***************************************************************************** * 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: St001892 ----------------------------------------------------------------------------- Collection: Signed permutations ----------------------------------------------------------------------------- Description: The flag excedance statistic of a signed permutation. This is the number of negative entries plus twice the number of excedances of the signed permutation. That is, $$fexc(\sigma) = 2exc(\sigma) + neg(\sigma),$$ where $$exc(\sigma) = |\{i \in [n-1] \,:\, \sigma(i) > i\}|$$ $$neg(\sigma) = |\{i \in [n] \,:\, \sigma(i) < 0\}|$$ It has the same distribution as the flag descent statistic. ----------------------------------------------------------------------------- References: [1] (service unreachable) [[MathSciNet:4339357]] [2] (service unreachable) [[MathSciNet:2501235]] ----------------------------------------------------------------------------- Code: ----------------------------------------------------------------------------- Statistic values: [1] => 0 [-1] => 1 [1,2] => 0 [1,-2] => 1 [-1,2] => 1 [-1,-2] => 2 [2,1] => 2 [2,-1] => 3 [-2,1] => 1 [-2,-1] => 2 [1,2,3] => 0 [1,2,-3] => 1 [1,-2,3] => 1 [1,-2,-3] => 2 [-1,2,3] => 1 [-1,2,-3] => 2 [-1,-2,3] => 2 [-1,-2,-3] => 3 [1,3,2] => 2 [1,3,-2] => 3 [1,-3,2] => 1 [1,-3,-2] => 2 [-1,3,2] => 3 [-1,3,-2] => 4 [-1,-3,2] => 2 [-1,-3,-2] => 3 [2,1,3] => 2 [2,1,-3] => 3 [2,-1,3] => 3 [2,-1,-3] => 4 [-2,1,3] => 1 [-2,1,-3] => 2 [-2,-1,3] => 2 [-2,-1,-3] => 3 [2,3,1] => 4 [2,3,-1] => 5 [2,-3,1] => 3 [2,-3,-1] => 4 [-2,3,1] => 3 [-2,3,-1] => 4 [-2,-3,1] => 2 [-2,-3,-1] => 3 [3,1,2] => 2 [3,1,-2] => 3 [3,-1,2] => 3 [3,-1,-2] => 4 [-3,1,2] => 1 [-3,1,-2] => 2 [-3,-1,2] => 2 [-3,-1,-2] => 3 [3,2,1] => 2 [3,2,-1] => 3 [3,-2,1] => 3 [3,-2,-1] => 4 [-3,2,1] => 1 [-3,2,-1] => 2 [-3,-2,1] => 2 [-3,-2,-1] => 3 [1,2,3,4] => 0 [1,2,3,-4] => 1 [1,2,-3,4] => 1 [1,2,-3,-4] => 2 [1,-2,3,4] => 1 [1,-2,3,-4] => 2 [1,-2,-3,4] => 2 [1,-2,-3,-4] => 3 [-1,2,3,4] => 1 [-1,2,3,-4] => 2 [-1,2,-3,4] => 2 [-1,2,-3,-4] => 3 [-1,-2,3,4] => 2 [-1,-2,3,-4] => 3 [-1,-2,-3,4] => 3 [-1,-2,-3,-4] => 4 [1,2,4,3] => 2 [1,2,4,-3] => 3 [1,2,-4,3] => 1 [1,2,-4,-3] => 2 [1,-2,4,3] => 3 [1,-2,4,-3] => 4 [1,-2,-4,3] => 2 [1,-2,-4,-3] => 3 [-1,2,4,3] => 3 [-1,2,4,-3] => 4 [-1,2,-4,3] => 2 [-1,2,-4,-3] => 3 [-1,-2,4,3] => 4 [-1,-2,4,-3] => 5 [-1,-2,-4,3] => 3 [-1,-2,-4,-3] => 4 [1,3,2,4] => 2 [1,3,2,-4] => 3 [1,3,-2,4] => 3 [1,3,-2,-4] => 4 [1,-3,2,4] => 1 [1,-3,2,-4] => 2 [1,-3,-2,4] => 2 [1,-3,-2,-4] => 3 [-1,3,2,4] => 3 [-1,3,2,-4] => 4 [-1,3,-2,4] => 4 [-1,3,-2,-4] => 5 [-1,-3,2,4] => 2 [-1,-3,2,-4] => 3 [-1,-3,-2,4] => 3 [-1,-3,-2,-4] => 4 [1,3,4,2] => 4 [1,3,4,-2] => 5 [1,3,-4,2] => 3 [1,3,-4,-2] => 4 [1,-3,4,2] => 3 [1,-3,4,-2] => 4 [1,-3,-4,2] => 2 [1,-3,-4,-2] => 3 [-1,3,4,2] => 5 [-1,3,4,-2] => 6 [-1,3,-4,2] => 4 [-1,3,-4,-2] => 5 [-1,-3,4,2] => 4 [-1,-3,4,-2] => 5 [-1,-3,-4,2] => 3 [-1,-3,-4,-2] => 4 [1,4,2,3] => 2 [1,4,2,-3] => 3 [1,4,-2,3] => 3 [1,4,-2,-3] => 4 [1,-4,2,3] => 1 [1,-4,2,-3] => 2 [1,-4,-2,3] => 2 [1,-4,-2,-3] => 3 [-1,4,2,3] => 3 [-1,4,2,-3] => 4 [-1,4,-2,3] => 4 [-1,4,-2,-3] => 5 [-1,-4,2,3] => 2 [-1,-4,2,-3] => 3 [-1,-4,-2,3] => 3 [-1,-4,-2,-3] => 4 [1,4,3,2] => 2 [1,4,3,-2] => 3 [1,4,-3,2] => 3 [1,4,-3,-2] => 4 [1,-4,3,2] => 1 [1,-4,3,-2] => 2 [1,-4,-3,2] => 2 [1,-4,-3,-2] => 3 [-1,4,3,2] => 3 [-1,4,3,-2] => 4 [-1,4,-3,2] => 4 [-1,4,-3,-2] => 5 [-1,-4,3,2] => 2 [-1,-4,3,-2] => 3 [-1,-4,-3,2] => 3 [-1,-4,-3,-2] => 4 [2,1,3,4] => 2 [2,1,3,-4] => 3 [2,1,-3,4] => 3 [2,1,-3,-4] => 4 [2,-1,3,4] => 3 [2,-1,3,-4] => 4 [2,-1,-3,4] => 4 [2,-1,-3,-4] => 5 [-2,1,3,4] => 1 [-2,1,3,-4] => 2 [-2,1,-3,4] => 2 [-2,1,-3,-4] => 3 [-2,-1,3,4] => 2 [-2,-1,3,-4] => 3 [-2,-1,-3,4] => 3 [-2,-1,-3,-4] => 4 [2,1,4,3] => 4 [2,1,4,-3] => 5 [2,1,-4,3] => 3 [2,1,-4,-3] => 4 [2,-1,4,3] => 5 [2,-1,4,-3] => 6 [2,-1,-4,3] => 4 [2,-1,-4,-3] => 5 [-2,1,4,3] => 3 [-2,1,4,-3] => 4 [-2,1,-4,3] => 2 [-2,1,-4,-3] => 3 [-2,-1,4,3] => 4 [-2,-1,4,-3] => 5 [-2,-1,-4,3] => 3 [-2,-1,-4,-3] => 4 [2,3,1,4] => 4 [2,3,1,-4] => 5 [2,3,-1,4] => 5 [2,3,-1,-4] => 6 [2,-3,1,4] => 3 [2,-3,1,-4] => 4 [2,-3,-1,4] => 4 [2,-3,-1,-4] => 5 [-2,3,1,4] => 3 [-2,3,1,-4] => 4 [-2,3,-1,4] => 4 [-2,3,-1,-4] => 5 [-2,-3,1,4] => 2 [-2,-3,1,-4] => 3 [-2,-3,-1,4] => 3 [-2,-3,-1,-4] => 4 [2,3,4,1] => 6 [2,3,4,-1] => 7 [2,3,-4,1] => 5 [2,3,-4,-1] => 6 [2,-3,4,1] => 5 [2,-3,4,-1] => 6 [2,-3,-4,1] => 4 [2,-3,-4,-1] => 5 [-2,3,4,1] => 5 [-2,3,4,-1] => 6 [-2,3,-4,1] => 4 [-2,3,-4,-1] => 5 [-2,-3,4,1] => 4 [-2,-3,4,-1] => 5 [-2,-3,-4,1] => 3 [-2,-3,-4,-1] => 4 [2,4,1,3] => 4 [2,4,1,-3] => 5 [2,4,-1,3] => 5 [2,4,-1,-3] => 6 [2,-4,1,3] => 3 [2,-4,1,-3] => 4 [2,-4,-1,3] => 4 [2,-4,-1,-3] => 5 [-2,4,1,3] => 3 [-2,4,1,-3] => 4 [-2,4,-1,3] => 4 [-2,4,-1,-3] => 5 [-2,-4,1,3] => 2 [-2,-4,1,-3] => 3 [-2,-4,-1,3] => 3 [-2,-4,-1,-3] => 4 [2,4,3,1] => 4 [2,4,3,-1] => 5 [2,4,-3,1] => 5 [2,4,-3,-1] => 6 [2,-4,3,1] => 3 [2,-4,3,-1] => 4 [2,-4,-3,1] => 4 [2,-4,-3,-1] => 5 [-2,4,3,1] => 3 [-2,4,3,-1] => 4 [-2,4,-3,1] => 4 [-2,4,-3,-1] => 5 [-2,-4,3,1] => 2 [-2,-4,3,-1] => 3 [-2,-4,-3,1] => 3 [-2,-4,-3,-1] => 4 [3,1,2,4] => 2 [3,1,2,-4] => 3 [3,1,-2,4] => 3 [3,1,-2,-4] => 4 [3,-1,2,4] => 3 [3,-1,2,-4] => 4 [3,-1,-2,4] => 4 [3,-1,-2,-4] => 5 [-3,1,2,4] => 1 [-3,1,2,-4] => 2 [-3,1,-2,4] => 2 [-3,1,-2,-4] => 3 [-3,-1,2,4] => 2 [-3,-1,2,-4] => 3 [-3,-1,-2,4] => 3 [-3,-1,-2,-4] => 4 [3,1,4,2] => 4 [3,1,4,-2] => 5 [3,1,-4,2] => 3 [3,1,-4,-2] => 4 [3,-1,4,2] => 5 [3,-1,4,-2] => 6 [3,-1,-4,2] => 4 [3,-1,-4,-2] => 5 [-3,1,4,2] => 3 [-3,1,4,-2] => 4 [-3,1,-4,2] => 2 [-3,1,-4,-2] => 3 [-3,-1,4,2] => 4 [-3,-1,4,-2] => 5 [-3,-1,-4,2] => 3 [-3,-1,-4,-2] => 4 [3,2,1,4] => 2 [3,2,1,-4] => 3 [3,2,-1,4] => 3 [3,2,-1,-4] => 4 [3,-2,1,4] => 3 [3,-2,1,-4] => 4 [3,-2,-1,4] => 4 [3,-2,-1,-4] => 5 [-3,2,1,4] => 