 [6,3,4,1,5,2] => 6 [6,3,4,2,1,5] => 6 [6,3,4,2,5,1] => 7 [6,3,4,5,1,2] => 7 [6,3,4,5,2,1] => 8 [6,3,5,1,2,4] => 5 [6,3,5,1,4,2] => 6 [6,3,5,2,1,4] => 6 [6,3,5,2,4,1] => 7 [6,3,5,4,1,2] => 7 [6,3,5,4,2,1] => 8 [6,4,1,2,3,5] => 3 [6,4,1,2,5,3] => 4 [6,4,1,3,2,5] => 4 [6,4,1,3,5,2] => 5 [6,4,1,5,2,3] => 5 [6,4,1,5,3,2] => 6 [6,4,2,1,3,5] => 4 [6,4,2,1,5,3] => 5 [6,4,2,3,1,5] => 5 [6,4,2,3,5,1] => 6 [6,4,2,5,1,3] => 6 [6,4,2,5,3,1] => 7 [6,4,3,1,2,5] => 5 [6,4,3,1,5,2] => 6 [6,4,3,2,1,5] => 6 [6,4,3,2,5,1] => 7 [6,4,3,5,1,2] => 7 [6,4,3,5,2,1] => 8 [6,4,5,1,2,3] => 6 [6,4,5,1,3,2] => 7 [6,4,5,2,1,3] => 7 [6,4,5,2,3,1] => 8 [6,4,5,3,1,2] => 8 [6,4,5,3,2,1] => 9 [6,5,1,2,3,4] => 3 [6,5,1,2,4,3] => 4 [6,5,1,3,2,4] => 4 [6,5,1,3,4,2] => 5 [6,5,1,4,2,3] => 5 [6,5,1,4,3,2] => 6 [6,5,2,1,3,4] => 4 [6,5,2,1,4,3] => 5 [6,5,2,3,1,4] => 5 [6,5,2,3,4,1] => 6 [6,5,2,4,1,3] => 6 [6,5,2,4,3,1] => 7 [6,5,3,1,2,4] => 5 [6,5,3,1,4,2] => 6 [6,5,3,2,1,4] => 6 [6,5,3,2,4,1] => 7 [6,5,3,4,1,2] => 7 [6,5,3,4,2,1] => 8 [6,5,4,1,2,3] => 6 [6,5,4,1,3,2] => 7 [6,5,4,2,1,3] => 7 [6,5,4,2,3,1] => 8 [6,5,4,3,1,2] => 8 [6,5,4,3,2,1] => 9 [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] => 2 [1,2,3,4,7,5,6] => 1 [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] => 2 [1,2,3,5,6,7,4] => 3 [1,2,3,5,7,4,6] => 2 [1,2,3,5,7,6,4] => 3 [1,2,3,6,4,5,7] => 1 [1,2,3,6,4,7,5] => 2 [1,2,3,6,5,4,7] => 2 [1,2,3,6,5,7,4] => 3 [1,2,3,6,7,4,5] => 3 [1,2,3,6,7,5,4] => 4 [1,2,3,7,4,5,6] => 1 [1,2,3,7,4,6,5] => 2 [1,2,3,7,5,4,6] => 2 [1,2,3,7,5,6,4] => 3 [1,2,3,7,6,4,5] => 3 [1,2,3,7,6,5,4] => 4 [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] => 3 [1,2,4,3,7,5,6] => 2 [1,2,4,3,7,6,5] => 3 [1,2,4,5,3,6,7] => 2 [1,2,4,5,3,7,6] => 3 [1,2,4,5,6,3,7] => 3 [1,2,4,5,6,7,3] => 4 [1,2,4,5,7,3,6] => 3 [1,2,4,5,7,6,3] => 4 [1,2,4,6,3,5,7] => 2 [1,2,4,6,3,7,5] => 3 [1,2,4,6,5,3,7] => 3 [1,2,4,6,5,7,3] => 4 [1,2,4,6,7,3,5] => 4 [1,2,4,6,7,5,3] => 5 [1,2,4,7,3,5,6] => 2 [1,2,4,7,3,6,5] => 3 [1,2,4,7,5,3,6] => 3 [1,2,4,7,5,6,3] => 