***************************************************************************** * 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: St000809 ----------------------------------------------------------------------------- Collection: Permutations ----------------------------------------------------------------------------- Description: The reduced reflection length of the permutation. Let $T$ be the set of reflections in a Coxeter group and let $\ell(w)$ be the usual length function. Then the reduced reflection length of $w$ is $$\min\{r\in\mathbb N \mid w = t_1\cdots t_r,\quad t_1,\dots,t_r \in T,\quad \ell(w)=\sum \ell(t_i)\}.$$ In the case of the symmetric group, this is twice the depth [[St000029]] minus the usual length [[St000018]]. ----------------------------------------------------------------------------- References: [1] Bagno, E., Biagioli, R., Novick, M., Woo, A. Depth in classical Coexter groups [[arXiv:1507.01180]] [2] Bemte Reference request: Reduced reflection length in Coxeter groups [[MathOverflow:270174]] ----------------------------------------------------------------------------- Code: def statistic(w): depth = sum(w[i]-i-1 for i in range(len(w)) if w[i]>i+1) return 2*depth-w.length() ----------------------------------------------------------------------------- Statistic values: [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] => 2 [3,2,1] => 1 [1,2,3,4] => 0 [1,2,4,3] => 1 [1,3,2,4] => 1 [1,3,4,2] => 2 [1,4,2,3] => 2 [1,4,3,2] => 1 [2,1,3,4] => 1 [2,1,4,3] => 2 [2,3,1,4] => 2 [2,3,4,1] => 3 [2,4,1,3] => 3 [2,4,3,1] => 2 [3,1,2,4] => 2 [3,1,4,2] => 3 [3,2,1,4] => 1 [3,2,4,1] => 2 [3,4,1,2] => 4 [3,4,2,1] => 3 [4,1,2,3] => 3 [4,1,3,2] => 2 [4,2,1,3] => 2 [4,2,3,1] => 1 [4,3,1,2] => 3 [4,3,2,1] => 2 [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] => 2 [1,2,5,4,3] => 1 [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] => 3 [1,3,5,4,2] => 2 [1,4,2,3,5] => 2 [1,4,2,5,3] => 3 [1,4,3,2,5] => 1 [1,4,3,5,2] => 2 [1,4,5,2,3] => 4 [1,4,5,3,2] => 3 [1,5,2,3,4] => 3 [1,5,2,4,3] => 2 [1,5,3,2,4] => 2 [1,5,3,4,2] => 1 [1,5,4,2,3] => 3 [1,5,4,3,2] => 2 [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] => 3 [2,1,5,4,3] => 2 [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] => 4 [2,3,5,4,1] => 3 [2,4,1,3,5] => 3 [2,4,1,5,3] => 4 [2,4,3,1,5] => 2 [2,4,3,5,1] => 3 [2,4,5,1,3] => 5 [2,4,5,3,1] => 4 [2,5,1,3,4] => 4 [2,5,1,4,3] => 3 [2,5,3,1,4] => 3 [2,5,3,4,1] => 2 [2,5,4,1,3] => 4 [2,5,4,3,1] => 3 [3,1,2,4,5] => 2 [3,1,2,5,4] => 3 [3,1,4,2,5] => 3 [3,1,4,5,2] => 4 [3,1,5,2,4] => 4 [3,1,5,4,2] => 3 [3,2,1,4,5] => 1 [3,2,1,5,4] => 2 [3,2,4,1,5] => 2 [3,2,4,5,1] => 3 [3,2,5,1,4] => 3 [3,2,5,4,1] => 2 [3,4,1,2,5] => 4 [3,4,1,5,2] => 5 [3,4,2,1,5] => 3 [3,4,2,5,1] => 4 [3,4,5,1,2] => 6 [3,4,5,2,1] => 5 [3,5,1,2,4] => 5 [3,5,1,4,2] => 4 [3,5,2,1,4] => 4 [3,5,2,4,1] => 3 [3,5,4,1,2] => 5 [3,5,4,2,1] => 4 [4,1,2,3,5] => 3 [4,1,2,5,3] => 