***************************************************************************** * 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: St001867 ----------------------------------------------------------------------------- Collection: Signed permutations ----------------------------------------------------------------------------- Description: The number of alignments of type EN of a signed permutation. An alignment of type EN of a signed permutation π∈Hn is a pair −n≤i≤j≤n, i,j≠0, such that one of the following conditions hold: * $-i < 0 < -\pi(i) < \pi(j) < j$ * $i \leq\pi(i) < \pi(j) < j$. ----------------------------------------------------------------------------- References: [1] Cho, S., Park, K. Permutation statistics and weak \B\ruhat order in permutation tableaux of type $B$ [[arXiv:1412.6290]] ----------------------------------------------------------------------------- Code: def statistic(pi): n = len(pi) A_EN = [(i, j) for i in range(1, n+1) for j in range(1, n+1) if (-i < 0 < -pi(i) < pi(j) < j) or (i <= pi(i) < pi(j) < j)] return len(A_EN) ----------------------------------------------------------------------------- Statistic values: [1] => 0 [-1] => 0 [1,2] => 0 [1,-2] => 0 [-1,2] => 0 [-1,-2] => 0 [2,1] => 0 [2,-1] => 0 [-2,1] => 0 [-2,-1] => 0 [1,2,3] => 0 [1,2,-3] => 0 [1,-2,3] => 0 [1,-2,-3] => 0 [-1,2,3] => 0 [-1,2,-3] => 0 [-1,-2,3] => 0 [-1,-2,-3] => 0 [1,3,2] => 1 [1,3,-2] => 0 [1,-3,2] => 1 [1,-3,-2] => 0 [-1,3,2] => 1 [-1,3,-2] => 0 [-1,-3,2] => 1 [-1,-3,-2] => 0 [2,1,3] => 0 [2,1,-3] => 0 [2,-1,3] => 0 [2,-1,-3] => 0 [-2,1,3] => 0 [-2,1,-3] => 0 [-2,-1,3] => 0 [-2,-1,-3] => 0 [2,3,1] => 0 [2,3,-1] => 0 [2,-3,1] => 0 [2,-3,-1] => 0 [-2,3,1] => 0 [-2,3,-1] => 0 [-2,-3,1] => 0 [-2,-3,-1] => 0 [3,1,2] => 0 [3,1,-2] => 0 [3,-1,2] => 1 [3,-1,-2] => 0 [-3,1,2] => 0 [-3,1,-2] => 0 [-3,-1,2] => 1 [-3,-1,-2] => 0 [3,2,1] => 0 [3,2,-1] => 0 [3,-2,1] => 0 [3,-2,-1] => 0 [-3,2,1] => 0 [-3,2,-1] => 0 [-3,-2,1] => 0 [-3,-2,-1] => 0 [1,2,3,4] => 0 [1,2,3,-4] => 0 [1,2,-3,4] => 0 [1,2,-3,-4] => 0 [1,-2,3,4] => 0 [1,-2,3,-4] => 0 [1,-2,-3,4] => 0 [1,-2,-3,-4] => 0 [-1,2,3,4] => 0 [-1,2,3,-4] => 0 [-1,2,-3,4] => 0 [-1,2,-3,-4] => 0 [-1,-2,3,4] => 0 [-1,-2,3,-4] => 0 [-1,-2,-3,4] => 0 [-1,-2,-3,-4] => 0 [1,2,4,3] => 2 [1,2,4,-3] => 0 [1,2,-4,3] => 2 [1,2,-4,-3] => 0 [1,-2,4,3] => 2 [1,-2,4,-3] => 0 [1,-2,-4,3] => 2 [1,-2,-4,-3] => 0 [-1,2,4,3] => 2 [-1,2,4,-3] => 0 [-1,2,-4,3] => 2 [-1,2,-4,-3] => 0 [-1,-2,4,3] => 2 [-1,-2,4,-3] => 0 [-1,-2,-4,3] => 2 [-1,-2,-4,-3] => 0 [1,3,2,4] => 1 [1,3,2,-4] => 1 [1,3,-2,4] => 0 [1,3,-2,-4] => 0 [1,-3,2,4] => 1 [1,-3,2,-4] => 1 [1,-3,-2,4] => 0 [1,-3,-2,-4] => 0 [-1,3,2,4] => 1 [-1,3,2,-4] => 1 [-1,3,-2,4] => 0 [-1,3,-2,-4] => 0 [-1,-3,2,4] => 1 [-1,-3,2,-4] => 1 [-1,-3,-2,4] => 0 [-1,-3,-2,-4] => 0 [1,3,4,2] => 1 [1,3,4,-2] => 0 [1,3,-4,2] => 1 [1,3,-4,-2] => 0 [1,-3,4,2] => 1 [1,-3,4,-2] => 0 [1,-3,-4,2] => 1 [1,-3,-4,-2] => 0 [-1,3,4,2] => 