***************************************************************************** * 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: St001511 ----------------------------------------------------------------------------- Collection: Permutations ----------------------------------------------------------------------------- Description: The minimal number of transpositions needed to sort a permutation in either direction. For a permutation $\sigma$, this is $\min\{ \operatorname{inv}(\sigma),\operatorname{inv}(\tau)\}$ where $\tau$ is the reverse permutation sending $i$ to $\sigma(n+1-i)$. ----------------------------------------------------------------------------- References: ----------------------------------------------------------------------------- Code: def statistic(pi): n = len(pi) l1 = len(pi.inversions()) l2 = binomial(n,2)-l1 return min(l1,l2) ----------------------------------------------------------------------------- Statistic values: [1] => 0 [1,2] => 0 [2,1] => 0 [1,2,3] => 0 [1,3,2] => 1 [2,1,3] => 1 [2,3,1] => 1 [3,1,2] => 1 [3,2,1] => 0 [1,2,3,4] => 0 [1,2,4,3] => 1 [1,3,2,4] => 1 [1,3,4,2] => 2 [1,4,2,3] => 2 [1,4,3,2] => 3 [2,1,3,4] => 1 [2,1,4,3] => 2 [2,3,1,4] => 2 [2,3,4,1] => 3 [2,4,1,3] => 3 [2,4,3,1] => 2 [3,1,2,4] => 2 [3,1,4,2] => 3 [3,2,1,4] => 3 [3,2,4,1] => 2 [3,4,1,2] => 2 [3,4,2,1] => 1 [4,1,2,3] => 3 [4,1,3,2] => 2 [4,2,1,3] => 2 [4,2,3,1] => 1 [4,3,1,2] => 1 [4,3,2,1] => 0 [1,2,3,4,5] => 0 [1,2,3,5,4] => 1 [1,2,4,3,5] => 1 [1,2,4,5,3] => 2 [1,2,5,3,4] => 2 [1,2,5,4,3] => 3 [1,3,2,4,5] => 1 [1,3,2,5,4] => 2 [1,3,4,2,5] => 2 [1,3,4,5,2] => 3 [1,3,5,2,4] => 3 [1,3,5,4,2] => 4 [1,4,2,3,5] => 2 [1,4,2,5,3] => 3 [1,4,3,2,5] => 3 [1,4,3,5,2] => 4 [1,4,5,2,3] => 4 [1,4,5,3,2] => 5 [1,5,2,3,4] => 3 [1,5,2,4,3] => 4 [1,5,3,2,4] => 4 [1,5,3,4,2] => 5 [1,5,4,2,3] => 5 [1,5,4,3,2] => 4 [2,1,3,4,5] => 1 [2,1,3,5,4] => 2 [2,1,4,3,5] => 2 [2,1,4,5,3] => 3 [2,1,5,3,4] => 3 [2,1,5,4,3] => 4 [2,3,1,4,5] => 2 [2,3,1,5,4] => 3 [2,3,4,1,5] => 3 [2,3,4,5,1] => 4 [2,3,5,1,4] => 4 [2,3,5,4,1] => 5 [2,4,1,3,5] => 3 [2,4,1,5,3] => 4 [2,4,3,1,5] => 4 [2,4,3,5,1] => 5 [2,4,5,1,3] => 5 [2,4,5,3,1] => 4 [2,5,1,3,4] => 4 [2,5,1,4,3] => 