4 [4,1,3,2,5] => 2 [4,1,3,5,2] => 3 [4,1,5,2,3] => 5 [4,1,5,3,2] => 4 [4,2,1,3,5] => 2 [4,2,1,5,3] => 3 [4,2,3,1,5] => 1 [4,2,3,5,1] => 2 [4,2,5,1,3] => 4 [4,2,5,3,1] => 3 [4,3,1,2,5] => 3 [4,3,1,5,2] => 4 [4,3,2,1,5] => 2 [4,3,2,5,1] => 3 [4,3,5,1,2] => 5 [4,3,5,2,1] => 4 [4,5,1,2,3] => 6 [4,5,1,3,2] => 5 [4,5,2,1,3] => 5 [4,5,2,3,1] => 4 [4,5,3,1,2] => 4 [4,5,3,2,1] => 3 [5,1,2,3,4] => 4 [5,1,2,4,3] => 3 [5,1,3,2,4] => 3 [5,1,3,4,2] => 2 [5,1,4,2,3] => 4 [5,1,4,3,2] => 3 [5,2,1,3,4] => 3 [5,2,1,4,3] => 2 [5,2,3,1,4] => 2 [5,2,3,4,1] => 1 [5,2,4,1,3] => 3 [5,2,4,3,1] => 2 [5,3,1,2,4] => 4 [5,3,1,4,2] => 3 [5,3,2,1,4] => 3 [5,3,2,4,1] => 2 [5,3,4,1,2] => 4 [5,3,4,2,1] => 3 [5,4,1,2,3] => 5 [5,4,1,3,2] => 4 [5,4,2,1,3] => 4 [5,4,2,3,1] => 3 [5,4,3,1,2] => 3 [5,4,3,2,1] => 2 [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] => 2 [1,2,3,6,5,4] => 1 [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] => 3 [1,2,4,6,5,3] => 2 [1,2,5,3,4,6] => 2 [1,2,5,3,6,4] => 3 [1,2,5,4,3,6] => 1 [1,2,5,4,6,3] => 2 [1,2,5,6,3,4] => 4 [1,2,5,6,4,3] => 3 [1,2,6,3,4,5] => 3 [1,2,6,3,5,4] => 2 [1,2,6,4,3,5] => 2 [1,2,6,4,5,3] => 1 [1,2,6,5,3,4] => 3 [1,2,6,5,4,3] => 2 [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] => 3 [1,3,2,6,5,4] => 2 [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] => 4 [1,3,4,6,5,2] => 3 [1,3,5,2,4,6] => 3 [1,3,5,2,6,4] => 4 [1,3,5,4,2,6] => 2 [1,3,5,4,6,2] => 3 [1,3,5,6,2,4] => 5 [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] => 2 [1,3,6,5,2,4] => 4 [1,3,6,5,4,2] => 3 [1,4,2,3,5,6] => 2 [1,4,2,3,6,5] => 3 [1,4,2,5,3,6] => 3 [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] => 1 [1,4,3,2,6,5] => 2 [1,4,3,5,2,6] => 2 [1,4,3,5,6,2] => 3 [1,4,3,6,2,5] => 3 [1,4,3,6,5,2] => 2 [1,4,5,2,3,6] => 4 [1,4,5,2,6,3] => 5 [1,4,5,3,2,6] => 3 [1,4,5,3,6,2] => 4 [1,4,5,6,2,3] => 6 [1,4,5,6,3,2] => 5 [1,4,6,2,3,5] => 5 [1,4,6,2,5,3] => 4 [1,4,6,3,2,5] => 4 [1,4,6,3,5,2] => 3 [1,4,6,5,2,3] => 5 [1,4,6,5,3,2] => 4 [1,5,2,3,4,6] => 3 [1,5,2,3,6,4] => 4 [1,5,2,4,3,6] => 2 [1,5,2,4,6,3] => 3 [1,5,2,6,3,4] => 5 [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] => 1 [1,5,3,4,6,2] => 2 [1,5,3,6,2,4] => 4 [1,5,3,6,4,2] => 3 [1,5,4,2,3,6] => 3 [1,5,4,2,6,3] => 4 [1,5,4,3,2,6] => 2 [1,5,4,3,6,2] => 3 [1,5,4,6,2,3] => 5 [1,5,4,6,3,2] => 4 [1,5,6,2,3,4] => 6 [1,5,6,2,4,3] => 5 [1,5,6,3,2,4] => 5 [1,5,6,3,4,2] => 4 [1,5,6,4,2,3] => 4 [1,5,6,4,3,2] => 3 [1,6,2,3,4,5] => 4 [1,6,2,3,5,4] => 3 [1,6,2,4,3,5] => 3 [1,6,2,4,5,3] => 2 [1,6,2,5,3,4] => 4 [1,6,2,5,4,3] => 3 [1,6,3,2,4,5] => 3 [1,6,3,2,5,4] => 2 [1,6,3,4,2,5] => 2 [1,6,3,4,5,2] => 1 [1,6,3,5,2,4] => 3 [1,6,3,5,4,2] => 2 [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] => 2 [1,6,4,5,2,3] => 4 [1,6,4,5,3,2] => 3 [1,6,5,2,3,4] => 5 [1,6,5,2,4,3] => 4 [1,6,5,3,2,4] => 4 [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] => 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] => 3 [2,1,3,6,5,4] => 2 [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] => 4 [2,1,4,6,5,3] => 3 [2,1,5,3,4,6] => 3 [2,1,5,3,6,4] => 4 [2,1,5,4,3,6] => 2 [2,1,5,4,6,3] => 3 [2,1,5,6,3,4] => 5 [2,1,5,6,4,3] => 4 [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] => 2 [2,1,6,5,3,4] => 4 [2,1,6,5,4,3] => 3 [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] => 4 [2,3,1,6,5,4] => 3 [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] => 5 [2,3,4,6,5,1] => 4 [2,3,5,1,4,6] => 4 [2,3,5,1,6,4] => 5 [2,3,5,4,1,6] => 3 [2,3,5,4,6,1] => 4 [2,3,5,6,1,4] => 6 [2,3,5,6,4,1] => 5 [2,3,6,1,4,5] => 5 [2,3,6,1,5,4] => 4 [2,3,6,4,1,5] => 4 [2,3,6,4,5,1] => 3 [2,3,6,5,1,4] => 5 [2,3,6,5,4,1] => 4 [2,4,1,3,5,6] => 3 [2,4,1,3,6,5] => 4 [2,4,1,5,3,6] => 4 [2,4,1,5,6,3] => 5 [2,4,1,6,3,5] => 5 [2,4,1,6,5,3] => 4 [2,4,3,1,5,6] => 2 [2,4,3,1,6,5] => 3 [2,4,3,5,1,6] => 3 [2,4,3,5,6,1] => 4 [2,4,3,6,1,5] => 4 [2,4,3,6,5,1] => 3 [2,4,5,1,3,6] => 5 [2,4,5,1,6,3] => 6 [2,4,5,3,1,6] => 4 [2,4,5,3,6,1] => 5 [2,4,5,6,1,3] => 7 [2,4,5,6,3,1] => 6 [2,4,6,1,3,5] => 6 [2,4,6,1,5,3] => 5 [2,4,6,3,1,5] => 5 [2,4,6,3,5,1] => 4 [2,4,6,5,1,3] => 6 [2,4,6,5,3,1] => 5 [2,5,1,3,4,6] => 4 [2,5,1,3,6,4] => 5 [2,5,1,4,3,6] => 3 [2,5,1,4,6,3] => 4 [2,5,1,6,3,4] => 6 [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] => 2 [2,5,3,4,6,1] => 3 [2,5,3,6,1,4] => 5 [2,5,3,6,4,1] => 4 [2,5,4,1,3,6] => 4 [2,5,4,1,6,3] => 5 [2,5,4,3,1,6] => 3 [2,5,4,3,6,1] => 4 [2,5,4,6,1,3] => 6 [2,5,4,6,3,1] => 5 [2,5,6,1,3,4] => 7 [2,5,6,1,4,3] => 6 [2,5,6,3,1,4] => 6 [2,5,6,3,4,1] => 5 [2,5,6,4,1,3] => 5 [2,5,6,4,3,1] => 4 [2,6,1,3,4,5] => 5 [2,6,1,3,5,4] => 4 [2,6,1,4,3,5] => 4 [2,6,1,4,5,3] => 3 [2,6,1,5,3,4] => 5 [2,6,1,5,4,3] => 4 [2,6,3,1,4,5] => 4 [2,6,3,1,5,4] => 3 [2,6,3,4,1,5] => 3 [2,6,3,4,5,1] => 2 [2,6,3,5,1,4] => 4 [2,6,3,5,4,1] => 3 [2,6,4,1,3,5] => 5 [2,6,4,1,5,3] => 4 [2,6,4,3,1,5] => 4 [2,6,4,3,5,1] => 3 [2,6,4,5,1,3] => 5 [2,6,4,5,3,1] => 4 [2,6,5,1,3,4] => 6 [2,6,5,1,4,3] => 5 [2,6,5,3,1,4] => 5 [2,6,5,3,4,1] => 4 [2,6,5,4,1,3] => 4 [2,6,5,4,3,1] => 3 [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] => 4 [3,1,2,6,4,5] => 4 [3,1,2,6,5,4] => 3 [3,1,4,2,5,6] => 3 [3,1,4,2,6,5] => 4 [3,1,4,5,2,6] => 4 [3,1,4,5,6,2] => 5 [3,1,4,6,2,5] => 5 [3,1,4,6,5,2] => 4 [3,1,5,2,4,6] => 4 [3,1,5,2,6,4] => 5 [3,1,5,4,2,6] => 3 [3,1,5,4,6,2] => 4 [3,1,5,6,2,4] => 6 [3,1,5,6,4,2] => 5 [3,1,6,2,4,5] => 5 [3,1,6,2,5,4] => 4 [3,1,6,4,2,5] => 4 [3,1,6,4,5,2] => 3 [3,1,6,5,2,4] => 5 [3,1,6,5,4,2] => 4 [3,2,1,4,5,6] => 1 [3,2,1,4,6,5] => 2 [3,2,1,5,4,6] => 2 [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] => 2 [3,2,4,1,6,5] => 3 [3,2,4,5,1,6] => 3 [3,2,4,5,6,1] => 4 [3,2,4,6,1,5] => 4 [3,2,4,6,5,1] => 3 [3,2,5,1,4,6] => 3 [3,2,5,1,6,4] => 4 [3,2,5,4,1,6] => 2 [3,2,5,4,6,1] => 3 [3,2,5,6,1,4] => 5 [3,2,5,6,4,1] => 4 [3,2,6,1,4,5] => 4 [3,2,6,1,5,4] => 3 [3,2,6,4,1,5] => 3 [3,2,6,4,5,1] => 2 [3,2,6,5,1,4] => 4 [3,2,6,5,4,1] => 3 [3,4,1,2,5,6] => 4 [3,4,1,2,6,5] => 5 [3,4,1,5,2,6] => 5 [3,4,1,5,6,2] => 6 [3,4,1,6,2,5] => 6 [3,4,1,6,5,2] => 5 [3,4,2,1,5,6] => 3 [3,4,2,1,6,5] => 4 [3,4,2,5,1,6] => 4 [3,4,2,5,6,1] => 5 [3,4,2,6,1,5] => 5 [3,4,2,6,5,1] => 4 [3,4,5,1,2,6] => 6 [3,4,5,1,6,2] => 7 [3,4,5,2,1,6] => 5 [3,4,5,2,6,1] => 6 [3,4,5,6,1,2] => 8 [3,4,5,6,2,1] => 7 [3,4,6,1,2,5] => 7 [3,4,6,1,5,2] => 6 [3,4,6,2,1,5] => 6 [3,4,6,2,5,1] => 5 [3,4,6,5,1,2] => 7 [3,4,6,5,2,1] => 6 [3,5,1,2,4,6] => 5 [3,5,1,2,6,4] => 6 [3,5,1,4,2,6] => 4 [3,5,1,4,6,2] => 5 [3,5,1,6,2,4] => 7 [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] => 3 [3,5,2,4,6,1] => 4 [3,5,2,6,1,4] => 6 [3,5,2,6,4,1] => 5 [3,5,4,1,2,6] => 5 [3,5,4,1,6,2] => 6 [3,5,4,2,1,6] => 4 [3,5,4,2,6,1] => 5 [3,5,4,6,1,2] => 7 [3,5,4,6,2,1] => 6 [3,5,6,1,2,4] => 8 [3,5,6,1,4,2] => 7 [3,5,6,2,1,4] => 7 [3,5,6,2,4,1] => 6 [3,5,6,4,1,2] => 6 [3,5,6,4,2,1] => 5 [3,6,1,2,4,5] => 6 [3,6,1,2,5,4] => 5 [3,6,1,4,2,5] => 5 [3,6,1,4,5,2] => 4 [3,6,1,5,2,4] => 6 [3,6,1,5,4,2] => 5 [3,6,2,1,4,5] => 5 [3,6,2,1,5,4] => 4 [3,6,2,4,1,5] => 4 [3,6,2,4,5,1] => 3 [3,6,2,5,1,4] => 5 [3,6,2,5,4,1] => 4 [3,6,4,1,2,5] => 6 [3,6,4,1,5,2] => 5 [3,6,4,2,1,5] => 5 [3,6,4,2,5,1] => 4 [3,6,4,5,1,2] => 6 [3,6,4,5,2,1] => 5 [3,6,5,1,2,4] => 7 [3,6,5,1,4,2] => 6 [3,6,5,2,1,4] => 6 [3,6,5,2,4,1] => 5 [3,6,5,4,1,2] => 5 [3,6,5,4,2,1] => 4 [4,1,2,3,5,6] => 3 [4,1,2,3,6,5] => 4 [4,1,2,5,3,6] => 4 [4,1,2,5,6,3] => 5 [4,1,2,6,3,5] => 5 [4,1,2,6,5,3] => 4 [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] => 4 [4,1,3,6,5,2] => 3 [4,1,5,2,3,6] => 5 [4,1,5,2,6,3] => 6 [4,1,5,3,2,6] => 4 [4,1,5,3,6,2] => 5 [4,1,5,6,2,3] => 7 [4,1,5,6,3,2] => 6 [4,1,6,2,3,5] => 6 [4,1,6,2,5,3] => 5 [4,1,6,3,2,5] => 5 [4,1,6,3,5,2] => 4 [4,1,6,5,2,3] => 6 [4,1,6,5,3,2] => 5 [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] => 4 [4,2,1,6,5,3] => 3 [4,2,3,1,5,6] => 1 [4,2,3,1,6,5] => 2 [4,2,3,5,1,6] => 2 [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] => 4 [4,2,5,1,6,3] => 5 [4,2,5,3,1,6] => 3 [4,2,5,3,6,1] => 4 [4,2,5,6,1,3] => 6 [4,2,5,6,3,1] => 5 [4,2,6,1,3,5] => 5 [4,2,6,1,5,3] => 4 [4,2,6,3,1,5] => 4 [4,2,6,3,5,1] => 3 [4,2,6,5,1,3] => 5 [4,2,6,5,3,1] => 4 [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] => 5 [4,3,1,6,5,2] => 4 [4,3,2,1,5,6] => 2 [4,3,2,1,6,5] => 3 [4,3,2,5,1,6] => 3 [4,3,2,5,6,1] => 4 [4,3,2,6,1,5] => 4 [4,3,2,6,5,1] => 3 [4,3,5,1,2,6] => 5 [4,3,5,1,6,2] => 6 [4,3,5,2,1,6] => 4 [4,3,5,2,6,1] => 5 [4,3,5,6,1,2] => 7 [4,3,5,6,2,1] => 6 [4,3,6,1,2,5] => 6 [4,3,6,1,5,2] => 5 [4,3,6,2,1,5] => 5 [4,3,6,2,5,1] => 4 [4,3,6,5,1,2] => 6 [4,3,6,5,2,1] => 5 [4,5,1,2,3,6] => 6 [4,5,1,2,6,3] => 7 [4,5,1,3,2,6] => 5 [4,5,1,3,6,2] => 6 [4,5,1,6,2,3] => 8 [4,5,1,6,3,2] => 7 [4,5,2,1,3,6] => 5 [4,5,2,1,6,3] => 6 [4,5,2,3,1,6] => 4 [4,5,2,3,6,1] => 5 [4,5,2,6,1,3] => 7 [4,5,2,6,3,1] => 6 [4,5,3,1,2,6] => 4 [4,5,3,1,6,2] => 5 [4,5,3,2,1,6] => 3 [4,5,3,2,6,1] => 4 [4,5,3,6,1,2] => 6 [4,5,3,6,2,1] => 5 [4,5,6,1,2,3] => 9 [4,5,6,1,3,2] => 8 [4,5,6,2,1,3] => 8 [4,5,6,2,3,1] => 7 [4,5,6,3,1,2] => 7 [4,5,6,3,2,1] => 6 [4,6,1,2,3,5] => 7 [4,6,1,2,5,3] => 6 [4,6,1,3,2,5] => 6 [4,6,1,3,5,2] => 5 [4,6,1,5,2,3] => 7 [4,6,1,5,3,2] => 6 [4,6,2,1,3,5] => 6 [4,6,2,1,5,3] => 5 [4,6,2,3,1,5] => 5 [4,6,2,3,5,1] => 4 [4,6,2,5,1,3] => 6 [4,6,2,5,3,1] => 5 [4,6,3,1,2,5] => 5 [4,6,3,1,5,2] => 4 [4,6,3,2,1,5] => 4 [4,6,3,2,5,1] => 3 [4,6,3,5,1,2] => 5 [4,6,3,5,2,1] => 4 [4,6,5,1,2,3] => 8 [4,6,5,1,3,2] => 7 [4,6,5,2,1,3] => 7 [4,6,5,2,3,1] => 6 [4,6,5,3,1,2] => 6 [4,6,5,3,2,1] => 5 [5,1,2,3,4,6] => 4 [5,1,2,3,6,4] => 5 [5,1,2,4,3,6] => 3 [5,1,2,4,6,3] => 4 [5,1,2,6,3,4] => 6 [5,1,2,6,4,3] => 5 [5,1,3,2,4,6] => 3 [5,1,3,2,6,4] => 4 [5,1,3,4,2,6] => 2 [5,1,3,4,6,2] => 3 [5,1,3,6,2,4] => 5 [5,1,3,6,4,2] => 4 [5,1,4,2,3,6] => 4 [5,1,4,2,6,3] => 5 [5,1,4,3,2,6] => 3 [5,1,4,3,6,2] => 4 [5,1,4,6,2,3] => 6 [5,1,4,6,3,2] => 5 [5,1,6,2,3,4] => 7 [5,1,6,2,4,3] => 6 [5,1,6,3,2,4] => 6 [5,1,6,3,4,2] => 5 [5,1,6,4,2,3] => 5 [5,1,6,4,3,2] => 4 [5,2,1,3,4,6] => 3 [5,2,1,3,6,4] => 4 [5,2,1,4,3,6] => 2 [5,2,1,4,6,3] => 3 [5,2,1,6,3,4] => 5 [5,2,1,6,4,3] => 4 [5,2,3,1,4,6] => 2 [5,2,3,1,6,4] => 3 [5,2,3,4,1,6] => 1 [5,2,3,4,6,1] => 2 [5,2,3,6,1,4] => 4 [5,2,3,6,4,1] => 3 [5,2,4,1,3,6] => 3 [5,2,4,1,6,3] => 4 [5,2,4,3,1,6] => 2 [5,2,4,3,6,1] => 3 [5,2,4,6,1,3] => 5 [5,2,4,6,3,1] => 4 [5,2,6,1,3,4] => 6 [5,2,6,1,4,3] => 5 [5,2,6,3,1,4] => 5 [5,2,6,3,4,1] => 4 [5,2,6,4,1,3] => 4 [5,2,6,4,3,1] => 3 [5,3,1,2,4,6] => 4 [5,3,1,2,6,4] => 5 [5,3,1,4,2,6] => 3 [5,3,1,4,6,2] => 4 [5,3,1,6,2,4] => 6 [5,3,1,6,4,2] => 5 [5,3,2,1,4,6] => 3 [5,3,2,1,6,4] => 4 [5,3,2,4,1,6] => 2 [5,3,2,4,6,1] => 3 [5,3,2,6,1,4] => 5 [5,3,2,6,4,1] => 4 [5,3,4,1,2,6] => 4 [5,3,4,1,6,2] => 5 [5,3,4,2,1,6] => 3 [5,3,4,2,6,1] => 4 [5,3,4,6,1,2] => 6 [5,3,4,6,2,1] => 5 [5,3,6,1,2,4] => 7 [5,3,6,1,4,2] => 6 [5,3,6,2,1,4] => 6 [5,3,6,2,4,1] => 5 [5,3,6,4,1,2] => 5 [5,3,6,4,2,1] => 4 [5,4,1,2,3,6] => 5 [5,4,1,2,6,3] => 6 [5,4,1,3,2,6] => 4 [5,4,1,3,6,2] => 5 [5,4,1,6,2,3] => 7 [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] => 3 [5,4,2,3,6,1] => 4 [5,4,2,6,1,3] => 6 [5,4,2,6,3,1] => 5 [5,4,3,1,2,6] => 3 [5,4,3,1,6,2] => 4 [5,4,3,2,1,6] => 2 [5,4,3,2,6,1] => 3 [5,4,3,6,1,2] => 5 [5,4,3,6,2,1] => 4 [5,4,6,1,2,3] => 8 [5,4,6,1,3,2] => 7 [5,4,6,2,1,3] => 7 [5,4,6,2,3,1] => 6 [5,4,6,3,1,2] => 6 [5,4,6,3,2,1] => 5 [5,6,1,2,3,4] => 8 [5,6,1,2,4,3] => 7 [5,6,1,3,2,4] => 7 [5,6,1,3,4,2] => 6 [5,6,1,4,2,3] => 6 [5,6,1,4,3,2] => 5 [5,6,2,1,3,4] => 7 [5,6,2,1,4,3] => 6 [5,6,2,3,1,4] => 6 [5,6,2,3,4,1] => 5 [5,6,2,4,1,3] => 5 [5,6,2,4,3,1] => 4 [5,6,3,1,2,4] => 6 [5,6,3,1,4,2] => 5 [5,6,3,2,1,4] => 5 [5,6,3,2,4,1] => 4 [5,6,3,4,1,2] => 4 [5,6,3,4,2,1] => 3 [5,6,4,1,2,3] => 7 [5,6,4,1,3,2] => 6 [5,6,4,2,1,3] => 6 [5,6,4,2,3,1] => 5 [5,6,4,3,1,2] => 5 [5,6,4,3,2,1] => 4 [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] => 