***************************************************************************** * 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: St000887 ----------------------------------------------------------------------------- Collection: Permutations ----------------------------------------------------------------------------- Description: The maximal number of nonzero entries on a diagonal of a permutation matrix. For example, the permutation matrix of $\pi=[3,1,2,5,4]$ is $$\begin{pmatrix} 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 1 & 0 \end{pmatrix},$$ and the entries corresponding to $\pi_2=1$, $\pi_3=2$ and $\pi_5=4$ are all on the fourth diagonal from the right. In other words, this is $\max_k \lvert\{i: \pi_i-i = k\}\rvert$ ----------------------------------------------------------------------------- References: [1] Nordh, G. A note on X-rays of permutations and a problem of Brualdi and Fritscher [[arXiv:1707.03928]] ----------------------------------------------------------------------------- Code: def statistic(pi): P = Permutation(pi).to_matrix() n = P.nrows() return max(sum(P[n-k+j][j] for j in range(max(0, k-n), min(k, n))) for k in range(1, 2*n)) ----------------------------------------------------------------------------- Statistic values: [1,2] => 2 [2,1] => 1 [1,2,3] => 3 [1,3,2] => 1 [2,1,3] => 1 [2,3,1] => 2 [3,1,2] => 2 [3,2,1] => 1 [1,2,3,4] => 4 [1,2,4,3] => 2 [1,3,2,4] => 2 [1,3,4,2] => 2 [1,4,2,3] => 2 [1,4,3,2] => 2 [2,1,3,4] => 2 [2,1,4,3] => 2 [2,3,1,4] => 2 [2,3,4,1] => 3 [2,4,1,3] => 1 [2,4,3,1] => 1 [3,1,2,4] => 2 [3,1,4,2] => 1 [3,2,1,4] => 2 [3,2,4,1] => 1 [3,4,1,2] => 2 [3,4,2,1] => 2 [4,1,2,3] => 3 [4,1,3,2] => 1 [4,2,1,3] => 1 [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] => 3 [1,2,4,3,5] => 3 [1,2,4,5,3] => 2 [1,2,5,3,4] => 2 [1,2,5,4,3] => 3 [1,3,2,4,5] => 3 [1,3,2,5,4] => 2 [1,3,4,2,5] => 2 [1,3,4,5,2] => 3 [1,3,5,2,4] => 1 [1,3,5,4,2] => 2 [1,4,2,3,5] => 2 [1,4,2,5,3] => 1 [1,4,3,2,5] => 3 [1,4,3,5,2] => 2 [1,4,5,2,3] => 2 [1,4,5,3,2] => 2 [1,5,2,3,4] => 3 [1,5,2,4,3] => 2 [1,5,3,2,4] => 2 [1,5,3,4,2] => 3 [1,5,4,2,3] => 2 [1,5,4,3,2] => 1 [2,1,3,4,5] => 3 [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] => 1 [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] => 2 [2,3,5,4,1] => 2 [2,4,1,3,5] => 1 [2,4,1,5,3] => 2 [2,4,3,1,5] => 2 [2,4,3,5,1] => 2 [2,4,5,1,3] => 2 [2,4,5,3,1] => 2 [2,5,1,3,4] => 2 [2,5,1,4,3] => 2 [2,5,3,1,4] => 1 [2,5,3,4,1] => 2 [2,5,4,1,3] => 2 [2,5,4,3,1] => 2 [3,1,2,4,5] => 2 [3,1,2,5,4] => 3 [3,1,4,2,5] => 1 [3,1,4,5,2] => 2 [3,1,5,2,4] => 2 [3,1,5,4,2] => 2 [3,2,1,4,5] => 3 [3,2,1,5,4] => 1 [3,2,4,1,5] => 2 [3,2,4,5,1] => 2 [3,2,5,1,4] => 2 [3,2,5,4,1] => 2 [3,4,1,2,5] => 2 [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] => 2 [3,5,1,4,2] => 1 [3,5,2,1,4] => 2 [3,5,2,4,1] => 1 [3,5,4,1,2] => 2 [3,5,4,2,1] => 1 [4,1,2,3,5] => 3 [4,1,2,5,3] => 2 [4,1,3,2,5] => 2 [4,1,3,5,2] => 1 [4,1,5,2,3] => 2 [4,1,5,3,2] => 2 [4,2,1,3,5] => 2 [4,2,1,5,3] => 2 [4,2,3,1,5] => 3 [4,2,3,5,1] => 2 [4,2,5,1,3] => 1 [4,2,5,3,1] => 1 [4,3,1,2,5] => 2 [4,3,1,5,2] => 2 [4,3,2,1,5] => 1 [4,3,2,5,1] => 2 [4,3,5,1,2] => 2 [4,3,5,2,1] => 1 [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] => 2 [5,1,3,2,4] => 2 [5,1,3,4,2] => 2 [5,1,4,2,3] => 2 [5,1,4,3,2] => 2 [5,2,1,3,4] => 2 [5,2,1,4,3] => 2 [5,2,3,1,4] => 2 [5,2,3,4,1] => 3 [5,2,4,1,3] => 1 [5,2,4,3,1] => 1 [5,3,1,2,4] => 2 [5,3,1,4,2] => 1 [5,3,2,1,4] => 2 [5,3,2,4,1] => 1 [5,3,4,1,2] => 2 [5,3,4,2,1] => 2 [5,4,1,2,3] => 3 [5,4,1,3,2] => 1 [5,4,2,1,3] => 1 [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] => 4 [1,2,3,5,4,6] => 4 [1,2,3,5,6,4] => 3 [1,2,3,6,4,5] => 3 [1,2,3,6,5,4] => 4 [1,2,4,3,5,6] => 4 [1,2,4,3,6,5] => 2 [1,2,4,5,3,6] => 3 [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] => 3 [1,2,5,3,6,4] => 2 [1,2,5,4,3,6] => 4 [1,2,5,4,6,3] => 3 [1,2,5,6,3,4] => 2 [1,2,5,6,4,3] => 2 [1,2,6,3,4,5] => 3 [1,2,6,3,5,4] => 3 [1,2,6,4,3,5] => 3 [1,2,6,4,5,3] => 4 [1,2,6,5,3,4] => 2 [1,2,6,5,4,3] => 2 [1,3,2,4,5,6] => 4 [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] => 3 [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] => 2 [1,3,4,6,5,2] => 2 [1,3,5,2,4,6] => 2 [1,3,5,2,6,4] => 2 [1,3,5,4,2,6] => 3 [1,3,5,4,6,2] => 2 [1,3,5,6,2,4] => 2 [1,3,5,6,4,2] => 2 [1,3,6,2,4,5] => 2 [1,3,6,2,5,4] => 2 [1,3,6,4,2,5] => 2 [1,3,6,4,5,2] => 3 [1,3,6,5,2,4] => 2 [1,3,6,5,4,2] => 2 [1,4,2,3,5,6] => 3 [1,4,2,3,6,5] => 3 [1,4,2,5,3,6] => 2 [1,4,2,5,6,3] => 2 [1,4,2,6,3,5] => 2 [1,4,2,6,5,3] => 2 [1,4,3,2,5,6] => 4 [1,4,3,2,6,5] => 2 [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] => 3 [1,4,5,2,3,6] => 2 [1,4,5,2,6,3] => 2 [1,4,5,3,2,6] => 2 [1,4,5,3,6,2] => 2 [1,4,5,6,2,3] => 3 [1,4,5,6,3,2] => 3 [1,4,6,2,3,5] => 2 [1,4,6,2,5,3] => 2 [1,4,6,3,2,5] => 2 [1,4,6,3,5,2] => 2 [1,4,6,5,2,3] => 2 [1,4,6,5,3,2] => 1 [1,5,2,3,4,6] => 3 [1,5,2,3,6,4] => 2 [1,5,2,4,3,6] => 3 [1,5,2,4,6,3] => 2 [1,5,2,6,3,4] => 2 [1,5,2,6,4,3] => 2 [1,5,3,2,4,6] => 3 [1,5,3,2,6,4] => 2 [1,5,3,4,2,6] => 4 [1,5,3,4,6,2] => 3 [1,5,3,6,2,4] => 2 [1,5,3,6,4,2] => 2 [1,5,4,2,3,6] => 2 [1,5,4,2,6,3] => 2 [1,5,4,3,2,6] => 2 [1,5,4,3,6,2] => 2 [1,5,4,6,2,3] => 2 [1,5,4,6,3,2] => 1 [1,5,6,2,3,4] => 3 [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] => 2 [1,5,6,4,3,2] => 2 [1,6,2,3,4,5] => 4 [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] => 2 [1,6,2,5,4,3] => 2 [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] => 2 [1,6,3,5,4,2] => 2 [1,6,4,2,3,5] => 2 [1,6,4,2,5,3] => 2 [1,6,4,3,2,5] => 2 [1,6,4,3,5,2] => 2 [1,6,4,5,2,3] => 2 [1,6,4,5,3,2] => 2 [1,6,5,2,3,4] => 3 [1,6,5,2,4,3] => 1 [1,6,5,3,2,4] => 1 [1,6,5,3,4,2] => 2 [1,6,5,4,2,3] => 2 [1,6,5,4,3,2] => 2 [2,1,3,4,5,6] => 4 [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] => 2 [2,1,4,6,5,3] => 2 [2,1,5,3,4,6] => 3 [2,1,5,3,6,4] => 2 [2,1,5,4,3,6] => 2 [2,1,5,4,6,3] => 2 [2,1,5,6,3,4] => 2 [2,1,5,6,4,3] => 2 [2,1,6,3,4,5] => 4 [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] => 2 [2,1,6,5,4,3] => 2 [2,3,1,4,5,6] => 3 [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] => 2 [2,3,1,6,5,4] => 2 [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] => 3 [2,3,4,6,5,1] => 3 [2,3,5,1,4,6] => 2 [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] => 2 [2,3,5,6,4,1] => 2 [2,3,6,1,4,5] => 2 [2,3,6,1,5,4] => 2 [2,3,6,4,1,5] => 2 [2,3,6,4,5,1] => 2 [2,3,6,5,1,4] => 3 [2,3,6,5,4,1] => 3 [2,4,1,3,5,6] => 2 [2,4,1,3,6,5] => 2 [2,4,1,5,3,6] => 2 [2,4,1,5,6,3] => 3 [2,4,1,6,3,5] => 2 [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] => 2 [2,4,3,5,6,1] => 3 [2,4,3,6,1,5] => 2 [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] => 2 [2,4,5,3,6,1] => 2 [2,4,5,6,1,3] => 3 [2,4,5,6,3,1] => 3 [2,4,6,1,3,5] => 1 [2,4,6,1,5,3] => 2 [2,4,6,3,1,5] => 2 [2,4,6,3,5,1] => 1 [2,4,6,5,1,3] => 2 [2,4,6,5,3,1] => 2 [2,5,1,3,4,6] => 2 [2,5,1,3,6,4] => 2 [2,5,1,4,3,6] => 2 [2,5,1,4,6,3] => 2 [2,5,1,6,3,4] => 3 [2,5,1,6,4,3] => 1 [2,5,3,1,4,6] => 2 [2,5,3,1,6,4] => 2 [2,5,3,4,1,6] => 3 [2,5,3,4,6,1] => 2 [2,5,3,6,1,4] => 1 [2,5,3,6,4,1] => 1 [2,5,4,1,3,6] => 2 [2,5,4,1,6,3] => 3 [2,5,4,3,1,6] => 2 [2,5,4,3,6,1] => 3 [2,5,4,6,1,3] => 2 [2,5,4,6,3,1] => 2 [2,5,6,1,3,4] => 2 [2,5,6,1,4,3] => 2 [2,5,6,3,1,4] => 2 [2,5,6,3,4,1] => 2 [2,5,6,4,1,3] => 2 [2,5,6,4,3,1] => 2 [2,6,1,3,4,5] => 3 [2,6,1,3,5,4] => 2 [2,6,1,4,3,5] => 2 [2,6,1,4,5,3] => 2 [2,6,1,5,3,4] => 3 [2,6,1,5,4,3] => 2 [2,6,3,1,4,5] => 2 [2,6,3,1,5,4] => 2 [2,6,3,4,1,5] => 2 [2,6,3,4,5,1] => 3 [2,6,3,5,1,4] => 2 [2,6,3,5,4,1] => 2 [2,6,4,1,3,5] => 2 [2,6,4,1,5,3] => 2 [2,6,4,3,1,5] => 2 [2,6,4,3,5,1] => 2 [2,6,4,5,1,3] => 3 [2,6,4,5,3,1] => 3 [2,6,5,1,3,4] => 2 [2,6,5,1,4,3] => 2 [2,6,5,3,1,4] => 1 [2,6,5,3,4,1] => 2 [2,6,5,4,1,3] => 1 [2,6,5,4,3,1] => 1 [3,1,2,4,5,6] => 3 [3,1,2,4,6,5] => 3 [3,1,2,5,4,6] => 3 [3,1,2,5,6,4] => 2 [3,1,2,6,4,5] => 4 [3,1,2,6,5,4] => 2 [3,1,4,2,5,6] => 2 [3,1,4,2,6,5] => 2 [3,1,4,5,2,6] => 2 [3,1,4,5,6,2] => 3 [3,1,4,6,2,5] => 2 [3,1,4,6,5,2] => 2 [3,1,5,2,4,6] => 2 [3,1,5,2,6,4] => 2 [3,1,5,4,2,6] => 2 [3,1,5,4,6,2] => 2 [3,1,5,6,2,4] => 3 [3,1,5,6,4,2] => 3 [3,1,6,2,4,5] => 3 [3,1,6,2,5,4] => 2 [3,1,6,4,2,5] => 2 [3,1,6,4,5,2] => 2 [3,1,6,5,2,4] => 1 [3,1,6,5,4,2] => 2 [3,2,1,4,5,6] => 4 [3,2,1,4,6,5] => 2 [3,2,1,5,4,6] => 2 [3,2,1,5,6,4] => 2 [3,2,1,6,4,5] => 2 [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] => 2 [3,2,4,5,6,1] => 3 [3,2,4,6,1,5] => 2 [3,2,4,6,5,1] => 2 [3,2,5,1,4,6] => 2 [3,2,5,1,6,4] => 2 [3,2,5,4,1,6] => 3 [3,2,5,4,6,1] => 2 [3,2,5,6,1,4] => 3 [3,2,5,6,4,1] => 3 [3,2,6,1,4,5] => 2 [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] => 1 [3,2,6,5,4,1] => 1 [3,4,1,2,5,6] => 2 [3,4,1,2,6,5] => 2 [3,4,1,5,2,6] => 2 [3,4,1,5,6,2] => 2 [3,4,1,6,2,5] => 3 [3,4,1,6,5,2] => 3 [3,4,2,1,5,6] => 2 [3,4,2,1,6,5] => 2 [3,4,2,5,1,6] => 2 [3,4,2,5,6,1] => 2 [3,4,2,6,1,5] => 3 [3,4,2,6,5,1] => 3 [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] => 2 [3,4,6,1,5,2] => 2 [3,4,6,2,1,5] => 2 [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] => 2 [3,5,1,2,6,4] => 3 [3,5,1,4,2,6] => 2 [3,5,1,4,6,2] => 1 [3,5,1,6,2,4] => 2 [3,5,1,6,4,2] => 2 [3,5,2,1,4,6] => 2 [3,5,2,1,6,4] => 1 [3,5,2,4,1,6] => 2 [3,5,2,4,6,1] => 1 [3,5,2,6,1,4] => 2 [3,5,2,6,4,1] => 2 [3,5,4,1,2,6] => 2 [3,5,4,1,6,2] => 2 [3,5,4,2,1,6] => 1 [3,5,4,2,6,1] => 2 [3,5,4,6,1,2] => 2 [3,5,4,6,2,1] => 2 [3,5,6,1,2,4] => 2 [3,5,6,1,4,2] => 2 [3,5,6,2,1,4] => 2 [3,5,6,2,4,1] => 2 [3,5,6,4,1,2] => 2 [3,5,6,4,2,1] => 2 [3,6,1,2,4,5] => 2 [3,6,1,2,5,4] => 3 [3,6,1,4,2,5] => 1 [3,6,1,4,5,2] => 2 [3,6,1,5,2,4] => 2 [3,6,1,5,4,2] => 1 [3,6,2,1,4,5] => 3 [3,6,2,1,5,4] => 1 [3,6,2,4,1,5] => 2 [3,6,2,4,5,1] => 2 [3,6,2,5,1,4] => 1 [3,6,2,5,4,1] => 2 [3,6,4,1,2,5] => 2 [3,6,4,1,5,2] => 1 [3,6,4,2,1,5] => 1 [3,6,4,2,5,1] => 1 [3,6,4,5,1,2] => 2 [3,6,4,5,2,1] => 2 [3,6,5,1,2,4] => 2 [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] => 3 [4,1,2,3,6,5] => 4 [4,1,2,5,3,6] => 2 [4,1,2,5,6,3] => 2 [4,1,2,6,3,5] => 3 [4,1,2,6,5,3] => 2 [4,1,3,2,5,6] => 3 [4,1,3,2,6,5] => 2 [4,1,3,5,2,6] => 2 [4,1,3,5,6,2] => 2 [4,1,3,6,2,5] => 2 [4,1,3,6,5,2] => 2 [4,1,5,2,3,6] => 2 [4,1,5,2,6,3] => 1 [4,1,5,3,2,6] => 2 [4,1,5,3,6,2] => 2 [4,1,5,6,2,3] => 2 [4,1,5,6,3,2] => 2 [4,1,6,2,3,5] => 2 [4,1,6,2,5,3] => 2 [4,1,6,3,2,5] => 3 [4,1,6,3,5,2] => 2 [4,1,6,5,2,3] => 2 [4,1,6,5,3,2] => 2 [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] => 2 [4,2,1,6,3,5] => 2 [4,2,1,6,5,3] => 2 [4,2,3,1,5,6] => 4 [4,2,3,1,6,5] => 2 [4,2,3,5,1,6] => 3 [4,2,3,5,6,1] => 2 [4,2,3,6,1,5] => 2 [4,2,3,6,5,1] => 3 [4,2,5,1,3,6] => 2 [4,2,5,1,6,3] => 2 [4,2,5,3,1,6] => 2 [4,2,5,3,6,1] => 1 [4,2,5,6,1,3] => 2 [4,2,5,6,3,1] => 2 [4,2,6,1,3,5] => 2 [4,2,6,1,5,3] => 2 [4,2,6,3,1,5] => 2 [4,2,6,3,5,1] => 2 [4,2,6,5,1,3] => 2 [4,2,6,5,3,1] => 2 [4,3,1,2,5,6] => 2 [4,3,1,2,6,5] => 2 [4,3,1,5,2,6] => 2 [4,3,1,5,6,2] => 3 [4,3,1,6,2,5] => 1 [4,3,1,6,5,2] => 1 [4,3,2,1,5,6] => 2 [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] => 1 [4,3,5,1,2,6] => 2 [4,3,5,1,6,2] => 2 [4,3,5,2,1,6] => 1 [4,3,5,2,6,1] => 2 [4,3,5,6,1,2] => 2 [4,3,5,6,2,1] => 2 [4,3,6,1,2,5] => 2 [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] => 3 [4,5,1,2,6,3] => 2 [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] => 2 [4,5,2,1,3,6] => 2 [4,5,2,1,6,3] => 2 [4,5,2,3,1,6] => 2 [4,5,2,3,6,1] => 2 [4,5,2,6,1,3] => 2 [4,5,2,6,3,1] => 2 [4,5,3,1,2,6] => 2 [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] => 3 [4,6,1,2,5,3] => 2 [4,6,1,3,2,5] => 2 [4,6,1,3,5,2] => 1 [4,6,1,5,2,3] => 2 [4,6,1,5,3,2] => 2 [4,6,2,1,3,5] => 2 [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] => 1 [4,6,2,5,3,1] => 1 [4,6,3,1,2,5] => 2 [4,6,3,1,5,2] => 2 [4,6,3,2,1,5] => 1 [4,6,3,2,5,1] => 2 [4,6,3,5,1,2] => 2 [4,6,3,5,2,1] => 1 [4,6,5,1,2,3] => 3 [4,6,5,1,3,2] => 1 [4,6,5,2,1,3] => 1 [4,6,5,2,3,1] => 2 [4,6,5,3,1,2] => 2 [4,6,5,3,2,1] => 1 [5,1,2,3,4,6] => 4 [5,1,2,3,6,4] => 3 [5,1,2,4,3,6] => 2 [5,1,2,4,6,3] => 2 [5,1,2,6,3,4] => 2 [5,1,2,6,4,3] => 3 [5,1,3,2,4,6] => 2 [5,1,3,2,6,4] => 2 [5,1,3,4,2,6] => 3 [5,1,3,4,6,2] => 2 [5,1,3,6,2,4] => 1 [5,1,3,6,4,2] => 2 [5,1,4,2,3,6] => 2 [5,1,4,2,6,3] => 2 [5,1,4,3,2,6] => 2 [5,1,4,3,6,2] => 2 [5,1,4,6,2,3] => 2 [5,1,4,6,3,2] => 1 [5,1,6,2,3,4] => 3 [5,1,6,2,4,3] => 2 [5,1,6,3,2,4] => 2 [5,1,6,3,4,2] => 3 [5,1,6,4,2,3] => 2 [5,1,6,4,3,2] => 1 [5,2,1,3,4,6] => 2 [5,2,1,3,6,4] => 2 [5,2,1,4,3,6] => 3 [5,2,1,4,6,3] => 2 [5,2,1,6,3,4] => 3 [5,2,1,6,4,3] => 1 [5,2,3,1,4,6] => 3 [5,2,3,1,6,4] => 2 [5,2,3,4,1,6] => 4 [5,2,3,4,6,1] => 3 [5,2,3,6,1,4] => 2 [5,2,3,6,4,1] => 2 [5,2,4,1,3,6] => 2 [5,2,4,1,6,3] => 2 [5,2,4,3,1,6] => 2 [5,2,4,3,6,1] => 2 [5,2,4,6,1,3] => 1 [5,2,4,6,3,1] => 1 [5,2,6,1,3,4] => 2 [5,2,6,1,4,3] => 2 [5,2,6,3,1,4] => 1 [5,2,6,3,4,1] => 2 [5,2,6,4,1,3] => 2 [5,2,6,4,3,1] => 2 [5,3,1,2,4,6] => 2 [5,3,1,2,6,4] => 3 [5,3,1,4,2,6] => 2 [5,3,1,4,6,2] => 2 [5,3,1,6,2,4] => 2 [5,3,1,6,4,2] => 1 [5,3,2,1,4,6] => 2 [5,3,2,1,6,4] => 2 [5,3,2,4,1,6] => 2 [5,3,2,4,6,1] => 2 [5,3,2,6,1,4] => 1 [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] => 2 [5,3,4,2,6,1] => 3 [5,3,4,6,1,2] => 2 [5,3,4,6,2,1] => 2 [5,3,6,1,2,4] => 2 [5,3,6,1,4,2] => 1 [5,3,6,2,1,4] => 2 [5,3,6,2,4,1] => 1 [5,3,6,4,1,2] => 2 [5,3,6,4,2,1] => 1 [5,4,1,2,3,6] => 3 [5,4,1,2,6,3] => 2 [5,4,1,3,2,6] => 1 [5,4,1,3,6,2] => 1 [5,4,1,6,2,3] => 2 [5,4,1,6,3,2] => 2 [5,4,2,1,3,6] => 1 [5,4,2,1,6,3] => 2 [5,4,2,3,1,6] => 2 [5,4,2,3,6,1] => 2 [5,4,2,6,1,3] => 2 [5,4,2,6,3,1] => 2 [5,4,3,1,2,6] => 2 [5,4,3,1,6,2] => 1 [5,4,3,2,1,6] => 2 [5,4,3,2,6,1] => 1 [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] => 1 [5,4,6,2,1,3] => 1 [5,4,6,2,3,1] => 2 [5,4,6,3,1,2] => 2 [5,4,6,3,2,1] => 1 [5,6,1,2,3,4] => 4 [5,6,1,2,4,3] => 2 [5,6,1,3,2,4] => 2 [5,6,1,3,4,2] => 2 [5,6,1,4,2,3] => 2 [5,6,1,4,3,2] => 2 [5,6,2,1,3,4] => 2 [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] => 2 [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] => 3 [6,1,2,4,3,5] => 3 [6,1,2,4,5,3] => 2 [6,1,2,5,3,4] => 2 [6,1,2,5,4,3] => 3 [6,1,3,2,4,5] => 3 [6,1,3,2,5,4] => 2 [6,1,3,4,2,5] => 2 [6,1,3,4,5,2] => 3 [6,1,3,5,2,4] => 1 [6,1,3,5,4,2] => 2 [6,1,4,2,3,5] => 2 [6,1,4,2,5,3] => 1 [6,1,4,3,2,5] => 3 [6,1,4,3,5,2] => 