***************************************************************************** * 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: St000886 ----------------------------------------------------------------------------- Collection: Permutations ----------------------------------------------------------------------------- Description: The number of permutations with the same antidiagonal sums. The X-ray of a permutation $\pi$ is the vector of the sums of the antidiagonals of the permutation matrix of $\pi$, read from left to right. For example, the permutation matrix of $\pi=[3,1,2,5,4]$ is $$\left(\begin{array}{rrrrr} 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 \\ 0 & 0 & 0 & 1 & 0 \end{array}\right),$$ so its X-ray is $(0, 1, 1, 1, 0, 0, 0, 2, 0)$. This statistic records the number of permutations having the same X-ray as the given permutation. In [1] this is called the degeneracy of the X-ray of the permutation. By [prop.1, 1], the number of different X-rays of permutations of size $n$ equals the number of nondecreasing differences of permutations of size $n$, [2]. ----------------------------------------------------------------------------- References: [1] Bebeacua, C., Mansour, T., Postnikov, A., Severini, S. On the X-rays of permutations [[arXiv:math/0506334]] [2] Number of nondecreasing sequences that are differences of two permutations of 1,2,...,n. [[OEIS:A019589]] ----------------------------------------------------------------------------- Code: def X_ray(pi): P = Permutation(pi).to_matrix() n = P.nrows() return tuple(sum(P[k-1-j][j] for j in range(max(0, k-n), min(k,n))) for k in range(1,2*n)) @cached_function def X_rays(n): return sorted(X_ray(pi) for pi in Permutations(n)) def statistic(pi): return X_rays(pi.size()).count(X_ray(pi)) ----------------------------------------------------------------------------- Statistic values: [1,2] => 1 [2,1] => 1 [1,2,3] => 1 [1,3,2] => 1 [2,1,3] => 1 [2,3,1] => 2 [3,1,2] => 2 [3,2,1] => 1 [1,2,3,4] => 1 [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] => 1 [2,3,1,4] => 2 [2,3,4,1] => 2 [2,4,1,3] => 2 [2,4,3,1] => 2 [3,1,2,4] => 2 [3,1,4,2] => 2 [3,2,1,4] => 1 [3,2,4,1] => 2 [3,4,1,2] => 1 [3,4,2,1] => 3 [4,1,2,3] => 2 [4,1,3,2] => 2 [4,2,1,3] => 2 [4,2,3,1] => 3 [4,3,1,2] => 3 [4,3,2,1] => 1 [1,2,3,4,5] => 1 [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] => 1 [1,3,4,2,5] => 2 [1,3,4,5,2] => 2 [1,3,5,2,4] => 2 [1,3,5,4,2] => 2 [1,4,2,3,5] => 2 [1,4,2,5,3] => 2 [1,4,3,2,5] => 1 [1,4,3,5,2] => 2 [1,4,5,2,3] => 1 [1,4,5,3,2] => 3 [1,5,2,3,4] => 2 [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] => 1 [2,1,3,4,5] => 1 [2,1,3,5,4] => 1 [2,1,4,3,5] => 1 [2,1,4,5,3] => 2 [2,1,5,3,4] => 2 [2,1,5,4,3] => 1 [2,3,1,4,5] => 2 [2,3,1,5,4] => 2 [2,3,4,1,5] => 2 [2,3,4,5,1] => 4 [2,3,5,1,4] => 2 [2,3,5,4,1] => 4 [2,4,1,3,5] => 2 [2,4,1,5,3] => 2 [2,4,3,1,5] => 2 [2,4,3,5,1] => 2 [2,4,5,1,3] => 4 [2,4,5,3,1] => 4 [2,5,1,3,4] => 2 [2,5,1,4,3] => 2 [2,5,3,1,4] => 4 [2,5,3,4,1] => 4 [2,5,4,1,3] => 2 [2,5,4,3,1] => 2 [3,1,2,4,5] => 2 [3,1,2,5,4] => 