3 [6,1,2,5,3,4] => 5 [6,1,2,5,4,3] => 4 [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] => 2 [6,1,3,5,2,4] => 4 [6,1,3,5,4,2] => 3 [6,1,4,2,3,5] => 5 [6,1,4,2,5,3] => 4 [6,1,4,3,2,5] => 4 [6,1,4,3,5,2] => 3 [6,1,4,5,2,3] => 5 [6,1,4,5,3,2] => 4 [6,1,5,2,3,4] => 6 [6,1,5,2,4,3] => 5 [6,1,5,3,2,4] => 5 [6,1,5,3,4,2] => 4 [6,1,5,4,2,3] => 4 [6,1,5,4,3,2] => 3 [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] => 2 [6,2,1,5,3,4] => 4 [6,2,1,5,4,3] => 3 [6,2,3,1,4,5] => 3 [6,2,3,1,5,4] => 2 [6,2,3,4,1,5] => 2 [6,2,3,4,5,1] => 1 [6,2,3,5,1,4] => 3 [6,2,3,5,4,1] => 2 [6,2,4,1,3,5] => 4 [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] => 4 [6,2,4,5,3,1] => 3 [6,2,5,1,3,4] => 5 [6,2,5,1,4,3] => 4 [6,2,5,3,1,4] => 4 [6,2,5,3,4,1] => 3 [6,2,5,4,1,3] => 3 [6,2,5,4,3,1] => 2 [6,3,1,2,4,5] => 5 [6,3,1,2,5,4] => 4 [6,3,1,4,2,5] => 4 [6,3,1,4,5,2] => 3 [6,3,1,5,2,4] => 5 [6,3,1,5,4,2] => 4 [6,3,2,1,4,5] => 4 [6,3,2,1,5,4] => 3 [6,3,2,4,1,5] => 3 [6,3,2,4,5,1] => 2 [6,3,2,5,1,4] => 4 [6,3,2,5,4,1] => 3 [6,3,4,1,2,5] => 5 [6,3,4,1,5,2] => 4 [6,3,4,2,1,5] => 4 [6,3,4,2,5,1] => 3 [6,3,4,5,1,2] => 5 [6,3,4,5,2,1] => 4 [6,3,5,1,2,4] => 6 [6,3,5,1,4,2] => 5 [6,3,5,2,1,4] => 5 [6,3,5,2,4,1] => 4 [6,3,5,4,1,2] => 4 [6,3,5,4,2,1] => 3 [6,4,1,2,3,5] => 6 [6,4,1,2,5,3] => 5 [6,4,1,3,2,5] => 5 [6,4,1,3,5,2] => 4 [6,4,1,5,2,3] => 6 [6,4,1,5,3,2] => 5 [6,4,2,1,3,5] => 5 [6,4,2,1,5,3] => 4 [6,4,2,3,1,5] => 4 [6,4,2,3,5,1] => 3 [6,4,2,5,1,3] => 5 [6,4,2,5,3,1] => 4 [6,4,3,1,2,5] => 4 [6,4,3,1,5,2] => 3 [6,4,3,2,1,5] => 3 [6,4,3,2,5,1] => 2 [6,4,3,5,1,2] => 4 [6,4,3,5,2,1] => 3 [6,4,5,1,2,3] => 7 [6,4,5,1,3,2] => 6 [6,4,5,2,1,3] => 6 [6,4,5,2,3,1] => 5 [6,4,5,3,1,2] => 5 [6,4,5,3,2,1] => 4 [6,5,1,2,3,4] => 7 [6,5,1,2,4,3] => 6 [6,5,1,3,2,4] => 6 [6,5,1,3,4,2] => 5 [6,5,1,4,2,3] => 5 [6,5,1,4,3,2] => 4 [6,5,2,1,3,4] => 6 [6,5,2,1,4,3] => 5 [6,5,2,3,1,4] => 5 [6,5,2,3,4,1] => 4 [6,5,2,4,1,3] => 4 [6,5,2,4,3,1] => 3 [6,5,3,1,2,4] => 5 [6,5,3,1,4,2] => 4 [6,5,3,2,1,4] => 4 [6,5,3,2,4,1] => 3 [6,5,3,4,1,2] => 3 [6,5,3,4,2,1] => 2 [6,5,4,1,2,3] => 6 [6,5,4,1,3,2] => 5 [6,5,4,2,1,3] => 5 [6,5,4,2,3,1] => 4 [6,5,4,3,1,2] => 4 [6,5,4,3,2,1] => 3 [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] => 2 [1,2,3,4,7,6,5] => 1 [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] => 3 [1,2,3,5,7,6,4] => 2 [1,2,3,6,4,5,7] => 2 [1,2,3,6,4,7,5] => 3 [1,2,3,6,5,4,7] => 1 [1,2,3,6,5,7,4] => 2 [1,2,3,6,7,4,5] => 4 [1,2,3,6,7,5,4] => 3 [1,2,3,7,4,5,6] => 3 [1,2,3,7,4,6,5] => 2 [1,2,3,7,5,4,6] => 2 [1,2,3,7,5,6,4] => 1 [1,2,3,7,6,4,5] => 3 [1,2,3,7,6,5,4] => 2 [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] => 3 [1,2,4,3,7,6,5] => 2 [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] => 4 [1,2,4,5,7,6,3] => 3 [1,2,4,6,3,5,7] => 3 [1,2,4,6,3,7,5] => 4 [1,2,4,6,5,3,7] => 2 [1,2,4,6,5,7,3] => 3 [1,2,4,6,7,3,5] => 5 [1,2,4,6,7,5,3] => 4 [1,2,4,7,3,5,6] => 