1 [-1,3,4,-2] => 0 [-1,3,-4,2] => 1 [-1,3,-4,-2] => 0 [-1,-3,4,2] => 1 [-1,-3,4,-2] => 0 [-1,-3,-4,2] => 1 [-1,-3,-4,-2] => 0 [1,4,2,3] => 2 [1,4,2,-3] => 1 [1,4,-2,3] => 2 [1,4,-2,-3] => 0 [1,-4,2,3] => 2 [1,-4,2,-3] => 1 [1,-4,-2,3] => 2 [1,-4,-2,-3] => 0 [-1,4,2,3] => 2 [-1,4,2,-3] => 1 [-1,4,-2,3] => 2 [-1,4,-2,-3] => 0 [-1,-4,2,3] => 2 [-1,-4,2,-3] => 1 [-1,-4,-2,3] => 2 [-1,-4,-2,-3] => 0 [1,4,3,2] => 1 [1,4,3,-2] => 0 [1,4,-3,2] => 1 [1,4,-3,-2] => 0 [1,-4,3,2] => 1 [1,-4,3,-2] => 0 [1,-4,-3,2] => 1 [1,-4,-3,-2] => 0 [-1,4,3,2] => 1 [-1,4,3,-2] => 0 [-1,4,-3,2] => 1 [-1,4,-3,-2] => 0 [-1,-4,3,2] => 1 [-1,-4,3,-2] => 0 [-1,-4,-3,2] => 1 [-1,-4,-3,-2] => 0 [2,1,3,4] => 0 [2,1,3,-4] => 0 [2,1,-3,4] => 0 [2,1,-3,-4] => 0 [2,-1,3,4] => 0 [2,-1,3,-4] => 0 [2,-1,-3,4] => 0 [2,-1,-3,-4] => 0 [-2,1,3,4] => 0 [-2,1,3,-4] => 0 [-2,1,-3,4] => 0 [-2,1,-3,-4] => 0 [-2,-1,3,4] => 0 [-2,-1,3,-4] => 0 [-2,-1,-3,4] => 0 [-2,-1,-3,-4] => 0 [2,1,4,3] => 1 [2,1,4,-3] => 0 [2,1,-4,3] => 1 [2,1,-4,-3] => 0 [2,-1,4,3] => 2 [2,-1,4,-3] => 0 [2,-1,-4,3] => 2 [2,-1,-4,-3] => 0 [-2,1,4,3] => 1 [-2,1,4,-3] => 0 [-2,1,-4,3] => 1 [-2,1,-4,-3] => 0 [-2,-1,4,3] => 2 [-2,-1,4,-3] => 0 [-2,-1,-4,3] => 2 [-2,-1,-4,-3] => 0 [2,3,1,4] => 0 [2,3,1,-4] => 0 [2,3,-1,4] => 0 [2,3,-1,-4] => 0 [2,-3,1,4] => 0 [2,-3,1,-4] => 0 [2,-3,-1,4] => 0 [2,-3,-1,-4] => 0 [-2,3,1,4] => 0 [-2,3,1,-4] => 0 [-2,3,-1,4] => 0 [-2,3,-1,-4] => 0 [-2,-3,1,4] => 0 [-2,-3,1,-4] => 0 [-2,-3,-1,4] => 0 [-2,-3,-1,-4] => 0 [2,3,4,1] => 0 [2,3,4,-1] => 0 [2,3,-4,1] => 0 [2,3,-4,-1] => 0 [2,-3,4,1] => 0 [2,-3,4,-1] => 0 [2,-3,-4,1] => 0 [2,-3,-4,-1] => 0 [-2,3,4,1] => 0 [-2,3,4,-1] => 0 [-2,3,-4,1] => 0 [-2,3,-4,-1] => 0 [-2,-3,4,1] => 0 [-2,-3,4,-1] => 0 [-2,-3,-4,1] => 0 [-2,-3,-4,-1] => 0 [2,4,1,3] => 1 [2,4,1,-3] => 0 [2,4,-1,3] => 2 [2,4,-1,-3] => 0 [2,-4,1,3] => 1 [2,-4,1,-3] => 0 [2,-4,-1,3] => 2 [2,-4,-1,-3] => 0 [-2,4,1,3] => 1 [-2,4,1,-3] => 0 [-2,4,-1,3] => 2 [-2,4,-1,-3] => 0 [-2,-4,1,3] => 1 [-2,-4,1,-3] => 0 [-2,-4,-1,3] => 2 [-2,-4,-1,-3] => 0 [2,4,3,1] => 0 [2,4,3,-1] => 0 [2,4,-3,1] => 0 [2,4,-3,-1] => 0 [2,-4,3,1] => 0 [2,-4,3,-1] => 0 [2,-4,-3,1] => 0 [2,-4,-3,-1] => 0 [-2,4,3,1] => 0 [-2,4,3,-1] => 0 [-2,4,-3,1] => 0 [-2,4,-3,-1] => 0 [-2,-4,3,1] => 0 [-2,-4,3,-1] => 0 [-2,-4,-3,1] => 0 [-2,-4,-3,-1] => 0 [3,1,2,4] => 0 [3,1,2,-4] => 0 [3,1,-2,4] => 0 [3,1,-2,-4] => 0 [3,-1,2,4] => 1 [3,-1,2,-4] => 1 [3,-1,-2,4] => 0 [3,-1,-2,-4] => 0 [-3,1,2,4] => 0 [-3,1,2,-4] => 0 [-3,1,-2,4] => 0 [-3,1,-2,-4] => 0 [-3,-1,2,4] => 1 [-3,-1,2,-4] => 1 [-3,-1,-2,4] => 0 [-3,-1,-2,-4] => 0 [3,1,4,2] => 0 [3,1,4,-2] => 0 [3,1,-4,2] => 0 [3,1,-4,-2] => 0 [3,-1,4,2] => 1 [3,-1,4,-2] => 0 [3,-1,-4,2] => 1 [3,-1,-4,-2] => 0 [-3,1,4,2] => 0 [-3,1,4,-2] => 0 [-3,1,-4,2] => 0 [-3,1,-4,-2] => 0 [-3,-1,4,2] => 1 [-3,-1,4,-2] => 0 [-3,-1,-4,2] => 1 [-3,-1,-4,-2] => 0 [3,2,1,4] => 0 [3,2,1,-4] => 0 [3,2,-1,4] => 0 [3,2,-1,-4] => 0 [3,-2,1,4] => 0 [3,-2,1,-4] => 0 [3,-2,-1,4] => 0 [3,-2,-1,-4] => 0 [-3,2,1,4] => 0 [-3,2,1,-4] => 0 [-3,2,-1,4] => 0 [-3,2,-1,-4] => 0 [-3,-2,1,4] => 0 [-3,-2,1,-4] => 0 [-3,-2,-1,4] => 0 [-3,-2,-1,-4] => 0 [3,2,4,1] => 0 [3,2,4,-1] => 0 [3,2,-4,1] => 0 [3,2,-4,-1] => 0 [3,-2,4,1] => 0 [3,-2,4,-1] => 0 [3,-2,-4,1] => 0 [3,-2,-4,-1] => 0 [-3,2,4,1] => 0 [-3,2,4,-1] => 0 [-3,2,-4,1] => 0 [-3,2,-4,-1] => 0 [-3,-2,4,1] => 0 [-3,-2,4,-1] => 0 [-3,-2,-4,1] => 0 [-3,-2,-4,-1] => 0 [3,4,1,2] => 0 [3,4,1,-2] => 0 [3,4,-1,2] => 1 [3,4,-1,-2] => 0 [3,-4,1,2] => 0 [3,-4,1,-2] => 0 [3,-4,-1,2] => 1 [3,-4,-1,-2] => 0 [-3,4,1,2] => 0 [-3,4,1,-2] => 0 [-3,4,-1,2] => 1 [-3,4,-1,-2] => 0 [-3,-4,1,2] => 0 [-3,-4,1,-2] => 0 [-3,-4,-1,2] => 1 [-3,-4,-1,-2] => 0 [3,4,2,1] => 0 [3,4,2,-1] => 1 [3,4,-2,1] => 0 [3,4,-2,-1] => 0 [3,-4,2,1] => 0 [3,-4,2,-1] => 1 [3,-4,-2,1] => 0 [3,-4,-2,-1] => 0 [-3,4,2,1] => 0 [-3,4,2,-1] => 1 [-3,4,-2,1] => 0 [-3,4,-2,-1] => 0 [-3,-4,2,1] => 0 [-3,-4,2,-1] => 1 [-3,-4,-2,1] => 0 [-3,-4,-2,-1] => 0 [4,1,2,3] => 0 [4,1,2,-3] => 0 [4,1,-2,3] => 1 [4,1,-2,-3] => 0 [4,-1,2,3] => 2 [4,-1,2,-3] => 1 [4,-1,-2,3] => 2 [4,-1,-2,-3] => 0 [-4,1,2,3] => 0 [-4,1,2,-3] => 0 [-4,1,-2,3] => 1 [-4,1,-2,-3] => 0 [-4,-1,2,3] => 2 [-4,-1,2,-3] => 1 [-4,-1,-2,3] => 2 [-4,-1,-2,-3] => 0 [4,1,3,2] => 0 [4,1,3,-2] => 0 [4,1,-3,2] => 0 [4,1,-3,-2] => 0 [4,-1,3,2] => 1 [4,-1,3,-2] => 0 [4,-1,-3,2] => 1 [4,-1,-3,-2] => 0 [-4,1,3,2] => 0 [-4,1,3,-2] => 0 [-4,1,-3,2] => 0 [-4,1,-3,-2] => 0 [-4,-1,3,2] => 1 [-4,-1,3,-2] => 0 [-4,-1,-3,2] => 1 [-4,-1,-3,-2] => 0 [4,2,1,3] => 1 [4,2,1,-3] => 0 [4,2,-1,3] => 2 [4,2,-1,-3] => 0 [4,-2,1,3] => 1 [4,-2,1,-3] => 0 [4,-2,-1,3] => 2 [4,-2,-1,-3] => 0 [-4,2,1,3] => 1 [-4,2,1,-3] => 0 [-4,2,-1,3] => 2 [-4,2,-1,-3] => 0 [-4,-2,1,3] => 1 [-4,-2,1,-3] => 0 [-4,-2,-1,3] => 2 [-4,-2,-1,-3] => 0 [4,2,3,1] => 0 [4,2,3,-1] => 0 [4,2,-3,1] => 0 [4,2,-3,-1] => 0 [4,-2,3,1] => 0 [4,-2,3,-1] => 0 [4,-2,-3,1] => 0 [4,-2,-3,-1] => 0 [-4,2,3,1] => 0 [-4,2,3,-1] => 0 [-4,2,-3,1] => 0 [-4,2,-3,-1] => 0 [-4,-2,3,1] => 0 [-4,-2,3,-1] => 0 [-4,-2,-3,1] => 0 [-4,-2,-3,-1] => 0 [4,3,1,2] => 0 [4,3,1,-2] => 0 [4,3,-1,2] => 1 [4,3,-1,-2] => 0 [4,-3,1,2] => 0 [4,-3,1,-2] => 0 [4,-3,-1,2] => 1 [4,-3,-1,-2] => 0 [-4,3,1,2] => 0 [-4,3,1,-2] => 0 [-4,3,-1,2] => 1 [-4,3,-1,-2] => 0 [-4,-3,1,2] => 0 [-4,-3,1,-2] => 0 [-4,-3,-1,2] => 1 [-4,-3,-1,-2] => 0 [4,3,2,1] => 0 [4,3,2,-1] => 1 [4,3,-2,1] => 0 [4,3,-2,-1] => 0 [4,-3,2,1] => 0 [4,-3,2,-1] => 1 [4,-3,-2,1] => 0 [4,-3,-2,-1] => 0 [-4,3,2,1] => 0 [-4,3,2,-1] => 1 [-4,3,-2,1] => 0 [-4,3,-2,-1] => 0 [-4,-3,2,1] => 0 [-4,-3,2,-1] => 1 [-4,-3,-2,1] => 0 [-4,-3,-2,-1] => 0 [1,2,3,4,5] => 0 [1,2,3,4,-5] => 0 [1,2,3,-4,5] => 0 [1,2,3,-4,-5] => 0 [1,2,-3,4,5] => 0 [1,2,-3,4,-5] => 0 [1,2,-3,-4,5] => 0 [1,2,-3,-4,-5] => 0 [1,-2,3,4,5] => 0 [1,-2,3,4,-5] => 0 [1,-2,3,-4,5] => 0 [1,-2,3,-4,-5] => 0 [1,-2,-3,4,5] => 0 [1,-2,-3,4,-5] => 0 [1,-2,-3,-4,5] => 0 [1,-2,-3,-4,-5] => 