2 [3,1,4,2,5] => 2 [3,1,4,5,2] => 2 [3,1,5,2,4] => 2 [3,1,5,4,2] => 2 [3,2,1,4,5] => 1 [3,2,1,5,4] => 1 [3,2,4,1,5] => 2 [3,2,4,5,1] => 4 [3,2,5,1,4] => 2 [3,2,5,4,1] => 2 [3,4,1,2,5] => 1 [3,4,1,5,2] => 4 [3,4,2,1,5] => 3 [3,4,2,5,1] => 4 [3,4,5,1,2] => 6 [3,4,5,2,1] => 3 [3,5,1,2,4] => 4 [3,5,1,4,2] => 1 [3,5,2,1,4] => 2 [3,5,2,4,1] => 6 [3,5,4,1,2] => 2 [3,5,4,2,1] => 3 [4,1,2,3,5] => 2 [4,1,2,5,3] => 2 [4,1,3,2,5] => 2 [4,1,3,5,2] => 4 [4,1,5,2,3] => 4 [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] => 4 [4,2,5,1,3] => 1 [4,2,5,3,1] => 6 [4,3,1,2,5] => 3 [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] => 3 [4,5,1,2,3] => 6 [4,5,1,3,2] => 2 [4,5,2,1,3] => 2 [4,5,2,3,1] => 3 [4,5,3,1,2] => 3 [4,5,3,2,1] => 4 [5,1,2,3,4] => 4 [5,1,2,4,3] => 4 [5,1,3,2,4] => 2 [5,1,3,4,2] => 4 [5,1,4,2,3] => 4 [5,1,4,3,2] => 2 [5,2,1,3,4] => 4 [5,2,1,4,3] => 2 [5,2,3,1,4] => 4 [5,2,3,4,1] => 3 [5,2,4,1,3] => 6 [5,2,4,3,1] => 3 [5,3,1,2,4] => 4 [5,3,1,4,2] => 6 [5,3,2,1,4] => 2 [5,3,2,4,1] => 3 [5,3,4,1,2] => 3 [5,3,4,2,1] => 4 [5,4,1,2,3] => 3 [5,4,1,3,2] => 3 [5,4,2,1,3] => 3 [5,4,2,3,1] => 4 [5,4,3,1,2] => 4 [5,4,3,2,1] => 1 [1,2,3,4,5,6] => 1 [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] => 1 [1,2,4,5,3,6] => 2 [1,2,4,5,6,3] => 2 [1,2,4,6,3,5] => 2 [1,2,4,6,5,3] => 2 [1,2,5,3,4,6] => 2 [1,2,5,3,6,4] => 2 [1,2,5,4,3,6] => 1 [1,2,5,4,6,3] => 2 [1,2,5,6,3,4] => 1 [1,2,5,6,4,3] => 3 [1,2,6,3,4,5] => 2 [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] => 1 [1,3,2,4,5,6] => 1 [1,3,2,4,6,5] => 1 [1,3,2,5,4,6] => 1 [1,3,2,5,6,4] => 2 [1,3,2,6,4,5] => 2 [1,3,2,6,5,4] => 1 [1,3,4,2,5,6] => 2 [1,3,4,2,6,5] => 2 [1,3,4,5,2,6] => 2 [1,3,4,5,6,2] => 4 [1,3,4,6,2,5] => 2 [1,3,4,6,5,2] => 4 [1,3,5,2,4,6] => 2 [1,3,5,2,6,4] => 2 [1,3,5,4,2,6] => 2 [1,3,5,4,6,2] => 2 [1,3,5,6,2,4] => 4 [1,3,5,6,4,2] => 4 [1,3,6,2,4,5] => 2 [1,3,6,2,5,4] => 2 [1,3,6,4,2,5] => 4 [1,3,6,4,5,2] => 4 [1,3,6,5,2,4] => 2 [1,3,6,5,4,2] => 2 [1,4,2,3,5,6] => 2 [1,4,2,3,6,5] => 2 [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] => 1 [1,4,3,2,6,5] => 1 [1,4,3,5,2,6] => 2 [1,4,3,5,6,2] => 4 [1,4,3,6,2,5] => 2 [1,4,3,6,5,2] => 2 [1,4,5,2,3,6] => 1 [1,4,5,2,6,3] => 4 [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] => 3 [1,4,6,2,3,5] => 4 [1,4,6,2,5,3] => 1 [1,4,6,3,2,5] => 2 [1,4,6,3,5,2] => 6 [1,4,6,5,2,3] => 2 [1,4,6,5,3,2] => 3 [1,5,2,3,4,6] => 2 [1,5,2,3,6,4] => 2 [1,5,2,4,3,6] => 2 [1,5,2,4,6,3] => 4 [1,5,2,6,3,4] => 4 [1,5,2,6,4,3] => 2 [1,5,3,2,4,6] => 2 [1,5,3,2,6,4] => 2 [1,5,3,4,2,6] => 3 [1,5,3,4,6,2] => 4 [1,5,3,6,2,4] => 1 [1,5,3,6,4,2] => 6 [1,5,4,2,3,6] => 3 [1,5,4,2,6,3] => 2 [1,5,4,3,2,6] => 1 [1,5,4,3,6,2] => 2 [1,5,4,6,2,3] => 2 [1,5,4,6,3,2] => 3 [1,5,6,2,3,4] => 6 [1,5,6,2,4,3] => 2 [1,5,6,3,2,4] => 2 [1,5,6,3,4,2] => 3 [1,5,6,4,2,3] => 3 [1,5,6,4,3,2] => 4 [1,6,2,3,4,5] => 4 [1,6,2,3,5,4] => 4 [1,6,2,4,3,5] => 2 [1,6,2,4,5,3] => 4 [1,6,2,5,3,4] => 4 [1,6,2,5,4,3] => 2 [1,6,3,2,4,5] => 4 [1,6,3,2,5,4] => 2 [1,6,3,4,2,5] => 4 [1,6,3,4,5,2] => 3 [1,6,3,5,2,4] => 6 [1,6,3,5,4,2] => 3 [1,6,4,2,3,5] => 