4 [1,2,4,7,3,6,5] => 3 [1,2,4,7,5,3,6] => 3 [1,2,4,7,5,6,3] => 2 [1,2,4,7,6,3,5] => 4 [1,2,4,7,6,5,3] => 3 [1,2,5,3,4,6,7] => 2 [1,2,5,3,4,7,6] => 3 [1,2,5,3,6,4,7] => 3 [1,2,5,3,6,7,4] => 4 [1,2,5,3,7,4,6] => 4 [1,2,5,3,7,6,4] => 3 [1,2,5,4,3,6,7] => 1 [1,2,5,4,3,7,6] => 2 [1,2,5,4,6,3,7] => 2 [1,2,5,4,6,7,3] => 3 [1,2,5,4,7,3,6] => 3 [1,2,5,4,7,6,3] => 2 [1,2,5,6,3,4,7] => 4 [1,2,5,6,3,7,4] => 5 [1,2,5,6,4,3,7] => 3 [1,2,5,6,4,7,3] => 4 [1,2,5,6,7,3,4] => 6 [1,2,5,6,7,4,3] => 5 [1,2,5,7,3,4,6] => 5 [1,2,5,7,3,6,4] => 4 [1,2,5,7,4,3,6] => 4 [1,2,5,7,4,6,3] => 3 [1,2,5,7,6,3,4] => 5 [1,2,5,7,6,4,3] => 4 [1,2,6,3,4,5,7] => 3 [1,2,6,3,4,7,5] => 4 [1,2,6,3,5,4,7] => 2 [1,2,6,3,5,7,4] => 3 [1,2,6,3,7,4,5] => 5 [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] => 1 [1,2,6,4,5,7,3] => 2 [1,2,6,4,7,3,5] => 4 [1,2,6,4,7,5,3] => 3 [1,2,6,5,3,4,7] => 3 [1,2,6,5,3,7,4] => 4 [1,2,6,5,4,3,7] => 2 [1,2,6,5,4,7,3] => 3 [1,2,6,5,7,3,4] => 5 [1,2,6,5,7,4,3] => 4 [1,2,6,7,3,4,5] => 6 [1,2,6,7,3,5,4] => 5 [1,2,6,7,4,3,5] => 5 [1,2,6,7,4,5,3] => 4 [1,2,6,7,5,3,4] => 4 [1,2,6,7,5,4,3] => 3 [1,2,7,3,4,5,6] => 4 [1,2,7,3,4,6,5] => 3 [1,2,7,3,5,4,6] => 3 [1,2,7,3,5,6,4] => 2 [1,2,7,3,6,4,5] => 4 [1,2,7,3,6,5,4] => 3 [1,2,7,4,3,5,6] => 3 [1,2,7,4,3,6,5] => 2 [1,2,7,4,5,3,6] => 2 [1,2,7,4,5,6,3] => 1 [1,2,7,4,6,3,5] => 3 [1,2,7,4,6,5,3] => 2 [1,2,7,5,3,4,6] => 4 [1,2,7,5,3,6,4] => 3 [1,2,7,5,4,3,6] => 3 [1,2,7,5,4,6,3] => 2 [1,2,7,5,6,3,4] => 4 [1,2,7,5,6,4,3] => 3 [1,2,7,6,3,4,5] => 5 [1,2,7,6,3,5,4] => 4 [1,2,7,6,4,3,5] => 4 [1,2,7,6,4,5,3] => 3 [1,2,7,6,5,3,4] => 3 [1,2,7,6,5,4,3] => 2 [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] => 3 [1,3,2,4,7,6,5] => 2 [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] => 4 [1,3,2,5,7,6,4] => 3 [1,3,2,6,4,5,7] => 3 [1,3,2,6,4,7,5] => 4 [1,3,2,6,5,4,7] => 2 [1,3,2,6,5,7,4] => 3 [1,3,2,6,7,4,5] => 5 [1,3,2,6,7,5,4] => 4 [1,3,2,7,4,5,6] => 4 [1,3,2,7,4,6,5] => 3 [1,3,2,7,5,4,6] => 3 [1,3,2,7,5,6,4] => 2 [1,3,2,7,6,4,5] => 4 [1,3,2,7,6,5,4] => 3 [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] => 4 [1,3,4,2,7,6,5] => 3 [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] => 5 [1,3,4,5,7,6,2] => 4 [1,3,4,6,2,5,7] => 4 [1,3,4,6,2,7,5] => 5 [1,3,4,6,5,2,7] => 3 [1,3,4,6,5,7,2] => 4 [1,3,4,6,7,2,5] => 6 [1,3,4,6,7,5,2] => 5 [1,3,4,7,2,5,6] => 5 [1,3,4,7,2,6,5] => 4 [1,3,4,7,5,2,6] => 4 [1,3,4,7,5,6,2] => 3 [1,3,4,7,6,2,5] => 5 [1,3,4,7,6,5,2] => 4 [1,3,5,2,4,6,7] => 3 [1,3,5,2,4,7,6] => 4 [1,3,5,2,6,4,7] => 4 [1,3,5,2,6,7,4] => 5 [1,3,5,2,7,4,6] => 5 [1,3,5,2,7,6,4] => 4 [1,3,5,4,2,6,7] => 2 [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] => 3 [1,3,5,6,2,4,7] => 5 [1,3,5,6,2,7,4] => 6 [1,3,5,6,4,2,7] => 4 [1,3,5,6,4,7,2] => 5 [1,3,5,6,7,2,4] => 7 [1,3,5,6,7,4,2] => 6 [1,3,5,7,2,4,6] => 6 [1,3,5,7,2,6,4] => 5 [1,3,5,7,4,2,6] => 5 [1,3,5,7,4,6,2] => 4 [1,3,5,7,6,2,4] => 6 [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] => 