5 [2,5,3,1,4] => 5 [2,5,3,4,1] => 4 [2,5,4,1,3] => 4 [2,5,4,3,1] => 3 [3,1,2,4,5] => 2 [3,1,2,5,4] => 3 [3,1,4,2,5] => 3 [3,1,4,5,2] => 4 [3,1,5,2,4] => 4 [3,1,5,4,2] => 5 [3,2,1,4,5] => 3 [3,2,1,5,4] => 4 [3,2,4,1,5] => 4 [3,2,4,5,1] => 5 [3,2,5,1,4] => 5 [3,2,5,4,1] => 4 [3,4,1,2,5] => 4 [3,4,1,5,2] => 5 [3,4,2,1,5] => 5 [3,4,2,5,1] => 4 [3,4,5,1,2] => 4 [3,4,5,2,1] => 3 [3,5,1,2,4] => 5 [3,5,1,4,2] => 4 [3,5,2,1,4] => 4 [3,5,2,4,1] => 3 [3,5,4,1,2] => 3 [3,5,4,2,1] => 2 [4,1,2,3,5] => 3 [4,1,2,5,3] => 4 [4,1,3,2,5] => 4 [4,1,3,5,2] => 5 [4,1,5,2,3] => 5 [4,1,5,3,2] => 4 [4,2,1,3,5] => 4 [4,2,1,5,3] => 5 [4,2,3,1,5] => 5 [4,2,3,5,1] => 4 [4,2,5,1,3] => 4 [4,2,5,3,1] => 3 [4,3,1,2,5] => 5 [4,3,1,5,2] => 4 [4,3,2,1,5] => 4 [4,3,2,5,1] => 3 [4,3,5,1,2] => 3 [4,3,5,2,1] => 2 [4,5,1,2,3] => 4 [4,5,1,3,2] => 3 [4,5,2,1,3] => 3 [4,5,2,3,1] => 2 [4,5,3,1,2] => 2 [4,5,3,2,1] => 1 [5,1,2,3,4] => 4 [5,1,2,4,3] => 5 [5,1,3,2,4] => 5 [5,1,3,4,2] => 4 [5,1,4,2,3] => 4 [5,1,4,3,2] => 3 [5,2,1,3,4] => 5 [5,2,1,4,3] => 4 [5,2,3,1,4] => 4 [5,2,3,4,1] => 3 [5,2,4,1,3] => 3 [5,2,4,3,1] => 2 [5,3,1,2,4] => 4 [5,3,1,4,2] => 3 [5,3,2,1,4] => 3 [5,3,2,4,1] => 2 [5,3,4,1,2] => 2 [5,3,4,2,1] => 1 [5,4,1,2,3] => 3 [5,4,1,3,2] => 2 [5,4,2,1,3] => 2 [5,4,2,3,1] => 1 [5,4,3,1,2] => 1 [5,4,3,2,1] => 0 [1,2,3,4,5,6] => 0 [1,2,3,4,6,5] => 1 [1,2,3,5,4,6] => 1 [1,2,3,5,6,4] => 2 [1,2,3,6,4,5] => 2 [1,2,3,6,5,4] => 3 [1,2,4,3,5,6] => 1 [1,2,4,3,6,5] => 2 [1,2,4,5,3,6] => 2 [1,2,4,5,6,3] => 3 [1,2,4,6,3,5] => 3 [1,2,4,6,5,3] => 4 [1,2,5,3,4,6] => 2 [1,2,5,3,6,4] => 3 [1,2,5,4,3,6] => 3 [1,2,5,4,6,3] => 4 [1,2,5,6,3,4] => 4 [1,2,5,6,4,3] => 5 [1,2,6,3,4,5] => 3 [1,2,6,3,5,4] => 4 [1,2,6,4,3,5] => 4 [1,2,6,4,5,3] => 5 [1,2,6,5,3,4] => 5 [1,2,6,5,4,3] => 6 [1,3,2,4,5,6] => 1 [1,3,2,4,6,5] => 2 [1,3,2,5,4,6] => 2 [1,3,2,5,6,4] => 3 [1,3,2,6,4,5] => 3 [1,3,2,6,5,4] => 4 [1,3,4,2,5,6] => 2 [1,3,4,2,6,5] => 3 [1,3,4,5,2,6] => 3 [1,3,4,5,6,2] => 4 [1,3,4,6,2,5] => 4 [1,3,4,6,5,2] => 5 [1,3,5,2,4,6] => 3 [1,3,5,2,6,4] => 4 [1,3,5,4,2,6] => 4 [1,3,5,4,6,2] => 5 [1,3,5,6,2,4] => 5 [1,3,5,6,4,2] => 6 [1,3,6,2,4,5] => 4 [1,3,6,2,5,4] => 5 [1,3,6,4,2,5] => 5 [1,3,6,4,5,2] => 6 [1,3,6,5,2,4] => 6 [1,3,6,5,4,2] => 7 [1,4,2,3,5,6] => 2 [1,4,2,3,6,5] => 3 [1,4,2,5,3,6] => 3 [1,4,2,5,6,3] => 4 [1,4,2,6,3,5] => 4 [1,4,2,6,5,3] => 5 [1,4,3,2,5,6] => 3 [1,4,3,2,6,5] => 4 [1,4,3,5,2,6] => 4 [1,4,3,5,6,2] => 5 [1,4,3,6,2,5] => 5 [1,4,3,6,5,2] => 6 [1,4,5,2,3,6] => 4 [1,4,5,2,6,3] => 5 [1,4,5,3,2,6] => 5 [1,4,5,3,6,2] => 6 [1,4,5,6,2,3] => 6 [1,4,5,6,3,2] => 7 [1,4,6,2,3,5] => 5 [1,4,6,2,5,3] => 6 [1,4,6,3,2,5] => 6 [1,4,6,3,5,2] => 7 [1,4,6,5,2,3] => 7 [1,4,6,5,3,2] => 7 [1,5,2,3,4,6] => 3 [1,5,2,3,6,4] => 4 [1,5,2,4,3,6] => 4 [1,5,2,4,6,3] => 5 [1,5,2,6,3,4] => 5 [1,5,2,6,4,3] => 6 [1,5,3,2,4,6] => 4 [1,5,3,2,6,4] => 5 [1,5,3,4,2,6] => 5 [1,5,3,4,6,2] => 6 [1,5,3,6,2,4] => 6 [1,5,3,6,4,2] => 7 [1,5,4,2,3,6] => 5 [1,5,4,2,6,3] => 6 [1,5,4,3,2,6] => 6 [1,5,4,3,6,2] => 7 [1,5,4,6,2,3] => 7 [1,5,4,6,3,2] => 7 [1,5,6,2,3,4] => 6 [1,5,6,2,4,3] => 7 [1,5,6,3,2,4] => 7 [1,5,6,3,4,2] => 7 [1,5,6,4,2,3] => 7 [1,5,6,4,3,2] => 6 [1,6,2,3,4,5] => 4 [1,6,2,3,5,4] => 5 [1,6,2,4,3,5] => 5 [1,6,2,4,5,3] => 6 [1,6,2,5,3,4] => 6 [1,6,2,5,4,3] => 7 [1,6,3,2,4,5] => 5 [1,6,3,2,5,4] => 6 [1,6,3,4,2,5] => 6 [1,6,3,4,5,2] => 7 [1,6,3,5,2,4] => 7 [1,6,3,5,4,2] => 7 [1,6,4,2,3,5] => 6 [1,6,4,2,5,3] => 7 [1,6,4,3,2,5] => 7 [1,6,4,3,5,2] => 7 [1,6,4,5,2,3] => 7 [1,6,4,5,3,2] => 6 [1,6,5,2,3,4] => 7 [1,6,5,2,4,3] => 7 [1,6,5,3,2,4] => 7 [1,6,5,3,4,2] => 6 [1,6,5,4,2,3] => 6 [1,6,5,4,3,2] => 5 [2,1,3,4,5,6] => 1 [2,1,3,4,6,5] => 2 [2,1,3,5,4,6] => 2 [2,1,3,5,6,4] => 3 [2,1,3,6,4,5] => 3 [2,1,3,6,5,4] => 4 [2,1,4,3,5,6] => 2 [2,1,4,3,6,5] => 3 [2,1,4,5,3,6] => 3 [2,1,4,5,6,3] => 4 [2,1,4,6,3,5] => 4 [2,1,4,6,5,3] => 5 [2,1,5,3,4,6] => 3 [2,1,5,3,6,4] => 4 [2,1,5,4,3,6] => 4 [2,1,5,4,6,3] => 5 [2,1,5,6,3,4] => 5 [2,1,5,6,4,3] => 6 [2,1,6,3,4,5] => 4 [2,1,6,3,5,4] => 5 [2,1,6,4,3,5] => 5 [2,1,6,4,5,3] => 6 [2,1,6,5,3,4] => 6 [2,1,6,5,4,3] => 7 [2,3,1,4,5,6] => 2 [2,3,1,4,6,5] => 3 [2,3,1,5,4,6] => 3 [2,3,1,5,6,4] => 4 [2,3,1,6,4,5] => 4 [2,3,1,6,5,4] => 5 [2,3,4,1,5,6] => 3 [2,3,4,1,6,5] => 4 [2,3,4,5,1,6] => 4 [2,3,4,5,6,1] => 5 [2,3,4,6,1,5] => 5 [2,3,4,6,5,1] => 6 [2,3,5,1,4,6] => 4 [2,3,5,1,6,4] => 5 [2,3,5,4,1,6] => 5 [2,3,5,4,6,1] => 6 [2,3,5,6,1,4] => 