***************************************************************************** * 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: St001461 ----------------------------------------------------------------------------- Collection: Permutations ----------------------------------------------------------------------------- Description: The number of topologically connected components of the chord diagram of a permutation. The chord diagram of a permutation $\pi\in\mathfrak S_n$ is obtained by placing labels $1,\dots,n$ in cyclic order on a cycle and drawing a (straight) arc from $i$ to $\pi(i)$ for every label $i$. This statistic records the number of topologically connected components in the chord diagram. In particular, if two arcs cross, all four labels connected by the two arcs are in the same component. The permutation $\pi\in\mathfrak S_n$ stabilizes an interval $I=\{a,a+1,\dots,b\}$ if $\pi(I)=I$. It is stabilized-interval-free, if the only interval $\pi$ stablizes is $\{1,\dots,n\}$. Thus, this statistic is $1$ if $\pi$ is stabilized-interval-free. ----------------------------------------------------------------------------- References: [1] Callan, D. Counting Stabilized-Interval-Free Permutations [[arXiv:math/0310157]] [2] Coefficients of power series A(x) such that n-th term of A(x)^n = n! x^(n-1) for n > 0. [[OEIS:A075834]] ----------------------------------------------------------------------------- Code: def factor(pi): """ Return smallest i such that pi([1,...,i]) equals [1,...,i] """ pi = list(pi) for i in range(1, len(pi)+1): A = pi[:i] if max(A) == i: return Permutation(A), Permutation([e-i for e in pi[i:]]) def rotate(pi): r = len(pi) pi1 = [x % r + 1 for x in pi] return Permutation(pi1[-1:] + pi1[:-1]) def orbit(pi): o = [pi] new_pi = rotate(pi) while pi != new_pi: o += [new_pi] new_pi = rotate(new_pi) return o @cached_function def statistic(pi): o = orbit(pi) for pi in o: A, B = factor(pi) if len(B) > 0: return statistic(A) + statistic(B) return 1 ----------------------------------------------------------------------------- Statistic values: [1] => 1 [1,2] => 2 [2,1] => 1 [1,2,3] => 3 [1,3,2] => 2 [2,1,3] => 2 [2,3,1] => 1 [3,1,2] => 1 [3,2,1] => 2 [1,2,3,4] => 4 [1,2,4,3] => 3 [1,3,2,4] => 3 [1,3,4,2] => 2 [1,4,2,3] => 2 [1,4,3,2] => 3 [2,1,3,4] => 3 [2,1,4,3] => 2 [2,3,1,4] => 2 [2,3,4,1] => 1 [2,4,1,3] => 1 [2,4,3,1] => 2 [3,1,2,4] => 2 [3,1,4,2] => 1 [3,2,1,4] => 3 [3,2,4,1] => 2 [3,4,1,2] => 1 [3,4,2,1] => 1 [4,1,2,3] => 1 [4,1,3,2] => 2 [4,2,1,3] => 2 [4,2,3,1] => 3 [4,3,1,2] => 1 [4,3,2,1] => 2 [1,2,3,4,5] => 5 [1,2,3,5,4] => 4 [1,2,4,3,5] => 4 [1,2,4,5,3] => 3 [1,2,5,3,4] => 3 [1,2,5,4,3] => 4 [1,3,2,4,5] => 4 [1,3,2,5,4] => 3 [1,3,4,2,5] => 3 [1,3,4,5,2] => 2 [1,3,5,2,4] => 2 [1,3,5,4,2] => 3 [1,4,2,3,5] => 3 [1,4,2,5,3] => 2 [1,4,3,2,5] => 4 [1,4,3,5,2] => 3 [1,4,5,2,3] => 2 [1,4,5,3,2] => 2 [1,5,2,3,4] => 2 [1,5,2,4,3] => 3 [1,5,3,2,4] => 3 [1,5,3,4,2] => 4 [1,5,4,2,3] => 2 [1,5,4,3,2] => 3 [2,1,3,4,5] => 4 [2,1,3,5,4] => 3 [2,1,4,3,5] => 3 [2,1,4,5,3] => 2 [2,1,5,3,4] => 2 [2,1,5,4,3] => 3 [2,3,1,4,5] => 3 [2,3,1,5,4] => 2 [2,3,4,1,5] => 2 [2,3,4,5,1] => 1 [2,3,5,1,4] => 1 [2,3,5,4,1] => 2 [2,4,1,3,5] => 2 [2,4,1,5,3] => 1 [2,4,3,1,5] => 3 [2,4,3,5,1] => 2 [2,4,5,1,3] => 1 [2,4,5,3,1] => 1 [2,5,1,3,4] => 1 [2,5,1,4,3] => 2 [2,5,3,1,4] => 2 [2,5,3,4,1] => 3 [2,5,4,1,3] => 1 [2,5,4,3,1] => 2 [3,1,2,4,5] => 3 [3,1,2,5,4] => 2 [3,1,4,2,5] => 2 [3,1,4,5,2] => 1 [3,1,5,2,4] => 1 [3,1,5,4,2] => 2 [3,2,1,4,5] => 4 [3,2,1,5,4] => 3 [3,2,4,1,5] => 3 [3,2,4,5,1] => 2 [3,2,5,1,4] => 2 [3,2,5,4,1] => 3 [3,4,1,2,5] => 2 [3,4,1,5,2] => 1 [3,4,2,1,5] => 2 [3,4,2,5,1] => 1 [3,4,5,1,2] => 1 [3,4,5,2,1] => 1 [3,5,1,2,4] => 1 [3,5,1,4,2] => 2 [3,5,2,1,4] => 1 [3,5,2,4,1] => 2 [3,5,4,1,2] => 1 [3,5,4,2,1] => 1 [4,1,2,3,5] => 2 [4,1,2,5,3] => 1 [4,1,3,2,5] => 3 [4,1,3,5,2] => 2 [4,1,5,2,3] => 1 [4,1,5,3,2] => 1 [4,2,1,3,5] => 3 [4,2,1,5,3] => 2 [4,2,3,1,5] => 4 [4,2,3,5,1] => 3 [4,2,5,1,3] => 2 [4,2,5,3,1] => 2 [4,3,1,2,5] => 2 [4,3,1,5,2] => 1 [4,3,2,1,5] => 3 [4,3,2,5,1] => 2 [4,3,5,1,2] => 1 [4,3,5,2,1] => 1 [4,5,1,2,3] => 1 [4,5,1,3,2] => 1 [4,5,2,1,3] => 1 [4,5,2,3,1] => 1 [4,5,3,1,2] => 2 [4,5,3,2,1] => 2 [5,1,2,3,4] => 1 [5,1,2,4,3] => 2 [5,1,3,2,4] => 2 [5,1,3,4,2] => 3 [5,1,4,2,3] => 1 [5,1,4,3,2] => 2 [5,2,1,3,4] => 2 [5,2,1,4,3] => 3 [5,2,3,1,4] => 3 [5,2,3,4,1] => 4 [5,2,4,1,3] => 2 [5,2,4,3,1] => 3 [5,3,1,2,4] => 1 [5,3,1,4,2] => 2 [5,3,2,1,4] => 2 [5,3,2,4,1] => 3 [5,3,4,1,2] => 1 [5,3,4,2,1] => 2 [5,4,1,2,3] => 1 [5,4,1,3,2] => 1 [5,4,2,1,3] => 1 [5,4,2,3,1] => 2 [5,4,3,1,2] => 2 [5,4,3,2,1] => 3 [1,2,3,4,5,6] => 6 [1,2,3,4,6,5] => 5 [1,2,3,5,4,6] => 5 [1,2,3,5,6,4] => 4 [1,2,3,6,4,5] => 4 [1,2,3,6,5,4] => 5 [1,2,4,3,5,6] => 5 [1,2,4,3,6,5] => 4 [1,2,4,5,3,6] => 4 [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] => 4 [1,2,5,3,6,4] => 3 [1,2,5,4,3,6] => 5 [1,2,5,4,6,3] => 4 [1,2,5,6,3,4] => 3 [1,2,5,6,4,3] => 3 [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] => 3 [1,2,6,5,4,3] => 4 [1,3,2,4,5,6] => 5 [1,3,2,4,6,5] => 4 [1,3,2,5,4,6] => 4 [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] => 4 [1,3,4,2,6,5] => 3 [1,3,4,5,2,6] => 3 [1,3,4,5,6,2] => 2 [1,3,4,6,2,5] => 2 [1,3,4,6,5,2] => 3 [1,3,5,2,4,6] => 3 [1,3,5,2,6,4] => 2 [1,3,5,4,2,6] => 4 [1,3,5,4,6,2] => 3 [1,3,5,6,2,4] => 2 [1,3,5,6,4,2] => 2 [1,3,6,2,4,5] => 2 [1,3,6,2,5,4] => 3 [1,3,6,4,2,5] => 3 [1,3,6,4,5,2] => 4 [1,3,6,5,2,4] => 2 [1,3,6,5,4,2] => 3 [1,4,2,3,5,6] => 4 [1,4,2,3,6,5] => 3 [1,4,2,5,3,6] => 3 [1,4,2,5,6,3] => 2 [1,4,2,6,3,5] => 2 [1,4,2,6,5,3] => 3 [1,4,3,2,5,6] => 5 [1,4,3,2,6,5] => 4 [1,4,3,5,2,6] => 4 [1,4,3,5,6,2] => 3 [1,4,3,6,2,5] => 3 [1,4,3,6,5,2] => 4 [1,4,5,2,3,6] => 3 [1,4,5,2,6,3] => 2 [1,4,5,3,2,6] => 3 [1,4,5,3,6,2] => 2 [1,4,5,6,2,3] => 2 [1,4,5,6,3,2] => 2 [1,4,6,2,3,5] => 2 [1,4,6,2,5,3] => 3 [1,4,6,3,2,5] => 2 [1,4,6,3,5,2] => 3 [1,4,6,5,2,3] => 2 [1,4,6,5,3,2] => 2 [1,5,2,3,4,6] => 3 [1,5,2,3,6,4] => 2 [1,5,2,4,3,6] => 4 [1,5,2,4,6,3] => 3 [1,5,2,6,3,4] => 2 [1,5,2,6,4,3] => 2 [1,5,3,2,4,6] => 4 [1,5,3,2,6,4] => 3 [1,5,3,4,2,6] => 5 [1,5,3,4,6,2] => 4 [1,5,3,6,2,4] => 3 [1,5,3,6,4,2] => 3 [1,5,4,2,3,6] => 3 [1,5,4,2,6,3] => 2 [1,5,4,3,2,6] => 4 [1,5,4,3,6,2] => 3 [1,5,4,6,2,3] => 2 [1,5,4,6,3,2] => 2 [1,5,6,2,3,4] => 2 [1,5,6,2,4,3] => 2 [1,5,6,3,2,4] => 2 [1,5,6,3,4,2] => 2 [1,5,6,4,2,3] => 3 [1,5,6,4,3,2] => 3 [1,6,2,3,4,5] => 2 [1,6,2,3,5,4] => 3 [1,6,2,4,3,5] => 3 [1,6,2,4,5,3] => 4 [1,6,2,5,3,4] => 2 [1,6,2,5,4,3] => 3 [1,6,3,2,4,5] => 3 [1,6,3,2,5,4] => 4 [1,6,3,4,2,5] => 4 [1,6,3,4,5,2] => 5 [1,6,3,5,2,4] => 3 [1,6,3,5,4,2] => 4 [1,6,4,2,3,5] => 2 [1,6,4,2,5,3] => 3 [1,6,4,3,2,5] => 3 [1,6,4,3,5,2] => 4 [1,6,4,5,2,3] => 2 [1,6,4,5,3,2] => 3 [1,6,5,2,3,4] => 2 [1,6,5,2,4,3] => 2 [1,6,5,3,2,4] => 2 [1,6,5,3,4,2] => 3 [1,6,5,4,2,3] => 3 [1,6,5,4,3,2] => 4 [2,1,3,4,5,6] => 5 [2,1,3,4,6,5] => 4 [2,1,3,5,4,6] => 4 [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] => 4 [2,1,4,3,6,5] => 3 [2,1,4,5,3,6] => 3 [2,1,4,5,6,3] => 2 [2,1,4,6,3,5] => 2 [2,1,4,6,5,3] => 3 [2,1,5,3,4,6] => 3 [2,1,5,3,6,4] => 2 [2,1,5,4,3,6] => 4 [2,1,5,4,6,3] => 3 [2,1,5,6,3,4] => 2 [2,1,5,6,4,3] => 2 [2,1,6,3,4,5] => 2 [2,1,6,3,5,4] => 3 [2,1,6,4,3,5] => 3 [2,1,6,4,5,3] => 4 [2,1,6,5,3,4] => 2 [2,1,6,5,4,3] => 3 [2,3,1,4,5,6] => 4 [2,3,1,4,6,5] => 3 [2,3,1,5,4,6] => 3 [2,3,1,5,6,4] => 2 [2,3,1,6,4,5] => 2 [2,3,1,6,5,4] => 3 [2,3,4,1,5,6] => 3 [2,3,4,1,6,5] => 2 [2,3,4,5,1,6] => 2 [2,3,4,5,6,1] => 1 [2,3,4,6,1,5] => 1 [2,3,4,6,5,1] => 2 [2,3,5,1,4,6] => 2 [2,3,5,1,6,4] => 1 [2,3,5,4,1,6] => 3 [2,3,5,4,6,1] => 2 [2,3,5,6,1,4] => 1 [2,3,5,6,4,1] => 1 [2,3,6,1,4,5] => 1 [2,3,6,1,5,4] => 2 [2,3,6,4,1,5] => 2 [2,3,6,4,5,1] => 3 [2,3,6,5,1,4] => 1 [2,3,6,5,4,1] => 2 [2,4,1,3,5,6] => 3 [2,4,1,3,6,5] => 2 [2,4,1,5,3,6] => 2 [2,4,1,5,6,3] => 1 [2,4,1,6,3,5] => 1 [2,4,1,6,5,3] => 2 [2,4,3,1,5,6] => 4 [2,4,3,1,6,5] => 3 [2,4,3,5,1,6] => 3 [2,4,3,5,6,1] => 2 [2,4,3,6,1,5] => 2 [2,4,3,6,5,1] => 3 [2,4,5,1,3,6] => 2 [2,4,5,1,6,3] => 1 [2,4,5,3,1,6] => 2 [2,4,5,3,6,1] => 1 [2,4,5,6,1,3] => 1 [2,4,5,6,3,1] => 1 [2,4,6,1,3,5] => 1 [2,4,6,1,5,3] => 2 [2,4,6,3,1,5] => 1 [2,4,6,3,5,1] => 2 [2,4,6,5,1,3] => 1 [2,4,6,5,3,1] => 1 [2,5,1,3,4,6] => 2 [2,5,1,3,6,4] => 1 [2,5,1,4,3,6] => 3 [2,5,1,4,6,3] => 2 [2,5,1,6,3,4] => 1 [2,5,1,6,4,3] => 1 [2,5,3,1,4,6] => 3 [2,5,3,1,6,4] => 2 [2,5,3,4,1,6] => 4 [2,5,3,4,6,1] => 3 [2,5,3,6,1,4] => 2 [2,5,3,6,4,1] => 2 [2,5,4,1,3,6] => 2 [2,5,4,1,6,3] => 1 [2,5,4,3,1,6] => 3 [2,5,4,3,6,1] => 2 [2,5,4,6,1,3] => 1 [2,5,4,6,3,1] => 1 [2,5,6,1,3,4] => 1 [2,5,6,1,4,3] => 1 [2,5,6,3,1,4] => 1 [2,5,6,3,4,1] => 1 [2,5,6,4,1,3] => 2 [2,5,6,4,3,1] => 2 [2,6,1,3,4,5] => 1 [2,6,1,3,5,4] => 2 [2,6,1,4,3,5] => 2 [2,6,1,4,5,3] => 3 [2,6,1,5,3,4] => 1 [2,6,1,5,4,3] => 2 [2,6,3,1,4,5] => 2 [2,6,3,1,5,4] => 3 [2,6,3,4,1,5] => 3 [2,6,3,4,5,1] => 4 [2,6,3,5,1,4] => 2 [2,6,3,5,4,1] => 3 [2,6,4,1,3,5] => 1 [2,6,4,1,5,3] => 2 [2,6,4,3,1,5] => 2 [2,6,4,3,5,1] => 3 [2,6,4,5,1,3] => 1 [2,6,4,5,3,1] => 2 [2,6,5,1,3,4] => 1 [2,6,5,1,4,3] => 1 [2,6,5,3,1,4] => 1 [2,6,5,3,4,1] => 2 [2,6,5,4,1,3] => 2 [2,6,5,4,3,1] => 3 [3,1,2,4,5,6] => 4 [3,1,2,4,6,5] => 3 [3,1,2,5,4,6] => 3 [3,1,2,5,6,4] => 2 [3,1,2,6,4,5] => 2 [3,1,2,6,5,4] => 3 [3,1,4,2,5,6] => 3 [3,1,4,2,6,5] => 2 [3,1,4,5,2,6] => 2 [3,1,4,5,6,2] => 1 [3,1,4,6,2,5] => 1 [3,1,4,6,5,2] => 2 [3,1,5,2,4,6] => 2 [3,1,5,2,6,4] => 1 [3,1,5,4,2,6] => 3 [3,1,5,4,6,2] => 2 [3,1,5,6,2,4] => 1 [3,1,5,6,4,2] => 1 [3,1,6,2,4,5] => 1 [3,1,6,2,5,4] => 2 [3,1,6,4,2,5] => 2 [3,1,6,4,5,2] => 3 [3,1,6,5,2,4] => 1 [3,1,6,5,4,2] => 2 [3,2,1,4,5,6] => 5 [3,2,1,4,6,5] => 4 [3,2,1,5,4,6] => 4 [3,2,1,5,6,4] => 3 [3,2,1,6,4,5] => 3 [3,2,1,6,5,4] => 4 [3,2,4,1,5,6] => 4 [3,2,4,1,6,5] => 3 [3,2,4,5,1,6] => 3 [3,2,4,5,6,1] => 2 [3,2,4,6,1,5] => 2 [3,2,4,6,5,1] => 3 [3,2,5,1,4,6] => 3 [3,2,5,1,6,4] => 2 [3,2,5,4,1,6] => 4 [3,2,5,4,6,1] => 3 [3,2,5,6,1,4] => 2 [3,2,5,6,4,1] => 2 [3,2,6,1,4,5] => 2 [3,2,6,1,5,4] => 3 [3,2,6,4,1,5] => 3 [3,2,6,4,5,1] => 4 [3,2,6,5,1,4] => 2 [3,2,6,5,4,1] => 3 [3,4,1,2,5,6] => 3 [3,4,1,2,6,5] => 2 [3,4,1,5,2,6] => 2 [3,4,1,5,6,2] => 1 [3,4,1,6,2,5] => 1 [3,4,1,6,5,2] => 2 [3,4,2,1,5,6] => 3 [3,4,2,1,6,5] => 2 [3,4,2,5,1,6] => 2 [3,4,2,5,6,1] => 1 [3,4,2,6,1,5] => 1 [3,4,2,6,5,1] => 2 [3,4,5,1,2,6] => 2 [3,4,5,1,6,2] => 1 [3,4,5,2,1,6] => 2 [3,4,5,2,6,1] => 1 [3,4,5,6,1,2] => 1 [3,4,5,6,2,1] => 1 [3,4,6,1,2,5] => 1 [3,4,6,1,5,2] => 2 [3,4,6,2,1,5] => 1 [3,4,6,2,5,1] => 2 [3,4,6,5,1,2] => 1 [3,4,6,5,2,1] => 1 [3,5,1,2,4,6] => 2 [3,5,1,2,6,4] => 1 [3,5,1,4,2,6] => 3 [3,5,1,4,6,2] => 2 [3,5,1,6,2,4] => 1 [3,5,1,6,4,2] => 1 [3,5,2,1,4,6] => 2 [3,5,2,1,6,4] => 1 [3,5,2,4,1,6] => 3 [3,5,2,4,6,1] => 2 [3,5,2,6,1,4] => 1 [3,5,2,6,4,1] => 1 [3,5,4,1,2,6] => 2 [3,5,4,1,6,2] => 1 [3,5,4,2,1,6] => 2 [3,5,4,2,6,1] => 1 [3,5,4,6,1,2] => 1 [3,5,4,6,2,1] => 1 [3,5,6,1,2,4] => 1 [3,5,6,1,4,2] => 1 [3,5,6,2,1,4] => 1 [3,5,6,2,4,1] => 1 [3,5,6,4,1,2] => 2 [3,5,6,4,2,1] => 2 [3,6,1,2,4,5] => 1 [3,6,1,2,5,4] => 2 [3,6,1,4,2,5] => 2 [3,6,1,4,5,2] => 3 [3,6,1,5,2,4] => 1 [3,6,1,5,4,2] => 2 [3,6,2,1,4,5] => 1 [3,6,2,1,5,4] => 2 [3,6,2,4,1,5] => 2 [3,6,2,4,5,1] => 3 [3,6,2,5,1,4] => 1 [3,6,2,5,4,1] => 2 [3,6,4,1,2,5] => 1 [3,6,4,1,5,2] => 2 [3,6,4,2,1,5] => 1 [3,6,4,2,5,1] => 2 [3,6,4,5,1,2] => 1 [3,6,4,5,2,1] => 1 [3,6,5,1,2,4] => 1 [3,6,5,1,4,2] => 1 [3,6,5,2,1,4] => 1 [3,6,5,2,4,1] => 1 [3,6,5,4,1,2] => 2 [3,6,5,4,2,1] => 2 [4,1,2,3,5,6] => 3 [4,1,2,3,6,5] => 2 [4,1,2,5,3,6] => 2 [4,1,2,5,6,3] => 1 [4,1,2,6,3,5] => 1 [4,1,2,6,5,3] => 2 [4,1,3,2,5,6] => 4 [4,1,3,2,6,5] => 3 [4,1,3,5,2,6] => 3 [4,1,3,5,6,2] => 2 [4,1,3,6,2,5] => 2 [4,1,3,6,5,2] => 3 [4,1,5,2,3,6] => 2 [4,1,5,2,6,3] => 1 [4,1,5,3,2,6] => 2 [4,1,5,3,6,2] => 1 [4,1,5,6,2,3] => 1 [4,1,5,6,3,2] => 1 [4,1,6,2,3,5] => 1 [4,1,6,2,5,3] => 2 [4,1,6,3,2,5] => 1 [4,1,6,3,5,2] => 2 [4,1,6,5,2,3] => 1 [4,1,6,5,3,2] => 1 [4,2,1,3,5,6] => 4 [4,2,1,3,6,5] => 3 [4,2,1,5,3,6] => 3 [4,2,1,5,6,3] => 2 [4,2,1,6,3,5] => 2 [4,2,1,6,5,3] => 3 [4,2,3,1,5,6] => 5 [4,2,3,1,6,5] => 4 [4,2,3,5,1,6] => 4 [4,2,3,5,6,1] => 3 [4,2,3,6,1,5] => 3 [4,2,3,6,5,1] => 4 [4,2,5,1,3,6] => 3 [4,2,5,1,6,3] => 2 [4,2,5,3,1,6] => 3 [4,2,5,3,6,1] => 2 [4,2,5,6,1,3] => 2 [4,2,5,6,3,1] => 2 [4,2,6,1,3,5] => 2 [4,2,6,1,5,3] => 3 [4,2,6,3,1,5] => 2 [4,2,6,3,5,1] => 3 [4,2,6,5,1,3] => 2 [4,2,6,5,3,1] => 2 [4,3,1,2,5,6] => 3 [4,3,1,2,6,5] => 2 [4,3,1,5,2,6] => 2 [4,3,1,5,6,2] => 1 [4,3,1,6,2,5] => 1 [4,3,1,6,5,2] => 2 [4,3,2,1,5,6] => 4 [4,3,2,1,6,5] => 3 [4,3,2,5,1,6] => 3 [4,3,2,5,6,1] => 2 [4,3,2,6,1,5] => 2 [4,3,2,6,5,1] => 3 [4,3,5,1,2,6] => 2 [4,3,5,1,6,2] => 1 [4,3,5,2,1,6] => 2 [4,3,5,2,6,1] => 1 [4,3,5,6,1,2] => 1 [4,3,5,6,2,1] => 1 [4,3,6,1,2,5] => 1 [4,3,6,1,5,2] => 2 [4,3,6,2,1,5] => 1 [4,3,6,2,5,1] => 2 [4,3,6,5,1,2] => 1 [4,3,6,5,2,1] => 1 [4,5,1,2,3,6] => 2 [4,5,1,2,6,3] => 1 [4,5,1,3,2,6] => 2 [4,5,1,3,6,2] => 1 [4,5,1,6,2,3] => 1 [4,5,1,6,3,2] => 1 [4,5,2,1,3,6] => 2 [4,5,2,1,6,3] => 1 [4,5,2,3,1,6] => 2 [4,5,2,3,6,1] => 1 [4,5,2,6,1,3] => 1 [4,5,2,6,3,1] => 1 [4,5,3,1,2,6] => 3 [4,5,3,1,6,2] => 2 [4,5,3,2,1,6] => 3 [4,5,3,2,6,1] => 2 [4,5,3,6,1,2] => 2 [4,5,3,6,2,1] => 2 [4,5,6,1,2,3] => 1 [4,5,6,1,3,2] => 1 [4,5,6,2,1,3] => 1 [4,5,6,2,3,1] => 1 [4,5,6,3,1,2] => 1 [4,5,6,3,2,1] => 1 [4,6,1,2,3,5] => 1 [4,6,1,2,5,3] => 2 [4,6,1,3,2,5] => 1 [4,6,1,3,5,2] => 2 [4,6,1,5,2,3] => 1 [4,6,1,5,3,2] => 1 [4,6,2,1,3,5] => 1 [4,6,2,1,5,3] => 2 [4,6,2,3,1,5] => 1 [4,6,2,3,5,1] => 2 [4,6,2,5,1,3] => 1 [4,6,2,5,3,1] => 1 [4,6,3,1,2,5] => 2 [4,6,3,1,5,2] => 3 [4,6,3,2,1,5] => 2 [4,6,3,2,5,1] => 3 [4,6,3,5,1,2] => 2 [4,6,3,5,2,1] => 2 [4,6,5,1,2,3] => 1 [4,6,5,1,3,2] => 1 [4,6,5,2,1,3] => 1 [4,6,5,2,3,1] => 1 [4,6,5,3,1,2] => 1 [4,6,5,3,2,1] => 1 [5,1,2,3,4,6] => 2 [5,1,2,3,6,4] => 1 [5,1,2,4,3,6] => 3 [5,1,2,4,6,3] => 2 [5,1,2,6,3,4] => 1 [5,1,2,6,4,3] => 1 [5,1,3,2,4,6] => 3 [5,1,3,2,6,4] => 2 [5,1,3,4,2,6] => 4 [5,1,3,4,6,2] => 3 [5,1,3,6,2,4] => 2 [5,1,3,6,4,2] => 2 [5,1,4,2,3,6] => 2 [5,1,4,2,6,3] => 1 [5,1,4,3,2,6] => 3 [5,1,4,3,6,2] => 2 [5,1,4,6,2,3] => 1 [5,1,4,6,3,2] => 1 [5,1,6,2,3,4] => 1 [5,1,6,2,4,3] => 1 [5,1,6,3,2,4] => 1 [5,1,6,3,4,2] => 1 [5,1,6,4,2,3] => 2 [5,1,6,4,3,2] => 2 [5,2,1,3,4,6] => 3 [5,2,1,3,6,4] => 2 [5,2,1,4,3,6] => 4 [5,2,1,4,6,3] => 3 [5,2,1,6,3,4] => 2 [5,2,1,6,4,3] => 2 [5,2,3,1,4,6] => 4 [5,2,3,1,6,4] => 3 [5,2,3,4,1,6] => 5 [5,2,3,4,6,1] => 4 [5,2,3,6,1,4] => 3 [5,2,3,6,4,1] => 3 [5,2,4,1,3,6] => 3 [5,2,4,1,6,3] => 2 [5,2,4,3,1,6] => 4 [5,2,4,3,6,1] => 3 [5,2,4,6,1,3] => 2 [5,2,4,6,3,1] => 2 [5,2,6,1,3,4] => 2 [5,2,6,1,4,3] => 2 [5,2,6,3,1,4] => 2 [5,2,6,3,4,1] => 2 [5,2,6,4,1,3] => 3 [5,2,6,4,3,1] => 3 [5,3,1,2,4,6] => 2 [5,3,1,2,6,4] => 1 [5,3,1,4,2,6] => 3 [5,3,1,4,6,2] => 2 [5,3,1,6,2,4] => 1 [5,3,1,6,4,2] => 1 [5,3,2,1,4,6] => 3 [5,3,2,1,6,4] => 2 [5,3,2,4,1,6] => 4 [5,3,2,4,6,1] => 3 [5,3,2,6,1,4] => 2 [5,3,2,6,4,1] => 2 [5,3,4,1,2,6] => 2 [5,3,4,1,6,2] => 1 [5,3,4,2,1,6] => 3 [5,3,4,2,6,1] => 2 [5,3,4,6,1,2] => 1 [5,3,4,6,2,1] => 1 [5,3,6,1,2,4] => 1 [5,3,6,1,4,2] => 1 [5,3,6,2,1,4] => 1 [5,3,6,2,4,1] => 1 [5,3,6,4,1,2] => 2 [5,3,6,4,2,1] => 2 [5,4,1,2,3,6] => 2 [5,4,1,2,6,3] => 1 [5,4,1,3,2,6] => 2 [5,4,1,3,6,2] => 1 [5,4,1,6,2,3] => 1 [5,4,1,6,3,2] => 1 [5,4,2,1,3,6] => 2 [5,4,2,1,6,3] => 1 [5,4,2,3,1,6] => 3 [5,4,2,3,6,1] => 2 [5,4,2,6,1,3] => 1 [5,4,2,6,3,1] => 1 [5,4,3,1,2,6] => 3 [5,4,3,1,6,2] => 2 [5,4,3,2,1,6] => 4 [5,4,3,2,6,1] => 3 [5,4,3,6,1,2] => 2 [5,4,3,6,2,1] => 2 [5,4,6,1,2,3] => 1 [5,4,6,1,3,2] => 1 [5,4,6,2,1,3] => 1 [5,4,6,2,3,1] => 1 [5,4,6,3,1,2] => 1 [5,4,6,3,2,1] => 1 [5,6,1,2,3,4] => 1 [5,6,1,2,4,3] => 1 [5,6,1,3,2,4] => 1 [5,6,1,3,4,2] => 1 [5,6,1,4,2,3] => 2 [5,6,1,4,3,2] => 2 [5,6,2,1,3,4] => 1 [5,6,2,1,4,3] => 1 [5,6,2,3,1,4] => 1 [5,6,2,3,4,1] => 1 [5,6,2,4,1,3] => 2 [5,6,2,4,3,1] => 2 [5,6,3,1,2,4] => 2 [5,6,3,1,4,2] => 