4 [1,2,4,7,6,3,5] => 4 [1,2,4,7,6,5,3] => 5 [1,2,5,3,4,6,7] => 1 [1,2,5,3,4,7,6] => 2 [1,2,5,3,6,4,7] => 2 [1,2,5,3,6,7,4] => 3 [1,2,5,3,7,4,6] => 2 [1,2,5,3,7,6,4] => 3 [1,2,5,4,3,6,7] => 2 [1,2,5,4,3,7,6] => 3 [1,2,5,4,6,3,7] => 3 [1,2,5,4,6,7,3] => 4 [1,2,5,4,7,3,6] => 3 [1,2,5,4,7,6,3] => 4 [1,2,5,6,3,4,7] => 3 [1,2,5,6,3,7,4] => 4 [1,2,5,6,4,3,7] => 4 [1,2,5,6,4,7,3] => 5 [1,2,5,6,7,3,4] => 5 [1,2,5,6,7,4,3] => 6 [1,2,5,7,3,4,6] => 3 [1,2,5,7,3,6,4] => 4 [1,2,5,7,4,3,6] => 4 [1,2,5,7,4,6,3] => 5 [1,2,5,7,6,3,4] => 5 [1,2,5,7,6,4,3] => 6 [1,2,6,3,4,5,7] => 1 [1,2,6,3,4,7,5] => 2 [1,2,6,3,5,4,7] => 2 [1,2,6,3,5,7,4] => 3 [1,2,6,3,7,4,5] => 3 [1,2,6,3,7,5,4] => 4 [1,2,6,4,3,5,7] => 2 [1,2,6,4,3,7,5] => 3 [1,2,6,4,5,3,7] => 3 [1,2,6,4,5,7,3] => 4 [1,2,6,4,7,3,5] => 4 [1,2,6,4,7,5,3] => 5 [1,2,6,5,3,4,7] => 3 [1,2,6,5,3,7,4] => 4 [1,2,6,5,4,3,7] => 4 [1,2,6,5,4,7,3] => 5 [1,2,6,5,7,3,4] => 5 [1,2,6,5,7,4,3] => 6 [1,2,6,7,3,4,5] => 3 [1,2,6,7,3,5,4] => 4 [1,2,6,7,4,3,5] => 4 [1,2,6,7,4,5,3] => 5 [1,2,6,7,5,3,4] => 5 [1,2,6,7,5,4,3] => 6 [1,2,7,3,4,5,6] => 1 [1,2,7,3,4,6,5] => 2 [1,2,7,3,5,4,6] => 2 [1,2,7,3,5,6,4] => 3 [1,2,7,3,6,4,5] => 3 [1,2,7,3,6,5,4] => 4 [1,2,7,4,3,5,6] => 2 [1,2,7,4,3,6,5] => 3 [1,2,7,4,5,3,6] => 3 [1,2,7,4,5,6,3] => 4 [1,2,7,4,6,3,5] => 4 [1,2,7,4,6,5,3] => 5 [1,2,7,5,3,4,6] => 3 [1,2,7,5,3,6,4] => 4 [1,2,7,5,4,3,6] => 4 [1,2,7,5,4,6,3] => 5 [1,2,7,5,6,3,4] => 5 [1,2,7,5,6,4,3] => 6 [1,2,7,6,3,4,5] => 3 [1,2,7,6,3,5,4] => 4 [1,2,7,6,4,3,5] => 4 [1,2,7,6,4,5,3] => 5 [1,2,7,6,5,3,4] => 5 [1,2,7,6,5,4,3] => 6 [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] => 3 [1,3,2,4,7,5,6] => 2 [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] => 3 [1,3,2,5,6,7,4] => 4 [1,3,2,5,7,4,6] => 3 [1,3,2,5,7,6,4] => 4 [1,3,2,6,4,5,7] => 2 [1,3,2,6,4,7,5] => 3 [1,3,2,6,5,4,7] => 3 [1,3,2,6,5,7,4] => 4 [1,3,2,6,7,4,5] => 4 [1,3,2,6,7,5,4] => 5 [1,3,2,7,4,5,6] => 2 [1,3,2,7,4,6,5] => 3 [1,3,2,7,5,4,6] => 3 [1,3,2,7,5,6,4] => 4 [1,3,2,7,6,4,5] => 4 [1,3,2,7,6,5,4] => 