2 [6,1,4,5,2,3] => 2 [6,1,4,5,3,2] => 2 [6,1,5,2,3,4] => 3 [6,1,5,2,4,3] => 2 [6,1,5,3,2,4] => 2 [6,1,5,3,4,2] => 3 [6,1,5,4,2,3] => 2 [6,1,5,4,3,2] => 1 [6,2,1,3,4,5] => 3 [6,2,1,3,5,4] => 2 [6,2,1,4,3,5] => 2 [6,2,1,4,5,3] => 3 [6,2,1,5,3,4] => 3 [6,2,1,5,4,3] => 1 [6,2,3,1,4,5] => 2 [6,2,3,1,5,4] => 3 [6,2,3,4,1,5] => 3 [6,2,3,4,5,1] => 4 [6,2,3,5,1,4] => 2 [6,2,3,5,4,1] => 2 [6,2,4,1,3,5] => 1 [6,2,4,1,5,3] => 2 [6,2,4,3,1,5] => 2 [6,2,4,3,5,1] => 2 [6,2,4,5,1,3] => 2 [6,2,4,5,3,1] => 2 [6,2,5,1,3,4] => 2 [6,2,5,1,4,3] => 2 [6,2,5,3,1,4] => 1 [6,2,5,3,4,1] => 2 [6,2,5,4,1,3] => 2 [6,2,5,4,3,1] => 2 [6,3,1,2,4,5] => 2 [6,3,1,2,5,4] => 3 [6,3,1,4,2,5] => 1 [6,3,1,4,5,2] => 2 [6,3,1,5,2,4] => 2 [6,3,1,5,4,2] => 2 [6,3,2,1,4,5] => 3 [6,3,2,1,5,4] => 1 [6,3,2,4,1,5] => 2 [6,3,2,4,5,1] => 2 [6,3,2,5,1,4] => 2 [6,3,2,5,4,1] => 2 [6,3,4,1,2,5] => 2 [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] => 2 [6,3,5,1,4,2] => 1 [6,3,5,2,1,4] => 2 [6,3,5,2,4,1] => 1 [6,3,5,4,1,2] => 2 [6,3,5,4,2,1] => 1 [6,4,1,2,3,5] => 3 [6,4,1,2,5,3] => 2 [6,4,1,3,2,5] => 2 [6,4,1,3,5,2] => 1 [6,4,1,5,2,3] => 2 [6,4,1,5,3,2] => 2 [6,4,2,1,3,5] => 2 [6,4,2,1,5,3] => 2 [6,4,2,3,1,5] => 3 [6,4,2,3,5,1] => 2 [6,4,2,5,1,3] => 1 [6,4,2,5,3,1] => 1 [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] => 2 [6,4,3,5,1,2] => 2 [6,4,3,5,2,1] => 1 [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] => 2 [6,5,1,3,2,4] => 2 [6,5,1,3,4,2] => 2 [6,5,1,4,2,3] => 2 [6,5,1,4,3,2] => 2 [6,5,2,1,3,4] => 2 [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] => 1 [6,5,2,4,3,1] => 1 [6,5,3,1,2,4] => 2 [6,5,3,1,4,2] => 1 [6,5,3,2,1,4] => 2 [6,5,3,2,4,1] => 1 [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] => 1 [6,5,4,2,1,3] => 1 [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 [1,2,3,4,5,7,6] => 5 [1,2,3,4,6,5,7] => 5 [1,2,3,4,6,7,5] => 4 [1,2,3,4,7,5,6] => 4 [1,2,3,4,7,6,5] => 5 [1,2,3,5,4,6,7] => 5 [1,2,3,5,4,7,6] => 3 [1,2,3,5,6,4,7] => 4 [1,2,3,5,6,7,4] => 3 [1,2,3,5,7,4,6] => 3 [1,2,3,5,7,6,4] => 4 [1,2,3,6,4,5,7] => 4 [1,2,3,6,4,7,5] => 3 [1,2,3,6,5,4,7] => 5 [1,2,3,6,5,7,4] => 4 [1,2,3,6,7,4,5] => 3 [1,2,3,6,7,5,4] => 3 [1,2,3,7,4,5,6] => 3 [1,2,3,7,4,6,5] => 4 [1,2,3,7,5,4,6] => 4 [1,2,3,7,5,6,4] => 5 [1,2,3,7,6,4,5] => 3 [1,2,3,7,6,5,4] => 3 [1,2,4,3,5,6,7] => 5 [1,2,4,3,5,7,6] => 3 [1,2,4,3,6,5,7] => 3 [1,2,4,3,6,7,5] => 3 [1,2,4,3,7,5,6] => 3 [1,2,4,3,7,6,5] => 3 [1,2,4,5,3,6,7] => 4 [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] => 2 [1,2,4,5,7,6,3] => 3 [1,2,4,6,3,5,7] => 3 [1,2,4,6,3,7,5] => 2 [1,2,4,6,5,3,7] => 4 [1,2,4,6,5,7,3] => 3 [1,2,4,6,7,3,5] => 2 [1,2,4,6,7,5,3] => 2 [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] => 2 [1,2,4,7,6,5,3] => 2 [1,2,5,3,4,6,7] => 4 [1,2,5,3,4,7,6] => 3 [1,2,5,3,6,4,7] => 3 [1,2,5,3,6,7,4] => 2 [1,2,5,3,7,4,6] => 2 [1,2,5,3,7,6,4] => 3 [1,2,5,4,3,6,7] => 5 [1,2,5,4,3,7,6] => 3 [1,2,5,4,6,3,7] => 4 [1,2,5,4,6,7,3] => 3 [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] => 2 [1,2,5,6,4,3,7] => 3 [1,2,5,6,4,7,3] => 2 [1,2,5,6,7,3,4] => 3 [1,2,5,6,7,4,3] => 3 [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] => 3 [1,2,6,3,4,7,5] => 2 [1,2,6,3,5,4,7] => 4 [1,2,6,3,5,7,4] => 3 [1,2,6,3,7,4,5] => 2 [1,2,6,3,7,5,4] => 2 [1,2,6,4,3,5,7] => 4 [1,2,6,4,3,7,5] => 3 [1,2,6,4,5,3,7] => 5 [1,2,6,4,5,7,3] => 4 [1,2,6,4,7,3,5] => 3 [1,2,6,4,7,5,3] => 3 [1,2,6,5,3,4,7] => 3 [1,2,6,5,3,7,4] => 2 [1,2,6,5,4,3,7] => 3 [1,2,6,5,4,7,3] => 2 [1,2,6,5,7,3,4] => 2 [1,2,6,5,7,4,3] => 2 [1,2,6,7,3,4,5] => 3 [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] => 3 [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] => 4 [1,2,7,3,6,4,5] => 2 [1,2,7,3,6,5,4] => 2 [1,2,7,4,3,5,6] => 3 [1,2,7,4,3,6,5] => 4 [1,2,7,4,5,3,6] => 4 [1,2,7,4,5,6,3] => 5 [1,2,7,4,6,3,5] => 3 [1,2,7,4,6,5,3] => 3 [1,2,7,5,3,4,6] => 2 [1,2,7,5,3,6,4] => 3 [1,2,7,5,4,3,6] => 2 [1,2,7,5,4,6,3] => 3 [1,2,7,5,6,3,4] => 2 [1,2,7,5,6,4,3] => 2 [1,2,7,6,3,4,5] => 3 [1,2,7,6,3,5,4] => 2 [1,2,7,6,4,3,5] => 2 [1,2,7,6,4,5,3] => 2 [1,2,7,6,5,3,4] => 3 [1,2,7,6,5,4,3] => 3 [1,3,2,4,5,6,7] => 5 [1,3,2,4,5,7,6] => 3 [1,3,2,4,6,5,7] => 3 [1,3,2,4,6,7,5] => 3 [1,3,2,4,7,5,6] => 3 [1,3,2,4,7,6,5] => 3 [1,3,2,5,4,6,7] => 3 [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] => 2 [1,3,2,5,7,6,4] => 2 [1,3,2,6,4,5,7] => 3 [1,3,2,6,4,7,5] => 2 [1,3,2,6,5,4,7] => 3 [1,3,2,6,5,7,4] => 2 [1,3,2,6,7,4,5] => 2 [1,3,2,6,7,5,4] => 2 [1,3,2,7,4,5,6] => 4 [1,3,2,7,4,6,5] => 2 [1,3,2,7,5,4,6] => 2 [1,3,2,7,5,6,4] => 3 [1,3,2,7,6,4,5] => 2 [1,3,2,7,6,5,4] => 2 [1,3,4,2,5,6,7] => 4 [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] => 2 [1,3,4,2,7,6,5] => 2 [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] => 3 [1,3,4,5,7,6,2] => 3 [1,3,4,6,2,5,7] => 2 [1,3,4,6,2,7,5] => 3 [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] => 2 [1,3,4,7,2,5,6] => 2 [1,3,4,7,2,6,5] => 2 [1,3,4,7,5,2,6] => 2 [1,3,4,7,5,6,2] => 3 [1,3,4,7,6,2,5] => 3 [1,3,4,7,6,5,2] => 3 [1,3,5,2,4,6,7] => 3 [1,3,5,2,4,7,6] => 2 [1,3,5,2,6,4,7] => 2 [1,3,5,2,6,7,4] => 3 [1,3,5,2,7,4,6] => 2 [1,3,5,2,7,6,4] => 2 [1,3,5,4,2,6,7] => 4 [1,3,5,4,2,7,6] => 2 [1,3,5,4,6,2,7] => 3 [1,3,5,4,6,7,2] => 3 [1,3,5,4,7,2,6] => 2 [1,3,5,4,7,6,2] => 3 [1,3,5,6,2,4,7] => 2 [1,3,5,6,2,7,4] => 2 [1,3,5,6,4,2,7] => 2 [1,3,5,6,4,7,2] => 2 [1,3,5,6,7,2,4] => 3 [1,3,5,6,7,4,2] => 3 [1,3,5,7,2,4,6] => 1 [1,3,5,7,2,6,4] => 2 [1,3,5,7,4,2,6] => 2 [1,3,5,7,4,6,2] => 2 [1,3,5,7,6,2,4] => 2 [1,3,5,7,6,4,2] => 2 [1,3,6,2,4,5,7] => 2 [1,3,6,2,4,7,5] => 2 [1,3,6,2,5,4,7] => 3 [1,3,6,2,5,7,4] => 2 [1,3,6,2,7,4,5] => 3 [1,3,6,2,7,5,4] => 1 [1,3,6,4,2,5,7] => 3 [1,3,6,4,2,7,5] => 2 [1,3,6,4,5,2,7] => 4 [1,3,6,4,5,7,2] => 