4 [1,6,4,2,5,3] => 6 [1,6,4,3,2,5] => 2 [1,6,4,3,5,2] => 3 [1,6,4,5,2,3] => 3 [1,6,4,5,3,2] => 4 [1,6,5,2,3,4] => 3 [1,6,5,2,4,3] => 3 [1,6,5,3,2,4] => 3 [1,6,5,3,4,2] => 4 [1,6,5,4,2,3] => 4 [1,6,5,4,3,2] => 1 [2,1,3,4,5,6] => 1 [2,1,3,4,6,5] => 1 [2,1,3,5,4,6] => 1 [2,1,3,5,6,4] => 2 [2,1,3,6,4,5] => 2 [2,1,3,6,5,4] => 1 [2,1,4,3,5,6] => 1 [2,1,4,3,6,5] => 1 [2,1,4,5,3,6] => 2 [2,1,4,5,6,3] => 2 [2,1,4,6,3,5] => 2 [2,1,4,6,5,3] => 2 [2,1,5,3,4,6] => 2 [2,1,5,3,6,4] => 2 [2,1,5,4,3,6] => 1 [2,1,5,4,6,3] => 2 [2,1,5,6,3,4] => 1 [2,1,5,6,4,3] => 3 [2,1,6,3,4,5] => 2 [2,1,6,3,5,4] => 2 [2,1,6,4,3,5] => 2 [2,1,6,4,5,3] => 3 [2,1,6,5,3,4] => 3 [2,1,6,5,4,3] => 1 [2,3,1,4,5,6] => 2 [2,3,1,4,6,5] => 2 [2,3,1,5,4,6] => 2 [2,3,1,5,6,4] => 4 [2,3,1,6,4,5] => 4 [2,3,1,6,5,4] => 2 [2,3,4,1,5,6] => 2 [2,3,4,1,6,5] => 2 [2,3,4,5,1,6] => 4 [2,3,4,5,6,1] => 4 [2,3,4,6,1,5] => 4 [2,3,4,6,5,1] => 2 [2,3,5,1,4,6] => 2 [2,3,5,1,6,4] => 2 [2,3,5,4,1,6] => 4 [2,3,5,4,6,1] => 4 [2,3,5,6,1,4] => 4 [2,3,5,6,4,1] => 8 [2,3,6,1,4,5] => 2 [2,3,6,1,5,4] => 2 [2,3,6,4,1,5] => 8 [2,3,6,4,5,1] => 8 [2,3,6,5,1,4] => 4 [2,3,6,5,4,1] => 4 [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] => 2 [2,4,1,6,3,5] => 2 [2,4,1,6,5,3] => 2 [2,4,3,1,5,6] => 2 [2,4,3,1,6,5] => 2 [2,4,3,5,1,6] => 2 [2,4,3,5,6,1] => 4 [2,4,3,6,1,5] => 2 [2,4,3,6,5,1] => 4 [2,4,5,1,3,6] => 4 [2,4,5,1,6,3] => 8 [2,4,5,3,1,6] => 4 [2,4,5,3,6,1] => 6 [2,4,5,6,1,3] => 4 [2,4,5,6,3,1] => 6 [2,4,6,1,3,5] => 8 [2,4,6,1,5,3] => 4 [2,4,6,3,1,5] => 4 [2,4,6,3,5,1] => 8 [2,4,6,5,1,3] => 2 [2,4,6,5,3,1] => 8 [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] => 4 [2,5,1,6,3,4] => 4 [2,5,1,6,4,3] => 2 [2,5,3,1,4,6] => 4 [2,5,3,1,6,4] => 4 [2,5,3,4,1,6] => 4 [2,5,3,4,6,1] => 6 [2,5,3,6,1,4] => 4 [2,5,3,6,4,1] => 8 [2,5,4,1,3,6] => 2 [2,5,4,1,6,3] => 4 [2,5,4,3,1,6] => 2 [2,5,4,3,6,1] => 2 [2,5,4,6,1,3] => 8 [2,5,4,6,3,1] => 4 [2,5,6,1,3,4] => 8 [2,5,6,1,4,3] => 4 [2,5,6,3,1,4] => 8 [2,5,6,3,4,1] => 2 [2,5,6,4,1,3] => 8 [2,5,6,4,3,1] => 6 [2,6,1,3,4,5] => 4 [2,6,1,3,5,4] => 4 [2,6,1,4,3,5] => 2 [2,6,1,4,5,3] => 4 [2,6,1,5,3,4] => 4 [2,6,1,5,4,3] => 2 [2,6,3,1,4,5] => 8 [2,6,3,1,5,4] => 4 [2,6,3,4,1,5] => 2 [2,6,3,4,5,1] => 6 [2,6,3,5,1,4] => 4 [2,6,3,5,4,1] => 8 [2,6,4,1,3,5] => 4 [2,6,4,1,5,3] => 8 [2,6,4,3,1,5] => 6 [2,6,4,3,5,1] => 4 [2,6,4,5,1,3] => 8 [2,6,4,5,3,1] => 6 [2,6,5,1,3,4] => 2 [2,6,5,1,4,3] => 2 [2,6,5,3,1,4] => 6 [2,6,5,3,4,1] => 6 [2,6,5,4,1,3] => 2 [2,6,5,4,3,1] => 2 [3,1,2,4,5,6] => 2 [3,1,2,4,6,5] => 2 [3,1,2,5,4,6] => 2 [3,1,2,5,6,4] => 4 [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] => 4 [3,1,4,6,2,5] => 2 [3,1,4,6,5,2] => 4 [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] => 4 [3,1,5,6,4,2] => 4 [3,1,6,2,4,5] => 2 [3,1,6,2,5,4] => 2 [3,1,6,4,2,5] => 4 [3,1,6,4,5,2] => 4 [3,1,6,5,2,4] => 2 [3,1,6,5,4,2] => 2 [3,2,1,4,5,6] => 1 [3,2,1,4,6,5] => 1 [3,2,1,5,4,6] => 1 [3,2,1,5,6,4] => 2 [3,2,1,6,4,5] => 2 [3,2,1,6,5,4] => 1 [3,2,4,1,5,6] => 2 [3,2,4,1,6,5] => 2 [3,2,4,5,1,6] => 4 [3,2,4,5,6,1] => 2 [3,2,4,6,1,5] => 4 [3,2,4,6,5,1] => 