2 [5,6,3,2,1,4] => 2 [5,6,3,2,4,1] => 2 [5,6,3,4,1,2] => 3 [5,6,3,4,2,1] => 3 [5,6,4,1,2,3] => 1 [5,6,4,1,3,2] => 1 [5,6,4,2,1,3] => 1 [5,6,4,2,3,1] => 1 [5,6,4,3,1,2] => 2 [5,6,4,3,2,1] => 2 [6,1,2,3,4,5] => 1 [6,1,2,3,5,4] => 2 [6,1,2,4,3,5] => 2 [6,1,2,4,5,3] => 3 [6,1,2,5,3,4] => 1 [6,1,2,5,4,3] => 2 [6,1,3,2,4,5] => 2 [6,1,3,2,5,4] => 3 [6,1,3,4,2,5] => 3 [6,1,3,4,5,2] => 4 [6,1,3,5,2,4] => 2 [6,1,3,5,4,2] => 3 [6,1,4,2,3,5] => 1 [6,1,4,2,5,3] => 2 [6,1,4,3,2,5] => 2 [6,1,4,3,5,2] => 3 [6,1,4,5,2,3] => 1 [6,1,4,5,3,2] => 2 [6,1,5,2,3,4] => 1 [6,1,5,2,4,3] => 1 [6,1,5,3,2,4] => 1 [6,1,5,3,4,2] => 2 [6,1,5,4,2,3] => 2 [6,1,5,4,3,2] => 3 [6,2,1,3,4,5] => 2 [6,2,1,3,5,4] => 3 [6,2,1,4,3,5] => 3 [6,2,1,4,5,3] => 4 [6,2,1,5,3,4] => 2 [6,2,1,5,4,3] => 3 [6,2,3,1,4,5] => 3 [6,2,3,1,5,4] => 4 [6,2,3,4,1,5] => 4 [6,2,3,4,5,1] => 5 [6,2,3,5,1,4] => 3 [6,2,3,5,4,1] => 4 [6,2,4,1,3,5] => 2 [6,2,4,1,5,3] => 3 [6,2,4,3,1,5] => 3 [6,2,4,3,5,1] => 4 [6,2,4,5,1,3] => 2 [6,2,4,5,3,1] => 3 [6,2,5,1,3,4] => 2 [6,2,5,1,4,3] => 2 [6,2,5,3,1,4] => 2 [6,2,5,3,4,1] => 3 [6,2,5,4,1,3] => 3 [6,2,5,4,3,1] => 4 [6,3,1,2,4,5] => 1 [6,3,1,2,5,4] => 2 [6,3,1,4,2,5] => 2 [6,3,1,4,5,2] => 3 [6,3,1,5,2,4] => 1 [6,3,1,5,4,2] => 2 [6,3,2,1,4,5] => 2 [6,3,2,1,5,4] => 3 [6,3,2,4,1,5] => 3 [6,3,2,4,5,1] => 4 [6,3,2,5,1,4] => 2 [6,3,2,5,4,1] => 3 [6,3,4,1,2,5] => 1 [6,3,4,1,5,2] => 2 [6,3,4,2,1,5] => 2 [6,3,4,2,5,1] => 3 [6,3,4,5,1,2] => 1 [6,3,4,5,2,1] => 2 [6,3,5,1,2,4] => 1 [6,3,5,1,4,2] => 1 [6,3,5,2,1,4] => 1 [6,3,5,2,4,1] => 2 [6,3,5,4,1,2] => 2 [6,3,5,4,2,1] => 3 [6,4,1,2,3,5] => 1 [6,4,1,2,5,3] => 2 [6,4,1,3,2,5] => 1 [6,4,1,3,5,2] => 2 [6,4,1,5,2,3] => 1 [6,4,1,5,3,2] => 1 [6,4,2,1,3,5] => 1 [6,4,2,1,5,3] => 2 [6,4,2,3,1,5] => 2 [6,4,2,3,5,1] => 3 [6,4,2,5,1,3] => 1 [6,4,2,5,3,1] => 2 [6,4,3,1,2,5] => 2 [6,4,3,1,5,2] => 3 [6,4,3,2,1,5] => 3 [6,4,3,2,5,1] => 4 [6,4,3,5,1,2] => 2 [6,4,3,5,2,1] => 3 [6,4,5,1,2,3] => 1 [6,4,5,1,3,2] => 1 [6,4,5,2,1,3] => 1 [6,4,5,2,3,1] => 2 [6,4,5,3,1,2] => 1 [6,4,5,3,2,1] => 2 [6,5,1,2,3,4] => 1 [6,5,1,2,4,3] => 1 [6,5,1,3,2,4] => 1 [6,5,1,3,4,2] => 1 [6,5,1,4,2,3] => 2 [6,5,1,4,3,2] => 2 [6,5,2,1,3,4] => 1 [6,5,2,1,4,3] => 1 [6,5,2,3,1,4] => 1 [6,5,2,3,4,1] => 2 [6,5,2,4,1,3] => 2 [6,5,2,4,3,1] => 3 [6,5,3,1,2,4] => 2 [6,5,3,1,4,2] => 2 [6,5,3,2,1,4] => 2 [6,5,3,2,4,1] => 3 [6,5,3,4,1,2] => 3 [6,5,3,4,2,1] => 4 [6,5,4,1,2,3] => 1 [6,5,4,1,3,2] => 1 [6,5,4,2,1,3] => 1 [6,5,4,2,3,1] => 2 [6,5,4,3,1,2] => 2 [6,5,4,3,2,1] => 3 [1,2,3,4,5,6,7] => 7 [1,2,3,4,5,7,6] => 6 [1,2,3,4,6,5,7] => 6 [1,2,3,4,6,7,5] => 5 [1,2,3,4,7,5,6] => 5 [1,2,3,4,7,6,5] => 6 [1,2,3,5,4,6,7] => 6 [1,2,3,5,4,7,6] => 5 [1,2,3,5,6,4,7] => 5 [1,2,3,5,6,7,4] => 4 [1,2,3,5,7,4,6] => 4 [1,2,3,5,7,6,4] => 5 [1,2,3,6,4,5,7] => 5 [1,2,3,6,4,7,5] => 4 [1,2,3,6,5,4,7] => 6 [1,2,3,6,5,7,4] => 5 [1,2,3,6,7,4,5] => 4 [1,2,3,6,7,5,4] => 4 [1,2,3,7,4,5,6] => 4 [1,2,3,7,4,6,5] => 5 [1,2,3,7,5,4,6] => 5 [1,2,3,7,5,6,4] => 6 [1,2,3,7,6,4,5] => 4 [1,2,3,7,6,5,4] => 5 [1,2,4,3,5,6,7] => 6 [1,2,4,3,5,7,6] => 5 [1,2,4,3,6,5,7] => 5 [1,2,4,3,6,7,5] => 4 [1,2,4,3,7,5,6] => 4 [1,2,4,3,7,6,5] => 5 [1,2,4,5,3,6,7] => 5 [1,2,4,5,3,7,6] => 