5 [1,3,4,2,5,6,7] => 2 [1,3,4,2,5,7,6] => 3 [1,3,4,2,6,5,7] => 3 [1,3,4,2,6,7,5] => 4 [1,3,4,2,7,5,6] => 3 [1,3,4,2,7,6,5] => 4 [1,3,4,5,2,6,7] => 3 [1,3,4,5,2,7,6] => 4 [1,3,4,5,6,2,7] => 4 [1,3,4,5,6,7,2] => 5 [1,3,4,5,7,2,6] => 4 [1,3,4,5,7,6,2] => 5 [1,3,4,6,2,5,7] => 3 [1,3,4,6,2,7,5] => 4 [1,3,4,6,5,2,7] => 4 [1,3,4,6,5,7,2] => 5 [1,3,4,6,7,2,5] => 5 [1,3,4,6,7,5,2] => 6 [1,3,4,7,2,5,6] => 3 [1,3,4,7,2,6,5] => 4 [1,3,4,7,5,2,6] => 4 [1,3,4,7,5,6,2] => 5 [1,3,4,7,6,2,5] => 5 [1,3,4,7,6,5,2] => 6 [1,3,5,2,4,6,7] => 2 [1,3,5,2,4,7,6] => 3 [1,3,5,2,6,4,7] => 3 [1,3,5,2,6,7,4] => 4 [1,3,5,2,7,4,6] => 3 [1,3,5,2,7,6,4] => 4 [1,3,5,4,2,6,7] => 3 [1,3,5,4,2,7,6] => 4 [1,3,5,4,6,2,7] => 4 [1,3,5,4,6,7,2] => 5 [1,3,5,4,7,2,6] => 4 [1,3,5,4,7,6,2] => 5 [1,3,5,6,2,4,7] => 4 [1,3,5,6,2,7,4] => 5 [1,3,5,6,4,2,7] => 5 [1,3,5,6,4,7,2] => 6 [1,3,5,6,7,2,4] => 6 [1,3,5,6,7,4,2] => 7 [1,3,5,7,2,4,6] => 4 [1,3,5,7,2,6,4] => 5 [1,3,5,7,4,2,6] => 5 [1,3,5,7,4,6,2] => 6 [1,3,5,7,6,2,4] => 6 [1,3,5,7,6,4,2] => 7 [1,3,6,2,4,5,7] => 2 [1,3,6,2,4,7,5] => 3 [1,3,6,2,5,4,7] => 3 [1,3,6,2,5,7,4] => 4 [1,3,6,2,7,4,5] => 4 [1,3,6,2,7,5,4] => 5 [1,3,6,4,2,5,7] => 3 [1,3,6,4,2,7,5] => 4 [1,3,6,4,5,2,7] => 4 [1,3,6,4,5,7,2] => 5 [1,3,6,4,7,2,5] => 5 [1,3,6,4,7,5,2] => 6 [1,3,6,5,2,4,7] => 4 [1,3,6,5,2,7,4] => 5 [1,3,6,5,4,2,7] => 5 [1,3,6,5,4,7,2] => 6 [1,3,6,5,7,2,4] => 6 [1,3,6,5,7,4,2] => 7 [1,3,6,7,2,4,5] => 4 [1,3,6,7,2,5,4] => 5 [1,3,6,7,4,2,5] => 5 [1,3,6,7,4,5,2] => 6 [1,3,6,7,5,2,4] => 6 [1,3,6,7,5,4,2] => 7 [1,3,7,2,4,5,6] => 2 [1,3,7,2,4,6,5] => 3 [1,3,7,2,5,4,6] => 3 [1,3,7,2,5,6,4] => 4 [1,3,7,2,6,4,5] => 4 [1,3,7,2,6,5,4] => 5 [1,3,7,4,2,5,6] => 3 [1,3,7,4,2,6,5] => 4 [1,3,7,4,5,2,6] => 4 [1,3,7,4,5,6,2] => 5 [1,3,7,4,6,2,5] => 5 [1,3,7,4,6,5,2] => 6 [1,3,7,5,2,4,6] => 4 [1,3,7,5,2,6,4] => 5 [1,3,7,5,4,2,6] => 5 [1,3,7,5,4,6,2] => 6 [1,3,7,5,6,2,4] => 6 [1,3,7,5,6,4,2] => 7 [1,3,7,6,2,4,5] => 4 [1,3,7,6,2,5,4] => 5 [1,3,7,6,4,2,5] => 5 [1,3,7,6,4,5,2] => 6 [1,3,7,6,5,2,4] => 6 [1,3,7,6,5,4,2] => 