3 [3,2,5,1,4,6] => 2 [3,2,5,1,6,4] => 2 [3,2,5,4,1,6] => 2 [3,2,5,4,6,1] => 4 [3,2,5,6,1,4] => 4 [3,2,5,6,4,1] => 6 [3,2,6,1,4,5] => 2 [3,2,6,1,5,4] => 2 [3,2,6,4,1,5] => 4 [3,2,6,4,5,1] => 6 [3,2,6,5,1,4] => 2 [3,2,6,5,4,1] => 2 [3,4,1,2,5,6] => 1 [3,4,1,2,6,5] => 1 [3,4,1,5,2,6] => 4 [3,4,1,5,6,2] => 4 [3,4,1,6,2,5] => 4 [3,4,1,6,5,2] => 4 [3,4,2,1,5,6] => 3 [3,4,2,1,6,5] => 3 [3,4,2,5,1,6] => 4 [3,4,2,5,6,1] => 8 [3,4,2,6,1,5] => 4 [3,4,2,6,5,1] => 6 [3,4,5,1,2,6] => 6 [3,4,5,1,6,2] => 4 [3,4,5,2,1,6] => 3 [3,4,5,2,6,1] => 6 [3,4,5,6,1,2] => 4 [3,4,5,6,2,1] => 9 [3,4,6,1,2,5] => 8 [3,4,6,1,5,2] => 6 [3,4,6,2,1,5] => 2 [3,4,6,2,5,1] => 8 [3,4,6,5,1,2] => 3 [3,4,6,5,2,1] => 7 [3,5,1,2,4,6] => 4 [3,5,1,2,6,4] => 4 [3,5,1,4,2,6] => 1 [3,5,1,4,6,2] => 4 [3,5,1,6,2,4] => 3 [3,5,1,6,4,2] => 6 [3,5,2,1,4,6] => 2 [3,5,2,1,6,4] => 2 [3,5,2,4,1,6] => 6 [3,5,2,4,6,1] => 8 [3,5,2,6,1,4] => 6 [3,5,2,6,4,1] => 6 [3,5,4,1,2,6] => 2 [3,5,4,1,6,2] => 8 [3,5,4,2,1,6] => 3 [3,5,4,2,6,1] => 4 [3,5,4,6,1,2] => 9 [3,5,4,6,2,1] => 3 [3,5,6,1,2,4] => 6 [3,5,6,1,4,2] => 6 [3,5,6,2,1,4] => 8 [3,5,6,2,4,1] => 7 [3,5,6,4,1,2] => 8 [3,5,6,4,2,1] => 6 [3,6,1,2,4,5] => 4 [3,6,1,2,5,4] => 4 [3,6,1,4,2,5] => 4 [3,6,1,4,5,2] => 1 [3,6,1,5,2,4] => 6 [3,6,1,5,4,2] => 1 [3,6,2,1,4,5] => 4 [3,6,2,1,5,4] => 2 [3,6,2,4,1,5] => 4 [3,6,2,4,5,1] => 8 [3,6,2,5,1,4] => 6 [3,6,2,5,4,1] => 6 [3,6,4,1,2,5] => 8 [3,6,4,1,5,2] => 8 [3,6,4,2,1,5] => 6 [3,6,4,2,5,1] => 9 [3,6,4,5,1,2] => 8 [3,6,4,5,2,1] => 6 [3,6,5,1,2,4] => 8 [3,6,5,1,4,2] => 2 [3,6,5,2,1,4] => 4 [3,6,5,2,4,1] => 8 [3,6,5,4,1,2] => 2 [3,6,5,4,2,1] => 3 [4,1,2,3,5,6] => 2 [4,1,2,3,6,5] => 2 [4,1,2,5,3,6] => 2 [4,1,2,5,6,3] => 2 [4,1,2,6,3,5] => 2 [4,1,2,6,5,3] => 2 [4,1,3,2,5,6] => 2 [4,1,3,2,6,5] => 2 [4,1,3,5,2,6] => 4 [4,1,3,5,6,2] => 8 [4,1,3,6,2,5] => 4 [4,1,3,6,5,2] => 4 [4,1,5,2,3,6] => 4 [4,1,5,2,6,3] => 8 [4,1,5,3,2,6] => 2 [4,1,5,3,6,2] => 4 [4,1,5,6,2,3] => 8 [4,1,5,6,3,2] => 2 [4,1,6,2,3,5] => 8 [4,1,6,2,5,3] => 4 [4,1,6,3,2,5] => 4 [4,1,6,3,5,2] => 8 [4,1,6,5,2,3] => 4 [4,1,6,5,3,2] => 2 [4,2,1,3,5,6] => 2 [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] => 3 [4,2,3,1,6,5] => 3 [4,2,3,5,1,6] => 4 [4,2,3,5,6,1] => 8 [4,2,3,6,1,5] => 4 [4,2,3,6,5,1] => 6 [4,2,5,1,3,6] => 1 [4,2,5,1,6,3] => 4 [4,2,5,3,1,6] => 6 [4,2,5,3,6,1] => 8 [4,2,5,6,1,3] => 6 [4,2,5,6,3,1] => 8 [4,2,6,1,3,5] => 4 [4,2,6,1,5,3] => 1 [4,2,6,3,1,5] => 8 [4,2,6,3,5,1] => 6 [4,2,6,5,1,3] => 2 [4,2,6,5,3,1] => 6 [4,3,1,2,5,6] => 3 [4,3,1,2,6,5] => 3 [4,3,1,5,2,6] => 2 [4,3,1,5,6,2] => 4 [4,3,1,6,2,5] => 2 [4,3,1,6,5,2] => 2 [4,3,2,1,5,6] => 1 [4,3,2,1,6,5] => 1 [4,3,2,5,1,6] => 2 [4,3,2,5,6,1] => 4 [4,3,2,6,1,5] => 2 [4,3,2,6,5,1] => 2 [4,3,5,1,2,6] => 2 [4,3,5,1,6,2] => 2 [4,3,5,2,1,6] => 3 [4,3,5,2,6,1] => 8 [4,3,5,6,1,2] => 3 [4,3,5,6,2,1] => 7 [4,3,6,1,2,5] => 4 [4,3,6,1,5,2] => 2 [4,3,6,2,1,5] => 2 [4,3,6,2,5,1] => 6 [4,3,6,5,1,2] => 4 [4,3,6,5,2,1] => 4 [4,5,1,2,3,6] => 6 [4,5,1,2,6,3] => 8 [4,5,1,3,2,6] => 2 [4,5,1,3,6,2] => 8 [4,5,1,6,2,3] => 6 [4,5,1,6,3,2] => 8 [4,5,2,1,3,6] => 2 [4,5,2,1,6,3] => 