3 [1,3,6,4,7,2,5] => 2 [1,3,6,4,7,5,2] => 2 [1,3,6,5,2,4,7] => 2 [1,3,6,5,2,7,4] => 3 [1,3,6,5,4,2,7] => 2 [1,3,6,5,4,7,2] => 3 [1,3,6,5,7,2,4] => 2 [1,3,6,5,7,4,2] => 2 [1,3,6,7,2,4,5] => 2 [1,3,6,7,2,5,4] => 2 [1,3,6,7,4,2,5] => 2 [1,3,6,7,4,5,2] => 2 [1,3,6,7,5,2,4] => 2 [1,3,6,7,5,4,2] => 2 [1,3,7,2,4,5,6] => 3 [1,3,7,2,4,6,5] => 2 [1,3,7,2,5,4,6] => 2 [1,3,7,2,5,6,4] => 3 [1,3,7,2,6,4,5] => 3 [1,3,7,2,6,5,4] => 2 [1,3,7,4,2,5,6] => 2 [1,3,7,4,2,6,5] => 3 [1,3,7,4,5,2,6] => 3 [1,3,7,4,5,6,2] => 4 [1,3,7,4,6,2,5] => 2 [1,3,7,4,6,5,2] => 2 [1,3,7,5,2,4,6] => 2 [1,3,7,5,2,6,4] => 2 [1,3,7,5,4,2,6] => 2 [1,3,7,5,4,6,2] => 2 [1,3,7,5,6,2,4] => 3 [1,3,7,5,6,4,2] => 3 [1,3,7,6,2,4,5] => 2 [1,3,7,6,2,5,4] => 2 [1,3,7,6,4,2,5] => 1 [1,3,7,6,4,5,2] => 2 [1,3,7,6,5,2,4] => 2 [1,3,7,6,5,4,2] => 2 [1,4,2,3,5,6,7] => 4 [1,4,2,3,5,7,6] => 3 [1,4,2,3,6,5,7] => 3 [1,4,2,3,6,7,5] => 2 [1,4,2,3,7,5,6] => 4 [1,4,2,3,7,6,5] => 2 [1,4,2,5,3,6,7] => 3 [1,4,2,5,3,7,6] => 2 [1,4,2,5,6,3,7] => 2 [1,4,2,5,6,7,3] => 3 [1,4,2,5,7,3,6] => 2 [1,4,2,5,7,6,3] => 2 [1,4,2,6,3,5,7] => 2 [1,4,2,6,3,7,5] => 2 [1,4,2,6,5,3,7] => 3 [1,4,2,6,5,7,3] => 2 [1,4,2,6,7,3,5] => 3 [1,4,2,6,7,5,3] => 3 [1,4,2,7,3,5,6] => 3 [1,4,2,7,3,6,5] => 2 [1,4,2,7,5,3,6] => 2 [1,4,2,7,5,6,3] => 3 [1,4,2,7,6,3,5] => 1 [1,4,2,7,6,5,3] => 2 [1,4,3,2,5,6,7] => 5 [1,4,3,2,5,7,6] => 3 [1,4,3,2,6,5,7] => 3 [1,4,3,2,6,7,5] => 2 [1,4,3,2,7,5,6] => 2 [1,4,3,2,7,6,5] => 3 [1,4,3,5,2,6,7] => 4 [1,4,3,5,2,7,6] => 2 [1,4,3,5,6,2,7] => 3 [1,4,3,5,6,7,2] => 3 [1,4,3,5,7,2,6] => 2 [1,4,3,5,7,6,2] => 3 [1,4,3,6,2,5,7] => 3 [1,4,3,6,2,7,5] => 2 [1,4,3,6,5,2,7] => 4 [1,4,3,6,5,7,2] => 3 [1,4,3,6,7,2,5] => 3 [1,4,3,6,7,5,2] => 3 [1,4,3,7,2,5,6] => 2 [1,4,3,7,2,6,5] => 3 [1,4,3,7,5,2,6] => 3 [1,4,3,7,5,6,2] => 4 [1,4,3,7,6,2,5] => 2 [1,4,3,7,6,5,2] => 2 [1,4,5,2,3,6,7] => 3 [1,4,5,2,3,7,6] => 2 [1,4,5,2,6,3,7] => 2 [1,4,5,2,6,7,3] => 2 [1,4,5,2,7,3,6] => 3 [1,4,5,2,7,6,3] => 3 [1,4,5,3,2,6,7] => 3 [1,4,5,3,2,7,6] => 2 [1,4,5,3,6,2,7] => 2 [1,4,5,3,6,7,2] => 2 [1,4,5,3,7,2,6] => 3 [1,4,5,3,7,6,2] => 3 [1,4,5,6,2,3,7] => 3 [1,4,5,6,2,7,3] => 3 [1,4,5,6,3,2,7] => 3 [1,4,5,6,3,7,2] => 3 [1,4,5,6,7,2,3] => 4 [1,4,5,6,7,3,2] => 4 [1,4,5,7,2,3,6] => 2 [1,4,5,7,2,6,3] => 2 [1,4,5,7,3,2,6] => 2 [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] => 2 [1,4,6,2,3,7,5] => 3 [1,4,6,2,5,3,7] => 3 [1,4,6,2,5,7,3] => 2 [1,4,6,2,7,3,5] => 2 [1,4,6,2,7,5,3] => 2 [1,4,6,3,2,5,7] => 2 [1,4,6,3,2,7,5] => 1 [1,4,6,3,5,2,7] => 3 [1,4,6,3,5,7,2] => 2 [1,4,6,3,7,2,5] => 2 [1,4,6,3,7,5,2] => 2 [1,4,6,5,2,3,7] => 2 [1,4,6,5,2,7,3] => 2 [1,4,6,5,3,2,7] => 2 [1,4,6,5,3,7,2] => 2 ----------------------------------------------------------------------------- Created: Jul 14, 2017 at 08:49 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Jul 17, 2017 at 07:31 by Martin Rubey