0 [-1,2,3,4,5] => 0 [-1,2,3,4,-5] => 0 [-1,2,3,-4,5] => 0 [-1,2,3,-4,-5] => 0 [-1,2,-3,4,5] => 0 [-1,2,-3,4,-5] => 0 [-1,2,-3,-4,5] => 0 [-1,2,-3,-4,-5] => 0 [-1,-2,3,4,5] => 0 [-1,-2,3,4,-5] => 0 [-1,-2,3,-4,5] => 0 [-1,-2,3,-4,-5] => 0 [-1,-2,-3,4,5] => 0 [-1,-2,-3,4,-5] => 0 [-1,-2,-3,-4,5] => 0 [-1,-2,-3,-4,-5] => 0 [1,2,3,5,4] => 3 [1,2,3,5,-4] => 0 [1,2,3,-5,4] => 3 [1,2,3,-5,-4] => 0 [1,2,-3,5,4] => 3 [1,2,-3,5,-4] => 0 [1,2,-3,-5,4] => 3 [1,2,-3,-5,-4] => 0 [1,-2,3,5,4] => 3 [1,-2,3,5,-4] => 0 [1,-2,3,-5,4] => 3 [1,-2,3,-5,-4] => 0 [1,-2,-3,5,4] => 3 [1,-2,-3,5,-4] => 0 [1,-2,-3,-5,4] => 3 [1,-2,-3,-5,-4] => 0 [-1,2,3,5,4] => 3 [-1,2,3,5,-4] => 0 [-1,2,3,-5,4] => 3 [-1,2,3,-5,-4] => 0 [-1,2,-3,5,4] => 3 [-1,2,-3,5,-4] => 0 [-1,2,-3,-5,4] => 3 [-1,2,-3,-5,-4] => 0 [-1,-2,3,5,4] => 3 [-1,-2,3,5,-4] => 0 [-1,-2,3,-5,4] => 3 [-1,-2,3,-5,-4] => 0 [-1,-2,-3,5,4] => 3 [-1,-2,-3,5,-4] => 0 [-1,-2,-3,-5,4] => 3 [-1,-2,-3,-5,-4] => 0 [1,2,4,3,5] => 2 [1,2,4,3,-5] => 2 [1,2,4,-3,5] => 0 [1,2,4,-3,-5] => 0 [1,2,-4,3,5] => 2 [1,2,-4,3,-5] => 2 [1,2,-4,-3,5] => 0 [1,2,-4,-3,-5] => 0 [1,-2,4,3,5] => 2 [1,-2,4,3,-5] => 2 [1,-2,4,-3,5] => 0 [1,-2,4,-3,-5] => 0 [1,-2,-4,3,5] => 2 [1,-2,-4,3,-5] => 2 [1,-2,-4,-3,5] => 0 [1,-2,-4,-3,-5] => 0 [-1,2,4,3,5] => 2 [-1,2,4,3,-5] => 2 [-1,2,4,-3,5] => 0 [-1,2,4,-3,-5] => 0 [-1,2,-4,3,5] => 2 [-1,2,-4,3,-5] => 2 [-1,2,-4,-3,5] => 0 [-1,2,-4,-3,-5] => 0 [-1,-2,4,3,5] => 2 [-1,-2,4,3,-5] => 2 [-1,-2,4,-3,5] => 0 [-1,-2,4,-3,-5] => 0 [-1,-2,-4,3,5] => 2 [-1,-2,-4,3,-5] => 2 [-1,-2,-4,-3,5] => 0 [-1,-2,-4,-3,-5] => 0 [1,2,4,5,3] => 2 [1,2,4,5,-3] => 0 [1,2,4,-5,3] => 2 [1,2,4,-5,-3] => 0 [1,2,-4,5,3] => 2 [1,2,-4,5,-3] => 0 [1,2,-4,-5,3] => 2 [1,2,-4,-5,-3] => 0 [1,-2,4,5,3] => 2 [1,-2,4,5,-3] => 0 [1,-2,4,-5,3] => 2 [1,-2,4,-5,-3] => 0 [1,-2,-4,5,3] => 2 [1,-2,-4,5,-3] => 0 [1,-2,-4,-5,3] => 2 [1,-2,-4,-5,-3] => 0 [-1,2,4,5,3] => 2 [-1,2,4,5,-3] => 0 [-1,2,4,-5,3] => 2 [-1,2,4,-5,-3] => 0 [-1,2,-4,5,3] => 2 [-1,2,-4,5,-3] => 0 [-1,2,-4,-5,3] => 2 [-1,2,-4,-5,-3] => 0 [-1,-2,4,5,3] => 2 [-1,-2,4,5,-3] => 0 [-1,-2,4,-5,3] => 2 [-1,-2,4,-5,-3] => 0 [-1,-2,-4,5,3] => 2 [-1,-2,-4,5,-3] => 0 [-1,-2,-4,-5,3] => 2 [-1,-2,-4,-5,-3] => 0 [1,2,5,3,4] => 4 [1,2,5,3,-4] => 2 [1,2,5,-3,4] => 3 [1,2,5,-3,-4] => 0 [1,2,-5,3,4] => 4 [1,2,-5,3,-4] => 2 [1,2,-5,-3,4] => 3 [1,2,-5,-3,-4] => 0 [1,-2,5,3,4] => 4 [1,-2,5,3,-4] => 2 [1,-2,5,-3,4] => 3 [1,-2,5,-3,-4] => 0 [1,-2,-5,3,4] => 4 [1,-2,-5,3,-4] => 2 [1,-2,-5,-3,4] => 3 [1,-2,-5,-3,-4] => 0 [-1,2,5,3,4] => 4 [-1,2,5,3,-4] => 2 [-1,2,5,-3,4] => 3 [-1,2,5,-3,-4] => 0 [-1,2,-5,3,4] => 4 [-1,2,-5,3,-4] => 2 [-1,2,-5,-3,4] => 3 [-1,2,-5,-3,-4] => 0 [-1,-2,5,3,4] => 4 [-1,-2,5,3,-4] => 2 [-1,-2,5,-3,4] => 3 [-1,-2,5,-3,-4] => 0 [-1,-2,-5,3,4] => 4 [-1,-2,-5,3,-4] => 2 [-1,-2,-5,-3,4] => 3 [-1,-2,-5,-3,-4] => 0 [1,2,5,4,3] => 2 [1,2,5,4,-3] => 0 [1,2,5,-4,3] => 2 [1,2,5,-4,-3] => 0 [1,2,-5,4,3] => 2 [1,2,-5,4,-3] => 0 [1,2,-5,-4,3] => 2 [1,2,-5,-4,-3] => 0 [1,-2,5,4,3] => 2 [1,-2,5,4,-3] => 0 [1,-2,5,-4,3] => 2 [1,-2,5,-4,-3] => 0 [1,-2,-5,4,3] => 2 [1,-2,-5,4,-3] => 0 [1,-2,-5,-4,3] => 2 [1,-2,-5,-4,-3] => 0 [-1,2,5,4,3] => 2 [-1,2,5,4,-3] => 0 [-1,2,5,-4,3] => 2 [-1,2,5,-4,-3] => 0 [-1,2,-5,4,3] => 2 [-1,2,-5,4,-3] => 0 [-1,2,-5,-4,3] => 2 [-1,2,-5,-4,-3] => 0 [-1,-2,5,4,3] => 2 [-1,-2,5,4,-3] => 0 [-1,-2,5,-4,3] => 2 [-1,-2,5,-4,-3] => 0 [-1,-2,-5,4,3] => 2 [-1,-2,-5,4,-3] => 0 [-1,-2,-5,-4,3] => 2 [-1,-2,-5,-4,-3] => 0 [1,3,2,4,5] => 1 [1,3,2,4,-5] => 1 [1,3,2,-4,5] => 1 [1,3,2,-4,-5] => 1 [1,3,-2,4,5] => 0 [1,3,-2,4,-5] => 0 [1,3,-2,-4,5] => 0 [1,3,-2,-4,-5] => 0 [1,-3,2,4,5] => 1 [1,-3,2,4,-5] => 1 [1,-3,2,-4,5] => 1 [1,-3,2,-4,-5] => 1 [1,-3,-2,4,5] => 0 [1,-3,-2,4,-5] => 0 [1,-3,-2,-4,5] => 0 [1,-3,-2,-4,-5] => 0 [-1,3,2,4,5] => 1 [-1,3,2,4,-5] => 1 [-1,3,2,-4,5] => 1 [-1,3,2,-4,-5] => 1 [-1,3,-2,4,5] => 0 [-1,3,-2,4,-5] => 0 [-1,3,-2,-4,5] => 0 [-1,3,-2,-4,-5] => 0 [-1,-3,2,4,5] => 1 [-1,-3,2,4,-5] => 1 [-1,-3,2,-4,5] => 1 [-1,-3,2,-4,-5] => 1 [-1,-3,-2,4,5] => 0 [-1,-3,-2,4,-5] => 0 [-1,-3,-2,-4,5] => 0 [-1,-3,-2,-4,-5] => 0 [1,3,2,5,4] => 3 [1,3,2,5,-4] => 1 [1,3,2,-5,4] => 3 [1,3,2,-5,-4] => 1 [1,3,-2,5,4] => 3 [1,3,-2,5,-4] => 0 [1,3,-2,-5,4] => 3 [1,3,-2,-5,-4] => 0 [1,-3,2,5,4] => 3 [1,-3,2,5,-4] => 1 [1,-3,2,-5,4] => 3 [1,-3,2,-5,-4] => 1 [1,-3,-2,5,4] => 3 [1,-3,-2,5,-4] => 0 [1,-3,-2,-5,4] => 3 [1,-3,-2,-5,-4] => 0 [-1,3,2,5,4] => 3 [-1,3,2,5,-4] => 1 [-1,3,2,-5,4] => 3 [-1,3,2,-5,-4] => 1 [-1,3,-2,5,4] => 3 [-1,3,-2,5,-4] => 0 [-1,3,-2,-5,4] => 3 [-1,3,-2,-5,-4] => 0 [-1,-3,2,5,4] => 3 [-1,-3,2,5,-4] => 1 [-1,-3,2,-5,4] => 3 [-1,-3,2,-5,-4] => 1 [-1,-3,-2,5,4] => 3 [-1,-3,-2,5,-4] => 0 [-1,-3,-2,-5,4] => 3 [-1,-3,-2,-5,-4] => 0 [1,3,4,2,5] => 1 [1,3,4,2,-5] => 1 [1,3,4,-2,5] => 0 [1,3,4,-2,-5] => 0 [1,3,-4,2,5] => 1 [1,3,-4,2,-5] => 1 [1,3,-4,-2,5] => 0 [1,3,-4,-2,-5] => 0 [1,-3,4,2,5] => 1 [1,-3,4,2,-5] => 1 [1,-3,4,-2,5] => 0 [1,-3,4,-2,-5] => 0 [1,-3,-4,2,5] => 1 [1,-3,-4,2,-5] => 1 [1,-3,-4,-2,5] => 0 [1,-3,-4,-2,-5] => 0 [-1,3,4,2,5] => 1 [-1,3,4,2,-5] => 1 [-1,3,4,-2,5] => 0 [-1,3,4,-2,-5] => 0 [-1,3,-4,2,5] => 1 [-1,3,-4,2,-5] => 1 [-1,3,-4,-2,5] => 0 [-1,3,-4,-2,-5] => 0 [-1,-3,4,2,5] => 1 [-1,-3,4,2,-5] => 1 [-1,-3,4,-2,5] => 0 [-1,-3,4,-2,-5] => 0 [-1,-3,-4,2,5] => 1 [-1,-3,-4,2,-5] => 1 [-1,-3,-4,-2,5] => 0 [-1,-3,-4,-2,-5] => 0 [1,3,4,5,2] => 1 [1,3,4,5,-2] => 0 [1,3,4,-5,2] => 1 [1,3,4,-5,-2] => 0 [1,3,-4,5,2] => 1 [1,3,-4,5,-2] => 0 [1,3,-4,-5,2] => 1 [1,3,-4,-5,-2] => 0 [1,-3,4,5,2] => 1 [1,-3,4,5,-2] => 0 [1,-3,4,-5,2] => 1 [1,-3,4,-5,-2] => 0 [1,-3,-4,5,2] => 1 [1,-3,-4,5,-2] => 0 [1,-3,-4,-5,2] => 1 [1,-3,-4,-5,-2] => 0 [-1,3,4,5,2] => 1 [-1,3,4,5,-2] => 0 [-1,3,4,-5,2] => 1 [-1,3,4,-5,-2] => 0 [-1,3,-4,5,2] => 1 [-1,3,-4,5,-2] => 0 [-1,3,-4,-5,2] => 1 [-1,3,-4,-5,-2] => 0 [-1,-3,4,5,2] => 1 [-1,-3,4,5,-2] => 0 [-1,-3,4,-5,2] => 1 [-1,-3,4,-5,-2] => 0 [-1,-3,-4,5,2] => 