***************************************************************************** * 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: St001081 ----------------------------------------------------------------------------- Collection: Permutations ----------------------------------------------------------------------------- Description: The number of minimal length factorizations of a permutation into star transpositions. For a permutation $\pi\in\mathfrak S_n$ a minimal length factorization into star transpositions is a factorization of the form $$\pi = \tau_{i_1} \cdots \tau_{i_k}, 2 \leq i_1,\ldots,i_k \leq n,$$ where $\tau_a = (1,a)$ for $2 \leq a \leq n$ and $k$ is minimal. [1, lem.2.1] shows that the minimal length of such a factorization 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 $1$, see [[St001077]]. [2, cor.2] shows that the number of such minimal factorizations is $$\frac{(n+m-2(k+1))!}{(n-k)!}\ell_1\cdots\ell_m,$$ where $\ell_1,\dots,\ell_m$ is the cycle type of $\pi$ and $k$ is the number of fixed point different from $1$. ----------------------------------------------------------------------------- References: [1] Irving, J., Rattan, A. Minimal factorizations of permutations into star transpositions [[MathSciNet:2721480]] ----------------------------------------------------------------------------- Code: def statistic(pi): L = pi.cycle_type() k = pi.number_of_fixed_points() if pi(1) == 1: k -= 1 m = len(L) n = len(pi) return factorial(n+m-2*(k+1))/factorial(n-k)*prod(L) ----------------------------------------------------------------------------- Statistic values: [1,2] => 1 [2,1] => 1 [1,2,3] => 1 [1,3,2] => 2 [2,1,3] => 1 [2,3,1] => 1 [3,1,2] => 1 [3,2,1] => 1 [1,2,3,4] => 1 [1,2,4,3] => 2 [1,3,2,4] => 2 [1,3,4,2] => 3 [1,4,2,3] => 3 [1,4,3,2] => 2 [2,1,3,4] => 1 [2,1,4,3] => 4 [2,3,1,4] => 1 [2,3,4,1] => 1 [2,4,1,3] => 1 [2,4,3,1] => 1 [3,1,2,4] => 1 [3,1,4,2] => 1 [3,2,1,4] => 1 [3,2,4,1] => 1 [3,4,1,2] => 4 [3,4,2,1] => 1 [4,1,2,3] => 1 [4,1,3,2] => 1 [4,2,1,3] => 1 [4,2,3,1] => 1 [4,3,1,2] => 1 [4,3,2,1] => 4 [1,2,3,4,5] => 1 [1,2,3,5,4] => 2 [1,2,4,3,5] => 2 [1,2,4,5,3] => 3 [1,2,5,3,4] => 3 [1,2,5,4,3] => 2 [1,3,2,4,5] => 2 [1,3,2,5,4] => 24 [1,3,4,2,5] => 3 [1,3,4,5,2] => 4 [1,3,5,2,4] => 4 [1,3,5,4,2] => 3 [1,4,2,3,5] => 3 [1,4,2,5,3] => 4 [1,4,3,2,5] => 2 [1,4,3,5,2] => 3 [1,4,5,2,3] => 24 [1,4,5,3,2] => 4 [1,5,2,3,4] => 4 [1,5,2,4,3] => 3 [1,5,3,2,4] => 3 [1,5,3,4,2] => 2 [1,5,4,2,3] => 4 [1,5,4,3,2] => 24 [2,1,3,4,5] => 1 [2,1,3,5,4] => 4 [2,1,4,3,5] => 4 [2,1,4,5,3] => 6 [2,1,5,3,4] => 6 [2,1,5,4,3] => 4 [2,3,1,4,5] => 1 [2,3,1,5,4] => 6 [2,3,4,1,5] => 1 [2,3,4,5,1] => 1 [2,3,5,1,4] => 1 [2,3,5,4,1] => 1 [2,4,1,3,5] => 1 [2,4,1,5,3] => 1 [2,4,3,1,5] => 1 [2,4,3,5,1] => 1 [2,4,5,1,3] => 6 [2,4,5,3,1] => 1 [2,5,1,3,4] => 1 [2,5,1,4,3] => 1 [2,5,3,1,4] => 1 [2,5,3,4,1] => 1 [2,5,4,1,3] => 1 [2,5,4,3,1] => 6 [3,1,2,4,5] => 1 [3,1,2,5,4] => 6 [3,1,4,2,5] => 1 [3,1,4,5,2] => 1 [3,1,5,2,4] => 1 [3,1,5,4,2] => 1 [3,2,1,4,5] => 1 [3,2,1,5,4] => 4 [3,2,4,1,5] => 1 [3,2,4,5,1] => 1 [3,2,5,1,4] => 1 [3,2,5,4,1] => 1 [3,4,1,2,5] => 4 [3,4,1,5,2] => 