1 [-3,2,1,-4] => 2 [-3,2,-1,4] => 2 [-3,2,-1,-4] => 3 [-3,-2,1,4] => 2 [-3,-2,1,-4] => 3 [-3,-2,-1,4] => 3 [-3,-2,-1,-4] => 4 [3,2,4,1] => 4 [3,2,4,-1] => 5 [3,2,-4,1] => 3 [3,2,-4,-1] => 4 [3,-2,4,1] => 5 [3,-2,4,-1] => 6 [3,-2,-4,1] => 4 [3,-2,-4,-1] => 5 [-3,2,4,1] => 3 [-3,2,4,-1] => 4 [-3,2,-4,1] => 2 [-3,2,-4,-1] => 3 [-3,-2,4,1] => 4 [-3,-2,4,-1] => 5 [-3,-2,-4,1] => 3 [-3,-2,-4,-1] => 4 [3,4,1,2] => 4 [3,4,1,-2] => 5 [3,4,-1,2] => 5 [3,4,-1,-2] => 6 [3,-4,1,2] => 3 [3,-4,1,-2] => 4 [3,-4,-1,2] => 4 [3,-4,-1,-2] => 5 [-3,4,1,2] => 3 [-3,4,1,-2] => 4 [-3,4,-1,2] => 4 [-3,4,-1,-2] => 5 [-3,-4,1,2] => 2 [-3,-4,1,-2] => 3 [-3,-4,-1,2] => 3 [-3,-4,-1,-2] => 4 [3,4,2,1] => 4 [3,4,2,-1] => 5 [3,4,-2,1] => 5 [3,4,-2,-1] => 6 [3,-4,2,1] => 3 [3,-4,2,-1] => 4 [3,-4,-2,1] => 4 [3,-4,-2,-1] => 5 [-3,4,2,1] => 3 [-3,4,2,-1] => 4 [-3,4,-2,1] => 4 [-3,4,-2,-1] => 5 [-3,-4,2,1] => 2 [-3,-4,2,-1] => 3 [-3,-4,-2,1] => 3 [-3,-4,-2,-1] => 4 [4,1,2,3] => 2 [4,1,2,-3] => 3 [4,1,-2,3] => 3 [4,1,-2,-3] => 4 [4,-1,2,3] => 3 [4,-1,2,-3] => 4 [4,-1,-2,3] => 4 [4,-1,-2,-3] => 5 [-4,1,2,3] => 1 [-4,1,2,-3] => 2 [-4,1,-2,3] => 2 [-4,1,-2,-3] => 3 [-4,-1,2,3] => 2 [-4,-1,2,-3] => 3 [-4,-1,-2,3] => 3 [-4,-1,-2,-3] => 4 [4,1,3,2] => 2 [4,1,3,-2] => 3 [4,1,-3,2] => 3 [4,1,-3,-2] => 4 [4,-1,3,2] => 3 [4,-1,3,-2] => 4 [4,-1,-3,2] => 4 [4,-1,-3,-2] => 5 [-4,1,3,2] => 1 [-4,1,3,-2] => 2 [-4,1,-3,2] => 2 [-4,1,-3,-2] => 3 [-4,-1,3,2] => 2 [-4,-1,3,-2] => 3 [-4,-1,-3,2] => 3 [-4,-1,-3,-2] => 4 [4,2,1,3] => 2 [4,2,1,-3] => 3 [4,2,-1,3] => 3 [4,2,-1,-3] => 4 [4,-2,1,3] => 3 [4,-2,1,-3] => 4 [4,-2,-1,3] => 4 [4,-2,-1,-3] => 5 [-4,2,1,3] => 1 [-4,2,1,-3] => 2 [-4,2,-1,3] => 2 [-4,2,-1,-3] => 3 [-4,-2,1,3] => 2 [-4,-2,1,-3] => 3 [-4,-2,-1,3] => 3 [-4,-2,-1,-3] => 4 [4,2,3,1] => 2 [4,2,3,-1] => 3 [4,2,-3,1] => 3 [4,2,-3,-1] => 4 [4,-2,3,1] => 3 [4,-2,3,-1] => 4 [4,-2,-3,1] => 4 [4,-2,-3,-1] => 5 [-4,2,3,1] => 1 [-4,2,3,-1] => 2 [-4,2,-3,1] => 2 [-4,2,-3,-1] => 3 [-4,-2,3,1] => 2 [-4,-2,3,-1] => 3 [-4,-2,-3,1] => 3 [-4,-2,-3,-1] => 4 [4,3,1,2] => 4 [4,3,1,-2] => 5 [4,3,-1,2] => 5 [4,3,-1,-2] => 6 [4,-3,1,2] => 3 [4,-3,1,-2] => 4 [4,-3,-1,2] => 4 [4,-3,-1,-2] => 5 [-4,3,1,2] => 3 [-4,3,1,-2] => 4 [-4,3,-1,2] => 4 [-4,3,-1,-2] => 5 [-4,-3,1,2] => 2 [-4,-3,1,-2] => 3 [-4,-3,-1,2] => 3 [-4,-3,-1,-2] => 4 [4,3,2,1] => 4 [4,3,2,-1] => 5 [4,3,-2,1] => 5 [4,3,-2,-1] => 6 [4,-3,2,1] => 3 [4,-3,2,-1] => 4 [4,-3,-2,1] => 4 [4,-3,-2,-1] => 5 [-4,3,2,1] => 3 [-4,3,2,-1] => 4 [-4,3,-2,1] => 4 [-4,3,-2,-1] => 5 [-4,-3,2,1] => 2 [-4,-3,2,-1] => 3 [-4,-3,-2,1] => 3 [-4,-3,-2,-1] => 4 [1,2,3,4,5] => 0 [1,2,3,4,-5] => 1 [1,2,3,-4,5] => 1 [1,2,3,-4,-5] => 2 [1,2,-3,4,5] => 1 [1,2,-3,4,-5] => 2 [1,2,-3,-4,5] => 2 [1,2,-3,-4,-5] => 3 [1,-2,3,4,5] => 1 [1,-2,3,4,-5] => 2 [1,-2,3,-4,5] => 2 [1,-2,3,-4,-5] => 3 [1,-2,-3,4,5] => 2 [1,-2,-3,4,-5] => 3 [1,-2,-3,-4,5] => 3 [1,-2,-3,-4,-5] => 4 [-1,2,3,4,5] => 1 [-1,2,3,4,-5] => 2 [-1,2,3,-4,5] => 2 [-1,2,3,-4,-5] => 3 [-1,2,-3,4,5] => 2 [-1,2,-3,4,-5] => 3 [-1,2,-3,-4,5] => 3 [-1,2,-3,-4,-5] => 4 [-1,-2,3,4,5] => 2 [-1,-2,3,4,-5] => 3 [-1,-2,3,-4,5] => 3 [-1,-2,3,-4,-5] => 4 [-1,-2,-3,4,5] => 3 [-1,-2,-3,4,-5] => 4 [-1,-2,-3,-4,5] => 4 [-1,-2,-3,-4,-5] => 5 [1,2,3,5,4] => 2 [1,2,3,5,-4] => 3 [1,2,3,-5,4] => 1 [1,2,3,-5,-4] => 2 [1,2,-3,5,4] => 3 [1,2,-3,5,-4] => 4 [1,2,-3,-5,4] => 2 [1,2,-3,-5,-4] => 3 [1,-2,3,5,4] => 3 [1,-2,3,5,-4] => 4 [1,-2,3,-5,4] => 2 [1,-2,3,-5,-4] => 3 [1,-2,-3,5,4] => 4 [1,-2,-3,5,-4] => 5 [1,-2,-3,-5,4] => 3 [1,-2,-3,-5,-4] => 4 [-1,2,3,5,4] => 3 [-1,2,3,5,-4] => 4 [-1,2,3,-5,4] => 2 [-1,2,3,-5,-4] => 3 [-1,2,-3,5,4] => 4 [-1,2,-3,5,-4] => 5 [-1,2,-3,-5,4] => 3 [-1,2,-3,-5,-4] => 4 [-1,-2,3,5,4] => 4 [-1,-2,3,5,-4] => 5 [-1,-2,3,-5,4] => 3 [-1,-2,3,-5,-4] => 4 [-1,-2,-3,5,4] => 5 [-1,-2,-3,5,-4] => 6 [-1,-2,-3,-5,4] => 4 [-1,-2,-3,-5,-4] => 5 [1,2,4,3,5] => 2 [1,2,4,3,-5] => 3 [1,2,4,-3,5] => 3 [1,2,4,-3,-5] => 4 [1,2,-4,3,5] => 1 [1,2,-4,3,-5] => 2 [1,2,-4,-3,5] => 2 [1,2,-4,-3,-5] => 3 [1,-2,4,3,5] => 3 [1,-2,4,3,-5] => 4 [1,-2,4,-3,5] => 4 [1,-2,4,-3,-5] => 5 [1,-2,-4,3,5] => 2 [1,-2,-4,3,-5] => 3 [1,-2,-4,-3,5] => 3 [1,-2,-4,-3,-5] => 4 [-1,2,4,3,5] => 3 [-1,2,4,3,-5] => 4 [-1,2,4,-3,5] => 4 [-1,2,4,-3,-5] => 5 [-1,2,-4,3,5] => 2 [-1,2,-4,3,-5] => 3 [-1,2,-4,-3,5] => 3 [-1,2,-4,-3,-5] => 4 [-1,-2,4,3,5] => 4 [-1,-2,4,3,-5] => 5 [-1,-2,4,-3,5] => 5 [-1,-2,4,-3,-5] => 6 [-1,-2,-4,3,5] => 3 [-1,-2,-4,3,-5] => 4 [-1,-2,-4,-3,5] => 4 [-1,-2,-4,-3,-5] => 5 [1,2,4,5,3] => 4 [1,2,4,5,-3] => 5 [1,2,4,-5,3] => 3 [1,2,4,-5,-3] => 4 [1,2,-4,5,3] => 3 [1,2,-4,5,-3] => 4 [1,2,-4,-5,3] => 2 [1,2,-4,-5,-3] => 3 [1,-2,4,5,3] => 5 [1,-2,4,5,-3] => 6 [1,-2,4,-5,3] => 4 [1,-2,4,-5,-3] => 5 [1,-2,-4,5,3] => 4 [1,-2,-4,5,-3] => 5 [1,-2,-4,-5,3] => 3 [1,-2,-4,-5,-3] => 4 [-1,2,4,5,3] => 5 [-1,2,4,5,-3] => 6 [-1,2,4,-5,3] => 4 [-1,2,4,-5,-3] => 5 [-1,2,-4,5,3] => 4 [-1,2,-4,5,-3] => 5 [-1,2,-4,-5,3] => 3 [-1,2,-4,-5,-3] => 4 [-1,-2,4,5,3] => 6 [-1,-2,4,5,-3] => 7 [-1,-2,4,-5,3] => 5 [-1,-2,4,-5,-3] => 6 [-1,-2,-4,5,3] => 5 [-1,-2,-4,5,-3] => 6 [-1,-2,-4,-5,3] => 4 [-1,-2,-4,-5,-3] => 5 [1,2,5,3,4] => 2 [1,2,5,3,-4] => 3 [1,2,5,-3,4] => 3 [1,2,5,-3,-4] => 4 [1,2,-5,3,4] => 1 [1,2,-5,3,-4] => 2 [1,2,-5,-3,4] => 2 [1,2,-5,-3,-4] => 3 [1,-2,5,3,4] => 3 [1,-2,5,3,-4] => 4 [1,-2,5,-3,4] => 4 [1,-2,5,-3,-4] => 5 [1,-2,-5,3,4] => 2 [1,-2,-5,3,-4] => 3 [1,-2,-5,-3,4] => 3 [1,-2,-5,-3,-4] => 4 [-1,2,5,3,4] => 3 [-1,2,5,3,-4] => 4 [-1,2,5,-3,4] => 4 [-1,2,5,-3,-4] => 5 [-1,2,-5,3,4] => 2 [-1,2,-5,3,-4] => 3 [-1,2,-5,-3,4] => 3 [-1,2,-5,-3,-4] => 4 [-1,-2,5,3,4] => 4 [-1,-2,5,3,-4] => 5 [-1,-2,5,-3,4] => 5 [-1,-2,5,-3,-4] => 6 [-1,-2,-5,3,4] => 3 [-1,-2,-5,3,-4] => 4 [-1,-2,-5,-3,4] => 4 [-1,-2,-5,-3,-4] => 5 [1,2,5,4,3] => 2 [1,2,5,4,-3] => 3 [1,2,5,-4,3] => 3 [1,2,5,-4,-3] => 4 [1,2,-5,4,3] => 1 [1,2,-5,4,-3] => 2 [1,2,-5,-4,3] => 2 [1,2,-5,-4,-3] => 3 [1,-2,5,4,3] => 3 [1,-2,5,4,-3] => 4 [1,-2,5,-4,3] => 4 [1,-2,5,-4,-3] => 5 [1,-2,-5,4,3] => 2 [1,-2,-5,4,-3] => 3 [1,-2,-5,-4,3] => 3 [1,-2,-5,-4,-3] => 4 [-1,2,5,4,3] => 3 [-1,2,5,4,-3] => 4 [-1,2,5,-4,3] => 4 [-1,2,5,-4,-3] => 5 [-1,2,-5,4,3] => 2 [-1,2,-5,4,-3] => 3 [-1,2,-5,-4,3] => 3 [-1,2,-5,-4,-3] => 4 [-1,-2,5,4,3] => 4 [-1,-2,5,4,-3] => 5 [-1,-2,5,-4,3] => 5 [-1,-2,5,-4,-3] => 6 [-1,-2,-5,4,3] => 3 [-1,-2,-5,4,-3] => 4 [-1,-2,-5,-4,3] => 4 [-1,-2,-5,-4,-3] => 5 [1,3,2,4,5] => 2 [1,3,2,4,-5] => 3 [1,3,2,-4,5] => 3 [1,3,2,-4,-5] => 4 [1,3,-2,4,5] => 3 [1,3,-2,4,-5] => 4 [1,3,-2,-4,5] => 4 [1,3,-2,-4,-5] => 5 [1,-3,2,4,5] => 1 [1,-3,2,4,-5] => 2 [1,-3,2,-4,5] => 2 [1,-3,2,-4,-5] => 3 [1,-3,-2,4,5] => 2 [1,-3,-2,4,-5] => 3 [1,-3,-2,-4,5] => 3 [1,-3,-2,-4,-5] => 4 [-1,3,2,4,5] => 3 [-1,3,2,4,-5] => 4 [-1,3,2,-4,5] => 4 [-1,3,2,-4,-5] => 5 [-1,3,-2,4,5] => 4 [-1,3,-2,4,-5] => 5 [-1,3,-2,-4,5] => 5 [-1,3,-2,-4,-5] => 6 [-1,-3,2,4,5] => 2 [-1,-3,2,4,-5] => 3 [-1,-3,2,-4,5] => 3 [-1,-3,2,-4,-5] => 4 [-1,-3,-2,4,5] => 3 [-1,-3,-2,4,-5] => 4 [-1,-3,-2,-4,5] => 4 [-1,-3,-2,-4,-5] => 5 [1,3,2,5,4] => 4 [1,3,2,5,-4] => 5 [1,3,2,-5,4] => 3 [1,3,2,-5,-4] => 4 [1,3,-2,5,4] => 5 [1,3,-2,5,-4] => 6 [1,3,-2,-5,4] => 4 [1,3,-2,-5,-4] => 5 [1,-3,2,5,4] => 3 [1,-3,2,5,-4] => 4 [1,-3,2,-5,4] => 2 [1,-3,2,-5,-4] => 3 [1,-3,-2,5,4] => 4 [1,-3,-2,5,-4] => 5 [1,-3,-2,-5,4] => 3 [1,-3,-2,-5,-4] => 4 [-1,3,2,5,4] => 5 [-1,3,2,5,-4] => 6 [-1,3,2,-5,4] => 4 [-1,3,2,-5,-4] => 5 [-1,3,-2,5,4] => 6 [-1,3,-2,5,-4] => 7 [-1,3,-2,-5,4] => 5 [-1,3,-2,-5,-4] => 6 [-1,-3,2,5,4] => 4 [-1,-3,2,5,-4] => 5 [-1,-3,2,-5,4] => 3 [-1,-3,2,-5,-4] => 4 [-1,-3,-2,5,4] => 5 [-1,-3,-2,5,-4] => 6 [-1,-3,-2,-5,4] => 4 [-1,-3,-2,-5,-4] => 5 [1,3,4,2,5] => 4 [1,3,4,2,-5] => 5 [1,3,4,-2,5] => 5 [1,3,4,-2,-5] => 6 [1,3,-4,2,5] => 3 [1,3,-4,2,-5] => 4 [1,3,-4,-2,5] => 4 [1,3,-4,-2,-5] => 5 [1,-3,4,2,5] => 3 [1,-3,4,2,-5] => 4 [1,-3,4,-2,5] => 4 [1,-3,4,-2,-5] => 5 [1,-3,-4,2,5] => 2 [1,-3,-4,2,-5] => 3 [1,-3,-4,-2,5] => 3 [1,-3,-4,-2,-5] => 4 [-1,3,4,2,5] => 5 [-1,3,4,2,-5] => 6 [-1,3,4,-2,5] => 6 [-1,3,4,-2,-5] => 7 [-1,3,-4,2,5] => 4 [-1,3,-4,2,-5] => 5 [-1,3,-4,-2,5] => 5 [-1,3,-4,-2,-5] => 6 [-1,-3,4,2,5] => 4 [-1,-3,4,2,-5] => 5 [-1,-3,4,-2,5] => 5 [-1,-3,4,-2,-5] => 6 [-1,-3,-4,2,5] => 3 [-1,-3,-4,2,-5] => 4 [-1,-3,-4,-2,5] => 4 [-1,-3,-4,-2,-5] => 5 [1,3,4,5,2] => 6 [1,3,4,5,-2] => 7 [1,3,4,-5,2] => 5 [1,3,4,-5,-2] => 6 [1,3,-4,5,2] => 5 [1,3,-4,5,-2] => 6 [1,3,-4,-5,2] => 4 [1,3,-4,-5,-2] => 5 [1,-3,4,5,2] => 5 [1,-3,4,5,-2] => 6 [1,-3,4,-5,2] => 4 [1,-3,4,-5,-2] => 5 [1,-3,-4,5,2] => 4 [1,-3,-4,5,-2] => 5 [1,-3,-4,-5,2] => 3 [1,-3,-4,-5,-2] => 4 [-1,3,4,5,2] => 7 [-1,3,4,5,-2] => 8 [-1,3,4,-5,2] => 6 [-1,3,4,-5,-2] => 7 [-1,3,-4,5,2] => 6 [-1,3,-4,5,-2] => 7 [-1,3,-4,-5,2] => 5 [-1,3,-4,-5,-2] => 6 [-1,-3,4,5,2] => 6 [-1,-3,4,5,-2] => 7 [-1,-3,4,-5,2] => 5 [-1,-3,4,-5,-2] => 6 [-1,-3,-4,5,2] => 5 [-1,-3,-4,5,-2] => 6 [-1,-3,-4,-5,2] => 4 [-1,-3,-4,-5,-2] => 5 [1,3,5,2,4] => 4 [1,3,5,2,-4] => 5 [1,3,5,-2,4] => 5 [1,3,5,-2,-4] => 6 [1,3,-5,2,4] => 3 [1,3,-5,2,-4] => 4 [1,3,-5,-2,4] => 4 [1,3,-5,-2,-4] => 5 [1,-3,5,2,4] => 3 [1,-3,5,2,-4] => 4 [1,-3,5,-2,4] => 4 [1,-3,5,-2,-4] => 5 [1,-3,-5,2,4] => 2 [1,-3,-5,2,-4] => 3 [1,-3,-5,-2,4] => 3 [1,-3,-5,-2,-4] => 4 [-1,3,5,2,4] => 5 [-1,3,5,2,-4] => 6 [-1,3,5,-2,4] => 6 [-1,3,5,-2,-4] => 7 [-1,3,-5,2,4] => 4 [-1,3,-5,2,-4] => 5 [-1,3,-5,-2,4] => 5 [-1,3,-5,-2,-4] => 6 [-1,-3,5,2,4] => 4 [-1,-3,5,2,-4] => 5 [-1,-3,5,-2,4] => 5 [-1,-3,5,-2,-4] => 6 [-1,-3,-5,2,4] => 3 [-1,-3,-5,2,-4] => 4 [-1,-3,-5,-2,4] => 4 [-1,-3,-5,-2,-4] => 5 [1,3,5,4,2] => 4 [1,3,5,4,-2] => 5 [1,3,5,-4,2] => 5 [1,3,5,-4,-2] => 6 [1,3,-5,4,2] => 3 [1,3,-5,4,-2] => 4 [1,3,-5,-4,2] => 4 [1,3,-5,-4,-2] => 5 [1,-3,5,4,2] => 3 [1,-3,5,4,-2] => 4 [1,-3,5,-4,2] => 4 [1,-3,5,-4,-2] => 5 [1,-3,-5,4,2] => 2 [1,-3,-5,4,-2] => 3 [1,-3,-5,-4,2] => 3 [1,-3,-5,-4,-2] => 4 [-1,3,5,4,2] => 5 [-1,3,5,4,-2] => 6 [-1,3,5,-4,2] => 6 [-1,3,5,-4,-2] => 7 [-1,3,-5,4,2] => 4 [-1,3,-5,4,-2] => 5 [-1,3,-5,-4,2] => 5 [-1,3,-5,-4,-2] => 6 [-1,-3,5,4,2] => 4 [-1,-3,5,4,-2] => 5 [-1,-3,5,-4,2] => 5 [-1,-3,5,-4,-2] => 6 [-1,-3,-5,4,2] => 3 [-1,-3,-5,4,-2] => 4 [-1,-3,-5,-4,2] => 4 [-1,-3,-5,-4,-2] => 5 [1,4,2,3,5] => 2 [1,4,2,3,-5] => 3 [1,4,2,-3,5] => 3 [1,4,2,-3,-5] => 4 [1,4,-2,3,5] => 3 [1,4,-2,3,-5] => 4 [1,4,-2,-3,5] => 4 [1,4,-2,-3,-5] => 5 [1,-4,2,3,5] => 1 [1,-4,2,3,-5] => 2 [1,-4,2,-3,5] => 2 [1,-4,2,-3,-5] => 3 [1,-4,-2,3,5] => 2 [1,-4,-2,3,-5] => 3 [1,-4,-2,-3,5] => 3 [1,-4,-2,-3,-5] => 4 [-1,4,2,3,5] => 3 [-1,4,2,3,-5] => 4 [-1,4,2,-3,5] => 4 [-1,4,2,-3,-5] => 5 [-1,4,-2,3,5] => 4 [-1,4,-2,3,-5] => 5 [-1,4,-2,-3,5] => 5 [-1,4,-2,-3,-5] => 6 [-1,-4,2,3,5] => 2 [-1,-4,2,3,-5] => 3 [-1,-4,2,-3,5] => 3 [-1,-4,2,-3,-5] => 4 [-1,-4,-2,3,5] => 3 [-1,-4,-2,3,-5] => 4 [-1,-4,-2,-3,5] => 4 [-1,-4,-2,-3,-5] => 5 [1,4,2,5,3] => 4 [1,4,2,5,-3] => 5 [1,4,2,-5,3] => 3 [1,4,2,-5,-3] => 4 [1,4,-2,5,3] => 5 [1,4,-2,5,-3] => 6 [1,4,-2,-5,3] => 4 [1,4,-2,-5,-3] => 5 [1,-4,2,5,3] => 3 [1,-4,2,5,-3] => 4 [1,-4,2,-5,3] => 2 [1,-4,2,-5,-3] => 3 [1,-4,-2,5,3] => 4 [1,-4,-2,5,-3] => 5 [1,-4,-2,-5,3] => 3 [1,-4,-2,-5,-3] => 4 [-1,4,2,5,3] => 5 [-1,4,2,5,-3] => 6 [-1,4,2,-5,3] => 4 [-1,4,2,-5,-3] => 5 [-1,4,-2,5,3] => 6 [-1,4,-2,5,-3] => 7 [-1,4,-2,-5,3] => 5 [-1,4,-2,-5,-3] => 6 [-1,-4,2,5,3] => 4 [-1,-4,2,5,-3] => 5 [-1,-4,2,-5,3] => 3 [-1,-4,2,-5,-3] => 4 [-1,-4,-2,5,3] => 5 [-1,-4,-2,5,-3] => 6 [-1,-4,-2,-5,3] => 4 [-1,-4,-2,-5,-3] => 5 [1,4,3,2,5] => 2 [1,4,3,2,-5] => 3 [1,4,3,-2,5] => 3 [1,4,3,-2,-5] => 4 [1,4,-3,2,5] => 3 [1,4,-3,2,-5] => 4 [1,4,-3,-2,5] => 4 [1,4,-3,-2,-5] => 5 [1,-4,3,2,5] => 1 [1,-4,3,2,-5] => 2 [1,-4,3,-2,5] => 2 [1,-4,3,-2,-5] => 3 [1,-4,-3,2,5] => 2 [1,-4,-3,2,-5] => 3 [1,-4,-3,-2,5] => 3 [1,-4,-3,-2,-5] => 4 [-1,4,3,2,5] => 3 [-1,4,3,2,-5] => 4 [-1,4,3,-2,5] => 4 [-1,4,3,-2,-5] => 5 [-1,4,-3,2,5] => 4 [-1,4,-3,2,-5] => 5 [-1,4,-3,-2,5] => 5 [-1,4,-3,-2,-5] => 6 [-1,-4,3,2,5] => 2 [-1,-4,3,2,-5] => 3 [-1,-4,3,-2,5] => 3 [-1,-4,3,-2,-5] => 4 [-1,-4,-3,2,5] => 3 [-1,-4,-3,2,-5] => 4 [-1,-4,-3,-2,5] => 4 [-1,-4,-3,-2,-5] => 5 [1,4,3,5,2] => 4 [1,4,3,5,-2] => 5 [1,4,3,-5,2] => 3 [1,4,3,-5,-2] => 4 [1,4,-3,5,2] => 5 [1,4,-3,5,-2] => 6 [1,4,-3,-5,2] => 4 [1,4,-3,-5,-2] => 5 [1,-4,3,5,2] => 3 [1,-4,3,5,-2] => 4 [1,-4,3,-5,2] => 2 [1,-4,3,-5,-2] => 3 [1,-4,-3,5,2] => 4 [1,-4,-3,5,-2] => 5 [1,-4,-3,-5,2] => 3 [1,-4,-3,-5,-2] => 4 [-1,4,3,5,2] => 5 [-1,4,3,5,-2] => 6 [-1,4,3,-5,2] => 4 [-1,4,3,-5,-2] => 5 [-1,4,-3,5,2] => 6 [-1,4,-3,5,-2] => 7 [-1,4,-3,-5,2] => 5 [-1,4,-3,-5,-2] => 6 [-1,-4,3,5,2] => 4 [-1,-4,3,5,-2] => 5 [-1,-4,3,-5,2] => 3 [-1,-4,3,-5,-2] => 4 [-1,-4,-3,5,2] => 5 [-1,-4,-3,5,-2] => 6 [-1,-4,-3,-5,2] => 4 [-1,-4,-3,-5,-2] => 5 [1,4,5,2,3] => 4 [1,4,5,2,-3] => 5 [1,4,5,-2,3] => 5 [1,4,5,-2,-3] => 6 [1,4,-5,2,3] => 3 [1,4,-5,2,-3] => 4 [1,4,-5,-2,3] => 4 [1,4,-5,-2,-3] => 5 [1,-4,5,2,3] => 3 [1,-4,5,2,-3] => 4 [1,-4,5,-2,3] => 4 [1,-4,5,-2,-3] => 5 [1,-4,-5,2,3] => 2 [1,-4,-5,2,-3] => 3 [1,-4,-5,-2,3] => 3 [1,-4,-5,-2,-3] => 4 [-1,4,5,2,3] => 5 [-1,4,5,2,-3] => 6 [-1,4,5,-2,3] => 6 [-1,4,5,-2,-3] => 7 [-1,4,-5,2,3] => 4 [-1,4,-5,2,-3] => 5 [-1,4,-5,-2,3] => 5 [-1,4,-5,-2,-3] => 6 [-1,-4,5,2,3] => 4 [-1,-4,5,2,-3] => 5 [-1,-4,5,-2,3] => 5 [-1,-4,5,-2,-3] => 6 [-1,-4,-5,2,3] => 3 [-1,-4,-5,2,-3] => 4 [-1,-4,-5,-2,3] => 4 [-1,-4,-5,-2,-3] => 5 [1,4,5,3,2] => 4 [1,4,5,3,-2] => 5 [1,4,5,-3,2] => 5 [1,4,5,-3,-2] => 6 [1,4,-5,3,2] => 3 [1,4,-5,3,-2] => 4 [1,4,-5,-3,2] => 4 [1,4,-5,-3,-2] => 5 [1,-4,5,3,2] => 3 [1,-4,5,3,-2] => 4 [1,-4,5,-3,2] => 4 [1,-4,5,-3,-2] => 5 [1,-4,-5,3,2] => 2 [1,-4,-5,3,-2] => 3 [1,-4,-5,-3,2] => 3 [1,-4,-5,-3,-2] => 4 [-1,4,5,3,2] => 5 [-1,4,5,3,-2] => 6 [-1,4,5,-3,2] => 6 [-1,4,5,-3,-2] => 7 [-1,4,-5,3,2] => 4 [-1,4,-5,3,-2] => 5 [-1,4,-5,-3,2] => 5 [-1,4,-5,-3,-2] => 6 [-1,-4,5,3,2] => 4 [-1,-4,5,3,-2] => 5 [-1,-4,5,-3,2] => 5 [-1,-4,5,-3,-2] => 6 [-1,-4,-5,3,2] => 3 [-1,-4,-5,3,-2] => 4 [-1,-4,-5,-3,2] => 4 [-1,-4,-5,-3,-2] => 5 [1,5,2,3,4] => 2 [1,5,2,3,-4] => 3 [1,5,2,-3,4] => 3 [1,5,2,-3,-4] => 4 [1,5,-2,3,4] => 3 [1,5,-2,3,-4] => 4 [1,5,-2,-3,4] => 4 [1,5,-2,-3,-4] => 5 [1,-5,2,3,4] => 1 [1,-5,2,3,-4] => 2 [1,-5,2,-3,4] => 2 [1,-5,2,-3,-4] => 3 [1,-5,-2,3,4] => 2 [1,-5,-2,3,-4] => 3 [1,-5,-2,-3,4] => 3 [1,-5,-2,-3,-4] => 4 [-1,5,2,3,4] => 3 [-1,5,2,3,-4] => 4 [-1,5,2,-3,4] => 4 [-1,5,2,-3,-4] => 5 [-1,5,-2,3,4] => 4 [-1,5,-2,3,-4] => 5 [-1,5,-2,-3,4] => 5 [-1,5,-2,-3,-4] => 6 [-1,-5,2,3,4] => 2 [-1,-5,2,3,-4] => 3 [-1,-5,2,-3,4] => 3 [-1,-5,2,-3,-4] => 4 [-1,-5,-2,3,4] => 3 [-1,-5,-2,3,-4] => 4 [-1,-5,-2,-3,4] => 4 [-1,-5,-2,-3,-4] => 5 [1,5,2,4,3] => 2 [1,5,2,4,-3] => 3 [1,5,2,-4,3] => 3 [1,5,2,-4,-3] => 4 [1,5,-2,4,3] => 3 [1,5,-2,4,-3] => 4 [1,5,-2,-4,3] => 4 [1,5,-2,-4,-3] => 5 [1,-5,2,4,3] => 1 [1,-5,2,4,-3] => 2 [1,-5,2,-4,3] => 2 [1,-5,2,-4,-3] => 3 [1,-5,-2,4,3] => 