6 [2,3,5,6,4,1] => 7 [2,3,6,1,4,5] => 5 [2,3,6,1,5,4] => 6 [2,3,6,4,1,5] => 6 [2,3,6,4,5,1] => 7 [2,3,6,5,1,4] => 7 [2,3,6,5,4,1] => 7 [2,4,1,3,5,6] => 3 [2,4,1,3,6,5] => 4 [2,4,1,5,3,6] => 4 [2,4,1,5,6,3] => 5 [2,4,1,6,3,5] => 5 [2,4,1,6,5,3] => 6 [2,4,3,1,5,6] => 4 [2,4,3,1,6,5] => 5 [2,4,3,5,1,6] => 5 [2,4,3,5,6,1] => 6 [2,4,3,6,1,5] => 6 [2,4,3,6,5,1] => 7 [2,4,5,1,3,6] => 5 [2,4,5,1,6,3] => 6 [2,4,5,3,1,6] => 6 [2,4,5,3,6,1] => 7 [2,4,5,6,1,3] => 7 [2,4,5,6,3,1] => 7 [2,4,6,1,3,5] => 6 [2,4,6,1,5,3] => 7 [2,4,6,3,1,5] => 7 [2,4,6,3,5,1] => 7 [2,4,6,5,1,3] => 7 [2,4,6,5,3,1] => 6 [2,5,1,3,4,6] => 4 [2,5,1,3,6,4] => 5 [2,5,1,4,3,6] => 5 [2,5,1,4,6,3] => 6 [2,5,1,6,3,4] => 6 [2,5,1,6,4,3] => 7 [2,5,3,1,4,6] => 5 [2,5,3,1,6,4] => 6 [2,5,3,4,1,6] => 6 [2,5,3,4,6,1] => 7 [2,5,3,6,1,4] => 7 [2,5,3,6,4,1] => 7 [2,5,4,1,3,6] => 6 [2,5,4,1,6,3] => 7 [2,5,4,3,1,6] => 7 [2,5,4,3,6,1] => 7 [2,5,4,6,1,3] => 7 [2,5,4,6,3,1] => 6 [2,5,6,1,3,4] => 7 [2,5,6,1,4,3] => 7 [2,5,6,3,1,4] => 7 [2,5,6,3,4,1] => 6 [2,5,6,4,1,3] => 6 [2,5,6,4,3,1] => 5 [2,6,1,3,4,5] => 5 [2,6,1,3,5,4] => 6 [2,6,1,4,3,5] => 6 [2,6,1,4,5,3] => 7 [2,6,1,5,3,4] => 7 [2,6,1,5,4,3] => 7 [2,6,3,1,4,5] => 6 [2,6,3,1,5,4] => 7 [2,6,3,4,1,5] => 7 [2,6,3,4,5,1] => 7 [2,6,3,5,1,4] => 7 [2,6,3,5,4,1] => 6 [2,6,4,1,3,5] => 7 [2,6,4,1,5,3] => 7 [2,6,4,3,1,5] => 7 [2,6,4,3,5,1] => 6 [2,6,4,5,1,3] => 6 [2,6,4,5,3,1] => 5 [2,6,5,1,3,4] => 7 [2,6,5,1,4,3] => 6 [2,6,5,3,1,4] => 6 [2,6,5,3,4,1] => 5 [2,6,5,4,1,3] => 5 [2,6,5,4,3,1] => 4 [3,1,2,4,5,6] => 2 [3,1,2,4,6,5] => 3 [3,1,2,5,4,6] => 3 [3,1,2,5,6,4] => 4 [3,1,2,6,4,5] => 4 [3,1,2,6,5,4] => 5 [3,1,4,2,5,6] => 3 [3,1,4,2,6,5] => 4 [3,1,4,5,2,6] => 4 [3,1,4,5,6,2] => 5 [3,1,4,6,2,5] => 5 [3,1,4,6,5,2] => 6 [3,1,5,2,4,6] => 4 [3,1,5,2,6,4] => 5 [3,1,5,4,2,6] => 5 [3,1,5,4,6,2] => 6 [3,1,5,6,2,4] => 6 [3,1,5,6,4,2] => 7 [3,1,6,2,4,5] => 5 [3,1,6,2,5,4] => 6 [3,1,6,4,2,5] => 6 [3,1,6,4,5,2] => 7 [3,1,6,5,2,4] => 7 [3,1,6,5,4,2] => 7 [3,2,1,4,5,6] => 3 [3,2,1,4,6,5] => 4 [3,2,1,5,4,6] => 4 [3,2,1,5,6,4] => 5 [3,2,1,6,4,5] => 5 [3,2,1,6,5,4] => 6 [3,2,4,1,5,6] => 4 [3,2,4,1,6,5] => 5 [3,2,4,5,1,6] => 5 [3,2,4,5,6,1] => 6 [3,2,4,6,1,5] => 6 [3,2,4,6,5,1] => 