6 [3,4,2,1,5] => 1 [3,4,2,5,1] => 1 [3,4,5,1,2] => 1 [3,4,5,2,1] => 6 [3,5,1,2,4] => 6 [3,5,1,4,2] => 4 [3,5,2,1,4] => 1 [3,5,2,4,1] => 1 [3,5,4,1,2] => 6 [3,5,4,2,1] => 1 [4,1,2,3,5] => 1 [4,1,2,5,3] => 1 [4,1,3,2,5] => 1 [4,1,3,5,2] => 1 [4,1,5,2,3] => 6 [4,1,5,3,2] => 1 [4,2,1,3,5] => 1 [4,2,1,5,3] => 1 [4,2,3,1,5] => 1 [4,2,3,5,1] => 1 [4,2,5,1,3] => 4 [4,2,5,3,1] => 1 [4,3,1,2,5] => 1 [4,3,1,5,2] => 1 [4,3,2,1,5] => 4 [4,3,2,5,1] => 6 [4,3,5,1,2] => 6 [4,3,5,2,1] => 1 [4,5,1,2,3] => 1 [4,5,1,3,2] => 6 [4,5,2,1,3] => 6 [4,5,2,3,1] => 1 [4,5,3,1,2] => 4 [4,5,3,2,1] => 1 [5,1,2,3,4] => 1 [5,1,2,4,3] => 1 [5,1,3,2,4] => 1 [5,1,3,4,2] => 1 [5,1,4,2,3] => 1 [5,1,4,3,2] => 6 [5,2,1,3,4] => 1 [5,2,1,4,3] => 1 [5,2,3,1,4] => 1 [5,2,3,4,1] => 1 [5,2,4,1,3] => 1 [5,2,4,3,1] => 4 [5,3,1,2,4] => 1 [5,3,1,4,2] => 1 [5,3,2,1,4] => 6 [5,3,2,4,1] => 4 [5,3,4,1,2] => 1 [5,3,4,2,1] => 6 [5,4,1,2,3] => 6 [5,4,1,3,2] => 1 [5,4,2,1,3] => 1 [5,4,2,3,1] => 6 [5,4,3,1,2] => 1 [5,4,3,2,1] => 4 [1,2,3,4,5,6] => 1 [1,2,3,4,6,5] => 2 [1,2,3,5,4,6] => 2 [1,2,3,5,6,4] => 3 [1,2,3,6,4,5] => 3 [1,2,3,6,5,4] => 2 [1,2,4,3,5,6] => 2 [1,2,4,3,6,5] => 24 [1,2,4,5,3,6] => 3 [1,2,4,5,6,3] => 4 [1,2,4,6,3,5] => 4 [1,2,4,6,5,3] => 3 [1,2,5,3,4,6] => 3 [1,2,5,3,6,4] => 4 [1,2,5,4,3,6] => 2 [1,2,5,4,6,3] => 3 [1,2,5,6,3,4] => 24 [1,2,5,6,4,3] => 4 [1,2,6,3,4,5] => 4 [1,2,6,3,5,4] => 3 [1,2,6,4,3,5] => 3 [1,2,6,4,5,3] => 2 [1,2,6,5,3,4] => 4 [1,2,6,5,4,3] => 24 [1,3,2,4,5,6] => 2 [1,3,2,4,6,5] => 24 [1,3,2,5,4,6] => 24 [1,3,2,5,6,4] => 42 [1,3,2,6,4,5] => 42 [1,3,2,6,5,4] => 24 [1,3,4,2,5,6] => 3 [1,3,4,2,6,5] => 42 [1,3,4,5,2,6] => 4 [1,3,4,5,6,2] => 5 [1,3,4,6,2,5] => 5 [1,3,4,6,5,2] => 4 [1,3,5,2,4,6] => 4 [1,3,5,2,6,4] => 5 [1,3,5,4,2,6] => 3 [1,3,5,4,6,2] => 4 [1,3,5,6,2,4] => 42 [1,3,5,6,4,2] => 5 [1,3,6,2,4,5] => 5 [1,3,6,2,5,4] => 4 [1,3,6,4,2,5] => 4 [1,3,6,4,5,2] => 3 [1,3,6,5,2,4] => 5 [1,3,6,5,4,2] => 42 [1,4,2,3,5,6] => 3 [1,4,2,3,6,5] => 42 [1,4,2,5,3,6] => 4 [1,4,2,5,6,3] => 5 [1,4,2,6,3,5] => 5 [1,4,2,6,5,3] => 4 [1,4,3,2,5,6] => 2 [1,4,3,2,6,5] => 24 [1,4,3,5,2,6] => 3 [1,4,3,5,6,2] => 4 [1,4,3,6,2,5] => 4 [1,4,3,6,5,2] => 3 [1,4,5,2,3,6] => 24 [1,4,5,2,6,3] => 42 [1,4,5,3,2,6] => 4 [1,4,5,3,6,2] => 5 [1,4,5,6,2,3] => 5 [1,4,5,6,3,2] => 42 [1,4,6,2,3,5] => 42 [1,4,6,2,5,3] => 24 [1,4,6,3,2,5] => 5 [1,4,6,3,5,2] => 4 [1,4,6,5,2,3] => 42 [1,4,6,5,3,2] => 5 [1,5,2,3,4,6] => 4 [1,5,2,3,6,4] => 5 [1,5,2,4,3,6] => 3 [1,5,2,4,6,3] => 4 [1,5,2,6,3,4] => 42 [1,5,2,6,4,3] => 5 [1,5,3,2,4,6] => 3 [1,5,3,2,6,4] => 4 [1,5,3,4,2,6] => 2 [1,5,3,4,6,2] => 3 [1,5,3,6,2,4] => 24 [1,5,3,6,4,2] => 4 [1,5,4,2,3,6] => 4 [1,5,4,2,6,3] => 5 [1,5,4,3,2,6] => 24 [1,5,4,3,6,2] => 42 [1,5,4,6,2,3] => 42 [1,5,4,6,3,2] => 5 [1,5,6,2,3,4] => 5 [1,5,6,2,4,3] => 42 [1,5,6,3,2,4] => 42 [1,5,6,3,4,2] => 5 [1,5,6,4,2,3] => 24 [1,5,6,4,3,2] => 4 [1,6,2,3,4,5] => 5 [1,6,2,3,5,4] => 4 [1,6,2,4,3,5] => 4 [1,6,2,4,5,3] => 3 [1,6,2,5,3,4] => 5 [1,6,2,5,4,3] => 42 [1,6,3,2,4,5] => 4 [1,6,3,2,5,4] => 3 [1,6,3,4,2,5] => 3 [1,6,3,4,5,2] => 2 [1,6,3,5,2,4] => 4 [1,6,3,5,4,2] => 24 [1,6,4,2,3,5] => 5 [1,6,4,2,5,3] => 4 [1,6,4,3,2,5] => 42 [1,6,4,3,5,2] => 24 [1,6,4,5,2,3] => 5 [1,6,4,5,3,2] => 42 [1,6,5,2,3,4] => 42 [1,6,5,2,4,3] => 5 [1,6,5,3,2,4] => 5 [1,6,5,3,4,2] => 42 [1,6,5,4,2,3] => 4 [1,6,5,4,3,2] => 24 [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] => 6 [2,1,3,6,4,5] => 6 [2,1,3,6,5,4] => 4 [2,1,4,3,5,6] => 4 [2,1,4,3,6,5] => 56 [2,1,4,5,3,6] => 6 [2,1,4,5,6,3] => 8 [2,1,4,6,3,5] => 8 [2,1,4,6,5,3] => 6 [2,1,5,3,4,6] => 6 [2,1,5,3,6,4] => 8 [2,1,5,4,3,6] => 4 [2,1,5,4,6,3] => 6 [2,1,5,6,3,4] => 56 [2,1,5,6,4,3] => 8 [2,1,6,3,4,5] => 8 [2,1,6,3,5,4] => 6 [2,1,6,4,3,5] => 6 [2,1,6,4,5,3] => 4 [2,1,6,5,3,4] => 8 [2,1,6,5,4,3] => 56 [2,3,1,4,5,6] => 1 [2,3,1,4,6,5] => 6 [2,3,1,5,4,6] => 6 [2,3,1,5,6,4] => 9 [2,3,1,6,4,5] => 9 [2,3,1,6,5,4] => 6 [2,3,4,1,5,6] => 1 [2,3,4,1,6,5] => 8 [2,3,4,5,1,6] => 1 [2,3,4,5,6,1] => 1 [2,3,4,6,1,5] => 1 [2,3,4,6,5,1] => 1 [2,3,5,1,4,6] => 1 [2,3,5,1,6,4] => 1 [2,3,5,4,1,6] => 1 [2,3,5,4,6,1] => 1 [2,3,5,6,1,4] => 8 [2,3,5,6,4,1] => 1 [2,3,6,1,4,5] => 1 [2,3,6,1,5,4] => 1 [2,3,6,4,1,5] => 1 [2,3,6,4,5,1] => 1 [2,3,6,5,1,4] => 1 [2,3,6,5,4,1] => 8 [2,4,1,3,5,6] => 1 [2,4,1,3,6,5] => 8 [2,4,1,5,3,6] => 1 [2,4,1,5,6,3] => 1 [2,4,1,6,3,5] => 1 [2,4,1,6,5,3] => 1 [2,4,3,1,5,6] => 1 [2,4,3,1,6,5] => 6 [2,4,3,5,1,6] => 1 [2,4,3,5,6,1] => 1 [2,4,3,6,1,5] => 1 [2,4,3,6,5,1] => 1 [2,4,5,1,3,6] => 6 [2,4,5,1,6,3] => 9 [2,4,5,3,1,6] => 1 [2,4,5,3,6,1] => 1 [2,4,5,6,1,3] => 1 [2,4,5,6,3,1] => 8 [2,4,6,1,3,5] => 9 [2,4,6,1,5,3] => 6 [2,4,6,3,1,5] => 1 [2,4,6,3,5,1] => 1 [2,4,6,5,1,3] => 8 [2,4,6,5,3,1] => 1 [2,5,1,3,4,6] => 1 [2,5,1,3,6,4] => 1 [2,5,1,4,3,6] => 1 [2,5,1,4,6,3] => 1 [2,5,1,6,3,4] => 8 [2,5,1,6,4,3] => 1 [2,5,3,1,4,6] => 1 [2,5,3,1,6,4] => 1 [2,5,3,4,1,6] => 1 [2,5,3,4,6,1] => 1 [2,5,3,6,1,4] => 6 [2,5,3,6,4,1] => 1 [2,5,4,1,3,6] => 1 [2,5,4,1,6,3] => 1 [2,5,4,3,1,6] => 6 [2,5,4,3,6,1] => 8 [2,5,4,6,1,3] => 9 [2,5,4,6,3,1] => 1 [2,5,6,1,3,4] => 1 [2,5,6,1,4,3] => 8 [2,5,6,3,1,4] => 9 [2,5,6,3,4,1] => 1 [2,5,6,4,1,3] => 6 [2,5,6,4,3,1] => 1 [2,6,1,3,4,5] => 1 [2,6,1,3,5,4] => 1 [2,6,1,4,3,5] => 1 [2,6,1,4,5,3] => 1 [2,6,1,5,3,4] => 1 [2,6,1,5,4,3] => 8 [2,6,3,1,4,5] => 1 [2,6,3,1,5,4] => 1 [2,6,3,4,1,5] => 1 [2,6,3,4,5,1] => 1 [2,6,3,5,1,4] => 1 [2,6,3,5,4,1] => 6 [2,6,4,1,3,5] => 1 [2,6,4,1,5,3] => 1 [2,6,4,3,1,5] => 8 [2,6,4,3,5,1] => 6 [2,6,4,5,1,3] => 1 [2,6,4,5,3,1] => 9 [2,6,5,1,3,4] => 8 [2,6,5,1,4,3] => 1 [2,6,5,3,1,4] => 1 [2,6,5,3,4,1] => 9 [2,6,5,4,1,3] => 1 [2,6,5,4,3,1] => 6 [3,1,2,4,5,6] => 1 [3,1,2,4,6,5] => 6 [3,1,2,5,4,6] => 6 [3,1,2,5,6,4] => 9 [3,1,2,6,4,5] => 9 [3,1,2,6,5,4] => 6 [3,1,4,2,5,6] => 1 [3,1,4,2,6,5] => 8 [3,1,4,5,2,6] => 1 [3,1,4,5,6,2] => 1 [3,1,4,6,2,5] => 1 [3,1,4,6,5,2] => 1 [3,1,5,2,4,6] => 1 [3,1,5,2,6,4] => 1 [3,1,5,4,2,6] => 1 [3,1,5,4,6,2] => 1 [3,1,5,6,2,4] => 8 [3,1,5,6,4,2] => 1 [3,1,6,2,4,5] => 1 [3,1,6,2,5,4] => 1 [3,1,6,4,2,5] => 1 [3,1,6,4,5,2] => 1 [3,1,6,5,2,4] => 1 [3,1,6,5,4,2] => 8 [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] => 6 [3,2,1,6,4,5] => 6 [3,2,1,6,5,4] => 4 [3,2,4,1,5,6] => 1 [3,2,4,1,6,5] => 6 [3,2,4,5,1,6] => 1 [3,2,4,5,6,1] => 1 [3,2,4,6,1,5] => 1 [3,2,4,6,5,1] => 1 [3,2,5,1,4,6] => 1 [3,2,5,1,6,4] => 1 [3,2,5,4,1,6] => 1 [3,2,5,4,6,1] => 1 [3,2,5,6,1,4] => 6 [3,2,5,6,4,1] => 1 [3,2,6,1,4,5] => 1 [3,2,6,1,5,4] => 1 [3,2,6,4,1,5] => 1 [3,2,6,4,5,1] => 1 [3,2,6,5,1,4] => 1 [3,2,6,5,4,1] => 6 [3,4,1,2,5,6] => 4 [3,4,1,2,6,5] => 56 [3,4,1,5,2,6] => 6 [3,4,1,5,6,2] => 8 [3,4,1,6,2,5] => 8 [3,4,1,6,5,2] => 6 [3,4,2,1,5,6] => 1 [3,4,2,1,6,5] => 8 [3,4,2,5,1,6] => 1 [3,4,2,5,6,1] => 1 [3,4,2,6,1,5] => 1 [3,4,2,6,5,1] => 1 [3,4,5,1,2,6] => 1 [3,4,5,1,6,2] => 1 [3,4,5,2,1,6] => 6 [3,4,5,2,6,1] => 8 [3,4,5,6,1,2] => 9 [3,4,5,6,2,1] => 1 [3,4,6,1,2,5] => 1 [3,4,6,1,5,2] => 1 [3,4,6,2,1,5] => 8 [3,4,6,2,5,1] => 6 [3,4,6,5,1,2] => 1 [3,4,6,5,2,1] => 9 [3,5,1,2,4,6] => 6 [3,5,1,2,6,4] => 8 [3,5,1,4,2,6] => 4 [3,5,1,4,6,2] => 6 [3,5,1,6,2,4] => 56 [3,5,1,6,4,2] => 8 [3,5,2,1,4,6] => 1 [3,5,2,1,6,4] => 1 [3,5,2,4,1,6] => 1 [3,5,2,4,6,1] => 1 [3,5,2,6,1,4] => 8 [3,5,2,6,4,1] => 1 [3,5,4,1,2,6] => 6 [3,5,4,1,6,2] => 9 [3,5,4,2,1,6] => 1 [3,5,4,2,6,1] => 1 [3,5,4,6,1,2] => 1 [3,5,4,6,2,1] => 8 [3,5,6,1,2,4] => 8 [3,5,6,1,4,2] => 1 [3,5,6,2,1,4] => 1 [3,5,6,2,4,1] => 9 [3,5,6,4,1,2] => 1 [3,5,6,4,2,1] => 6 [3,6,1,2,4,5] => 8 [3,6,1,2,5,4] => 6 [3,6,1,4,2,5] => 6 [3,6,1,4,5,2] => 4 [3,6,1,5,2,4] => 8 [3,6,1,5,4,2] => 56 [3,6,2,1,4,5] => 1 [3,6,2,1,5,4] => 1 [3,6,2,4,1,5] => 1 [3,6,2,4,5,1] => 1 [3,6,2,5,1,4] => 1 [3,6,2,5,4,1] => 8 [3,6,4,1,2,5] => 9 [3,6,4,1,5,2] => 6 [3,6,4,2,1,5] => 1 [3,6,4,2,5,1] => 1 [3,6,4,5,1,2] => 8 [3,6,4,5,2,1] => 1 [3,6,5,1,2,4] => 1 [3,6,5,1,4,2] => 8 [3,6,5,2,1,4] => 9 [3,6,5,2,4,1] => 1 [3,6,5,4,1,2] => 6 [3,6,5,4,2,1] => 1 [4,1,2,3,5,6] => 1 [4,1,2,3,6,5] => 8 [4,1,2,5,3,6] => 1 [4,1,2,5,6,3] => 1 [4,1,2,6,3,5] => 1 [4,1,2,6,5,3] => 1 [4,1,3,2,5,6] => 1 [4,1,3,2,6,5] => 6 [4,1,3,5,2,6] => 1 [4,1,3,5,6,2] => 1 [4,1,3,6,2,5] => 1 [4,1,3,6,5,2] => 1 [4,1,5,2,3,6] => 6 [4,1,5,2,6,3] => 9 [4,1,5,3,2,6] => 1 [4,1,5,3,6,2] => 1 [4,1,5,6,2,3] => 1 [4,1,5,6,3,2] => 8 [4,1,6,2,3,5] => 9 [4,1,6,2,5,3] => 6 [4,1,6,3,2,5] => 1 [4,1,6,3,5,2] => 1 [4,1,6,5,2,3] => 8 [4,1,6,5,3,2] => 1 [4,2,1,3,5,6] => 1 [4,2,1,3,6,5] => 6 [4,2,1,5,3,6] => 1 [4,2,1,5,6,3] => 1 [4,2,1,6,3,5] => 1 [4,2,1,6,5,3] => 1 [4,2,3,1,5,6] => 1 [4,2,3,1,6,5] => 4 [4,2,3,5,1,6] => 1 [4,2,3,5,6,1] => 1 [4,2,3,6,1,5] => 1 [4,2,3,6,5,1] => 1 [4,2,5,1,3,6] => 4 [4,2,5,1,6,3] => 6 [4,2,5,3,1,6] => 1 [4,2,5,3,6,1] => 1 [4,2,5,6,1,3] => 1 [4,2,5,6,3,1] => 6 [4,2,6,1,3,5] => 6 [4,2,6,1,5,3] => 4 [4,2,6,3,1,5] => 1 [4,2,6,3,5,1] => 1 [4,2,6,5,1,3] => 6 [4,2,6,5,3,1] => 1 [4,3,1,2,5,6] => 1 [4,3,1,2,6,5] => 8 [4,3,1,5,2,6] => 1 [4,3,1,5,6,2] => 1 [4,3,1,6,2,5] => 1 [4,3,1,6,5,2] => 1 [4,3,2,1,5,6] => 4 [4,3,2,1,6,5] => 56 [4,3,2,5,1,6] => 6 [4,3,2,5,6,1] => 8 [4,3,2,6,1,5] => 8 [4,3,2,6,5,1] => 6 [4,3,5,1,2,6] => 6 [4,3,5,1,6,2] => 8 [4,3,5,2,1,6] => 1 [4,3,5,2,6,1] => 1 [4,3,5,6,1,2] => 1 [4,3,5,6,2,1] => 9 [4,3,6,1,2,5] => 8 [4,3,6,1,5,2] => 6 [4,3,6,2,1,5] => 1 [4,3,6,2,5,1] => 1 [4,3,6,5,1,2] => 9 [4,3,6,5,2,1] => 1 [4,5,1,2,3,6] => 1 [4,5,1,2,6,3] => 1 [4,5,1,3,2,6] => 6 [4,5,1,3,6,2] => 9 [4,5,1,6,2,3] => 8 [4,5,1,6,3,2] => 1 [4,5,2,1,3,6] => 6 [4,5,2,1,6,3] => 8 [4,5,2,3,1,6] => 1 [4,5,2,3,6,1] => 