4 [1,2,4,5,6,3,7] => 4 [1,2,4,5,6,7,3] => 3 [1,2,4,5,7,3,6] => 3 [1,2,4,5,7,6,3] => 4 [1,2,4,6,3,5,7] => 4 [1,2,4,6,3,7,5] => 3 [1,2,4,6,5,3,7] => 5 [1,2,4,6,5,7,3] => 4 [1,2,4,6,7,3,5] => 3 [1,2,4,6,7,5,3] => 3 [1,2,4,7,3,5,6] => 3 [1,2,4,7,3,6,5] => 4 [1,2,4,7,5,3,6] => 4 [1,2,4,7,5,6,3] => 5 [1,2,4,7,6,3,5] => 3 [1,2,4,7,6,5,3] => 4 [1,2,5,3,4,6,7] => 5 [1,2,5,3,4,7,6] => 4 [1,2,5,3,6,4,7] => 4 [1,2,5,3,6,7,4] => 3 [1,2,5,3,7,4,6] => 3 [1,2,5,3,7,6,4] => 4 [1,2,5,4,3,6,7] => 6 [1,2,5,4,3,7,6] => 5 [1,2,5,4,6,3,7] => 5 [1,2,5,4,6,7,3] => 4 [1,2,5,4,7,3,6] => 4 [1,2,5,4,7,6,3] => 5 [1,2,5,6,3,4,7] => 4 [1,2,5,6,3,7,4] => 3 [1,2,5,6,4,3,7] => 4 [1,2,5,6,4,7,3] => 3 [1,2,5,6,7,3,4] => 3 [1,2,5,6,7,4,3] => 3 [1,2,5,7,3,4,6] => 3 [1,2,5,7,3,6,4] => 4 [1,2,5,7,4,3,6] => 3 [1,2,5,7,4,6,3] => 4 [1,2,5,7,6,3,4] => 3 [1,2,5,7,6,4,3] => 3 [1,2,6,3,4,5,7] => 4 [1,2,6,3,4,7,5] => 3 [1,2,6,3,5,4,7] => 5 [1,2,6,3,5,7,4] => 4 [1,2,6,3,7,4,5] => 3 [1,2,6,3,7,5,4] => 3 [1,2,6,4,3,5,7] => 5 [1,2,6,4,3,7,5] => 4 [1,2,6,4,5,3,7] => 6 [1,2,6,4,5,7,3] => 5 [1,2,6,4,7,3,5] => 4 [1,2,6,4,7,5,3] => 4 [1,2,6,5,3,4,7] => 4 [1,2,6,5,3,7,4] => 3 [1,2,6,5,4,3,7] => 5 [1,2,6,5,4,7,3] => 4 [1,2,6,5,7,3,4] => 3 [1,2,6,5,7,4,3] => 3 [1,2,6,7,3,4,5] => 3 [1,2,6,7,3,5,4] => 3 [1,2,6,7,4,3,5] => 3 [1,2,6,7,4,5,3] => 3 [1,2,6,7,5,3,4] => 4 [1,2,6,7,5,4,3] => 4 [1,2,7,3,4,5,6] => 3 [1,2,7,3,4,6,5] => 4 [1,2,7,3,5,4,6] => 4 [1,2,7,3,5,6,4] => 5 [1,2,7,3,6,4,5] => 3 [1,2,7,3,6,5,4] => 4 [1,2,7,4,3,5,6] => 4 [1,2,7,4,3,6,5] => 5 [1,2,7,4,5,3,6] => 5 [1,2,7,4,5,6,3] => 6 [1,2,7,4,6,3,5] => 4 [1,2,7,4,6,5,3] => 5 [1,2,7,5,3,4,6] => 3 [1,2,7,5,3,6,4] => 4 [1,2,7,5,4,3,6] => 4 [1,2,7,5,4,6,3] => 5 [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] => 5 [1,3,2,4,5,6,7] => 6 [1,3,2,4,5,7,6] => 5 [1,3,2,4,6,5,7] => 5 [1,3,2,4,6,7,5] => 4 [1,3,2,4,7,5,6] => 4 [1,3,2,4,7,6,5] => 5 [1,3,2,5,4,6,7] => 5 [1,3,2,5,4,7,6] => 4 [1,3,2,5,6,4,7] => 4 [1,3,2,5,6,7,4] => 3 [1,3,2,5,7,4,6] => 3 [1,3,2,5,7,6,4] => 4 [1,3,2,6,4,5,7] => 4 [1,3,2,6,4,7,5] => 3 [1,3,2,6,5,4,7] => 5 [1,3,2,6,5,7,4] => 4 [1,3,2,6,7,4,5] => 3 [1,3,2,6,7,5,4] => 3 [1,3,2,7,4,5,6] => 3 [1,3,2,7,4,6,5] => 4 [1,3,2,7,5,4,6] => 4 [1,3,2,7,5,6,4] => 5 [1,3,2,7,6,4,5] => 3 [1,3,2,7,6,5,4] => 4 [1,3,4,2,5,6,7] => 5 [1,3,4,2,5,7,6] => 4 [1,3,4,2,6,5,7] => 4 [1,3,4,2,6,7,5] => 3 [1,3,4,2,7,5,6] => 3 [1,3,4,2,7,6,5] => 4 [1,3,4,5,2,6,7] => 4 [1,3,4,5,2,7,6] => 3 [1,3,4,5,6,2,7] => 3 [1,3,4,5,6,7,2] => 2 [1,3,4,5,7,2,6] => 2 [1,3,4,5,7,6,2] => 3 [1,3,4,6,2,5,7] => 3 [1,3,4,6,2,7,5] => 2 [1,3,4,6,5,2,7] => 4 [1,3,4,6,5,7,2] => 3 [1,3,4,6,7,2,5] => 2 [1,3,4,6,7,5,2] => 2 [1,3,4,7,2,5,6] => 2 [1,3,4,7,2,6,5] => 3 [1,3,4,7,5,2,6] => 3 [1,3,4,7,5,6,2] => 4 [1,3,4,7,6,2,5] => 2 [1,3,4,7,6,5,2] => 3 [1,3,5,2,4,6,7] => 4 [1,3,5,2,4,7,6] => 3 [1,3,5,2,6,4,7] => 3 [1,3,5,2,6,7,4] => 2 [1,3,5,2,7,4,6] => 2 [1,3,5,2,7,6,4] => 3 [1,3,5,4,2,6,7] => 5 [1,3,5,4,2,7,6] => 4 [1,3,5,4,6,2,7] => 4 [1,3,5,4,6,7,2] => 3 [1,3,5,4,7,2,6] => 3 [1,3,5,4,7,6,2] => 4 [1,3,5,6,2,4,7] => 3 [1,3,5,6,2,7,4] => 2 [1,3,5,6,4,2,7] => 3 [1,3,5,6,4,7,2] => 2 [1,3,5,6,7,2,4] => 2 [1,3,5,6,7,4,2] => 2 [1,3,5,7,2,4,6] => 