7 [3,2,5,1,4,6] => 5 [3,2,5,1,6,4] => 6 [3,2,5,4,1,6] => 6 [3,2,5,4,6,1] => 7 [3,2,5,6,1,4] => 7 [3,2,5,6,4,1] => 7 [3,2,6,1,4,5] => 6 [3,2,6,1,5,4] => 7 [3,2,6,4,1,5] => 7 [3,2,6,4,5,1] => 7 [3,2,6,5,1,4] => 7 [3,2,6,5,4,1] => 6 [3,4,1,2,5,6] => 4 [3,4,1,2,6,5] => 5 [3,4,1,5,2,6] => 5 [3,4,1,5,6,2] => 6 [3,4,1,6,2,5] => 6 [3,4,1,6,5,2] => 7 [3,4,2,1,5,6] => 5 [3,4,2,1,6,5] => 6 [3,4,2,5,1,6] => 6 [3,4,2,5,6,1] => 7 [3,4,2,6,1,5] => 7 [3,4,2,6,5,1] => 7 [3,4,5,1,2,6] => 6 [3,4,5,1,6,2] => 7 [3,4,5,2,1,6] => 7 [3,4,5,2,6,1] => 7 [3,4,5,6,1,2] => 7 [3,4,5,6,2,1] => 6 [3,4,6,1,2,5] => 7 [3,4,6,1,5,2] => 7 [3,4,6,2,1,5] => 7 [3,4,6,2,5,1] => 6 [3,4,6,5,1,2] => 6 [3,4,6,5,2,1] => 5 [3,5,1,2,4,6] => 5 [3,5,1,2,6,4] => 6 [3,5,1,4,2,6] => 6 [3,5,1,4,6,2] => 7 [3,5,1,6,2,4] => 7 [3,5,1,6,4,2] => 7 [3,5,2,1,4,6] => 6 [3,5,2,1,6,4] => 7 [3,5,2,4,1,6] => 7 [3,5,2,4,6,1] => 7 [3,5,2,6,1,4] => 7 [3,5,2,6,4,1] => 6 [3,5,4,1,2,6] => 7 [3,5,4,1,6,2] => 7 [3,5,4,2,1,6] => 7 [3,5,4,2,6,1] => 6 [3,5,4,6,1,2] => 6 [3,5,4,6,2,1] => 5 [3,5,6,1,2,4] => 7 [3,5,6,1,4,2] => 6 [3,5,6,2,1,4] => 6 [3,5,6,2,4,1] => 5 [3,5,6,4,1,2] => 5 [3,5,6,4,2,1] => 4 [3,6,1,2,4,5] => 6 [3,6,1,2,5,4] => 7 [3,6,1,4,2,5] => 7 [3,6,1,4,5,2] => 7 [3,6,1,5,2,4] => 7 [3,6,1,5,4,2] => 6 [3,6,2,1,4,5] => 7 [3,6,2,1,5,4] => 7 [3,6,2,4,1,5] => 7 [3,6,2,4,5,1] => 6 [3,6,2,5,1,4] => 6 [3,6,2,5,4,1] => 5 [3,6,4,1,2,5] => 7 [3,6,4,1,5,2] => 6 [3,6,4,2,1,5] => 6 [3,6,4,2,5,1] => 5 [3,6,4,5,1,2] => 5 [3,6,4,5,2,1] => 4 [3,6,5,1,2,4] => 6 [3,6,5,1,4,2] => 5 [3,6,5,2,1,4] => 5 [3,6,5,2,4,1] => 4 [3,6,5,4,1,2] => 4 [3,6,5,4,2,1] => 3 [4,1,2,3,5,6] => 3 [4,1,2,3,6,5] => 4 [4,1,2,5,3,6] => 4 [4,1,2,5,6,3] => 5 [4,1,2,6,3,5] => 5 [4,1,2,6,5,3] => 6 [4,1,3,2,5,6] => 4 [4,1,3,2,6,5] => 5 [4,1,3,5,2,6] => 5 [4,1,3,5,6,2] => 6 [4,1,3,6,2,5] => 6 [4,1,3,6,5,2] => 7 [4,1,5,2,3,6] => 5 [4,1,5,2,6,3] => 6 [4,1,5,3,2,6] => 6 [4,1,5,3,6,2] => 7 [4,1,5,6,2,3] => 7 [4,1,5,6,3,2] => 7 [4,1,6,2,3,5] => 6 [4,1,6,2,5,3] => 7 [4,1,6,3,2,5] => 7 [4,1,6,3,5,2] => 7 [4,1,6,5,2,3] => 7 [4,1,6,5,3,2] => 6 [4,2,1,3,5,6] => 4 [4,2,1,3,6,5] => 5 [4,2,1,5,3,6] => 5 [4,2,1,5,6,3] => 6 [4,2,1,6,3,5] => 6 [4,2,1,6,5,3] => 7 [4,2,3,1,5,6] => 5 [4,2,3,1,6,5] => 6 [4,2,3,5,1,6] => 6 [4,2,3,5,6,1] => 7 [4,2,3,6,1,5] => 7 [4,2,3,6,5,1] => 7 [4,2,5,1,3,6] => 6 [4,2,5,1,6,3] => 7 [4,2,5,3,1,6] => 7 [4,2,5,3,6,1] => 7 [4,2,5,6,1,3] => 7 [4,2,5,6,3,1] => 6 [4,2,6,1,3,5] => 7 [4,2,6,1,5,3] => 7 [4,2,6,3,1,5] => 7 [4,2,6,3,5,1] => 6 [4,2,6,5,1,3] => 6 [4,2,6,5,3,1] => 5 [4,3,1,2,5,6] => 5 [4,3,1,2,6,5] => 6 [4,3,1,5,2,6] => 6 [4,3,1,5,6,2] => 7 [4,3,1,6,2,5] => 7 [4,3,1,6,5,2] => 7 [4,3,2,1,5,6] => 6 [4,3,2,1,6,5] => 7 [4,3,2,5,1,6] => 7 [4,3,2,5,6,1] => 7 [4,3,2,6,1,5] => 7 [4,3,2,6,5,1] => 6 [4,3,5,1,2,6] => 7 [4,3,5,1,6,2] => 7 [4,3,5,2,1,6] => 7 [4,3,5,2,6,1] => 6 [4,3,5,6,1,2] => 6 [4,3,5,6,2,1] => 5 [4,3,6,1,2,5] => 7 [4,3,6,1,5,2] => 6 [4,3,6,2,1,5] => 6 [4,3,6,2,5,1] => 5 [4,3,6,5,1,2] => 5 [4,3,6,5,2,1] => 4 [4,5,1,2,3,6] => 6 [4,5,1,2,6,3] => 7 [4,5,1,3,2,6] => 7 [4,5,1,3,6,2] => 7 [4,5,1,6,2,3] => 7 [4,5,1,6,3,2] => 6 [4,5,2,1,3,6] => 7 [4,5,2,1,6,3] => 7 [4,5,2,3,1,6] => 7 [4,5,2,3,6,1] => 6 [4,5,2,6,1,3] => 6 [4,5,2,6,3,1] => 5 [4,5,3,1,2,6] => 7 [4,5,3,1,6,2] => 6 [4,5,3,2,1,6] => 6 [4,5,3,2,6,1] => 5 [4,5,3,6,1,2] => 5 [4,5,3,6,2,1] => 4 [4,5,6,1,2,3] => 6 [4,5,6,1,3,2] => 5 [4,5,6,2,1,3] => 5 [4,5,6,2,3,1] => 4 [4,5,6,3,1,2] => 4 [4,5,6,3,2,1] => 3 [4,6,1,2,3,5] => 7 [4,6,1,2,5,3] => 7 [4,6,1,3,2,5] => 7 [4,6,1,3,5,2] => 6 [4,6,1,5,2,3] => 6 [4,6,1,5,3,2] => 5 [4,6,2,1,3,5] => 7 [4,6,2,1,5,3] => 6 [4,6,2,3,1,5] => 6 [4,6,2,3,5,1] => 5 [4,6,2,5,1,3] => 5 [4,6,2,5,3,1] => 4 [4,6,3,1,2,5] => 6 [4,6,3,1,5,2] => 5 [4,6,3,2,1,5] => 5 [4,6,3,2,5,1] => 4 [4,6,3,5,1,2] => 4 [4,6,3,5,2,1] => 3 [4,6,5,1,2,3] => 5 [4,6,5,1,3,2] => 4 [4,6,5,2,1,3] => 4 [4,6,5,2,3,1] => 3 [4,6,5,3,1,2] => 3 [4,6,5,3,2,1] => 2 [5,1,2,3,4,6] => 4 [5,1,2,3,6,4] => 5 [5,1,2,4,3,6] => 5 [5,1,2,4,6,3] => 6 [5,1,2,6,3,4] => 6 [5,1,2,6,4,3] => 7 [5,1,3,2,4,6] => 5 [5,1,3,2,6,4] => 6 [5,1,3,4,2,6] => 6 [5,1,3,4,6,2] => 7 [5,1,3,6,2,4] => 7 [5,1,3,6,4,2] => 7 [5,1,4,2,3,6] => 6 [5,1,4,2,6,3] => 7 [5,1,4,3,2,6] => 7 [5,1,4,3,6,2] => 7 [5,1,4,6,2,3] => 7 [5,1,4,6,3,2] => 6 [5,1,6,2,3,4] => 7 [5,1,6,2,4,3] => 7 [5,1,6,3,2,4] => 7 [5,1,6,3,4,2] => 6 [5,1,6,4,2,3] => 6 [5,1,6,4,3,2] => 5 [5,2,1,3,4,6] => 