1 [-1,-3,-4,5,-2] => 0 [-1,-3,-4,-5,2] => 1 [-1,-3,-4,-5,-2] => 0 [1,3,5,2,4] => 3 [1,3,5,2,-4] => 1 [1,3,5,-2,4] => 3 [1,3,5,-2,-4] => 0 [1,3,-5,2,4] => 3 [1,3,-5,2,-4] => 1 [1,3,-5,-2,4] => 3 [1,3,-5,-2,-4] => 0 [1,-3,5,2,4] => 3 [1,-3,5,2,-4] => 1 [1,-3,5,-2,4] => 3 [1,-3,5,-2,-4] => 0 [1,-3,-5,2,4] => 3 [1,-3,-5,2,-4] => 1 [1,-3,-5,-2,4] => 3 [1,-3,-5,-2,-4] => 0 [-1,3,5,2,4] => 3 [-1,3,5,2,-4] => 1 [-1,3,5,-2,4] => 3 [-1,3,5,-2,-4] => 0 [-1,3,-5,2,4] => 3 [-1,3,-5,2,-4] => 1 [-1,3,-5,-2,4] => 3 [-1,3,-5,-2,-4] => 0 [-1,-3,5,2,4] => 3 [-1,-3,5,2,-4] => 1 [-1,-3,5,-2,4] => 3 [-1,-3,5,-2,-4] => 0 [-1,-3,-5,2,4] => 3 [-1,-3,-5,2,-4] => 1 [-1,-3,-5,-2,4] => 3 [-1,-3,-5,-2,-4] => 0 [1,3,5,4,2] => 1 [1,3,5,4,-2] => 0 [1,3,5,-4,2] => 1 [1,3,5,-4,-2] => 0 [1,3,-5,4,2] => 1 [1,3,-5,4,-2] => 0 [1,3,-5,-4,2] => 1 [1,3,-5,-4,-2] => 0 [1,-3,5,4,2] => 1 [1,-3,5,4,-2] => 0 [1,-3,5,-4,2] => 1 [1,-3,5,-4,-2] => 0 [1,-3,-5,4,2] => 1 [1,-3,-5,4,-2] => 0 [1,-3,-5,-4,2] => 1 [1,-3,-5,-4,-2] => 0 [-1,3,5,4,2] => 1 [-1,3,5,4,-2] => 0 [-1,3,5,-4,2] => 1 [-1,3,5,-4,-2] => 0 [-1,3,-5,4,2] => 1 [-1,3,-5,4,-2] => 0 [-1,3,-5,-4,2] => 1 [-1,3,-5,-4,-2] => 0 [-1,-3,5,4,2] => 1 [-1,-3,5,4,-2] => 0 [-1,-3,5,-4,2] => 1 [-1,-3,5,-4,-2] => 0 [-1,-3,-5,4,2] => 1 [-1,-3,-5,4,-2] => 0 [-1,-3,-5,-4,2] => 1 [-1,-3,-5,-4,-2] => 0 [1,4,2,3,5] => 2 [1,4,2,3,-5] => 2 [1,4,2,-3,5] => 1 [1,4,2,-3,-5] => 1 [1,4,-2,3,5] => 2 [1,4,-2,3,-5] => 2 [1,4,-2,-3,5] => 0 [1,4,-2,-3,-5] => 0 [1,-4,2,3,5] => 2 [1,-4,2,3,-5] => 2 [1,-4,2,-3,5] => 1 [1,-4,2,-3,-5] => 1 [1,-4,-2,3,5] => 2 [1,-4,-2,3,-5] => 2 [1,-4,-2,-3,5] => 0 [1,-4,-2,-3,-5] => 0 [-1,4,2,3,5] => 2 [-1,4,2,3,-5] => 2 [-1,4,2,-3,5] => 1 [-1,4,2,-3,-5] => 1 [-1,4,-2,3,5] => 2 [-1,4,-2,3,-5] => 2 [-1,4,-2,-3,5] => 0 [-1,4,-2,-3,-5] => 0 [-1,-4,2,3,5] => 2 [-1,-4,2,3,-5] => 2 [-1,-4,2,-3,5] => 1 [-1,-4,2,-3,-5] => 1 [-1,-4,-2,3,5] => 2 [-1,-4,-2,3,-5] => 2 [-1,-4,-2,-3,5] => 0 [-1,-4,-2,-3,-5] => 0 [1,4,2,5,3] => 2 [1,4,2,5,-3] => 1 [1,4,2,-5,3] => 2 [1,4,2,-5,-3] => 1 [1,4,-2,5,3] => 2 [1,4,-2,5,-3] => 0 [1,4,-2,-5,3] => 2 [1,4,-2,-5,-3] => 0 [1,-4,2,5,3] => 2 [1,-4,2,5,-3] => 1 [1,-4,2,-5,3] => 2 [1,-4,2,-5,-3] => 1 [1,-4,-2,5,3] => 2 [1,-4,-2,5,-3] => 0 [1,-4,-2,-5,3] => 2 [1,-4,-2,-5,-3] => 0 [-1,4,2,5,3] => 2 [-1,4,2,5,-3] => 1 [-1,4,2,-5,3] => 2 [-1,4,2,-5,-3] => 1 [-1,4,-2,5,3] => 2 [-1,4,-2,5,-3] => 0 [-1,4,-2,-5,3] => 2 [-1,4,-2,-5,-3] => 0 [-1,-4,2,5,3] => 2 [-1,-4,2,5,-3] => 1 [-1,-4,2,-5,3] => 2 [-1,-4,2,-5,-3] => 1 [-1,-4,-2,5,3] => 2 [-1,-4,-2,5,-3] => 0 [-1,-4,-2,-5,3] => 2 [-1,-4,-2,-5,-3] => 0 [1,4,3,2,5] => 1 [1,4,3,2,-5] => 1 [1,4,3,-2,5] => 0 [1,4,3,-2,-5] => 0 [1,4,-3,2,5] => 1 [1,4,-3,2,-5] => 1 [1,4,-3,-2,5] => 0 [1,4,-3,-2,-5] => 0 [1,-4,3,2,5] => 1 [1,-4,3,2,-5] => 1 [1,-4,3,-2,5] => 0 [1,-4,3,-2,-5] => 0 [1,-4,-3,2,5] => 1 [1,-4,-3,2,-5] => 1 [1,-4,-3,-2,5] => 0 [1,-4,-3,-2,-5] => 0 [-1,4,3,2,5] => 1 [-1,4,3,2,-5] => 1 [-1,4,3,-2,5] => 0 [-1,4,3,-2,-5] => 0 [-1,4,-3,2,5] => 1 [-1,4,-3,2,-5] => 1 [-1,4,-3,-2,5] => 0 [-1,4,-3,-2,-5] => 0 [-1,-4,3,2,5] => 1 [-1,-4,3,2,-5] => 1 [-1,-4,3,-2,5] => 0 [-1,-4,3,-2,-5] => 0 [-1,-4,-3,2,5] => 1 [-1,-4,-3,2,-5] => 1 [-1,-4,-3,-2,5] => 0 [-1,-4,-3,-2,-5] => 0 [1,4,3,5,2] => 1 [1,4,3,5,-2] => 0 [1,4,3,-5,2] => 1 [1,4,3,-5,-2] => 0 [1,4,-3,5,2] => 1 [1,4,-3,5,-2] => 0 [1,4,-3,-5,2] => 1 [1,4,-3,-5,-2] => 0 [1,-4,3,5,2] => 1 [1,-4,3,5,-2] => 0 [1,-4,3,-5,2] => 1 [1,-4,3,-5,-2] => 0 [1,-4,-3,5,2] => 1 [1,-4,-3,5,-2] => 0 [1,-4,-3,-5,2] => 1 [1,-4,-3,-5,-2] => 0 [-1,4,3,5,2] => 1 [-1,4,3,5,-2] => 0 [-1,4,3,-5,2] => 1 [-1,4,3,-5,-2] => 0 [-1,4,-3,5,2] => 1 [-1,4,-3,5,-2] => 0 [-1,4,-3,-5,2] => 1 [-1,4,-3,-5,-2] => 0 [-1,-4,3,5,2] => 1 [-1,-4,3,5,-2] => 0 [-1,-4,3,-5,2] => 1 [-1,-4,3,-5,-2] => 0 [-1,-4,-3,5,2] => 1 [-1,-4,-3,5,-2] => 0 [-1,-4,-3,-5,2] => 1 [-1,-4,-3,-5,-2] => 0 [1,4,5,2,3] => 2 [1,4,5,2,-3] => 1 [1,4,5,-2,3] => 2 [1,4,5,-2,-3] => 0 [1,4,-5,2,3] => 2 [1,4,-5,2,-3] => 1 [1,4,-5,-2,3] => 2 [1,4,-5,-2,-3] => 0 [1,-4,5,2,3] => 2 [1,-4,5,2,-3] => 1 [1,-4,5,-2,3] => 2 [1,-4,5,-2,-3] => 0 [1,-4,-5,2,3] => 2 [1,-4,-5,2,-3] => 1 [1,-4,-5,-2,3] => 2 [1,-4,-5,-2,-3] => 0 [-1,4,5,2,3] => 2 [-1,4,5,2,-3] => 1 [-1,4,5,-2,3] => 2 [-1,4,5,-2,-3] => 0 [-1,4,-5,2,3] => 2 [-1,4,-5,2,-3] => 1 [-1,4,-5,-2,3] => 2 [-1,4,-5,-2,-3] => 0 [-1,-4,5,2,3] => 2 [-1,-4,5,2,-3] => 1 [-1,-4,5,-2,3] => 2 [-1,-4,5,-2,-3] => 0 [-1,-4,-5,2,3] => 2 [-1,-4,-5,2,-3] => 1 [-1,-4,-5,-2,3] => 2 [-1,-4,-5,-2,-3] => 0 [1,4,5,3,2] => 2 [1,4,5,3,-2] => 2 [1,4,5,-3,2] => 1 [1,4,5,-3,-2] => 0 [1,4,-5,3,2] => 2 [1,4,-5,3,-2] => 2 [1,4,-5,-3,2] => 1 [1,4,-5,-3,-2] => 0 [1,-4,5,3,2] => 2 [1,-4,5,3,-2] => 2 [1,-4,5,-3,2] => 1 [1,-4,5,-3,-2] => 0 [1,-4,-5,3,2] => 2 [1,-4,-5,3,-2] => 2 [1,-4,-5,-3,2] => 1 [1,-4,-5,-3,-2] => 0 [-1,4,5,3,2] => 2 [-1,4,5,3,-2] => 2 [-1,4,5,-3,2] => 1 [-1,4,5,-3,-2] => 0 [-1,4,-5,3,2] => 2 [-1,4,-5,3,-2] => 2 [-1,4,-5,-3,2] => 1 [-1,4,-5,-3,-2] => 0 [-1,-4,5,3,2] => 2 [-1,-4,5,3,-2] => 2 [-1,-4,5,-3,2] => 1 [-1,-4,5,-3,-2] => 0 [-1,-4,-5,3,2] => 2 [-1,-4,-5,3,-2] => 2 [-1,-4,-5,-3,2] => 1 [-1,-4,-5,-3,-2] => 0 [1,5,2,3,4] => 3 [1,5,2,3,-4] => 2 [1,5,2,-3,4] => 3 [1,5,2,-3,-4] => 1 [1,5,-2,3,4] => 4 [1,5,-2,3,-4] => 2 [1,5,-2,-3,4] => 3 [1,5,-2,-3,-4] => 0 [1,-5,2,3,4] => 3 [1,-5,2,3,-4] => 2 [1,-5,2,-3,4] => 3 [1,-5,2,-3,-4] => 1 [1,-5,-2,3,4] => 4 [1,-5,-2,3,-4] => 2 [1,-5,-2,-3,4] => 3 [1,-5,-2,-3,-4] => 0 [-1,5,2,3,4] => 3 [-1,5,2,3,-4] => 2 [-1,5,2,-3,4] => 3 [-1,5,2,-3,-4] => 1 [-1,5,-2,3,4] => 4 [-1,5,-2,3,-4] => 2 [-1,5,-2,-3,4] => 3 [-1,5,-2,-3,-4] => 0 [-1,-5,2,3,4] => 3 [-1,-5,2,3,-4] => 2 [-1,-5,2,-3,4] => 3 [-1,-5,2,-3,-4] => 1 [-1,-5,-2,3,4] => 4 [-1,-5,-2,3,-4] => 2 [-1,-5,-2,-3,4] => 3 [-1,-5,-2,-3,-4] => 0 [1,5,2,4,3] => 2 [1,5,2,4,-3] => 1 [1,5,2,-4,3] => 2 [1,5,2,-4,-3] => 1 [1,5,-2,4,3] => 2 [1,5,-2,4,-3] => 0 [1,5,-2,-4,3] => 2 [1,5,-2,-4,-3] => 0 [1,-5,2,4,3] => 2 [1,-5,2,4,-3] => 