2 [1,-5,-2,4,-3] => 3 [1,-5,-2,-4,3] => 3 [1,-5,-2,-4,-3] => 4 [-1,5,2,4,3] => 3 [-1,5,2,4,-3] => 4 [-1,5,2,-4,3] => 4 [-1,5,2,-4,-3] => 5 [-1,5,-2,4,3] => 4 [-1,5,-2,4,-3] => 5 [-1,5,-2,-4,3] => 5 [-1,5,-2,-4,-3] => 6 [-1,-5,2,4,3] => 2 [-1,-5,2,4,-3] => 3 [-1,-5,2,-4,3] => 3 [-1,-5,2,-4,-3] => 4 [-1,-5,-2,4,3] => 3 [-1,-5,-2,4,-3] => 4 [-1,-5,-2,-4,3] => 4 [-1,-5,-2,-4,-3] => 5 [1,5,3,2,4] => 2 [1,5,3,2,-4] => 3 [1,5,3,-2,4] => 3 [1,5,3,-2,-4] => 4 [1,5,-3,2,4] => 3 [1,5,-3,2,-4] => 4 [1,5,-3,-2,4] => 4 [1,5,-3,-2,-4] => 5 [1,-5,3,2,4] => 1 [1,-5,3,2,-4] => 2 [1,-5,3,-2,4] => 2 [1,-5,3,-2,-4] => 3 [1,-5,-3,2,4] => 2 [1,-5,-3,2,-4] => 3 [1,-5,-3,-2,4] => 3 [1,-5,-3,-2,-4] => 4 [-1,5,3,2,4] => 3 [-1,5,3,2,-4] => 4 [-1,5,3,-2,4] => 4 [-1,5,3,-2,-4] => 5 [-1,5,-3,2,4] => 4 [-1,5,-3,2,-4] => 5 [-1,5,-3,-2,4] => 5 [-1,5,-3,-2,-4] => 6 [-1,-5,3,2,4] => 2 [-1,-5,3,2,-4] => 3 [-1,-5,3,-2,4] => 3 [-1,-5,3,-2,-4] => 4 [-1,-5,-3,2,4] => 3 [-1,-5,-3,2,-4] => 4 [-1,-5,-3,-2,4] => 4 [-1,-5,-3,-2,-4] => 5 [1,5,3,4,2] => 2 [1,5,3,4,-2] => 3 [1,5,3,-4,2] => 3 [1,5,3,-4,-2] => 4 [1,5,-3,4,2] => 3 [1,5,-3,4,-2] => 4 [1,5,-3,-4,2] => 4 [1,5,-3,-4,-2] => 5 [1,-5,3,4,2] => 1 [1,-5,3,4,-2] => 2 [1,-5,3,-4,2] => 2 [1,-5,3,-4,-2] => 3 [1,-5,-3,4,2] => 2 [1,-5,-3,4,-2] => 3 [1,-5,-3,-4,2] => 3 [1,-5,-3,-4,-2] => 4 [-1,5,3,4,2] => 3 [-1,5,3,4,-2] => 4 [-1,5,3,-4,2] => 4 [-1,5,3,-4,-2] => 5 [-1,5,-3,4,2] => 4 [-1,5,-3,4,-2] => 5 [-1,5,-3,-4,2] => 5 [-1,5,-3,-4,-2] => 6 [-1,-5,3,4,2] => 2 [-1,-5,3,4,-2] => 3 [-1,-5,3,-4,2] => 3 [-1,-5,3,-4,-2] => 4 [-1,-5,-3,4,2] => 3 [-1,-5,-3,4,-2] => 4 [-1,-5,-3,-4,2] => 4 [-1,-5,-3,-4,-2] => 5 [1,5,4,2,3] => 4 [1,5,4,2,-3] => 5 [1,5,4,-2,3] => 5 [1,5,4,-2,-3] => 6 [1,5,-4,2,3] => 3 [1,5,-4,2,-3] => 4 [1,5,-4,-2,3] => 4 [1,5,-4,-2,-3] => 5 [1,-5,4,2,3] => 3 [1,-5,4,2,-3] => 4 [1,-5,4,-2,3] => 4 [1,-5,4,-2,-3] => 5 [1,-5,-4,2,3] => 2 [1,-5,-4,2,-3] => 3 [1,-5,-4,-2,3] => 3 [1,-5,-4,-2,-3] => 4 [-1,5,4,2,3] => 5 [-1,5,4,2,-3] => 6 [-1,5,4,-2,3] => 6 [-1,5,4,-2,-3] => 7 [-1,5,-4,2,3] => 4 [-1,5,-4,2,-3] => 5 [-1,5,-4,-2,3] => 5 [-1,5,-4,-2,-3] => 6 [-1,-5,4,2,3] => 4 [-1,-5,4,2,-3] => 5 [-1,-5,4,-2,3] => 5 [-1,-5,4,-2,-3] => 6 [-1,-5,-4,2,3] => 3 [-1,-5,-4,2,-3] => 4 [-1,-5,-4,-2,3] => 4 [-1,-5,-4,-2,-3] => 5 [1,5,4,3,2] => 4 [1,5,4,3,-2] => 5 [1,5,4,-3,2] => 5 [1,5,4,-3,-2] => 6 [1,5,-4,3,2] => 3 [1,5,-4,3,-2] => 4 [1,5,-4,-3,2] => 4 [1,5,-4,-3,-2] => 5 [1,-5,4,3,2] => 3 [1,-5,4,3,-2] => 4 [1,-5,4,-3,2] => 4 [1,-5,4,-3,-2] => 5 [1,-5,-4,3,2] => 2 [1,-5,-4,3,-2] => 3 [1,-5,-4,-3,2] => 3 [1,-5,-4,-3,-2] => 4 [-1,5,4,3,2] => 5 [-1,5,4,3,-2] => 6 [-1,5,4,-3,2] => 6 [-1,5,4,-3,-2] => 7 [-1,5,-4,3,2] => 4 [-1,5,-4,3,-2] => 5 ----------------------------------------------------------------------------- Created: Mar 31, 2023 at 09:34 by Jose Bastidas ----------------------------------------------------------------------------- Last Updated: Jul 05, 2023 at 17:38 by Jose Bastidas