5 [5,2,1,3,6,4] => 6 [5,2,1,4,3,6] => 6 [5,2,1,4,6,3] => 7 [5,2,1,6,3,4] => 7 [5,2,1,6,4,3] => 7 [5,2,3,1,4,6] => 6 [5,2,3,1,6,4] => 7 [5,2,3,4,1,6] => 7 [5,2,3,4,6,1] => 7 [5,2,3,6,1,4] => 7 [5,2,3,6,4,1] => 6 [5,2,4,1,3,6] => 7 [5,2,4,1,6,3] => 7 [5,2,4,3,1,6] => 7 [5,2,4,3,6,1] => 6 [5,2,4,6,1,3] => 6 [5,2,4,6,3,1] => 5 [5,2,6,1,3,4] => 7 [5,2,6,1,4,3] => 6 [5,2,6,3,1,4] => 6 [5,2,6,3,4,1] => 5 [5,2,6,4,1,3] => 5 [5,2,6,4,3,1] => 4 [5,3,1,2,4,6] => 6 [5,3,1,2,6,4] => 7 [5,3,1,4,2,6] => 7 [5,3,1,4,6,2] => 7 [5,3,1,6,2,4] => 7 [5,3,1,6,4,2] => 6 [5,3,2,1,4,6] => 7 [5,3,2,1,6,4] => 7 [5,3,2,4,1,6] => 7 [5,3,2,4,6,1] => 6 [5,3,2,6,1,4] => 6 [5,3,2,6,4,1] => 5 [5,3,4,1,2,6] => 7 [5,3,4,1,6,2] => 6 [5,3,4,2,1,6] => 6 [5,3,4,2,6,1] => 5 [5,3,4,6,1,2] => 5 [5,3,4,6,2,1] => 4 [5,3,6,1,2,4] => 6 [5,3,6,1,4,2] => 5 [5,3,6,2,1,4] => 5 [5,3,6,2,4,1] => 4 [5,3,6,4,1,2] => 4 [5,3,6,4,2,1] => 3 [5,4,1,2,3,6] => 7 [5,4,1,2,6,3] => 7 [5,4,1,3,2,6] => 7 [5,4,1,3,6,2] => 6 [5,4,1,6,2,3] => 6 [5,4,1,6,3,2] => 5 [5,4,2,1,3,6] => 7 [5,4,2,1,6,3] => 6 [5,4,2,3,1,6] => 6 [5,4,2,3,6,1] => 5 [5,4,2,6,1,3] => 5 [5,4,2,6,3,1] => 4 [5,4,3,1,2,6] => 6 [5,4,3,1,6,2] => 5 [5,4,3,2,1,6] => 5 [5,4,3,2,6,1] => 4 [5,4,3,6,1,2] => 4 [5,4,3,6,2,1] => 3 [5,4,6,1,2,3] => 5 [5,4,6,1,3,2] => 4 [5,4,6,2,1,3] => 4 [5,4,6,2,3,1] => 3 [5,4,6,3,1,2] => 3 [5,4,6,3,2,1] => 2 [5,6,1,2,3,4] => 7 [5,6,1,2,4,3] => 6 [5,6,1,3,2,4] => 6 [5,6,1,3,4,2] => 5 [5,6,1,4,2,3] => 5 [5,6,1,4,3,2] => 4 [5,6,2,1,3,4] => 6 [5,6,2,1,4,3] => 5 [5,6,2,3,1,4] => 5 [5,6,2,3,4,1] => 4 [5,6,2,4,1,3] => 4 [5,6,2,4,3,1] => 3 [5,6,3,1,2,4] => 5 [5,6,3,1,4,2] => 4 [5,6,3,2,1,4] => 4 [5,6,3,2,4,1] => 3 [5,6,3,4,1,2] => 3 [5,6,3,4,2,1] => 2 [5,6,4,1,2,3] => 4 [5,6,4,1,3,2] => 3 [5,6,4,2,1,3] => 3 [5,6,4,2,3,1] => 2 [5,6,4,3,1,2] => 2 [5,6,4,3,2,1] => 1 [6,1,2,3,4,5] => 5 [6,1,2,3,5,4] => 6 [6,1,2,4,3,5] => 6 [6,1,2,4,5,3] => 7 [6,1,2,5,3,4] => 7 [6,1,2,5,4,3] => 7 [6,1,3,2,4,5] => 6 [6,1,3,2,5,4] => 7 [6,1,3,4,2,5] => 7 [6,1,3,4,5,2] => 7 [6,1,3,5,2,4] => 7 [6,1,3,5,4,2] => 6 [6,1,4,2,3,5] => 7 [6,1,4,2,5,3] => 7 [6,1,4,3,2,5] => 7 [6,1,4,3,5,2] => 6 [6,1,4,5,2,3] => 6 [6,1,4,5,3,2] => 5 [6,1,5,2,3,4] => 7 [6,1,5,2,4,3] => 6 [6,1,5,3,2,4] => 6 [6,1,5,3,4,2] => 5 [6,1,5,4,2,3] => 5 [6,1,5,4,3,2] => 4 [6,2,1,3,4,5] => 6 [6,2,1,3,5,4] => 7 [6,2,1,4,3,5] => 7 [6,2,1,4,5,3] => 7 [6,2,1,5,3,4] => 7 [6,2,1,5,4,3] => 6 [6,2,3,1,4,5] => 7 [6,2,3,1,5,4] => 7 [6,2,3,4,1,5] => 7 [6,2,3,4,5,1] => 6 [6,2,3,5,1,4] => 6 [6,2,3,5,4,1] => 5 [6,2,4,1,3,5] => 7 [6,2,4,1,5,3] => 6 [6,2,4,3,1,5] => 6 [6,2,4,3,5,1] => 5 [6,2,4,5,1,3] => 5 [6,2,4,5,3,1] => 4 [6,2,5,1,3,4] => 6 [6,2,5,1,4,3] => 5 [6,2,5,3,1,4] => 5 [6,2,5,3,4,1] => 4 [6,2,5,4,1,3] => 4 [6,2,5,4,3,1] => 3 [6,3,1,2,4,5] => 7 [6,3,1,2,5,4] => 7 [6,3,1,4,2,5] => 7 [6,3,1,4,5,2] => 6 [6,3,1,5,2,4] => 6 [6,3,1,5,4,2] => 5 [6,3,2,1,4,5] => 7 [6,3,2,1,5,4] => 6 [6,3,2,4,1,5] => 6 [6,3,2,4,5,1] => 5 [6,3,2,5,1,4] => 5 [6,3,2,5,4,1] => 4 [6,3,4,1,2,5] => 6 [6,3,4,1,5,2] => 5 [6,3,4,2,1,5] => 5 [6,3,4,2,5,1] => 4 [6,3,4,5,1,2] => 4 [6,3,4,5,2,1] => 3 [6,3,5,1,2,4] => 5 [6,3,5,1,4,2] => 4 [6,3,5,2,1,4] => 4 [6,3,5,2,4,1] => 3 [6,3,5,4,1,2] => 3 [6,3,5,4,2,1] => 2 [6,4,1,2,3,5] => 7 [6,4,1,2,5,3] => 6 [6,4,1,3,2,5] => 6 [6,4,1,3,5,2] => 5 [6,4,1,5,2,3] => 5 [6,4,1,5,3,2] => 4 [6,4,2,1,3,5] => 6 [6,4,2,1,5,3] => 5 [6,4,2,3,1,5] => 5 [6,4,2,3,5,1] => 4 [6,4,2,5,1,3] => 4 [6,4,2,5,3,1] => 3 [6,4,3,1,2,5] => 5 [6,4,3,1,5,2] => 4 [6,4,3,2,1,5] => 4 [6,4,3,2,5,1] => 3 [6,4,3,5,1,2] => 3 [6,4,3,5,2,1] => 2 [6,4,5,1,2,3] => 4 [6,4,5,1,3,2] => 3 [6,4,5,2,1,3] => 3 [6,4,5,2,3,1] => 2 [6,4,5,3,1,2] => 2 [6,4,5,3,2,1] => 1 [6,5,1,2,3,4] => 6 [6,5,1,2,4,3] => 5 [6,5,1,3,2,4] => 5 [6,5,1,3,4,2] => 4 [6,5,1,4,2,3] => 4 [6,5,1,4,3,2] => 3 [6,5,2,1,3,4] => 5 [6,5,2,1,4,3] => 4 [6,5,2,3,1,4] => 4 [6,5,2,3,4,1] => 3 [6,5,2,4,1,3] => 3 [6,5,2,4,3,1] => 2 [6,5,3,1,2,4] => 4 [6,5,3,1,4,2] => 3 [6,5,3,2,1,4] => 3 [6,5,3,2,4,1] => 2 [6,5,3,4,1,2] => 2 [6,5,3,4,2,1] => 1 [6,5,4,1,2,3] => 3 [6,5,4,1,3,2] => 2 [6,5,4,2,1,3] => 2 [6,5,4,2,3,1] => 1 [6,5,4,3,1,2] => 1 [6,5,4,3,2,1] => 0 ----------------------------------------------------------------------------- Created: Dec 01, 2019 at 14:50 by Christian Stump ----------------------------------------------------------------------------- Last Updated: Dec 01, 2019 at 14:50 by Christian Stump