1 [1,-5,2,-4,3] => 2 [1,-5,2,-4,-3] => 1 [1,-5,-2,4,3] => 2 [1,-5,-2,4,-3] => 0 [1,-5,-2,-4,3] => 2 [1,-5,-2,-4,-3] => 0 [-1,5,2,4,3] => 2 [-1,5,2,4,-3] => 1 [-1,5,2,-4,3] => 2 [-1,5,2,-4,-3] => 1 [-1,5,-2,4,3] => 2 [-1,5,-2,4,-3] => 0 [-1,5,-2,-4,3] => 2 [-1,5,-2,-4,-3] => 0 [-1,-5,2,4,3] => 2 [-1,-5,2,4,-3] => 1 [-1,-5,2,-4,3] => 2 [-1,-5,2,-4,-3] => 1 [-1,-5,-2,4,3] => 2 [-1,-5,-2,4,-3] => 0 [-1,-5,-2,-4,3] => 2 [-1,-5,-2,-4,-3] => 0 [1,5,3,2,4] => 3 [1,5,3,2,-4] => 1 [1,5,3,-2,4] => 3 [1,5,3,-2,-4] => 0 [1,5,-3,2,4] => 3 [1,5,-3,2,-4] => 1 [1,5,-3,-2,4] => 3 [1,5,-3,-2,-4] => 0 [1,-5,3,2,4] => 3 [1,-5,3,2,-4] => 1 [1,-5,3,-2,4] => 3 [1,-5,3,-2,-4] => 0 [1,-5,-3,2,4] => 3 [1,-5,-3,2,-4] => 1 [1,-5,-3,-2,4] => 3 [1,-5,-3,-2,-4] => 0 [-1,5,3,2,4] => 3 [-1,5,3,2,-4] => 1 [-1,5,3,-2,4] => 3 [-1,5,3,-2,-4] => 0 [-1,5,-3,2,4] => 3 [-1,5,-3,2,-4] => 1 [-1,5,-3,-2,4] => 3 [-1,5,-3,-2,-4] => 0 [-1,-5,3,2,4] => 3 [-1,-5,3,2,-4] => 1 [-1,-5,3,-2,4] => 3 [-1,-5,3,-2,-4] => 0 [-1,-5,-3,2,4] => 3 [-1,-5,-3,2,-4] => 1 [-1,-5,-3,-2,4] => 3 [-1,-5,-3,-2,-4] => 0 [1,5,3,4,2] => 1 [1,5,3,4,-2] => 0 [1,5,3,-4,2] => 1 [1,5,3,-4,-2] => 0 [1,5,-3,4,2] => 1 [1,5,-3,4,-2] => 0 [1,5,-3,-4,2] => 1 [1,5,-3,-4,-2] => 0 [1,-5,3,4,2] => 1 [1,-5,3,4,-2] => 0 [1,-5,3,-4,2] => 1 [1,-5,3,-4,-2] => 0 [1,-5,-3,4,2] => 1 [1,-5,-3,4,-2] => 0 [1,-5,-3,-4,2] => 1 [1,-5,-3,-4,-2] => 0 [-1,5,3,4,2] => 1 [-1,5,3,4,-2] => 0 [-1,5,3,-4,2] => 1 [-1,5,3,-4,-2] => 0 [-1,5,-3,4,2] => 1 [-1,5,-3,4,-2] => 0 [-1,5,-3,-4,2] => 1 [-1,5,-3,-4,-2] => 0 [-1,-5,3,4,2] => 1 [-1,-5,3,4,-2] => 0 [-1,-5,3,-4,2] => 1 [-1,-5,3,-4,-2] => 0 [-1,-5,-3,4,2] => 1 [-1,-5,-3,4,-2] => 0 [-1,-5,-3,-4,2] => 1 [-1,-5,-3,-4,-2] => 0 [1,5,4,2,3] => 2 [1,5,4,2,-3] => 1 [1,5,4,-2,3] => 2 [1,5,4,-2,-3] => 0 [1,5,-4,2,3] => 2 [1,5,-4,2,-3] => 1 [1,5,-4,-2,3] => 2 [1,5,-4,-2,-3] => 0 [1,-5,4,2,3] => 2 [1,-5,4,2,-3] => 1 [1,-5,4,-2,3] => 2 [1,-5,4,-2,-3] => 0 [1,-5,-4,2,3] => 2 [1,-5,-4,2,-3] => 1 [1,-5,-4,-2,3] => 2 [1,-5,-4,-2,-3] => 0 [-1,5,4,2,3] => 2 [-1,5,4,2,-3] => 1 [-1,5,4,-2,3] => 2 [-1,5,4,-2,-3] => 0 [-1,5,-4,2,3] => 2 [-1,5,-4,2,-3] => 1 [-1,5,-4,-2,3] => 2 [-1,5,-4,-2,-3] => 0 [-1,-5,4,2,3] => 2 [-1,-5,4,2,-3] => 1 [-1,-5,4,-2,3] => 2 [-1,-5,4,-2,-3] => 0 [-1,-5,-4,2,3] => 2 [-1,-5,-4,2,-3] => 1 [-1,-5,-4,-2,3] => 2 [-1,-5,-4,-2,-3] => 0 [1,5,4,3,2] => 2 [1,5,4,3,-2] => 2 [1,5,4,-3,2] => 1 [1,5,4,-3,-2] => 0 [1,5,-4,3,2] => 2 [1,5,-4,3,-2] => 2 [1,5,-4,-3,2] => 1 [1,5,-4,-3,-2] => 0 [1,-5,4,3,2] => 2 [1,-5,4,3,-2] => 2 [1,-5,4,-3,2] => 1 [1,-5,4,-3,-2] => 0 [1,-5,-4,3,2] => 2 [1,-5,-4,3,-2] => 2 [1,-5,-4,-3,2] => 1 [1,-5,-4,-3,-2] => 0 [-1,5,4,3,2] => 2 [-1,5,4,3,-2] => 2 [-1,5,4,-3,2] => 1 [-1,5,4,-3,-2] => 0 [-1,5,-4,3,2] => 2 [-1,5,-4,3,-2] => 2 ----------------------------------------------------------------------------- Created: Dec 01, 2022 at 11:41 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Dec 01, 2022 at 11:41 by Martin Rubey