1 [4,5,2,6,1,3] => 1 [4,5,2,6,3,1] => 9 [4,5,3,1,2,6] => 4 [4,5,3,1,6,2] => 6 [4,5,3,2,1,6] => 1 [4,5,3,2,6,1] => 1 [4,5,3,6,1,2] => 1 [4,5,3,6,2,1] => 6 [4,5,6,1,2,3] => 56 [4,5,6,1,3,2] => 8 [4,5,6,2,1,3] => 8 [4,5,6,2,3,1] => 1 [4,5,6,3,1,2] => 1 [4,5,6,3,2,1] => 8 [4,6,1,2,3,5] => 1 [4,6,1,2,5,3] => 1 [4,6,1,3,2,5] => 9 [4,6,1,3,5,2] => 6 [4,6,1,5,2,3] => 1 [4,6,1,5,3,2] => 8 [4,6,2,1,3,5] => 8 [4,6,2,1,5,3] => 6 [4,6,2,3,1,5] => 1 [4,6,2,3,5,1] => 1 [4,6,2,5,1,3] => 9 [4,6,2,5,3,1] => 1 [4,6,3,1,2,5] => 6 [4,6,3,1,5,2] => 4 [4,6,3,2,1,5] => 1 [4,6,3,2,5,1] => 1 [4,6,3,5,1,2] => 6 [4,6,3,5,2,1] => 1 [4,6,5,1,2,3] => 8 [4,6,5,1,3,2] => 56 [4,6,5,2,1,3] => 1 [4,6,5,2,3,1] => 8 [4,6,5,3,1,2] => 8 [4,6,5,3,2,1] => 1 [5,1,2,3,4,6] => 1 [5,1,2,3,6,4] => 1 [5,1,2,4,3,6] => 1 [5,1,2,4,6,3] => 1 [5,1,2,6,3,4] => 8 [5,1,2,6,4,3] => 1 [5,1,3,2,4,6] => 1 [5,1,3,2,6,4] => 1 [5,1,3,4,2,6] => 1 [5,1,3,4,6,2] => 1 [5,1,3,6,2,4] => 6 [5,1,3,6,4,2] => 1 [5,1,4,2,3,6] => 1 [5,1,4,2,6,3] => 1 [5,1,4,3,2,6] => 6 [5,1,4,3,6,2] => 8 [5,1,4,6,2,3] => 9 [5,1,4,6,3,2] => 1 [5,1,6,2,3,4] => 1 [5,1,6,2,4,3] => 8 [5,1,6,3,2,4] => 9 [5,1,6,3,4,2] => 1 [5,1,6,4,2,3] => 6 [5,1,6,4,3,2] => 1 [5,2,1,3,4,6] => 1 [5,2,1,3,6,4] => 1 [5,2,1,4,3,6] => 1 [5,2,1,4,6,3] => 1 [5,2,1,6,3,4] => 6 [5,2,1,6,4,3] => 1 [5,2,3,1,4,6] => 1 [5,2,3,1,6,4] => 1 [5,2,3,4,1,6] => 1 [5,2,3,4,6,1] => 1 [5,2,3,6,1,4] => 4 [5,2,3,6,4,1] => 1 [5,2,4,1,3,6] => 1 [5,2,4,1,6,3] => 1 [5,2,4,3,1,6] => 4 [5,2,4,3,6,1] => 6 [5,2,4,6,1,3] => 6 [5,2,4,6,3,1] => 1 [5,2,6,1,3,4] => 1 [5,2,6,1,4,3] => 6 [5,2,6,3,1,4] => 6 [5,2,6,3,4,1] => 1 [5,2,6,4,1,3] => 4 [5,2,6,4,3,1] => 1 [5,3,1,2,4,6] => 1 [5,3,1,2,6,4] => 1 [5,3,1,4,2,6] => 1 [5,3,1,4,6,2] => 1 [5,3,1,6,2,4] => 8 [5,3,1,6,4,2] => 1 [5,3,2,1,4,6] => 6 [5,3,2,1,6,4] => 8 [5,3,2,4,1,6] => 4 [5,3,2,4,6,1] => 6 [5,3,2,6,1,4] => 56 [5,3,2,6,4,1] => 8 [5,3,4,1,2,6] => 1 [5,3,4,1,6,2] => 1 [5,3,4,2,1,6] => 6 [5,3,4,2,6,1] => 9 [5,3,4,6,1,2] => 8 [5,3,4,6,2,1] => 1 [5,3,6,1,2,4] => 1 [5,3,6,1,4,2] => 9 [5,3,6,2,1,4] => 8 [5,3,6,2,4,1] => 1 [5,3,6,4,1,2] => 6 [5,3,6,4,2,1] => 1 [5,4,1,2,3,6] => 6 [5,4,1,2,6,3] => 8 [5,4,1,3,2,6] => 1 [5,4,1,3,6,2] => 1 [5,4,1,6,2,3] => 1 [5,4,1,6,3,2] => 9 [5,4,2,1,3,6] => 1 [5,4,2,1,6,3] => 1 [5,4,2,3,1,6] => 6 [5,4,2,3,6,1] => 9 [5,4,2,6,1,3] => 8 [5,4,2,6,3,1] => 1 [5,4,3,1,2,6] => 1 [5,4,3,1,6,2] => 1 [5,4,3,2,1,6] => 4 [5,4,3,2,6,1] => 6 [5,4,3,6,1,2] => 6 [5,4,3,6,2,1] => 1 [5,4,6,1,2,3] => 8 [5,4,6,1,3,2] => 1 [5,4,6,2,1,3] => 56 [5,4,6,2,3,1] => 8 [5,4,6,3,1,2] => 8 [5,4,6,3,2,1] => 1 [5,6,1,2,3,4] => 9 [5,6,1,2,4,3] => 1 [5,6,1,3,2,4] => 1 [5,6,1,3,4,2] => 8 [5,6,1,4,2,3] => 1 [5,6,1,4,3,2] => 6 [5,6,2,1,3,4] => 1 [5,6,2,1,4,3] => 9 [5,6,2,3,1,4] => 8 [5,6,2,3,4,1] => 1 [5,6,2,4,1,3] => 6 [5,6,2,4,3,1] => 1 [5,6,3,1,2,4] => 1 [5,6,3,1,4,2] => 6 [5,6,3,2,1,4] => 6 [5,6,3,2,4,1] => 1 [5,6,3,4,1,2] => 4 [5,6,3,4,2,1] => 1 [5,6,4,1,2,3] => 1 [5,6,4,1,3,2] => 8 [5,6,4,2,1,3] => 8 [5,6,4,2,3,1] => 1 [5,6,4,3,1,2] => 56 [5,6,4,3,2,1] => 8 [6,1,2,3,4,5] => 1 [6,1,2,3,5,4] => 1 [6,1,2,4,3,5] => 1 [6,1,2,4,5,3] => 1 [6,1,2,5,3,4] => 1 [6,1,2,5,4,3] => 8 [6,1,3,2,4,5] => 1 [6,1,3,2,5,4] => 1 [6,1,3,4,2,5] => 1 [6,1,3,4,5,2] => 1 [6,1,3,5,2,4] => 1 [6,1,3,5,4,2] => 6 [6,1,4,2,3,5] => 1 [6,1,4,2,5,3] => 1 [6,1,4,3,2,5] => 8 [6,1,4,3,5,2] => 6 [6,1,4,5,2,3] => 1 [6,1,4,5,3,2] => 9 [6,1,5,2,3,4] => 8 [6,1,5,2,4,3] => 1 [6,1,5,3,2,4] => 1 [6,1,5,3,4,2] => 9 [6,1,5,4,2,3] => 1 [6,1,5,4,3,2] => 6 [6,2,1,3,4,5] => 1 [6,2,1,3,5,4] => 1 [6,2,1,4,3,5] => 1 [6,2,1,4,5,3] => 1 [6,2,1,5,3,4] => 1 [6,2,1,5,4,3] => 6 [6,2,3,1,4,5] => 1 [6,2,3,1,5,4] => 1 [6,2,3,4,1,5] => 1 [6,2,3,4,5,1] => 1 [6,2,3,5,1,4] => 1 [6,2,3,5,4,1] => 4 [6,2,4,1,3,5] => 1 [6,2,4,1,5,3] => 1 [6,2,4,3,1,5] => 6 [6,2,4,3,5,1] => 4 [6,2,4,5,1,3] => 1 [6,2,4,5,3,1] => 6 [6,2,5,1,3,4] => 6 [6,2,5,1,4,3] => 1 [6,2,5,3,1,4] => 1 [6,2,5,3,4,1] => 6 [6,2,5,4,1,3] => 1 [6,2,5,4,3,1] => 4 [6,3,1,2,4,5] => 1 [6,3,1,2,5,4] => 1 [6,3,1,4,2,5] => 1 [6,3,1,4,5,2] => 1 [6,3,1,5,2,4] => 1 [6,3,1,5,4,2] => 8 [6,3,2,1,4,5] => 8 [6,3,2,1,5,4] => 6 [6,3,2,4,1,5] => 6 [6,3,2,4,5,1] => 4 [6,3,2,5,1,4] => 8 [6,3,2,5,4,1] => 56 [6,3,4,1,2,5] => 1 [6,3,4,1,5,2] => 1 [6,3,4,2,1,5] => 9 [6,3,4,2,5,1] => 6 [6,3,4,5,1,2] => 1 [6,3,4,5,2,1] => 8 [6,3,5,1,2,4] => 9 [6,3,5,1,4,2] => 1 [6,3,5,2,1,4] => 1 [6,3,5,2,4,1] => 8 [6,3,5,4,1,2] => 1 [6,3,5,4,2,1] => 6 [6,4,1,2,3,5] => 8 [6,4,1,2,5,3] => 6 [6,4,1,3,2,5] => 1 [6,4,1,3,5,2] => 1 [6,4,1,5,2,3] => 9 [6,4,1,5,3,2] => 1 [6,4,2,1,3,5] => 1 [6,4,2,1,5,3] => 1 [6,4,2,3,1,5] => 9 [6,4,2,3,5,1] => 6 [6,4,2,5,1,3] => 1 [6,4,2,5,3,1] => 8 [6,4,3,1,2,5] => 1 [6,4,3,1,5,2] => 1 [6,4,3,2,1,5] => 6 [6,4,3,2,5,1] => 4 [6,4,3,5,1,2] => 1 [6,4,3,5,2,1] => 6 [6,4,5,1,2,3] => 1 [6,4,5,1,3,2] => 8 [6,4,5,2,1,3] => 8 [6,4,5,2,3,1] => 56 [6,4,5,3,1,2] => 1 [6,4,5,3,2,1] => 8 [6,5,1,2,3,4] => 1 [6,5,1,2,4,3] => 9 [6,5,1,3,2,4] => 8 [6,5,1,3,4,2] => 1 [6,5,1,4,2,3] => 6 [6,5,1,4,3,2] => 1 [6,5,2,1,3,4] => 9 [6,5,2,1,4,3] => 1 [6,5,2,3,1,4] => 1 [6,5,2,3,4,1] => 8 [6,5,2,4,1,3] => 1 [6,5,2,4,3,1] => 6 [6,5,3,1,2,4] => 6 [6,5,3,1,4,2] => 1 [6,5,3,2,1,4] => 1 [6,5,3,2,4,1] => 6 [6,5,3,4,1,2] => 1 [6,5,3,4,2,1] => 4 [6,5,4,1,2,3] => 8 [6,5,4,1,3,2] => 1 [6,5,4,2,1,3] => 1 [6,5,4,2,3,1] => 8 [6,5,4,3,1,2] => 8 [6,5,4,3,2,1] => 56 [1,2,3,4,5,6,7] => 1 [1,2,3,4,5,7,6] => 2 [1,2,3,4,6,5,7] => 2 [1,2,3,4,6,7,5] => 3 [1,2,3,4,7,5,6] => 3 [1,2,3,4,7,6,5] => 2 [1,2,3,5,4,6,7] => 2 [1,2,3,5,4,7,6] => 24 [1,2,3,5,6,4,7] => 3 [1,2,3,5,6,7,4] => 4 [1,2,3,5,7,4,6] => 4 [1,2,3,5,7,6,4] => 3 [1,2,3,6,4,5,7] => 3 [1,2,3,6,4,7,5] => 4 [1,2,3,6,5,4,7] => 2 [1,2,3,6,5,7,4] => 3 [1,2,3,6,7,4,5] => 24 [1,2,3,6,7,5,4] => 4 [1,2,3,7,4,5,6] => 4 [1,2,3,7,4,6,5] => 3 [1,2,3,7,5,4,6] => 3 [1,2,3,7,5,6,4] => 2 [1,2,3,7,6,4,5] => 4 [1,2,3,7,6,5,4] => 24 [1,2,4,3,5,6,7] => 2 [1,2,4,3,5,7,6] => 24 [1,2,4,3,6,5,7] => 24 [1,2,4,3,6,7,5] => 42 [1,2,4,3,7,5,6] => 42 [1,2,4,3,7,6,5] => 24 [1,2,4,5,3,6,7] => 3 [1,2,4,5,3,7,6] => 42 [1,2,4,5,6,3,7] => 4 [1,2,4,5,6,7,3] => 5 [1,2,4,5,7,3,6] => 5 [1,2,4,5,7,6,3] => 4 [1,2,4,6,3,5,7] => 4 [1,2,4,6,3,7,5] => 5 [1,2,4,6,5,3,7] => 3 [1,2,4,6,5,7,3] => 4 [1,2,4,6,7,3,5] => 42 [1,2,4,6,7,5,3] => 5 [1,2,4,7,3,5,6] => 5 [1,2,4,7,3,6,5] => 4 [1,2,4,7,5,3,6] => 4 [1,2,4,7,5,6,3] => 3 [1,2,4,7,6,3,5] => 5 [1,2,4,7,6,5,3] => 42 [1,2,5,3,4,6,7] => 3 [1,2,5,3,4,7,6] => 42 [1,2,5,3,6,4,7] => 4 [1,2,5,3,6,7,4] => 5 [1,2,5,3,7,4,6] => 5 [1,2,5,3,7,6,4] => 4 [1,2,5,4,3,6,7] => 2 [1,2,5,4,3,7,6] => 24 [1,2,5,4,6,3,7] => 3 [1,2,5,4,6,7,3] => 4 [1,2,5,4,7,3,6] => 4 [1,2,5,4,7,6,3] => 3 [1,2,5,6,3,4,7] => 24 [1,2,5,6,3,7,4] => 42 [1,2,5,6,4,3,7] => 4 [1,2,5,6,4,7,3] => 5 [1,2,5,6,7,3,4] => 5 [1,2,5,6,7,4,3] => 42 [1,2,5,7,3,4,6] => 42 [1,2,5,7,3,6,4] => 24 [1,2,5,7,4,3,6] => 5 [1,2,5,7,4,6,3] => 4 [1,2,5,7,6,3,4] => 42 [1,2,5,7,6,4,3] => 5 [1,2,6,3,4,5,7] => 4 [1,2,6,3,4,7,5] => 5 [1,2,6,3,5,4,7] => 3 [1,2,6,3,5,7,4] => 4 [1,2,6,3,7,4,5] => 42 [1,2,6,3,7,5,4] => 5 [1,2,6,4,3,5,7] => 3 [1,2,6,4,3,7,5] => 4 [1,2,6,4,5,3,7] => 2 [1,2,6,4,5,7,3] => 3 [1,2,6,4,7,3,5] => 24 [1,2,6,4,7,5,3] => 4 [1,2,6,5,3,4,7] => 4 [1,2,6,5,3,7,4] => 5 [1,2,6,5,4,3,7] => 24 [1,2,6,5,4,7,3] => 42 [1,2,6,5,7,3,4] => 42 [1,2,6,5,7,4,3] => 5 [1,2,6,7,3,4,5] => 5 [1,2,6,7,3,5,4] => 42 [1,2,6,7,4,3,5] => 42 [1,2,6,7,4,5,3] => 5 [1,2,6,7,5,3,4] => 24 [1,2,6,7,5,4,3] => 4 [1,2,7,3,4,5,6] => 5 [1,2,7,3,4,6,5] => 4 [1,2,7,3,5,4,6] => 4 [1,2,7,3,5,6,4] => 3 [1,2,7,3,6,4,5] => 5 [1,2,7,3,6,5,4] => 42 [1,2,7,4,3,5,6] => 4 [1,2,7,4,3,6,5] => 3 [1,2,7,4,5,3,6] => 3 [1,2,7,4,5,6,3] => 2 [1,2,7,4,6,3,5] => 4 [1,2,7,4,6,5,3] => 24 [1,2,7,5,3,4,6] => 5 [1,2,7,5,3,6,4] => 4 [1,2,7,5,4,3,6] => 42 [1,2,7,5,4,6,3] => 24 [1,2,7,5,6,3,4] => 5 [1,2,7,5,6,4,3] => 42 [1,2,7,6,3,4,5] => 42 [1,2,7,6,3,5,4] => 5 [1,2,7,6,4,3,5] => 5 [1,2,7,6,4,5,3] => 42 [1,2,7,6,5,3,4] => 4 [1,2,7,6,5,4,3] => 24 [1,3,2,4,5,6,7] => 2 [1,3,2,4,5,7,6] => 24 [1,3,2,4,6,5,7] => 24 [1,3,2,4,6,7,5] => 42 [1,3,2,4,7,5,6] => 42 [1,3,2,4,7,6,5] => 24 [1,3,2,5,4,6,7] => 24 [1,3,2,5,4,7,6] => 576 [1,3,2,5,6,4,7] => 42 [1,3,2,5,6,7,4] => 64 [1,3,2,5,7,4,6] => 64 [1,3,2,5,7,6,4] => 42 [1,3,2,6,4,5,7] => 42 [1,3,2,6,4,7,5] => 64 [1,3,2,6,5,4,7] => 24 [1,3,2,6,5,7,4] => 42 [1,3,2,6,7,4,5] => 576 [1,3,2,6,7,5,4] => 64 [1,3,2,7,4,5,6] => 64 [1,3,2,7,4,6,5] => 42 [1,3,2,7,5,4,6] => 42 [1,3,2,7,5,6,4] => 24 [1,3,2,7,6,4,5] => 64 [1,3,2,7,6,5,4] => 576 [1,3,4,2,5,6,7] => 3 [1,3,4,2,5,7,6] => 42 [1,3,4,2,6,5,7] => 42 [1,3,4,2,6,7,5] => 72 [1,3,4,2,7,5,6] => 72 [1,3,4,2,7,6,5] => 42 [1,3,4,5,2,6,7] => 4 [1,3,4,5,2,7,6] => 64 [1,3,4,5,6,2,7] => 5 [1,3,4,5,6,7,2] => 6 [1,3,4,5,7,2,6] => 6 [1,3,4,5,7,6,2] => 5 [1,3,4,6,2,5,7] => 5 [1,3,4,6,2,7,5] => 6 [1,3,4,6,5,2,7] => 4 [1,3,4,6,5,7,2] => 5 [1,3,4,6,7,2,5] => 64 [1,3,4,6,7,5,2] => 6 [1,3,4,7,2,5,6] => 6 [1,3,4,7,2,6,5] => 5 [1,3,4,7,5,2,6] => 5 [1,3,4,7,5,6,2] => 4 [1,3,4,7,6,2,5] => 6 [1,3,4,7,6,5,2] => 64 [1,3,5,2,4,6,7] => 4 [1,3,5,2,4,7,6] => 64 [1,3,5,2,6,4,7] => 5 [1,3,5,2,6,7,4] => 6 [1,3,5,2,7,4,6] => 6 [1,3,5,2,7,6,4] => 5 [1,3,5,4,2,6,7] => 3 [1,3,5,4,2,7,6] => 42 [1,3,5,4,6,2,7] => 4 [1,3,5,4,6,7,2] => 5 [1,3,5,4,7,2,6] => 5 [1,3,5,4,7,6,2] => 4 [1,3,5,6,2,4,7] => 42 [1,3,5,6,2,7,4] => 72 [1,3,5,6,4,2,7] => 5 [1,3,5,6,4,7,2] => 6 [1,3,5,6,7,2,4] => 6 [1,3,5,6,7,4,2] => 64 [1,3,5,7,2,4,6] => 72 [1,3,5,7,2,6,4] => 42 [1,3,5,7,4,2,6] => 6 [1,3,5,7,4,6,2] => 5 [1,3,5,7,6,2,4] => 64 [1,3,5,7,6,4,2] => 6 [1,3,6,2,4,5,7] => 5 [1,3,6,2,4,7,5] => 6 [1,3,6,2,5,4,7] => 4 [1,3,6,2,5,7,4] => 5 [1,3,6,2,7,4,5] => 64 [1,3,6,2,7,5,4] => 6 [1,3,6,4,2,5,7] => 4 [1,3,6,4,2,7,5] => 5 [1,3,6,4,5,2,7] => 3 [1,3,6,4,5,7,2] => 4 [1,3,6,4,7,2,5] => 42 [1,3,6,4,7,5,2] => 5 [1,3,6,5,2,4,7] => 5 [1,3,6,5,2,7,4] => 6 [1,3,6,5,4,2,7] => 42 [1,3,6,5,4,7,2] => 64 [1,3,6,5,7,2,4] => 72 [1,3,6,5,7,4,2] => 6 [1,3,6,7,2,4,5] => 6 [1,3,6,7,2,5,4] => 64 [1,3,6,7,4,2,5] => 72 [1,3,6,7,4,5,2] => 6 [1,3,6,7,5,2,4] => 42 [1,3,6,7,5,4,2] => 5 [1,3,7,2,4,5,6] => 6 [1,3,7,2,4,6,5] => 5 [1,3,7,2,5,4,6] => 5 [1,3,7,2,5,6,4] => 4 [1,3,7,2,6,4,5] => 6 [1,3,7,2,6,5,4] => 64 [1,3,7,4,2,5,6] => 5 [1,3,7,4,2,6,5] => 4 [1,3,7,4,5,2,6] => 4 [1,3,7,4,5,6,2] => 3 [1,3,7,4,6,2,5] => 5 [1,3,7,4,6,5,2] => 42 [1,3,7,5,2,4,6] => 6 [1,3,7,5,2,6,4] => 5 [1,3,7,5,4,2,6] => 64 [1,3,7,5,4,6,2] => 42 [1,3,7,5,6,2,4] => 6 [1,3,7,5,6,4,2] => 72 [1,3,7,6,2,4,5] => 64 [1,3,7,6,2,5,4] => 6 [1,3,7,6,4,2,5] => 6 [1,3,7,6,4,5,2] => 72 [1,3,7,6,5,2,4] => 5 [1,3,7,6,5,4,2] => 42 [1,4,2,3,5,6,7] => 3 [1,4,2,3,5,7,6] => 42 [1,4,2,3,6,5,7] => 42 [1,4,2,3,6,7,5] => 72 [1,4,2,3,7,5,6] => 72 [1,4,2,3,7,6,5] => 42 [1,4,2,5,3,6,7] => 4 [1,4,2,5,3,7,6] => 64 [1,4,2,5,6,3,7] => 5 [1,4,2,5,6,7,3] => 6 [1,4,2,5,7,3,6] => 6 [1,4,2,5,7,6,3] => 5 [1,4,2,6,3,5,7] => 5 [1,4,2,6,3,7,5] => 6 [1,4,2,6,5,3,7] => 4 [1,4,2,6,5,7,3] => 5 [1,4,2,6,7,3,5] => 64 [1,4,2,6,7,5,3] => 6 [1,4,2,7,3,5,6] => 6 [1,4,2,7,3,6,5] => 5 [1,4,2,7,5,3,6] => 5 [1,4,2,7,5,6,3] => 4 [1,4,2,7,6,3,5] => 6 [1,4,2,7,6,5,3] => 64 [1,4,3,2,5,6,7] => 2 [1,4,3,2,5,7,6] => 24 [1,4,3,2,6,5,7] => 24 [1,4,3,2,6,7,5] => 42 [1,4,3,2,7,5,6] => 42 [1,4,3,2,7,6,5] => 24 [1,4,3,5,2,6,7] => 3 [1,4,3,5,2,7,6] => 42 [1,4,3,5,6,2,7] => 4 [1,4,3,5,6,7,2] => 5 [1,4,3,5,7,2,6] => 5 [1,4,3,5,7,6,2] => 4 [1,4,3,6,2,5,7] => 4 [1,4,3,6,2,7,5] => 5 [1,4,3,6,5,2,7] => 3 [1,4,3,6,5,7,2] => 4 [1,4,3,6,7,2,5] => 42 [1,4,3,6,7,5,2] => 5 [1,4,3,7,2,5,6] => 5 [1,4,3,7,2,6,5] => 4 [1,4,3,7,5,2,6] => 4 [1,4,3,7,5,6,2] => 3 [1,4,3,7,6,2,5] => 5 [1,4,3,7,6,5,2] => 42 [1,4,5,2,3,6,7] => 24 [1,4,5,2,3,7,6] => 576 [1,4,5,2,6,3,7] => 42 [1,4,5,2,6,7,3] => 64 [1,4,5,2,7,3,6] => 64 [1,4,5,2,7,6,3] => 42 [1,4,5,3,2,6,7] => 4 [1,4,5,3,2,7,6] => 64 [1,4,5,3,6,2,7] => 5 [1,4,5,3,6,7,2] => 6 [1,4,5,3,7,2,6] => 6 [1,4,5,3,7,6,2] => 5 [1,4,5,6,2,3,7] => 5 [1,4,5,6,2,7,3] => 6 [1,4,5,6,3,2,7] => 42 [1,4,5,6,3,7,2] => 64 [1,4,5,6,7,2,3] => 72 [1,4,5,6,7,3,2] => 6 [1,4,5,7,2,3,6] => 6 [1,4,5,7,2,6,3] => 5 [1,4,5,7,3,2,6] => 64 [1,4,5,7,3,6,2] => 42 [1,4,5,7,6,2,3] => 6 [1,4,5,7,6,3,2] => 72 [1,4,6,2,3,5,7] => 42 [1,4,6,2,3,7,5] => 64 [1,4,6,2,5,3,7] => 24 [1,4,6,2,5,7,3] => 42 [1,4,6,2,7,3,5] => 576 [1,4,6,2,7,5,3] => 64 [1,4,6,3,2,5,7] => 5 [1,4,6,3,2,7,5] => 6 [1,4,6,3,5,2,7] => 4 [1,4,6,3,5,7,2] => 5 [1,4,6,3,7,2,5] => 64 [1,4,6,3,7,5,2] => 6 [1,4,6,5,2,3,7] => 42 [1,4,6,5,2,7,3] => 72 [1,4,6,5,3,2,7] => 5 [1,4,6,5,3,7,2] => 6 ----------------------------------------------------------------------------- Created: Jan 09, 2018 at 21:52 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Jan 09, 2018 at 21:52 by Martin Rubey