4 [4,5,2,3,1,6] => 3 [4,5,2,3,6,1] => 2 [4,5,2,6,1,3] => 6 [4,5,2,6,3,1] => 7 [4,5,3,1,2,6] => 3 [4,5,3,1,6,2] => 8 [4,5,3,2,1,6] => 4 [4,5,3,2,6,1] => 6 [4,5,3,6,1,2] => 8 [4,5,3,6,2,1] => 6 [4,5,6,1,2,3] => 4 [4,5,6,1,3,2] => 4 [4,5,6,2,1,3] => 4 [4,5,6,2,3,1] => 12 [4,5,6,3,1,2] => 12 [4,5,6,3,2,1] => 4 [4,6,1,2,3,5] => 4 [4,6,1,2,5,3] => 6 [4,6,1,3,2,5] => 8 [4,6,1,3,5,2] => 8 [4,6,1,5,2,3] => 6 [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] => 8 [4,6,2,3,5,1] => 7 [4,6,2,5,1,3] => 4 [4,6,2,5,3,1] => 4 [4,6,3,1,2,5] => 8 [4,6,3,1,5,2] => 3 [4,6,3,2,1,5] => 2 [4,6,3,2,5,1] => 8 [4,6,3,5,1,2] => 6 [4,6,3,5,2,1] => 12 [4,6,5,1,2,3] => 4 [4,6,5,1,3,2] => 1 [4,6,5,2,1,3] => 6 [4,6,5,2,3,1] => 6 [4,6,5,3,1,2] => 6 [4,6,5,3,2,1] => 4 [5,1,2,3,4,6] => 4 [5,1,2,3,6,4] => 4 [5,1,2,4,3,6] => 4 [5,1,2,4,6,3] => 8 [5,1,2,6,3,4] => 4 [5,1,2,6,4,3] => 4 [5,1,3,2,4,6] => 2 [5,1,3,2,6,4] => 2 [5,1,3,4,2,6] => 4 [5,1,3,4,6,2] => 2 [5,1,3,6,2,4] => 4 [5,1,3,6,4,2] => 4 [5,1,4,2,3,6] => 4 [5,1,4,2,6,3] => 4 [5,1,4,3,2,6] => 2 [5,1,4,3,6,2] => 6 [5,1,4,6,2,3] => 8 [5,1,4,6,3,2] => 6 [5,1,6,2,3,4] => 4 [5,1,6,2,4,3] => 2 [5,1,6,3,2,4] => 8 [5,1,6,3,4,2] => 8 [5,1,6,4,2,3] => 8 [5,1,6,4,3,2] => 2 [5,2,1,3,4,6] => 4 [5,2,1,3,6,4] => 4 [5,2,1,4,3,6] => 2 [5,2,1,4,6,3] => 4 [5,2,1,6,3,4] => 4 [5,2,1,6,4,3] => 2 [5,2,3,1,4,6] => 4 [5,2,3,1,6,4] => 4 [5,2,3,4,1,6] => 3 [5,2,3,4,6,1] => 6 [5,2,3,6,1,4] => 1 [5,2,3,6,4,1] => 8 [5,2,4,1,3,6] => 6 [5,2,4,1,6,3] => 8 [5,2,4,3,1,6] => 3 [5,2,4,3,6,1] => 4 [5,2,4,6,1,3] => 8 [5,2,4,6,3,1] => 9 [5,2,6,1,3,4] => 6 [5,2,6,1,4,3] => 2 [5,2,6,3,1,4] => 8 [5,2,6,3,4,1] => 7 [5,2,6,4,1,3] => 3 [5,2,6,4,3,1] => 8 [5,3,1,2,4,6] => 4 [5,3,1,2,6,4] => 4 [5,3,1,4,2,6] => 6 [5,3,1,4,6,2] => 4 [5,3,1,6,2,4] => 6 [5,3,1,6,4,2] => 6 [5,3,2,1,4,6] => 2 [5,3,2,1,6,4] => 2 [5,3,2,4,1,6] => 3 [5,3,2,4,6,1] => 8 [5,3,2,6,1,4] => 1 [5,3,2,6,4,1] => 6 [5,3,4,1,2,6] => 3 [5,3,4,1,6,2] => 8 [5,3,4,2,1,6] => 4 [5,3,4,2,6,1] => 6 [5,3,4,6,1,2] => 8 [5,3,4,6,2,1] => 6 [5,3,6,1,2,4] => 6 [5,3,6,1,4,2] => 4 [5,3,6,2,1,4] => 2 [5,3,6,2,4,1] => 4 [5,3,6,4,1,2] => 6 [5,3,6,4,2,1] => 12 [5,4,1,2,3,6] => 3 [5,4,1,2,6,3] => 2 [5,4,1,3,2,6] => 3 [5,4,1,3,6,2] => 6 [5,4,1,6,2,3] => 8 [5,4,1,6,3,2] => 4 [5,4,2,1,3,6] => 3 [5,4,2,1,6,3] => 2 [5,4,2,3,1,6] => 4 [5,4,2,3,6,1] => 6 [5,4,2,6,1,3] => 2 [5,4,2,6,3,1] => 8 [5,4,3,1,2,6] => 4 [5,4,3,1,6,2] => 2 [5,4,3,2,1,6] => 1 [5,4,3,2,6,1] => 2 [5,4,3,6,1,2] => 2 [5,4,3,6,2,1] => 3 [5,4,6,1,2,3] => 4 [5,4,6,1,3,2] => 6 [5,4,6,2,1,3] => 1 [5,4,6,2,3,1] => 6 [5,4,6,3,1,2] => 6 [5,4,6,3,2,1] => 4 [5,6,1,2,3,4] => 4 [5,6,1,2,4,3] => 3 [5,6,1,3,2,4] => 9 [5,6,1,3,4,2] => 8 [5,6,1,4,2,3] => 8 [5,6,1,4,3,2] => 2 [5,6,2,1,3,4] => 3 [5,6,2,1,4,3] => 4 [5,6,2,3,1,4] => 8 [5,6,2,3,4,1] => 12 [5,6,2,4,1,3] => 6 [5,6,2,4,3,1] => 6 [5,6,3,1,2,4] => 8 [5,6,3,1,4,2] => 6 [5,6,3,2,1,4] => 2 [5,6,3,2,4,1] => 6 [5,6,3,4,1,2] => 1 [5,6,3,4,2,1] => 6 [5,6,4,1,2,3] => 12 [5,6,4,1,3,2] => 6 [5,6,4,2,1,3] => 6 [5,6,4,2,3,1] => 6 [5,6,4,3,1,2] => 6 [5,6,4,3,2,1] => 5 [6,1,2,3,4,5] => 4 [6,1,2,3,5,4] => 2 [6,1,2,4,3,5] => 4 [6,1,2,4,5,3] => 8 [6,1,2,5,3,4] => 8 [6,1,2,5,4,3] => 4 [6,1,3,2,4,5] => 4 [6,1,3,2,5,4] => 4 [6,1,3,4,2,5] => 6 [6,1,3,4,5,2] => 6 [6,1,3,5,2,4] => 8 [6,1,3,5,4,2] => 8 [6,1,4,2,3,5] => 6 [6,1,4,2,5,3] => 8 [6,1,4,3,2,5] => 2 [6,1,4,3,5,2] => 4 [6,1,4,5,2,3] => 2 [6,1,4,5,3,2] => 6 [6,1,5,2,3,4] => 6 [6,1,5,2,4,3] => 8 [6,1,5,3,2,4] => 4 [6,1,5,3,4,2] => 6 [6,1,5,4,2,3] => 6 [6,1,5,4,3,2] => 2 [6,2,1,3,4,5] => 2 [6,2,1,3,5,4] => 3 [6,2,1,4,3,5] => 4 [6,2,1,4,5,3] => 6 [6,2,1,5,3,4] => 6 [6,2,1,5,4,3] => 2 [6,2,3,1,4,5] => 8 [6,2,3,1,5,4] => 6 [6,2,3,4,1,5] => 6 [6,2,3,4,5,1] => 9 [6,2,3,5,1,4] => 8 [6,2,3,5,4,1] => 7 [6,2,4,1,3,5] => 8 [6,2,4,1,5,3] => 6 [6,2,4,3,1,5] => 4 [6,2,4,3,5,1] => 3 [6,2,4,5,1,3] => 7 [6,2,4,5,3,1] => 6 [6,2,5,1,3,4] => 8 [6,2,5,1,4,3] => 6 [6,2,5,3,1,4] => 9 [6,2,5,3,4,1] => 6 [6,2,5,4,1,3] => 8 [6,2,5,4,3,1] => 3 [6,3,1,2,4,5] => 8 [6,3,1,2,5,4] => 6 [6,3,1,4,2,5] => 8 [6,3,1,4,5,2] => 8 [6,3,1,5,2,4] => 6 [6,3,1,5,4,2] => 6 [6,3,2,1,4,5] => 4 [6,3,2,1,5,4] => 2 [6,3,2,4,1,5] => 8 [6,3,2,4,5,1] => 7 [6,3,2,5,1,4] => 6 [6,3,2,5,4,1] => 4 [6,3,4,1,2,5] => 2 [6,3,4,1,5,2] => 7 [6,3,4,2,1,5] => 6 [6,3,4,2,5,1] => 6 [6,3,4,5,1,2] => 12 [6,3,4,5,2,1] => 4 [6,3,5,1,2,4] => 7 [6,3,5,1,4,2] => 4 [6,3,5,2,1,4] => 8 [6,3,5,2,4,1] => 12 [6,3,5,4,1,2] => 6 [6,3,5,4,2,1] => 4 [6,4,1,2,3,5] => 6 [6,4,1,2,5,3] => 8 [6,4,1,3,2,5] => 4 [6,4,1,3,5,2] => 9 [6,4,1,5,2,3] => 7 [6,4,1,5,3,2] => 8 [6,4,2,1,3,5] => 8 [6,4,2,1,5,3] => 6 [6,4,2,3,1,5] => 6 [6,4,2,3,5,1] => 6 [6,4,2,5,1,3] => 4 [6,4,2,5,3,1] => 12 [6,4,3,1,2,5] => 6 [6,4,3,1,5,2] => 8 [6,4,3,2,1,5] => 2 [6,4,3,2,5,1] => 3 [6,4,3,5,1,2] => 6 [6,4,3,5,2,1] => 4 [6,4,5,1,2,3] => 12 [6,4,5,1,3,2] => 6 [6,4,5,2,1,3] => 6 [6,4,5,2,3,1] => 6 [6,4,5,3,1,2] => 6 [6,4,5,3,2,1] => 5 [6,5,1,2,3,4] => 9 [6,5,1,2,4,3] => 7 [6,5,1,3,2,4] => 3 [6,5,1,3,4,2] => 6 [6,5,1,4,2,3] => 6 [6,5,1,4,3,2] => 3 [6,5,2,1,3,4] => 7 [6,5,2,1,4,3] => 4 [6,5,2,3,1,4] => 6 [6,5,2,3,4,1] => 4 [6,5,2,4,1,3] => 12 [6,5,2,4,3,1] => 4 [6,5,3,1,2,4] => 6 [6,5,3,1,4,2] => 12 [6,5,3,2,1,4] => 3 [6,5,3,2,4,1] => 4 [6,5,3,4,1,2] => 6 [6,5,3,4,2,1] => 5 [6,5,4,1,2,3] => 4 [6,5,4,1,3,2] => 4 [6,5,4,2,1,3] => 4 [6,5,4,2,3,1] => 5 [6,5,4,3,1,2] => 5 [6,5,4,3,2,1] => 1 [1,2,3,4,5,6,7] => 1 [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] => 1 [1,2,3,5,6,4,7] => 2 [1,2,3,5,6,7,4] => 2 [1,2,3,5,7,4,6] => 2 [1,2,3,5,7,6,4] => 2 [1,2,3,6,4,5,7] => 2 [1,2,3,6,4,7,5] => 2 [1,2,3,6,5,4,7] => 1 [1,2,3,6,5,7,4] => 2 [1,2,3,6,7,4,5] => 1 [1,2,3,6,7,5,4] => 3 [1,2,3,7,4,5,6] => 2 [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] => 1 [1,2,4,3,5,6,7] => 1 [1,2,4,3,5,7,6] => 1 [1,2,4,3,6,5,7] => 1 [1,2,4,3,6,7,5] => 2 [1,2,4,3,7,5,6] => 2 [1,2,4,3,7,6,5] => 1 [1,2,4,5,3,6,7] => 2 [1,2,4,5,3,7,6] => 2 [1,2,4,5,6,3,7] => 2 [1,2,4,5,6,7,3] => 4 [1,2,4,5,7,3,6] => 2 [1,2,4,5,7,6,3] => 4 [1,2,4,6,3,5,7] => 2 [1,2,4,6,3,7,5] => 2 [1,2,4,6,5,3,7] => 2 [1,2,4,6,5,7,3] => 2 [1,2,4,6,7,3,5] => 4 [1,2,4,6,7,5,3] => 4 [1,2,4,7,3,5,6] => 2 [1,2,4,7,3,6,5] => 