7 [1,4,2,3,5,6,7] => 1 [1,4,2,3,5,7,6] => 2 [1,4,2,3,6,5,7] => 2 [1,4,2,3,6,7,5] => 3 [1,4,2,3,7,5,6] => 2 [1,4,2,3,7,6,5] => 3 [1,4,2,5,3,6,7] => 2 [1,4,2,5,3,7,6] => 3 [1,4,2,5,6,3,7] => 3 [1,4,2,5,6,7,3] => 4 [1,4,2,5,7,3,6] => 3 [1,4,2,5,7,6,3] => 4 [1,4,2,6,3,5,7] => 2 [1,4,2,6,3,7,5] => 3 [1,4,2,6,5,3,7] => 3 [1,4,2,6,5,7,3] => 4 [1,4,2,6,7,3,5] => 4 [1,4,2,6,7,5,3] => 5 [1,4,2,7,3,5,6] => 2 [1,4,2,7,3,6,5] => 3 [1,4,2,7,5,3,6] => 3 [1,4,2,7,5,6,3] => 4 [1,4,2,7,6,3,5] => 4 [1,4,2,7,6,5,3] => 5 [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] => 4 [1,4,3,2,7,5,6] => 3 [1,4,3,2,7,6,5] => 4 [1,4,3,5,2,6,7] => 3 [1,4,3,5,2,7,6] => 4 [1,4,3,5,6,2,7] => 4 [1,4,3,5,6,7,2] => 5 [1,4,3,5,7,2,6] => 4 [1,4,3,5,7,6,2] => 5 [1,4,3,6,2,5,7] => 3 [1,4,3,6,2,7,5] => 4 [1,4,3,6,5,2,7] => 4 [1,4,3,6,5,7,2] => 5 [1,4,3,6,7,2,5] => 5 [1,4,3,6,7,5,2] => 6 [1,4,3,7,2,5,6] => 3 [1,4,3,7,2,6,5] => 4 [1,4,3,7,5,2,6] => 4 [1,4,3,7,5,6,2] => 5 [1,4,3,7,6,2,5] => 5 [1,4,3,7,6,5,2] => 6 [1,4,5,2,3,6,7] => 3 [1,4,5,2,3,7,6] => 4 [1,4,5,2,6,3,7] => 4 [1,4,5,2,6,7,3] => 5 [1,4,5,2,7,3,6] => 4 [1,4,5,2,7,6,3] => 5 [1,4,5,3,2,6,7] => 4 [1,4,5,3,2,7,6] => 5 [1,4,5,3,6,2,7] => 5 [1,4,5,3,6,7,2] => 6 [1,4,5,3,7,2,6] => 5 [1,4,5,3,7,6,2] => 6 [1,4,5,6,2,3,7] => 5 [1,4,5,6,2,7,3] => 6 [1,4,5,6,3,2,7] => 6 [1,4,5,6,3,7,2] => 7 [1,4,5,6,7,2,3] => 7 [1,4,5,6,7,3,2] => 8 [1,4,5,7,2,3,6] => 5 [1,4,5,7,2,6,3] => 6 [1,4,5,7,3,2,6] => 6 [1,4,5,7,3,6,2] => 7 [1,4,5,7,6,2,3] => 7 [1,4,5,7,6,3,2] => 8 [1,4,6,2,3,5,7] => 3 [1,4,6,2,3,7,5] => 4 [1,4,6,2,5,3,7] => 4 [1,4,6,2,5,7,3] => 5 [1,4,6,2,7,3,5] => 5 [1,4,6,2,7,5,3] => 6 [1,4,6,3,2,5,7] => 4 [1,4,6,3,2,7,5] => 5 [1,4,6,3,5,2,7] => 5 [1,4,6,3,5,7,2] => 6 [1,4,6,3,7,2,5] => 6 [1,4,6,3,7,5,2] => 7 [1,4,6,5,2,3,7] => 5 [1,4,6,5,2,7,3] => 6 [1,4,6,5,3,2,7] => 6 ----------------------------------------------------------------------------- Created: Jun 14, 2021 at 12:56 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Jun 14, 2021 at 20:20 by Zachary Hamaker