2 [1,3,5,7,2,6,4] => 3 [1,3,5,7,4,2,6] => 2 [1,3,5,7,4,6,2] => 3 [1,3,5,7,6,2,4] => 2 [1,3,5,7,6,4,2] => 2 [1,3,6,2,4,5,7] => 3 [1,3,6,2,4,7,5] => 2 [1,3,6,2,5,4,7] => 4 [1,3,6,2,5,7,4] => 3 [1,3,6,2,7,4,5] => 2 [1,3,6,2,7,5,4] => 2 [1,3,6,4,2,5,7] => 4 [1,3,6,4,2,7,5] => 3 [1,3,6,4,5,2,7] => 5 [1,3,6,4,5,7,2] => 4 [1,3,6,4,7,2,5] => 3 [1,3,6,4,7,5,2] => 3 [1,3,6,5,2,4,7] => 3 [1,3,6,5,2,7,4] => 2 [1,3,6,5,4,2,7] => 4 [1,3,6,5,4,7,2] => 3 [1,3,6,5,7,2,4] => 2 [1,3,6,5,7,4,2] => 2 [1,3,6,7,2,4,5] => 2 [1,3,6,7,2,5,4] => 2 [1,3,6,7,4,2,5] => 2 [1,3,6,7,4,5,2] => 2 [1,3,6,7,5,2,4] => 3 [1,3,6,7,5,4,2] => 3 [1,3,7,2,4,5,6] => 2 [1,3,7,2,4,6,5] => 3 [1,3,7,2,5,4,6] => 3 [1,3,7,2,5,6,4] => 4 [1,3,7,2,6,4,5] => 2 [1,3,7,2,6,5,4] => 3 [1,3,7,4,2,5,6] => 3 [1,3,7,4,2,6,5] => 4 [1,3,7,4,5,2,6] => 4 [1,3,7,4,5,6,2] => 5 [1,3,7,4,6,2,5] => 3 [1,3,7,4,6,5,2] => 4 [1,3,7,5,2,4,6] => 2 [1,3,7,5,2,6,4] => 3 [1,3,7,5,4,2,6] => 3 [1,3,7,5,4,6,2] => 4 [1,3,7,5,6,2,4] => 2 [1,3,7,5,6,4,2] => 3 [1,3,7,6,2,4,5] => 2 [1,3,7,6,2,5,4] => 2 [1,3,7,6,4,2,5] => 2 [1,3,7,6,4,5,2] => 3 [1,3,7,6,5,2,4] => 3 [1,3,7,6,5,4,2] => 4 [1,4,2,3,5,6,7] => 5 [1,4,2,3,5,7,6] => 4 [1,4,2,3,6,5,7] => 4 [1,4,2,3,6,7,5] => 3 [1,4,2,3,7,5,6] => 3 [1,4,2,3,7,6,5] => 4 [1,4,2,5,3,6,7] => 4 [1,4,2,5,3,7,6] => 3 [1,4,2,5,6,3,7] => 3 [1,4,2,5,6,7,3] => 2 [1,4,2,5,7,3,6] => 2 [1,4,2,5,7,6,3] => 3 [1,4,2,6,3,5,7] => 3 [1,4,2,6,3,7,5] => 2 [1,4,2,6,5,3,7] => 4 [1,4,2,6,5,7,3] => 3 [1,4,2,6,7,3,5] => 2 [1,4,2,6,7,5,3] => 2 [1,4,2,7,3,5,6] => 2 [1,4,2,7,3,6,5] => 3 [1,4,2,7,5,3,6] => 3 [1,4,2,7,5,6,3] => 4 [1,4,2,7,6,3,5] => 2 [1,4,2,7,6,5,3] => 3 [1,4,3,2,5,6,7] => 6 [1,4,3,2,5,7,6] => 5 [1,4,3,2,6,5,7] => 5 [1,4,3,2,6,7,5] => 4 [1,4,3,2,7,5,6] => 4 [1,4,3,2,7,6,5] => 5 [1,4,3,5,2,6,7] => 5 [1,4,3,5,2,7,6] => 4 [1,4,3,5,6,2,7] => 4 [1,4,3,5,6,7,2] => 3 [1,4,3,5,7,2,6] => 3 [1,4,3,5,7,6,2] => 4 [1,4,3,6,2,5,7] => 4 [1,4,3,6,2,7,5] => 3 [1,4,3,6,5,2,7] => 5 [1,4,3,6,5,7,2] => 4 [1,4,3,6,7,2,5] => 3 [1,4,3,6,7,5,2] => 3 [1,4,3,7,2,5,6] => 3 [1,4,3,7,2,6,5] => 4 [1,4,3,7,5,2,6] => 4 [1,4,3,7,5,6,2] => 5 [1,4,3,7,6,2,5] => 3 [1,4,3,7,6,5,2] => 4 [1,4,5,2,3,6,7] => 4 [1,4,5,2,3,7,6] => 3 [1,4,5,2,6,3,7] => 3 [1,4,5,2,6,7,3] => 2 [1,4,5,2,7,3,6] => 2 [1,4,5,2,7,6,3] => 3 [1,4,5,3,2,6,7] => 4 [1,4,5,3,2,7,6] => 3 [1,4,5,3,6,2,7] => 3 [1,4,5,3,6,7,2] => 2 [1,4,5,3,7,2,6] => 2 [1,4,5,3,7,6,2] => 3 [1,4,5,6,2,3,7] => 3 [1,4,5,6,2,7,3] => 2 [1,4,5,6,3,2,7] => 3 [1,4,5,6,3,7,2] => 2 [1,4,5,6,7,2,3] => 2 [1,4,5,6,7,3,2] => 2 [1,4,5,7,2,3,6] => 2 [1,4,5,7,2,6,3] => 3 [1,4,5,7,3,2,6] => 2 [1,4,5,7,3,6,2] => 3 [1,4,5,7,6,2,3] => 2 [1,4,5,7,6,3,2] => 2 [1,4,6,2,3,5,7] => 3 [1,4,6,2,3,7,5] => 2 [1,4,6,2,5,3,7] => 4 [1,4,6,2,5,7,3] => 3 [1,4,6,2,7,3,5] => 2 [1,4,6,2,7,5,3] => 2 [1,4,6,3,2,5,7] => 3 [1,4,6,3,2,7,5] => 2 [1,4,6,3,5,2,7] => 4 [1,4,6,3,5,7,2] => 3 [1,4,6,3,7,2,5] => 2 [1,4,6,3,7,5,2] => 2 [1,4,6,5,2,3,7] => 3 [1,4,6,5,2,7,3] => 2 [1,4,6,5,3,2,7] => 3 ----------------------------------------------------------------------------- Created: Aug 09, 2019 at 21:30 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Aug 09, 2019 at 21:30 by Martin Rubey