2 [1,2,4,7,5,3,6] => 4 [1,2,4,7,5,6,3] => 4 [1,2,4,7,6,3,5] => 2 [1,2,4,7,6,5,3] => 2 [1,2,5,3,4,6,7] => 2 [1,2,5,3,4,7,6] => 2 [1,2,5,3,6,4,7] => 2 [1,2,5,3,6,7,4] => 2 [1,2,5,3,7,4,6] => 2 [1,2,5,3,7,6,4] => 2 [1,2,5,4,3,6,7] => 1 [1,2,5,4,3,7,6] => 1 [1,2,5,4,6,3,7] => 2 [1,2,5,4,6,7,3] => 4 [1,2,5,4,7,3,6] => 2 [1,2,5,4,7,6,3] => 2 [1,2,5,6,3,4,7] => 1 [1,2,5,6,3,7,4] => 4 [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] => 3 [1,2,5,7,3,4,6] => 4 [1,2,5,7,3,6,4] => 1 [1,2,5,7,4,3,6] => 2 [1,2,5,7,4,6,3] => 6 [1,2,5,7,6,3,4] => 2 [1,2,5,7,6,4,3] => 3 [1,2,6,3,4,5,7] => 2 [1,2,6,3,4,7,5] => 2 [1,2,6,3,5,4,7] => 2 [1,2,6,3,5,7,4] => 4 [1,2,6,3,7,4,5] => 4 [1,2,6,3,7,5,4] => 2 [1,2,6,4,3,5,7] => 2 [1,2,6,4,3,7,5] => 2 [1,2,6,4,5,3,7] => 3 [1,2,6,4,5,7,3] => 4 [1,2,6,4,7,3,5] => 1 [1,2,6,4,7,5,3] => 6 [1,2,6,5,3,4,7] => 3 [1,2,6,5,3,7,4] => 2 [1,2,6,5,4,3,7] => 1 [1,2,6,5,4,7,3] => 2 [1,2,6,5,7,3,4] => 2 [1,2,6,5,7,4,3] => 3 [1,2,6,7,3,4,5] => 6 [1,2,6,7,3,5,4] => 2 [1,2,6,7,4,3,5] => 2 [1,2,6,7,4,5,3] => 3 [1,2,6,7,5,3,4] => 3 [1,2,6,7,5,4,3] => 4 [1,2,7,3,4,5,6] => 4 [1,2,7,3,4,6,5] => 4 [1,2,7,3,5,4,6] => 2 [1,2,7,3,5,6,4] => 4 [1,2,7,3,6,4,5] => 4 [1,2,7,3,6,5,4] => 2 [1,2,7,4,3,5,6] => 4 [1,2,7,4,3,6,5] => 2 [1,2,7,4,5,3,6] => 4 [1,2,7,4,5,6,3] => 3 [1,2,7,4,6,3,5] => 6 [1,2,7,4,6,5,3] => 3 [1,2,7,5,3,4,6] => 4 [1,2,7,5,3,6,4] => 6 [1,2,7,5,4,3,6] => 2 [1,2,7,5,4,6,3] => 3 [1,2,7,5,6,3,4] => 3 [1,2,7,5,6,4,3] => 4 [1,2,7,6,3,4,5] => 3 [1,2,7,6,3,5,4] => 3 [1,2,7,6,4,3,5] => 3 [1,2,7,6,4,5,3] => 4 [1,2,7,6,5,3,4] => 4 [1,2,7,6,5,4,3] => 1 [1,3,2,4,5,6,7] => 1 [1,3,2,4,5,7,6] => 1 [1,3,2,4,6,5,7] => 1 [1,3,2,4,6,7,5] => 2 [1,3,2,4,7,5,6] => 2 [1,3,2,4,7,6,5] => 1 [1,3,2,5,4,6,7] => 1 [1,3,2,5,4,7,6] => 1 [1,3,2,5,6,4,7] => 2 [1,3,2,5,6,7,4] => 2 [1,3,2,5,7,4,6] => 2 [1,3,2,5,7,6,4] => 2 [1,3,2,6,4,5,7] => 2 [1,3,2,6,4,7,5] => 2 [1,3,2,6,5,4,7] => 1 [1,3,2,6,5,7,4] => 2 [1,3,2,6,7,4,5] => 1 [1,3,2,6,7,5,4] => 3 [1,3,2,7,4,5,6] => 2 [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] => 3 [1,3,2,7,6,5,4] => 1 [1,3,4,2,5,6,7] => 2 [1,3,4,2,5,7,6] => 2 [1,3,4,2,6,5,7] => 2 [1,3,4,2,6,7,5] => 4 [1,3,4,2,7,5,6] => 4 [1,3,4,2,7,6,5] => 2 [1,3,4,5,2,6,7] => 2 [1,3,4,5,2,7,6] => 2 [1,3,4,5,6,2,7] => 4 [1,3,4,5,6,7,2] => 4 [1,3,4,5,7,2,6] => 4 [1,3,4,5,7,6,2] => 2 [1,3,4,6,2,5,7] => 2 [1,3,4,6,2,7,5] => 2 [1,3,4,6,5,2,7] => 4 [1,3,4,6,5,7,2] => 4 [1,3,4,6,7,2,5] => 4 [1,3,4,6,7,5,2] => 8 [1,3,4,7,2,5,6] => 2 [1,3,4,7,2,6,5] => 2 [1,3,4,7,5,2,6] => 8 [1,3,4,7,5,6,2] => 8 [1,3,4,7,6,2,5] => 4 [1,3,4,7,6,5,2] => 4 [1,3,5,2,4,6,7] => 2 [1,3,5,2,4,7,6] => 2 [1,3,5,2,6,4,7] => 2 [1,3,5,2,6,7,4] => 2 [1,3,5,2,7,4,6] => 2 [1,3,5,2,7,6,4] => 2 [1,3,5,4,2,6,7] => 2 [1,3,5,4,2,7,6] => 2 [1,3,5,4,6,2,7] => 2 [1,3,5,4,6,7,2] => 4 [1,3,5,4,7,2,6] => 2 [1,3,5,4,7,6,2] => 4 [1,3,5,6,2,4,7] => 4 [1,3,5,6,2,7,4] => 8 [1,3,5,6,4,2,7] => 4 [1,3,5,6,4,7,2] => 6 [1,3,5,6,7,2,4] => 4 [1,3,5,6,7,4,2] => 6 [1,3,5,7,2,4,6] => 8 [1,3,5,7,2,6,4] => 4 [1,3,5,7,4,2,6] => 4 [1,3,5,7,4,6,2] => 8 [1,3,5,7,6,2,4] => 2 [1,3,5,7,6,4,2] => 