***************************************************************************** * 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: St001077 ----------------------------------------------------------------------------- Collection: Permutations ----------------------------------------------------------------------------- Description: The prefix exchange distance of a permutation. This is the number of star transpositions needed to write a permutation. In symbols, for a permutation $\pi\in\mathfrak S_n$ this is $$\min\{ k \mid \pi = \tau_{i_1} \cdots \tau_{i_k}, 2 \leq i_1,\ldots,i_k \leq n\},$$ where $\tau_a = (1,a)$ for $2 \leq a \leq n$. [1, Lem. 2.1] shows that the this length is $n+m-a-1$, where $m$ is the number of non-trival cycles not containing the element $1$, and $a$ is the number of fixed points different from $1$. One may find in [2] explicit formulas for its generating function and a combinatorial proof that it is asymptotically normal. ----------------------------------------------------------------------------- References: [1] Pak, I. Reduced decompositions of permutations in terms of star transpositions, generalized Catalan numbers and $k$-ary trees [[MathSciNet:1691876]] [2] Grusea, S., Labarre, A. Asymptotic normality and combinatorial aspects of the prefix exchange distance distribution [[MathSciNet:3497998]] ----------------------------------------------------------------------------- Code: def statistic(pi): ct = pi.cycle_tuples() one = None # cycle containing 1 two = 0 # other cycles of length at least 2 fix = 0 # other fixed points for c in ct: if one is None and 1 in c: one = True elif len(c) > 1: two += 1 else: fix += 1 return len(pi) + two - fix - 1 ----------------------------------------------------------------------------- Statistic values: [1,2] => 0 [2,1] => 1 [1,2,3] => 0 [1,3,2] => 3 [2,1,3] => 1 [2,3,1] => 2 [3,1,2] => 2 [3,2,1] => 1 [1,2,3,4] => 0 [1,2,4,3] => 3 [1,3,2,4] => 3 [1,3,4,2] => 4 [1,4,2,3] => 4 [1,4,3,2] => 3 [2,1,3,4] => 1 [2,1,4,3] => 4 [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] => 1 [3,2,4,1] => 2 [3,4,1,2] => 4 [3,4,2,1] => 3 [4,1,2,3] => 3 [4,1,3,2] => 2 [4,2,1,3] => 2 [4,2,3,1] => 1 [4,3,1,2] => 3 [4,3,2,1] => 4 [1,2,3,4,5] => 0 [1,2,3,5,4] => 3 [1,2,4,3,5] => 3 [1,2,4,5,3] => 4 [1,2,5,3,4] => 4 [1,2,5,4,3] => 3 [1,3,2,4,5] => 3 [1,3,2,5,4] => 6 [1,3,4,2,5] => 4 [1,3,4,5,2] => 5 [1,3,5,2,4] => 5 [1,3,5,4,2] => 4 [1,4,2,3,5] => 4 [1,4,2,5,3] => 5 [1,4,3,2,5] => 3 [1,4,3,5,2] => 4 [1,4,5,2,3] => 6 [1,4,5,3,2] => 5 [1,5,2,3,4] => 5 [1,5,2,4,3] => 4 [1,5,3,2,4] => 4 [1,5,3,4,2] => 3 [1,5,4,2,3] => 5 [1,5,4,3,2] => 6 [2,1,3,4,5] => 1 [2,1,3,5,4] => 4 [2,1,4,3,5] => 4 [2,1,4,5,3] => 5 [2,1,5,3,4] => 5 [2,1,5,4,3] => 4 [2,3,1,4,5] => 2 [2,3,1,5,4] => 5 [2,3,4,1,5] => 3 [2,3,4,5,1] => 4 [2,3,5,1,4] => 4 [2,3,5,4,1] => 3 [2,4,1,3,5] => 3 [2,4,1,5,3] => 4 [2,4,3,1,5] => 2 [2,4,3,5,1] => 3 [2,4,5,1,3] => 5 [2,4,5,3,1] => 4 [2,5,1,3,4] => 4 [2,5,1,4,3] => 3 [2,5,3,1,4] => 3 [2,5,3,4,1] => 2 [2,5,4,1,3] => 4 [2,5,4,3,1] => 5 [3,1,2,4,5] => 2 [3,1,2,5,4] => 5 [3,1,4,2,5] => 3 [3,1,4,5,2] => 4 [3,1,5,2,4] => 4 [3,1,5,4,2] => 3 [3,2,1,4,5] => 1 [3,2,1,5,4] => 4 [3,2,4,1,5] => 2 [3,2,4,5,1] => 3 [3,2,5,1,4] => 3 [3,2,5,4,1] => 2 [3,4,1,2,5] => 4 [3,4,1,5,2] => 5 [3,4,2,1,5] => 3 [3,4,2,5,1] => 4 [3,4,5,1,2] => 4 [3,4,5,2,1] => 5 [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] => 5 [3,5,4,2,1] => 4 [4,1,2,3,5] => 3 [4,1,2,5,3] => 4 [4,1,3,2,5] => 2 [4,1,3,5,2] => 3 [4,1,5,2,3] => 5 [4,1,5,3,2] => 4 [4,2,1,3,5] => 2 [4,2,1,5,3] => 3 [4,2,3,1,5] => 1 [4,2,3,5,1] => 2 [4,2,5,1,3] => 4 [4,2,5,3,1] => 3 [4,3,1,2,5] => 3 [4,3,1,5,2] => 4 [4,3,2,1,5] => 4 [4,3,2,5,1] => 5 [4,3,5,1,2] => 5 [4,3,5,2,1] => 4 [4,5,1,2,3] => 4 [4,5,1,3,2] => 5 [4,5,2,1,3] => 5 [4,5,2,3,1] => 4 [4,5,3,1,2] => 4 [4,5,3,2,1] => 3 [5,1,2,3,4] => 4 [5,1,2,4,3] => 3 [5,1,3,2,4] => 3 [5,1,3,4,2] => 2 [5,1,4,2,3] => 4 [5,1,4,3,2] => 5 [5,2,1,3,4] => 3 [5,2,1,4,3] => 2 [5,2,3,1,4] => 2 [5,2,3,4,1] => 1 [5,2,4,1,3] => 3 [5,2,4,3,1] => 4 [5,3,1,2,4] => 4 [5,3,1,4,2] => 3 [5,3,2,1,4] => 5 [5,3,2,4,1] => 4 [5,3,4,1,2] => 4 [5,3,4,2,1] => 5 [5,4,1,2,3] => 5 [5,4,1,3,2] => 4 [5,4,2,1,3] => 4 [5,4,2,3,1] => 5 [5,4,3,1,2] => 3 [5,4,3,2,1] => 4 [1,2,3,4,5,6] => 0 [1,2,3,4,6,5] => 3 [1,2,3,5,4,6] => 3 [1,2,3,5,6,4] => 4 [1,2,3,6,4,5] => 4 [1,2,3,6,5,4] => 3 [1,2,4,3,5,6] => 3 [1,2,4,3,6,5] => 6 [1,2,4,5,3,6] => 4 [1,2,4,5,6,3] => 5 [1,2,4,6,3,5] => 5 [1,2,4,6,5,3] => 4 [1,2,5,3,4,6] => 4 [1,2,5,3,6,4] => 5 [1,2,5,4,3,6] => 3 [1,2,5,4,6,3] => 4 [1,2,5,6,3,4] => 6 [1,2,5,6,4,3] => 5 [1,2,6,3,4,5] => 5 [1,2,6,3,5,4] => 4 [1,2,6,4,3,5] => 4 [1,2,6,4,5,3] => 3 [1,2,6,5,3,4] => 5 [1,2,6,5,4,3] => 6 [1,3,2,4,5,6] => 3 [1,3,2,4,6,5] => 6 [1,3,2,5,4,6] => 6 [1,3,2,5,6,4] => 7 [1,3,2,6,4,5] => 7 [1,3,2,6,5,4] => 6 [1,3,4,2,5,6] => 4 [1,3,4,2,6,5] => 7 [1,3,4,5,2,6] => 5 [1,3,4,5,6,2] => 6 [1,3,4,6,2,5] => 6 [1,3,4,6,5,2] => 5 [1,3,5,2,4,6] => 5 [1,3,5,2,6,4] => 6 [1,3,5,4,2,6] => 4 [1,3,5,4,6,2] => 5 [1,3,5,6,2,4] => 7 [1,3,5,6,4,2] => 6 [1,3,6,2,4,5] => 6 [1,3,6,2,5,4] => 5 [1,3,6,4,2,5] => 5 [1,3,6,4,5,2] => 4 [1,3,6,5,2,4] => 6 [1,3,6,5,4,2] => 7 [1,4,2,3,5,6] => 4 [1,4,2,3,6,5] => 7 [1,4,2,5,3,6] => 5 [1,4,2,5,6,3] => 6 [1,4,2,6,3,5] => 6 [1,4,2,6,5,3] => 5 [1,4,3,2,5,6] => 3 [1,4,3,2,6,5] => 6 [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] => 4 [1,4,5,2,3,6] => 6 [1,4,5,2,6,3] => 7 [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] => 7 [1,4,6,2,5,3] => 6 [1,4,6,3,2,5] => 6 [1,4,6,3,5,2] => 5 [1,4,6,5,2,3] => 7 [1,4,6,5,3,2] => 6 [1,5,2,3,4,6] => 5 [1,5,2,3,6,4] => 6 [1,5,2,4,3,6] => 4 [1,5,2,4,6,3] => 5 [1,5,2,6,3,4] => 7 [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] => 3 [1,5,3,4,6,2] => 4 [1,5,3,6,2,4] => 6 [1,5,3,6,4,2] => 5 [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] => 6 [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] => 6 [1,5,6,4,2,3] => 6 [1,5,6,4,3,2] => 5 [1,6,2,3,4,5] => 6 [1,6,2,3,5,4] => 5 [1,6,2,4,3,5] => 5 [1,6,2,4,5,3] => 4 [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] => 4 [1,6,3,4,2,5] => 4 [1,6,3,4,5,2] => 3 [1,6,3,5,2,4] => 5 [1,6,3,5,4,2] => 6 [1,6,4,2,3,5] => 6 [1,6,4,2,5,3] => 5 [1,6,4,3,2,5] => 7 [1,6,4,3,5,2] => 6 [1,6,4,5,2,3] => 6 [1,6,4,5,3,2] => 7 [1,6,5,2,3,4] => 7 [1,6,5,2,4,3] => 6 [1,6,5,3,2,4] => 6 [1,6,5,3,4,2] => 7 [1,6,5,4,2,3] => 5 [1,6,5,4,3,2] => 6 [2,1,3,4,5,6] => 1 [2,1,3,4,6,5] => 4 [2,1,3,5,4,6] => 4 [2,1,3,5,6,4] => 5 [2,1,3,6,4,5] => 5 [2,1,3,6,5,4] => 4 [2,1,4,3,5,6] => 4 [2,1,4,3,6,5] => 7 [2,1,4,5,3,6] => 5 [2,1,4,5,6,3] => 6 [2,1,4,6,3,5] => 6 [2,1,4,6,5,3] => 5 [2,1,5,3,4,6] => 5 [2,1,5,3,6,4] => 6 [2,1,5,4,3,6] => 4 [2,1,5,4,6,3] => 5 [2,1,5,6,3,4] => 7 [2,1,5,6,4,3] => 6 [2,1,6,3,4,5] => 6 [2,1,6,3,5,4] => 5 [2,1,6,4,3,5] => 5 [2,1,6,4,5,3] => 4 [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] => 5 [2,3,1,5,4,6] => 5 [2,3,1,5,6,4] => 6 [2,3,1,6,4,5] => 6 [2,3,1,6,5,4] => 5 [2,3,4,1,5,6] => 3 [2,3,4,1,6,5] => 6 [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] => 4 [2,3,5,1,4,6] => 4 [2,3,5,1,6,4] => 5 [2,3,5,4,1,6] => 3 [2,3,5,4,6,1] => 4 [2,3,5,6,1,4] => 6 [2,3,5,6,4,1] => 5 [2,3,6,1,4,5] => 5 [2,3,6,1,5,4] => 4 [2,3,6,4,1,5] => 4 [2,3,6,4,5,1] => 3 [2,3,6,5,1,4] => 5 [2,3,6,5,4,1] => 6 [2,4,1,3,5,6] => 3 [2,4,1,3,6,5] => 6 [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] => 4 [2,4,3,1,5,6] => 2 [2,4,3,1,6,5] => 5 [2,4,3,5,1,6] => 3 [2,4,3,5,6,1] => 4 [2,4,3,6,1,5] => 4 [2,4,3,6,5,1] => 3 [2,4,5,1,3,6] => 5 [2,4,5,1,6,3] => 6 [2,4,5,3,1,6] => 4 [2,4,5,3,6,1] => 5 [2,4,5,6,1,3] => 5 [2,4,5,6,3,1] => 6 [2,4,6,1,3,5] => 6 [2,4,6,1,5,3] => 5 [2,4,6,3,1,5] => 5 [2,4,6,3,5,1] => 4 [2,4,6,5,1,3] => 6 [2,4,6,5,3,1] => 5 [2,5,1,3,4,6] => 4 [2,5,1,3,6,4] => 5 [2,5,1,4,3,6] => 3 [2,5,1,4,6,3] => 4 [2,5,1,6,3,4] => 6 [2,5,1,6,4,3] => 5 [2,5,3,1,4,6] => 3 [2,5,3,1,6,4] => 4 [2,5,3,4,1,6] => 2 [2,5,3,4,6,1] => 3 [2,5,3,6,1,4] => 5 [2,5,3,6,4,1] => 4 [2,5,4,1,3,6] => 4 [2,5,4,1,6,3] => 5 [2,5,4,3,1,6] => 5 [2,5,4,3,6,1] => 6 [2,5,4,6,1,3] => 6 [2,5,4,6,3,1] => 5 [2,5,6,1,3,4] => 5 [2,5,6,1,4,3] => 6 [2,5,6,3,1,4] => 6 [2,5,6,3,4,1] => 5 [2,5,6,4,1,3] => 5 [2,5,6,4,3,1] => 4 [2,6,1,3,4,5] => 5 [2,6,1,3,5,4] => 4 [2,6,1,4,3,5] => 4 [2,6,1,4,5,3] => 3 [2,6,1,5,3,4] => 5 [2,6,1,5,4,3] => 6 [2,6,3,1,4,5] => 4 [2,6,3,1,5,4] => 3 [2,6,3,4,1,5] => 3 [2,6,3,4,5,1] => 2 [2,6,3,5,1,4] => 4 [2,6,3,5,4,1] => 5 [2,6,4,1,3,5] => 5 [2,6,4,1,5,3] => 4 [2,6,4,3,1,5] => 6 [2,6,4,3,5,1] => 5 [2,6,4,5,1,3] => 5 [2,6,4,5,3,1] => 6 [2,6,5,1,3,4] => 6 [2,6,5,1,4,3] => 5 [2,6,5,3,1,4] => 5 [2,6,5,3,4,1] => 6 [2,6,5,4,1,3] => 4 [2,6,5,4,3,1] => 5 [3,1,2,4,5,6] => 2 [3,1,2,4,6,5] => 5 [3,1,2,5,4,6] => 5 [3,1,2,5,6,4] => 6 [3,1,2,6,4,5] => 6 [3,1,2,6,5,4] => 5 [3,1,4,2,5,6] => 3 [3,1,4,2,6,5] => 6 [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] => 4 [3,1,5,2,4,6] => 4 [3,1,5,2,6,4] => 5 [3,1,5,4,2,6] => 3 [3,1,5,4,6,2] => 4 [3,1,5,6,2,4] => 6 [3,1,5,6,4,2] => 5 [3,1,6,2,4,5] => 5 [3,1,6,2,5,4] => 4 [3,1,6,4,2,5] => 4 [3,1,6,4,5,2] => 3 [3,1,6,5,2,4] => 5 [3,1,6,5,4,2] => 6 [3,2,1,4,5,6] => 1 [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] => 4 [3,2,4,1,5,6] => 2 [3,2,4,1,6,5] => 5 [3,2,4,5,1,6] => 3 [3,2,4,5,6,1] => 4 [3,2,4,6,1,5] => 4 [3,2,4,6,5,1] => 3 [3,2,5,1,4,6] => 3 [3,2,5,1,6,4] => 4 [3,2,5,4,1,6] => 2 [3,2,5,4,6,1] => 3 [3,2,5,6,1,4] => 5 [3,2,5,6,4,1] => 4 [3,2,6,1,4,5] => 4 [3,2,6,1,5,4] => 3 [3,2,6,4,1,5] => 3 [3,2,6,4,5,1] => 2 [3,2,6,5,1,4] => 4 [3,2,6,5,4,1] => 5 [3,4,1,2,5,6] => 4 [3,4,1,2,6,5] => 7 [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] => 5 [3,4,2,1,5,6] => 3 [3,4,2,1,6,5] => 6 [3,4,2,5,1,6] => 4 [3,4,2,5,6,1] => 5 [3,4,2,6,1,5] => 5 [3,4,2,6,5,1] => 4 [3,4,5,1,2,6] => 4 [3,4,5,1,6,2] => 5 [3,4,5,2,1,6] => 5 [3,4,5,2,6,1] => 6 [3,4,5,6,1,2] => 6 [3,4,5,6,2,1] => 5 [3,4,6,1,2,5] => 5 [3,4,6,1,5,2] => 4 [3,4,6,2,1,5] => 6 [3,4,6,2,5,1] => 5 [3,4,6,5,1,2] => 5 [3,4,6,5,2,1] => 6 [3,5,1,2,4,6] => 5 [3,5,1,2,6,4] => 6 [3,5,1,4,2,6] => 4 [3,5,1,4,6,2] => 5 [3,5,1,6,2,4] => 7 [3,5,1,6,4,2] => 6 [3,5,2,1,4,6] => 4 [3,5,2,1,6,4] => 5 [3,5,2,4,1,6] => 3 [3,5,2,4,6,1] => 4 [3,5,2,6,1,4] => 6 [3,5,2,6,4,1] => 5 [3,5,4,1,2,6] => 5 [3,5,4,1,6,2] => 6 [3,5,4,2,1,6] => 4 [3,5,4,2,6,1] => 5 [3,5,4,6,1,2] => 5 [3,5,4,6,2,1] => 6 [3,5,6,1,2,4] => 6 [3,5,6,1,4,2] => 5 [3,5,6,2,1,4] => 5 [3,5,6,2,4,1] => 6 [3,5,6,4,1,2] => 4 [3,5,6,4,2,1] => 5 [3,6,1,2,4,5] => 6 [3,6,1,2,5,4] => 5 [3,6,1,4,2,5] => 5 [3,6,1,4,5,2] => 4 [3,6,1,5,2,4] => 6 [3,6,1,5,4,2] => 7 [3,6,2,1,4,5] => 5 [3,6,2,1,5,4] => 4 [3,6,2,4,1,5] => 4 [3,6,2,4,5,1] => 3 [3,6,2,5,1,4] => 5 [3,6,2,5,4,1] => 6 [3,6,4,1,2,5] => 6 [3,6,4,1,5,2] => 5 [3,6,4,2,1,5] => 5 [3,6,4,2,5,1] => 4 [3,6,4,5,1,2] => 6 [3,6,4,5,2,1] => 5 [3,6,5,1,2,4] => 5 [3,6,5,1,4,2] => 6 [3,6,5,2,1,4] => 6 [3,6,5,2,4,1] => 5 [3,6,5,4,1,2] => 5 [3,6,5,4,2,1] => 4 [4,1,2,3,5,6] => 3 [4,1,2,3,6,5] => 6 [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] => 4 [4,1,3,2,5,6] => 2 [4,1,3,2,6,5] => 5 [4,1,3,5,2,6] => 3 [4,1,3,5,6,2] => 4 [4,1,3,6,2,5] => 4 [4,1,3,6,5,2] => 3 [4,1,5,2,3,6] => 5 [4,1,5,2,6,3] => 6 [4,1,5,3,2,6] => 4 [4,1,5,3,6,2] => 5 [4,1,5,6,2,3] => 5 [4,1,5,6,3,2] => 6 [4,1,6,2,3,5] => 6 [4,1,6,2,5,3] => 5 [4,1,6,3,2,5] => 5 [4,1,6,3,5,2] => 4 [4,1,6,5,2,3] => 6 [4,1,6,5,3,2] => 5 [4,2,1,3,5,6] => 2 [4,2,1,3,6,5] => 5 [4,2,1,5,3,6] => 3 [4,2,1,5,6,3] => 4 [4,2,1,6,3,5] => 4 [4,2,1,6,5,3] => 3 [4,2,3,1,5,6] => 1 [4,2,3,1,6,5] => 4 [4,2,3,5,1,6] => 2 [4,2,3,5,6,1] => 3 [4,2,3,6,1,5] => 3 [4,2,3,6,5,1] => 2 [4,2,5,1,3,6] => 4 [4,2,5,1,6,3] => 5 [4,2,5,3,1,6] => 3 [4,2,5,3,6,1] => 4 [4,2,5,6,1,3] => 4 [4,2,5,6,3,1] => 5 [4,2,6,1,3,5] => 5 [4,2,6,1,5,3] => 4 [4,2,6,3,1,5] => 4 [4,2,6,3,5,1] => 3 [4,2,6,5,1,3] => 5 [4,2,6,5,3,1] => 4 [4,3,1,2,5,6] => 3 [4,3,1,2,6,5] => 6 [4,3,1,5,2,6] => 4 [4,3,1,5,6,2] => 5 [4,3,1,6,2,5] => 5 [4,3,1,6,5,2] => 4 [4,3,2,1,5,6] => 4 [4,3,2,1,6,5] => 7 [4,3,2,5,1,6] => 5 [4,3,2,5,6,1] => 6 [4,3,2,6,1,5] => 6 [4,3,2,6,5,1] => 5 [4,3,5,1,2,6] => 5 [4,3,5,1,6,2] => 6 [4,3,5,2,1,6] => 4 [4,3,5,2,6,1] => 5 [4,3,5,6,1,2] => 5 [4,3,5,6,2,1] => 6 [4,3,6,1,2,5] => 6 [4,3,6,1,5,2] => 5 [4,3,6,2,1,5] => 5 [4,3,6,2,5,1] => 4 [4,3,6,5,1,2] => 6 [4,3,6,5,2,1] => 5 [4,5,1,2,3,6] => 4 [4,5,1,2,6,3] => 5 [4,5,1,3,2,6] => 5 [4,5,1,3,6,2] => 6 [4,5,1,6,2,3] => 6 [4,5,1,6,3,2] => 5 [4,5,2,1,3,6] => 5 [4,5,2,1,6,3] => 6 [4,5,2,3,1,6] => 4 [4,5,2,3,6,1] => 5 [4,5,2,6,1,3] => 5 [4,5,2,6,3,1] => 6 [4,5,3,1,2,6] => 4 [4,5,3,1,6,2] => 5 [4,5,3,2,1,6] => 3 [4,5,3,2,6,1] => 4 [4,5,3,6,1,2] => 4 [4,5,3,6,2,1] => 5 [4,5,6,1,2,3] => 7 [4,5,6,1,3,2] => 6 [4,5,6,2,1,3] => 6 [4,5,6,2,3,1] => 5 [4,5,6,3,1,2] => 5 [4,5,6,3,2,1] => 6 [4,6,1,2,3,5] => 5 [4,6,1,2,5,3] => 4 [4,6,1,3,2,5] => 6 [4,6,1,3,5,2] => 5 [4,6,1,5,2,3] => 5 [4,6,1,5,3,2] => 6 [4,6,2,1,3,5] => 6 [4,6,2,1,5,3] => 5 [4,6,2,3,1,5] => 5 [4,6,2,3,5,1] => 4 [4,6,2,5,1,3] => 6 [4,6,2,5,3,1] => 5 [4,6,3,1,2,5] => 5 [4,6,3,1,5,2] => 4 [4,6,3,2,1,5] => 4 [4,6,3,2,5,1] => 3 [4,6,3,5,1,2] => 5 [4,6,3,5,2,1] => 4 [4,6,5,1,2,3] => 6 [4,6,5,1,3,2] => 7 [4,6,5,2,1,3] => 5 [4,6,5,2,3,1] => 6 [4,6,5,3,1,2] => 6 [4,6,5,3,2,1] => 5 [5,1,2,3,4,6] => 4 [5,1,2,3,6,4] => 5 [5,1,2,4,3,6] => 3 [5,1,2,4,6,3] => 4 [5,1,2,6,3,4] => 6 [5,1,2,6,4,3] => 5 [5,1,3,2,4,6] => 3 [5,1,3,2,6,4] => 4 [5,1,3,4,2,6] => 2 [5,1,3,4,6,2] => 3 [5,1,3,6,2,4] => 5 [5,1,3,6,4,2] => 4 [5,1,4,2,3,6] => 4 [5,1,4,2,6,3] => 5 [5,1,4,3,2,6] => 5 [5,1,4,3,6,2] => 6 [5,1,4,6,2,3] => 6 [5,1,4,6,3,2] => 5 [5,1,6,2,3,4] => 5 [5,1,6,2,4,3] => 6 [5,1,6,3,2,4] => 6 [5,1,6,3,4,2] => 5 [5,1,6,4,2,3] => 5 [5,1,6,4,3,2] => 4 [5,2,1,3,4,6] => 3 [5,2,1,3,6,4] => 4 [5,2,1,4,3,6] => 2 [5,2,1,4,6,3] => 3 [5,2,1,6,3,4] => 5 [5,2,1,6,4,3] => 4 [5,2,3,1,4,6] => 2 [5,2,3,1,6,4] => 3 [5,2,3,4,1,6] => 1 [5,2,3,4,6,1] => 2 [5,2,3,6,1,4] => 4 [5,2,3,6,4,1] => 3 [5,2,4,1,3,6] => 3 [5,2,4,1,6,3] => 4 [5,2,4,3,1,6] => 4 [5,2,4,3,6,1] => 5 [5,2,4,6,1,3] => 5 [5,2,4,6,3,1] => 4 [5,2,6,1,3,4] => 4 [5,2,6,1,4,3] => 5 [5,2,6,3,1,4] => 5 [5,2,6,3,4,1] => 4 [5,2,6,4,1,3] => 4 [5,2,6,4,3,1] => 3 [5,3,1,2,4,6] => 4 [5,3,1,2,6,4] => 5 [5,3,1,4,2,6] => 3 [5,3,1,4,6,2] => 4 [5,3,1,6,2,4] => 6 [5,3,1,6,4,2] => 5 [5,3,2,1,4,6] => 5 [5,3,2,1,6,4] => 6 [5,3,2,4,1,6] => 4 [5,3,2,4,6,1] => 5 [5,3,2,6,1,4] => 7 [5,3,2,6,4,1] => 6 [5,3,4,1,2,6] => 4 [5,3,4,1,6,2] => 5 [5,3,4,2,1,6] => 5 [5,3,4,2,6,1] => 6 [5,3,4,6,1,2] => 6 [5,3,4,6,2,1] => 5 [5,3,6,1,2,4] => 5 [5,3,6,1,4,2] => 6 [5,3,6,2,1,4] => 6 [5,3,6,2,4,1] => 5 [5,3,6,4,1,2] => 5 [5,3,6,4,2,1] => 4 [5,4,1,2,3,6] => 5 [5,4,1,2,6,3] => 6 [5,4,1,3,2,6] => 4 [5,4,1,3,6,2] => 5 [5,4,1,6,2,3] => 5 [5,4,1,6,3,2] => 6 [5,4,2,1,3,6] => 4 [5,4,2,1,6,3] => 5 [5,4,2,3,1,6] => 5 [5,4,2,3,6,1] => 6 [5,4,2,6,1,3] => 6 [5,4,2,6,3,1] => 5 [5,4,3,1,2,6] => 3 [5,4,3,1,6,2] => 4 [5,4,3,2,1,6] => 4 [5,4,3,2,6,1] => 5 [5,4,3,6,1,2] => 5 [5,4,3,6,2,1] => 4 [5,4,6,1,2,3] => 6 [5,4,6,1,3,2] => 5 [5,4,6,2,1,3] => 7 [5,4,6,2,3,1] => 6 [5,4,6,3,1,2] => 6 [5,4,6,3,2,1] => 5 [5,6,1,2,3,4] => 6 [5,6,1,2,4,3] => 5 [5,6,1,3,2,4] => 5 [5,6,1,3,4,2] => 6 [5,6,1,4,2,3] => 4 [5,6,1,4,3,2] => 5 [5,6,2,1,3,4] => 5 [5,6,2,1,4,3] => 6 [5,6,2,3,1,4] => 6 [5,6,2,3,4,1] => 5 [5,6,2,4,1,3] => 5 [5,6,2,4,3,1] => 4 [5,6,3,1,2,4] => 4 [5,6,3,1,4,2] => 5 [5,6,3,2,1,4] => 5 [5,6,3,2,4,1] => 4 [5,6,3,4,1,2] => 4 [5,6,3,4,2,1] => 3 [5,6,4,1,2,3] => 5 [5,6,4,1,3,2] => 6 [5,6,4,2,1,3] => 6 [5,6,4,2,3,1] => 5 [5,6,4,3,1,2] => 7 [5,6,4,3,2,1] => 6 [6,1,2,3,4,5] => 5 [6,1,2,3,5,4] => 4 [6,1,2,4,3,5] => 4 [6,1,2,4,5,3] => 3 [6,1,2,5,3,4] => 5 [6,1,2,5,4,3] => 6 [6,1,3,2,4,5] => 4 [6,1,3,2,5,4] => 3 [6,1,3,4,2,5] => 3 [6,1,3,4,5,2] => 2 [6,1,3,5,2,4] => 4 [6,1,3,5,4,2] => 5 [6,1,4,2,3,5] => 5 [6,1,4,2,5,3] => 4 [6,1,4,3,2,5] => 6 [6,1,4,3,5,2] => 5 [6,1,4,5,2,3] => 5 [6,1,4,5,3,2] => 6 [6,1,5,2,3,4] => 6 [6,1,5,2,4,3] => 5 [6,1,5,3,2,4] => 5 [6,1,5,3,4,2] => 6 [6,1,5,4,2,3] => 4 [6,1,5,4,3,2] => 5 [6,2,1,3,4,5] => 4 [6,2,1,3,5,4] => 3 [6,2,1,4,3,5] => 3 [6,2,1,4,5,3] => 2 [6,2,1,5,3,4] => 4 [6,2,1,5,4,3] => 5 [6,2,3,1,4,5] => 3 [6,2,3,1,5,4] => 2 [6,2,3,4,1,5] => 2 [6,2,3,4,5,1] => 1 [6,2,3,5,1,4] => 3 [6,2,3,5,4,1] => 4 [6,2,4,1,3,5] => 4 [6,2,4,1,5,3] => 3 [6,2,4,3,1,5] => 5 [6,2,4,3,5,1] => 4 [6,2,4,5,1,3] => 4 [6,2,4,5,3,1] => 5 [6,2,5,1,3,4] => 5 [6,2,5,1,4,3] => 4 [6,2,5,3,1,4] => 4 [6,2,5,3,4,1] => 5 [6,2,5,4,1,3] => 3 [6,2,5,4,3,1] => 4 [6,3,1,2,4,5] => 5 [6,3,1,2,5,4] => 4 [6,3,1,4,2,5] => 4 [6,3,1,4,5,2] => 3 [6,3,1,5,2,4] => 5 [6,3,1,5,4,2] => 6 [6,3,2,1,4,5] => 6 [6,3,2,1,5,4] => 5 [6,3,2,4,1,5] => 5 [6,3,2,4,5,1] => 4 [6,3,2,5,1,4] => 6 [6,3,2,5,4,1] => 7 [6,3,4,1,2,5] => 5 [6,3,4,1,5,2] => 4 [6,3,4,2,1,5] => 6 [6,3,4,2,5,1] => 5 [6,3,4,5,1,2] => 5 [6,3,4,5,2,1] => 6 [6,3,5,1,2,4] => 6 [6,3,5,1,4,2] => 5 [6,3,5,2,1,4] => 5 [6,3,5,2,4,1] => 6 [6,3,5,4,1,2] => 4 [6,3,5,4,2,1] => 5 [6,4,1,2,3,5] => 6 [6,4,1,2,5,3] => 5 [6,4,1,3,2,5] => 5 [6,4,1,3,5,2] => 4 [6,4,1,5,2,3] => 6 [6,4,1,5,3,2] => 5 [6,4,2,1,3,5] => 5 [6,4,2,1,5,3] => 4 [6,4,2,3,1,5] => 6 [6,4,2,3,5,1] => 5 [6,4,2,5,1,3] => 5 [6,4,2,5,3,1] => 6 [6,4,3,1,2,5] => 4 [6,4,3,1,5,2] => 3 [6,4,3,2,1,5] => 5 [6,4,3,2,5,1] => 4 [6,4,3,5,1,2] => 4 [6,4,3,5,2,1] => 5 [6,4,5,1,2,3] => 5 [6,4,5,1,3,2] => 6 [6,4,5,2,1,3] => 6 [6,4,5,2,3,1] => 7 [6,4,5,3,1,2] => 5 [6,4,5,3,2,1] => 6 [6,5,1,2,3,4] => 5 [6,5,1,2,4,3] => 6 [6,5,1,3,2,4] => 6 [6,5,1,3,4,2] => 5 [6,5,1,4,2,3] => 5 [6,5,1,4,3,2] => 4 [6,5,2,1,3,4] => 6 [6,5,2,1,4,3] => 5 [6,5,2,3,1,4] => 5 [6,5,2,3,4,1] => 6 [6,5,2,4,1,3] => 4 [6,5,2,4,3,1] => 5 [6,5,3,1,2,4] => 5 [6,5,3,1,4,2] => 4 [6,5,3,2,1,4] => 4 [6,5,3,2,4,1] => 5 [6,5,3,4,1,2] => 3 [6,5,3,4,2,1] => 4 [6,5,4,1,2,3] => 6 [6,5,4,1,3,2] => 5 [6,5,4,2,1,3] => 5 [6,5,4,2,3,1] => 6 [6,5,4,3,1,2] => 6 [6,5,4,3,2,1] => 7 [1,2,3,4,5,6,7] => 0 [1,2,3,4,5,7,6] => 3 [1,2,3,4,6,5,7] => 3 [1,2,3,4,6,7,5] => 4 [1,2,3,4,7,5,6] => 4 [1,2,3,4,7,6,5] => 3 [1,2,3,5,4,6,7] => 3 [1,2,3,5,4,7,6] => 6 [1,2,3,5,6,4,7] => 4 [1,2,3,5,6,7,4] => 5 [1,2,3,5,7,4,6] => 5 [1,2,3,5,7,6,4] => 4 [1,2,3,6,4,5,7] => 4 [1,2,3,6,4,7,5] => 5 [1,2,3,6,5,4,7] => 3 [1,2,3,6,5,7,4] => 4 [1,2,3,6,7,4,5] => 6 [1,2,3,6,7,5,4] => 5 [1,2,3,7,4,5,6] => 5 [1,2,3,7,4,6,5] => 4 [1,2,3,7,5,4,6] => 4 [1,2,3,7,5,6,4] => 3 [1,2,3,7,6,4,5] => 5 [1,2,3,7,6,5,4] => 6 [1,2,4,3,5,6,7] => 3 [1,2,4,3,5,7,6] => 6 [1,2,4,3,6,5,7] => 6 [1,2,4,3,6,7,5] => 7 [1,2,4,3,7,5,6] => 7 [1,2,4,3,7,6,5] => 6 [1,2,4,5,3,6,7] => 4 [1,2,4,5,3,7,6] => 7 [1,2,4,5,6,3,7] => 5 [1,2,4,5,6,7,3] => 6 [1,2,4,5,7,3,6] => 6 [1,2,4,5,7,6,3] => 5 [1,2,4,6,3,5,7] => 5 [1,2,4,6,3,7,5] => 6 [1,2,4,6,5,3,7] => 4 [1,2,4,6,5,7,3] => 5 [1,2,4,6,7,3,5] => 7 [1,2,4,6,7,5,3] => 6 [1,2,4,7,3,5,6] => 6 [1,2,4,7,3,6,5] => 5 [1,2,4,7,5,3,6] => 5 [1,2,4,7,5,6,3] => 4 [1,2,4,7,6,3,5] => 6 [1,2,4,7,6,5,3] => 7 [1,2,5,3,4,6,7] => 4 [1,2,5,3,4,7,6] => 7 [1,2,5,3,6,4,7] => 5 [1,2,5,3,6,7,4] => 6 [1,2,5,3,7,4,6] => 6 [1,2,5,3,7,6,4] => 5 [1,2,5,4,3,6,7] => 3 [1,2,5,4,3,7,6] => 6 [1,2,5,4,6,3,7] => 4 [1,2,5,4,6,7,3] => 5 [1,2,5,4,7,3,6] => 5 [1,2,5,4,7,6,3] => 4 [1,2,5,6,3,4,7] => 6 [1,2,5,6,3,7,4] => 7 [1,2,5,6,4,3,7] => 5 [1,2,5,6,4,7,3] => 6 [1,2,5,6,7,3,4] => 6 [1,2,5,6,7,4,3] => 7 [1,2,5,7,3,4,6] => 7 [1,2,5,7,3,6,4] => 6 [1,2,5,7,4,3,6] => 6 [1,2,5,7,4,6,3] => 5 [1,2,5,7,6,3,4] => 7 [1,2,5,7,6,4,3] => 6 [1,2,6,3,4,5,7] => 5 [1,2,6,3,4,7,5] => 6 [1,2,6,3,5,4,7] => 4 [1,2,6,3,5,7,4] => 5 [1,2,6,3,7,4,5] => 7 [1,2,6,3,7,5,4] => 6 [1,2,6,4,3,5,7] => 4 [1,2,6,4,3,7,5] => 5 [1,2,6,4,5,3,7] => 3 [1,2,6,4,5,7,3] => 4 [1,2,6,4,7,3,5] => 6 [1,2,6,4,7,5,3] => 5 [1,2,6,5,3,4,7] => 5 [1,2,6,5,3,7,4] => 6 [1,2,6,5,4,3,7] => 6 [1,2,6,5,4,7,3] => 7 [1,2,6,5,7,3,4] => 7 [1,2,6,5,7,4,3] => 6 [1,2,6,7,3,4,5] => 6 [1,2,6,7,3,5,4] => 7 [1,2,6,7,4,3,5] => 7 [1,2,6,7,4,5,3] => 6 [1,2,6,7,5,3,4] => 6 [1,2,6,7,5,4,3] => 5 [1,2,7,3,4,5,6] => 6 [1,2,7,3,4,6,5] => 5 [1,2,7,3,5,4,6] => 5 [1,2,7,3,5,6,4] => 4 [1,2,7,3,6,4,5] => 6 [1,2,7,3,6,5,4] => 7 [1,2,7,4,3,5,6] => 5 [1,2,7,4,3,6,5] => 4 [1,2,7,4,5,3,6] => 4 [1,2,7,4,5,6,3] => 3 [1,2,7,4,6,3,5] => 5 [1,2,7,4,6,5,3] => 6 [1,2,7,5,3,4,6] => 6 [1,2,7,5,3,6,4] => 5 [1,2,7,5,4,3,6] => 7 [1,2,7,5,4,6,3] => 6 [1,2,7,5,6,3,4] => 6 [1,2,7,5,6,4,3] => 7 [1,2,7,6,3,4,5] => 7 [1,2,7,6,3,5,4] => 6 [1,2,7,6,4,3,5] => 6 [1,2,7,6,4,5,3] => 7 [1,2,7,6,5,3,4] => 5 [1,2,7,6,5,4,3] => 6 [1,3,2,4,5,6,7] => 3 [1,3,2,4,5,7,6] => 6 [1,3,2,4,6,5,7] => 6 [1,3,2,4,6,7,5] => 7 [1,3,2,4,7,5,6] => 7 [1,3,2,4,7,6,5] => 6 [1,3,2,5,4,6,7] => 6 [1,3,2,5,4,7,6] => 9 [1,3,2,5,6,4,7] => 7 [1,3,2,5,6,7,4] => 8 [1,3,2,5,7,4,6] => 8 [1,3,2,5,7,6,4] => 7 [1,3,2,6,4,5,7] => 7 [1,3,2,6,4,7,5] => 8 [1,3,2,6,5,4,7] => 6 [1,3,2,6,5,7,4] => 7 [1,3,2,6,7,4,5] => 9 [1,3,2,6,7,5,4] => 8 [1,3,2,7,4,5,6] => 8 [1,3,2,7,4,6,5] => 7 [1,3,2,7,5,4,6] => 7 [1,3,2,7,5,6,4] => 6 [1,3,2,7,6,4,5] => 8 [1,3,2,7,6,5,4] => 9 [1,3,4,2,5,6,7] => 4 [1,3,4,2,5,7,6] => 7 [1,3,4,2,6,5,7] => 7 [1,3,4,2,6,7,5] => 8 [1,3,4,2,7,5,6] => 8 [1,3,4,2,7,6,5] => 7 [1,3,4,5,2,6,7] => 5 [1,3,4,5,2,7,6] => 8 [1,3,4,5,6,2,7] => 6 [1,3,4,5,6,7,2] => 7 [1,3,4,5,7,2,6] => 7 [1,3,4,5,7,6,2] => 6 [1,3,4,6,2,5,7] => 6 [1,3,4,6,2,7,5] => 7 [1,3,4,6,5,2,7] => 5 [1,3,4,6,5,7,2] => 6 [1,3,4,6,7,2,5] => 8 [1,3,4,6,7,5,2] => 7 [1,3,4,7,2,5,6] => 7 [1,3,4,7,2,6,5] => 6 [1,3,4,7,5,2,6] => 6 [1,3,4,7,5,6,2] => 5 [1,3,4,7,6,2,5] => 7 [1,3,4,7,6,5,2] => 8 [1,3,5,2,4,6,7] => 5 [1,3,5,2,4,7,6] => 8 [1,3,5,2,6,4,7] => 6 [1,3,5,2,6,7,4] => 7 [1,3,5,2,7,4,6] => 7 [1,3,5,2,7,6,4] => 6 [1,3,5,4,2,6,7] => 4 [1,3,5,4,2,7,6] => 7 [1,3,5,4,6,2,7] => 5 [1,3,5,4,6,7,2] => 6 [1,3,5,4,7,2,6] => 6 [1,3,5,4,7,6,2] => 5 [1,3,5,6,2,4,7] => 7 [1,3,5,6,2,7,4] => 8 [1,3,5,6,4,2,7] => 6 [1,3,5,6,4,7,2] => 7 [1,3,5,6,7,2,4] => 7 [1,3,5,6,7,4,2] => 8 [1,3,5,7,2,4,6] => 8 [1,3,5,7,2,6,4] => 7 [1,3,5,7,4,2,6] => 7 [1,3,5,7,4,6,2] => 6 [1,3,5,7,6,2,4] => 8 [1,3,5,7,6,4,2] => 7 [1,3,6,2,4,5,7] => 6 [1,3,6,2,4,7,5] => 7 [1,3,6,2,5,4,7] => 5 [1,3,6,2,5,7,4] => 6 [1,3,6,2,7,4,5] => 8 [1,3,6,2,7,5,4] => 7 [1,3,6,4,2,5,7] => 5 [1,3,6,4,2,7,5] => 6 [1,3,6,4,5,2,7] => 4 [1,3,6,4,5,7,2] => 5 [1,3,6,4,7,2,5] => 7 [1,3,6,4,7,5,2] => 6 [1,3,6,5,2,4,7] => 6 [1,3,6,5,2,7,4] => 7 [1,3,6,5,4,2,7] => 7 [1,3,6,5,4,7,2] => 8 [1,3,6,5,7,2,4] => 8 [1,3,6,5,7,4,2] => 7 [1,3,6,7,2,4,5] => 7 [1,3,6,7,2,5,4] => 8 [1,3,6,7,4,2,5] => 8 [1,3,6,7,4,5,2] => 7 [1,3,6,7,5,2,4] => 7 [1,3,6,7,5,4,2] => 6 [1,3,7,2,4,5,6] => 7 [1,3,7,2,4,6,5] => 6 [1,3,7,2,5,4,6] => 6 [1,3,7,2,5,6,4] => 5 [1,3,7,2,6,4,5] => 7 [1,3,7,2,6,5,4] => 8 [1,3,7,4,2,5,6] => 6 [1,3,7,4,2,6,5] => 5 [1,3,7,4,5,2,6] => 5 [1,3,7,4,5,6,2] => 4 [1,3,7,4,6,2,5] => 6 [1,3,7,4,6,5,2] => 7 [1,3,7,5,2,4,6] => 7 [1,3,7,5,2,6,4] => 6 [1,3,7,5,4,2,6] => 8 [1,3,7,5,4,6,2] => 7 [1,3,7,5,6,2,4] => 7 [1,3,7,5,6,4,2] => 8 [1,3,7,6,2,4,5] => 8 [1,3,7,6,2,5,4] => 7 [1,3,7,6,4,2,5] => 7 [1,3,7,6,4,5,2] => 8 [1,3,7,6,5,2,4] => 6 [1,3,7,6,5,4,2] => 7 [1,4,2,3,5,6,7] => 4 [1,4,2,3,5,7,6] => 7 [1,4,2,3,6,5,7] => 7 [1,4,2,3,6,7,5] => 8 [1,4,2,3,7,5,6] => 8 [1,4,2,3,7,6,5] => 7 [1,4,2,5,3,6,7] => 5 [1,4,2,5,3,7,6] => 8 [1,4,2,5,6,3,7] => 6 [1,4,2,5,6,7,3] => 7 [1,4,2,5,7,3,6] => 7 [1,4,2,5,7,6,3] => 6 [1,4,2,6,3,5,7] => 6 [1,4,2,6,3,7,5] => 7 [1,4,2,6,5,3,7] => 5 [1,4,2,6,5,7,3] => 6 [1,4,2,6,7,3,5] => 8 [1,4,2,6,7,5,3] => 7 [1,4,2,7,3,5,6] => 7 [1,4,2,7,3,6,5] => 6 [1,4,2,7,5,3,6] => 6 [1,4,2,7,5,6,3] => 5 [1,4,2,7,6,3,5] => 7 [1,4,2,7,6,5,3] => 8 [1,4,3,2,5,6,7] => 3 [1,4,3,2,5,7,6] => 6 [1,4,3,2,6,5,7] => 6 [1,4,3,2,6,7,5] => 7 [1,4,3,2,7,5,6] => 7 [1,4,3,2,7,6,5] => 6 [1,4,3,5,2,6,7] => 4 [1,4,3,5,2,7,6] => 7 [1,4,3,5,6,2,7] => 5 [1,4,3,5,6,7,2] => 6 [1,4,3,5,7,2,6] => 6 [1,4,3,5,7,6,2] => 5 [1,4,3,6,2,5,7] => 5 [1,4,3,6,2,7,5] => 6 [1,4,3,6,5,2,7] => 4 [1,4,3,6,5,7,2] => 5 [1,4,3,6,7,2,5] => 7 [1,4,3,6,7,5,2] => 6 [1,4,3,7,2,5,6] => 6 [1,4,3,7,2,6,5] => 5 [1,4,3,7,5,2,6] => 5 [1,4,3,7,5,6,2] => 4 [1,4,3,7,6,2,5] => 6 [1,4,3,7,6,5,2] => 7 [1,4,5,2,3,6,7] => 6 [1,4,5,2,3,7,6] => 9 [1,4,5,2,6,3,7] => 7 [1,4,5,2,6,7,3] => 8 [1,4,5,2,7,3,6] => 8 [1,4,5,2,7,6,3] => 7 [1,4,5,3,2,6,7] => 5 [1,4,5,3,2,7,6] => 8 [1,4,5,3,6,2,7] => 6 [1,4,5,3,6,7,2] => 7 [1,4,5,3,7,2,6] => 7 [1,4,5,3,7,6,2] => 6 [1,4,5,6,2,3,7] => 6 [1,4,5,6,2,7,3] => 7 [1,4,5,6,3,2,7] => 7 [1,4,5,6,3,7,2] => 8 [1,4,5,6,7,2,3] => 8 [1,4,5,6,7,3,2] => 7 [1,4,5,7,2,3,6] => 7 [1,4,5,7,2,6,3] => 6 [1,4,5,7,3,2,6] => 8 [1,4,5,7,3,6,2] => 7 [1,4,5,7,6,2,3] => 7 [1,4,5,7,6,3,2] => 8 [1,4,6,2,3,5,7] => 7 [1,4,6,2,3,7,5] => 8 [1,4,6,2,5,3,7] => 6 [1,4,6,2,5,7,3] => 7 [1,4,6,2,7,3,5] => 9 [1,4,6,2,7,5,3] => 8 [1,4,6,3,2,5,7] => 6 [1,4,6,3,2,7,5] => 7 [1,4,6,3,5,2,7] => 5 [1,4,6,3,5,7,2] => 6 [1,4,6,3,7,2,5] => 8 [1,4,6,3,7,5,2] => 7 [1,4,6,5,2,3,7] => 7 [1,4,6,5,2,7,3] => 8 [1,4,6,5,3,2,7] => 6 [1,4,6,5,3,7,2] => 7 ----------------------------------------------------------------------------- Created: Jan 08, 2018 at 23:01 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Aug 15, 2019 at 12:55 by Christian Stump