3 [1,3,6,2,5,7,4] => 4 [1,3,6,2,7,4,5] => 6 [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] => 2 [1,3,6,4,5,7,2] => 3 [1,3,6,4,7,2,5] => 5 [1,3,6,4,7,5,2] => 4 [1,3,6,5,2,4,7] => 4 [1,3,6,5,2,7,4] => 5 [1,3,6,5,4,2,7] => 3 [1,3,6,5,4,7,2] => 4 [1,3,6,5,7,2,4] => 6 [1,3,6,5,7,4,2] => 5 [1,3,6,7,2,4,5] => 7 [1,3,6,7,2,5,4] => 6 [1,3,6,7,4,2,5] => 6 [1,3,6,7,4,5,2] => 5 [1,3,6,7,5,2,4] => 5 [1,3,6,7,5,4,2] => 4 [1,3,7,2,4,5,6] => 5 [1,3,7,2,4,6,5] => 4 [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] => 4 [1,3,7,4,2,5,6] => 4 [1,3,7,4,2,6,5] => 3 [1,3,7,4,5,2,6] => 3 [1,3,7,4,5,6,2] => 2 [1,3,7,4,6,2,5] => 4 [1,3,7,4,6,5,2] => 3 [1,3,7,5,2,4,6] => 5 [1,3,7,5,2,6,4] => 4 [1,3,7,5,4,2,6] => 4 [1,3,7,5,4,6,2] => 3 [1,3,7,5,6,2,4] => 5 [1,3,7,5,6,4,2] => 4 [1,3,7,6,2,4,5] => 6 [1,3,7,6,2,5,4] => 5 [1,3,7,6,4,2,5] => 5 [1,3,7,6,4,5,2] => 4 [1,3,7,6,5,2,4] => 4 [1,3,7,6,5,4,2] => 3 [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] => 4 [1,4,2,3,7,5,6] => 4 [1,4,2,3,7,6,5] => 3 [1,4,2,5,3,6,7] => 3 [1,4,2,5,3,7,6] => 4 [1,4,2,5,6,3,7] => 4 [1,4,2,5,6,7,3] => 5 [1,4,2,5,7,3,6] => 5 [1,4,2,5,7,6,3] => 4 [1,4,2,6,3,5,7] => 4 [1,4,2,6,3,7,5] => 5 [1,4,2,6,5,3,7] => 3 [1,4,2,6,5,7,3] => 4 [1,4,2,6,7,3,5] => 6 [1,4,2,6,7,5,3] => 5 [1,4,2,7,3,5,6] => 5 [1,4,2,7,3,6,5] => 4 [1,4,2,7,5,3,6] => 4 [1,4,2,7,5,6,3] => 3 [1,4,2,7,6,3,5] => 5 [1,4,2,7,6,5,3] => 4 [1,4,3,2,5,6,7] => 1 [1,4,3,2,5,7,6] => 2 [1,4,3,2,6,5,7] => 2 [1,4,3,2,6,7,5] => 3 [1,4,3,2,7,5,6] => 3 [1,4,3,2,7,6,5] => 2 [1,4,3,5,2,6,7] => 2 [1,4,3,5,2,7,6] => 3 [1,4,3,5,6,2,7] => 3 [1,4,3,5,6,7,2] => 4 [1,4,3,5,7,2,6] => 4 [1,4,3,5,7,6,2] => 3 [1,4,3,6,2,5,7] => 3 [1,4,3,6,2,7,5] => 4 [1,4,3,6,5,2,7] => 2 [1,4,3,6,5,7,2] => 3 [1,4,3,6,7,2,5] => 5 [1,4,3,6,7,5,2] => 4 [1,4,3,7,2,5,6] => 4 [1,4,3,7,2,6,5] => 3 [1,4,3,7,5,2,6] => 3 [1,4,3,7,5,6,2] => 2 [1,4,3,7,6,2,5] => 4 [1,4,3,7,6,5,2] => 3 [1,4,5,2,3,6,7] => 4 [1,4,5,2,3,7,6] => 5 [1,4,5,2,6,3,7] => 5 [1,4,5,2,6,7,3] => 6 [1,4,5,2,7,3,6] => 6 [1,4,5,2,7,6,3] => 5 [1,4,5,3,2,6,7] => 3 [1,4,5,3,2,7,6] => 4 [1,4,5,3,6,2,7] => 4 [1,4,5,3,6,7,2] => 5 [1,4,5,3,7,2,6] => 5 [1,4,5,3,7,6,2] => 4 [1,4,5,6,2,3,7] => 6 [1,4,5,6,2,7,3] => 7 [1,4,5,6,3,2,7] => 5 [1,4,5,6,3,7,2] => 6 [1,4,5,6,7,2,3] => 8 [1,4,5,6,7,3,2] => 7 [1,4,5,7,2,3,6] => 7 [1,4,5,7,2,6,3] => 6 [1,4,5,7,3,2,6] => 6 [1,4,5,7,3,6,2] => 5 [1,4,5,7,6,2,3] => 7 [1,4,5,7,6,3,2] => 6 [1,4,6,2,3,5,7] => 5 [1,4,6,2,3,7,5] => 6 [1,4,6,2,5,3,7] => 4 [1,4,6,2,5,7,3] => 5 [1,4,6,2,7,3,5] => 7 [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] => 3 [1,4,6,3,5,7,2] => 4 [1,4,6,3,7,2,5] => 6 [1,4,6,3,7,5,2] => 5 [1,4,6,5,2,3,7] => 5 [1,4,6,5,2,7,3] => 6 [1,4,6,5,3,2,7] => 4 [1,4,6,5,3,7,2] => 5 ----------------------------------------------------------------------------- Created: May 19, 2017 at 18:36 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: May 19, 2017 at 18:36 by Martin Rubey