8 [1,3,6,2,4,5,7] => 2 [1,3,6,2,4,7,5] => 2 [1,3,6,2,5,4,7] => 2 [1,3,6,2,5,7,4] => 4 [1,3,6,2,7,4,5] => 4 [1,3,6,2,7,5,4] => 2 [1,3,6,4,2,5,7] => 4 [1,3,6,4,2,7,5] => 4 [1,3,6,4,5,2,7] => 4 [1,3,6,4,5,7,2] => 6 [1,3,6,4,7,2,5] => 4 [1,3,6,4,7,5,2] => 8 [1,3,6,5,2,4,7] => 2 [1,3,6,5,2,7,4] => 4 [1,3,6,5,4,2,7] => 2 [1,3,6,5,4,7,2] => 2 [1,3,6,5,7,2,4] => 8 [1,3,6,5,7,4,2] => 4 [1,3,6,7,2,4,5] => 8 [1,3,6,7,2,5,4] => 4 [1,3,6,7,4,2,5] => 8 [1,3,6,7,4,5,2] => 2 [1,3,6,7,5,2,4] => 8 [1,3,6,7,5,4,2] => 6 [1,3,7,2,4,5,6] => 4 [1,3,7,2,4,6,5] => 4 [1,3,7,2,5,4,6] => 2 [1,3,7,2,5,6,4] => 4 [1,3,7,2,6,4,5] => 4 [1,3,7,2,6,5,4] => 2 [1,3,7,4,2,5,6] => 8 [1,3,7,4,2,6,5] => 4 [1,3,7,4,5,2,6] => 2 [1,3,7,4,5,6,2] => 6 [1,3,7,4,6,2,5] => 4 [1,3,7,4,6,5,2] => 8 [1,3,7,5,2,4,6] => 4 [1,3,7,5,2,6,4] => 8 [1,3,7,5,4,2,6] => 6 [1,3,7,5,4,6,2] => 4 [1,3,7,5,6,2,4] => 8 [1,3,7,5,6,4,2] => 6 [1,3,7,6,2,4,5] => 2 [1,3,7,6,2,5,4] => 2 [1,3,7,6,4,2,5] => 6 [1,3,7,6,4,5,2] => 6 [1,3,7,6,5,2,4] => 2 [1,3,7,6,5,4,2] => 2 [1,4,2,3,5,6,7] => 2 [1,4,2,3,5,7,6] => 2 [1,4,2,3,6,5,7] => 2 [1,4,2,3,6,7,5] => 4 [1,4,2,3,7,5,6] => 4 [1,4,2,3,7,6,5] => 2 [1,4,2,5,3,6,7] => 2 [1,4,2,5,3,7,6] => 2 [1,4,2,5,6,3,7] => 2 [1,4,2,5,6,7,3] => 4 [1,4,2,5,7,3,6] => 2 [1,4,2,5,7,6,3] => 4 [1,4,2,6,3,5,7] => 2 [1,4,2,6,3,7,5] => 2 [1,4,2,6,5,3,7] => 2 [1,4,2,6,5,7,3] => 2 [1,4,2,6,7,3,5] => 4 [1,4,2,6,7,5,3] => 4 [1,4,2,7,3,5,6] => 2 [1,4,2,7,3,6,5] => 2 [1,4,2,7,5,3,6] => 4 [1,4,2,7,5,6,3] => 4 [1,4,2,7,6,3,5] => 2 [1,4,2,7,6,5,3] => 2 [1,4,3,2,5,6,7] => 1 [1,4,3,2,5,7,6] => 1 [1,4,3,2,6,5,7] => 1 [1,4,3,2,6,7,5] => 2 [1,4,3,2,7,5,6] => 2 [1,4,3,2,7,6,5] => 1 [1,4,3,5,2,6,7] => 2 [1,4,3,5,2,7,6] => 2 [1,4,3,5,6,2,7] => 4 [1,4,3,5,6,7,2] => 2 [1,4,3,5,7,2,6] => 4 [1,4,3,5,7,6,2] => 3 [1,4,3,6,2,5,7] => 2 [1,4,3,6,2,7,5] => 2 [1,4,3,6,5,2,7] => 2 [1,4,3,6,5,7,2] => 4 [1,4,3,6,7,2,5] => 4 [1,4,3,6,7,5,2] => 6 [1,4,3,7,2,5,6] => 2 [1,4,3,7,2,6,5] => 2 [1,4,3,7,5,2,6] => 4 [1,4,3,7,5,6,2] => 6 [1,4,3,7,6,2,5] => 2 [1,4,3,7,6,5,2] => 2 [1,4,5,2,3,6,7] => 1 [1,4,5,2,3,7,6] => 1 [1,4,5,2,6,3,7] => 4 [1,4,5,2,6,7,3] => 4 [1,4,5,2,7,3,6] => 4 [1,4,5,2,7,6,3] => 4 [1,4,5,3,2,6,7] => 3 [1,4,5,3,2,7,6] => 3 [1,4,5,3,6,2,7] => 4 [1,4,5,3,6,7,2] => 8 [1,4,5,3,7,2,6] => 4 [1,4,5,3,7,6,2] => 6 [1,4,5,6,2,3,7] => 6 [1,4,5,6,2,7,3] => 4 [1,4,5,6,3,2,7] => 3 [1,4,5,6,3,7,2] => 6 [1,4,5,6,7,2,3] => 4 [1,4,5,6,7,3,2] => 9 [1,4,5,7,2,3,6] => 8 [1,4,5,7,2,6,3] => 6 [1,4,5,7,3,2,6] => 2 [1,4,5,7,3,6,2] => 8 [1,4,5,7,6,2,3] => 3 [1,4,5,7,6,3,2] => 7 [1,4,6,2,3,5,7] => 4 [1,4,6,2,3,7,5] => 4 [1,4,6,2,5,3,7] => 1 [1,4,6,2,5,7,3] => 4 [1,4,6,2,7,3,5] => 3 [1,4,6,2,7,5,3] => 6 [1,4,6,3,2,5,7] => 2 [1,4,6,3,2,7,5] => 2 [1,4,6,3,5,2,7] => 6 [1,4,6,3,5,7,2] => 8 [1,4,6,3,7,2,5] => 6 [1,4,6,3,7,5,2] => 6 [1,4,6,5,2,3,7] => 2 [1,4,6,5,2,7,3] => 8 [1,4,6,5,3,2,7] => 3 [1,4,6,5,3,7,2] => 4 ----------------------------------------------------------------------------- Created: Jul 14, 2017 at 09:26 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Jul 14, 2017 at 11:53 by Martin Rubey