***************************************************************************** * 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: St000677 ----------------------------------------------------------------------------- Collection: Permutations ----------------------------------------------------------------------------- Description: The standardized bi-alternating inversion number of a permutation. The bi-alternating inversion number $i(\pi)$ is $\sum_{1\leq y < x\leq n} (-1)^{y+x} \mathrm{sgn}(\pi(x)-\pi(y))$, see Section 3.1 of [1]. It takes values in between $-\lfloor\frac n2\rfloor^2$ and $\lfloor\frac n2\rfloor^2$, and $i(\pi)+\lfloor\frac n2\rfloor^2$ is even, so we standardize it to $(i(\pi)+\lfloor\frac n2\rfloor^2)/2$. For odd $n$ the bi-alternating inversion is invariant under rotation, that is, conjugation with the long cycle. ----------------------------------------------------------------------------- References: [1] Even-Zohar, C. The Writhe of Permutations and Random Framed Knots [[arXiv:1511.09469]] ----------------------------------------------------------------------------- Code: def statistic(pi): """ sage: all(statistic(Permutation([e+1 if e < len(pi) else 1 for e in [pi[-1]] + pi[:-1]])) == statistic(pi) for r in range(1,8,2) for pi in Permutations(r)) True """ return 1/2*((len(pi)//2)^2+sum((-1)^(y+x) if pi(x) > pi(y) else -(-1)^(y+x) for x in range(1,len(pi)+1) for y in range(1,x))) ----------------------------------------------------------------------------- Statistic values: [1,2] => 0 [2,1] => 1 [1,2,3] => 0 [1,3,2] => 1 [2,1,3] => 1 [2,3,1] => 0 [3,1,2] => 0 [3,2,1] => 1 [1,2,3,4] => 1 [1,2,4,3] => 2 [1,3,2,4] => 2 [1,3,4,2] => 1 [1,4,2,3] => 1 [1,4,3,2] => 2 [2,1,3,4] => 2 [2,1,4,3] => 3 [2,3,1,4] => 1 [2,3,4,1] => 2 [2,4,1,3] => 0 [2,4,3,1] => 3 [3,1,2,4] => 1 [3,1,4,2] => 4 [3,2,1,4] => 2 [3,2,4,1] => 3 [3,4,1,2] => 1 [3,4,2,1] => 2 [4,1,2,3] => 2 [4,1,3,2] => 3 [4,2,1,3] => 3 [4,2,3,1] => 2 [4,3,1,2] => 2 [4,3,2,1] => 3 [1,2,3,4,5] => 1 [1,2,3,5,4] => 2 [1,2,4,3,5] => 2 [1,2,4,5,3] => 1 [1,2,5,3,4] => 1 [1,2,5,4,3] => 2 [1,3,2,4,5] => 2 [1,3,2,5,4] => 3 [1,3,4,2,5] => 1 [1,3,4,5,2] => 2 [1,3,5,2,4] => 0 [1,3,5,4,2] => 3 [1,4,2,3,5] => 1 [1,4,2,5,3] => 4 [1,4,3,2,5] => 2 [1,4,3,5,2] => 3 [1,4,5,2,3] => 1 [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] => 2 [1,5,4,2,3] => 2 [1,5,4,3,2] => 3 [2,1,3,4,5] => 2 [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] => 1 [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] => 0 [2,4,1,5,3] => 3 [2,4,3,1,5] => 3 [2,4,3,5,1] => 2 [2,4,5,1,3] => 2 [2,4,5,3,1] => 1 [2,5,1,3,4] => 1 [2,5,1,4,3] => 2 [2,5,3,1,4] => 4 [2,5,3,4,1] => 1 [2,5,4,1,3] => 3 [2,5,4,3,1] => 2 [3,1,2,4,5] => 1 [3,1,2,5,4] => 2 [3,1,4,2,5] => 4 [3,1,4,5,2] => 1 [3,1,5,2,4] => 3 [3,1,5,4,2] => 2 [3,2,1,4,5] => 2 [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] => 1 [3,4,1,5,2] => 2 [3,4,2,1,5] => 2 [3,4,2,5,1] => 1 [3,4,5,1,2] => 1 [3,4,5,2,1] => 2 [3,5,1,2,4] => 2 [3,5,1,4,2] => 1 [3,5,2,1,4] => 3 [3,5,2,4,1] => 0 [3,5,4,1,2] => 2 [3,5,4,2,1] => 3 [4,1,2,3,5] => 2 [4,1,2,5,3] => 1 [4,1,3,2,5] => 3 [4,1,3,5,2] => 0 [4,1,5,2,3] => 2 [4,1,5,3,2] => 3 [4,2,1,3,5] => 3 [4,2,1,5,3] => 2 [4,2,3,1,5] => 2 [4,2,3,5,1] => 1 [4,2,5,1,3] => 1 [4,2,5,3,1] => 4 [4,3,1,2,5] => 2 [4,3,1,5,2] => 3 [4,3,2,1,5] => 3 [4,3,2,5,1] => 2 [4,3,5,1,2] => 2 [4,3,5,2,1] => 3 [4,5,1,2,3] => 1 [4,5,1,3,2] => 2 [4,5,2,1,3] => 2 [4,5,2,3,1] => 1 [4,5,3,1,2] => 1 [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] => 1 [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] => 1 [5,2,3,4,1] => 2 [5,2,4,1,3] => 0 [5,2,4,3,1] => 3 [5,3,1,2,4] => 1 [5,3,1,4,2] => 4 [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] => 2 [5,4,1,3,2] => 3 [5,4,2,1,3] => 3 [5,4,2,3,1] => 2 [5,4,3,1,2] => 2 [5,4,3,2,1] => 3 [1,2,3,4,5,6] => 3 [1,2,3,4,6,5] => 4 [1,2,3,5,4,6] => 4 [1,2,3,5,6,4] => 3 [1,2,3,6,4,5] => 3 [1,2,3,6,5,4] => 4 [1,2,4,3,5,6] => 4 [1,2,4,3,6,5] => 5 [1,2,4,5,3,6] => 3 [1,2,4,5,6,3] => 4 [1,2,4,6,3,5] => 2 [1,2,4,6,5,3] => 5 [1,2,5,3,4,6] => 3 [1,2,5,3,6,4] => 6 [1,2,5,4,3,6] => 4 [1,2,5,4,6,3] => 5 [1,2,5,6,3,4] => 3 [1,2,5,6,4,3] => 4 [1,2,6,3,4,5] => 4 [1,2,6,3,5,4] => 5 [1,2,6,4,3,5] => 5 [1,2,6,4,5,3] => 4 [1,2,6,5,3,4] => 4 [1,2,6,5,4,3] => 5 [1,3,2,4,5,6] => 4 [1,3,2,4,6,5] => 5 [1,3,2,5,4,6] => 5 [1,3,2,5,6,4] => 4 [1,3,2,6,4,5] => 4 [1,3,2,6,5,4] => 5 [1,3,4,2,5,6] => 3 [1,3,4,2,6,5] => 4 [1,3,4,5,2,6] => 4 [1,3,4,5,6,2] => 3 [1,3,4,6,2,5] => 3 [1,3,4,6,5,2] => 4 [1,3,5,2,4,6] => 2 [1,3,5,2,6,4] => 5 [1,3,5,4,2,6] => 5 [1,3,5,4,6,2] => 4 [1,3,5,6,2,4] => 4 [1,3,5,6,4,2] => 3 [1,3,6,2,4,5] => 3 [1,3,6,2,5,4] => 4 [1,3,6,4,2,5] => 6 [1,3,6,4,5,2] => 3 [1,3,6,5,2,4] => 5 [1,3,6,5,4,2] => 4 [1,4,2,3,5,6] => 3 [1,4,2,3,6,5] => 4 [1,4,2,5,3,6] => 6 [1,4,2,5,6,3] => 3 [1,4,2,6,3,5] => 5 [1,4,2,6,5,3] => 4 [1,4,3,2,5,6] => 4 [1,4,3,2,6,5] => 5 [1,4,3,5,2,6] => 5 [1,4,3,5,6,2] => 4 [1,4,3,6,2,5] => 4 [1,4,3,6,5,2] => 5 [1,4,5,2,3,6] => 3 [1,4,5,2,6,3] => 4 [1,4,5,3,2,6] => 4 [1,4,5,3,6,2] => 3 [1,4,5,6,2,3] => 3 [1,4,5,6,3,2] => 4 [1,4,6,2,3,5] => 4 [1,4,6,2,5,3] => 3 [1,4,6,3,2,5] => 5 [1,4,6,3,5,2] => 2 [1,4,6,5,2,3] => 4 [1,4,6,5,3,2] => 5 [1,5,2,3,4,6] => 4 [1,5,2,3,6,4] => 3 [1,5,2,4,3,6] => 5 [1,5,2,4,6,3] => 2 [1,5,2,6,3,4] => 4 [1,5,2,6,4,3] => 5 [1,5,3,2,4,6] => 5 [1,5,3,2,6,4] => 4 [1,5,3,4,2,6] => 4 [1,5,3,4,6,2] => 3 [1,5,3,6,2,4] => 3 [1,5,3,6,4,2] => 6 [1,5,4,2,3,6] => 4 [1,5,4,2,6,3] => 5 [1,5,4,3,2,6] => 5 [1,5,4,3,6,2] => 4 [1,5,4,6,2,3] => 4 [1,5,4,6,3,2] => 5 [1,5,6,2,3,4] => 3 [1,5,6,2,4,3] => 4 [1,5,6,3,2,4] => 4 [1,5,6,3,4,2] => 3 [1,5,6,4,2,3] => 3 [1,5,6,4,3,2] => 4 [1,6,2,3,4,5] => 3 [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] => 3 [1,6,2,5,4,3] => 4 [1,6,3,2,4,5] => 4 [1,6,3,2,5,4] => 5 [1,6,3,4,2,5] => 3 [1,6,3,4,5,2] => 4 [1,6,3,5,2,4] => 2 [1,6,3,5,4,2] => 5 [1,6,4,2,3,5] => 3 [1,6,4,2,5,3] => 6 [1,6,4,3,2,5] => 4 [1,6,4,3,5,2] => 5 [1,6,4,5,2,3] => 3 [1,6,4,5,3,2] => 4 [1,6,5,2,3,4] => 4 [1,6,5,2,4,3] => 5 [1,6,5,3,2,4] => 5 [1,6,5,3,4,2] => 4 [1,6,5,4,2,3] => 4 [1,6,5,4,3,2] => 5 [2,1,3,4,5,6] => 4 [2,1,3,4,6,5] => 5 [2,1,3,5,4,6] => 5 [2,1,3,5,6,4] => 4 [2,1,3,6,4,5] => 4 [2,1,3,6,5,4] => 5 [2,1,4,3,5,6] => 5 [2,1,4,3,6,5] => 6 [2,1,4,5,3,6] => 4 [2,1,4,5,6,3] => 5 [2,1,4,6,3,5] => 3 [2,1,4,6,5,3] => 6 [2,1,5,3,4,6] => 4 [2,1,5,3,6,4] => 7 [2,1,5,4,3,6] => 5 [2,1,5,4,6,3] => 6 [2,1,5,6,3,4] => 4 [2,1,5,6,4,3] => 5 [2,1,6,3,4,5] => 5 [2,1,6,3,5,4] => 6 [2,1,6,4,3,5] => 6 [2,1,6,4,5,3] => 5 [2,1,6,5,3,4] => 5 [2,1,6,5,4,3] => 6 [2,3,1,4,5,6] => 3 [2,3,1,4,6,5] => 4 [2,3,1,5,4,6] => 4 [2,3,1,5,6,4] => 3 [2,3,1,6,4,5] => 3 [2,3,1,6,5,4] => 4 [2,3,4,1,5,6] => 4 [2,3,4,1,6,5] => 5 [2,3,4,5,1,6] => 3 [2,3,4,5,6,1] => 4 [2,3,4,6,1,5] => 2 [2,3,4,6,5,1] => 5 [2,3,5,1,4,6] => 3 [2,3,5,1,6,4] => 6 [2,3,5,4,1,6] => 4 [2,3,5,4,6,1] => 5 [2,3,5,6,1,4] => 3 [2,3,5,6,4,1] => 4 [2,3,6,1,4,5] => 4 [2,3,6,1,5,4] => 5 [2,3,6,4,1,5] => 5 [2,3,6,4,5,1] => 4 [2,3,6,5,1,4] => 4 [2,3,6,5,4,1] => 5 [2,4,1,3,5,6] => 2 [2,4,1,3,6,5] => 3 [2,4,1,5,3,6] => 5 [2,4,1,5,6,3] => 2 [2,4,1,6,3,5] => 4 [2,4,1,6,5,3] => 3 [2,4,3,1,5,6] => 5 [2,4,3,1,6,5] => 6 [2,4,3,5,1,6] => 4 [2,4,3,5,6,1] => 5 [2,4,3,6,1,5] => 3 [2,4,3,6,5,1] => 6 [2,4,5,1,3,6] => 4 [2,4,5,1,6,3] => 5 [2,4,5,3,1,6] => 3 [2,4,5,3,6,1] => 4 [2,4,5,6,1,3] => 2 [2,4,5,6,3,1] => 5 [2,4,6,1,3,5] => 5 [2,4,6,1,5,3] => 4 [2,4,6,3,1,5] => 4 [2,4,6,3,5,1] => 3 [2,4,6,5,1,3] => 3 [2,4,6,5,3,1] => 6 [2,5,1,3,4,6] => 3 [2,5,1,3,6,4] => 2 [2,5,1,4,3,6] => 4 [2,5,1,4,6,3] => 1 [2,5,1,6,3,4] => 3 [2,5,1,6,4,3] => 4 [2,5,3,1,4,6] => 6 [2,5,3,1,6,4] => 5 [2,5,3,4,1,6] => 3 [2,5,3,4,6,1] => 4 [2,5,3,6,1,4] => 2 [2,5,3,6,4,1] => 7 [2,5,4,1,3,6] => 5 [2,5,4,1,6,3] => 6 [2,5,4,3,1,6] => 4 [2,5,4,3,6,1] => 5 [2,5,4,6,1,3] => 3 [2,5,4,6,3,1] => 6 [2,5,6,1,3,4] => 4 [2,5,6,1,4,3] => 5 [2,5,6,3,1,4] => 3 [2,5,6,3,4,1] => 4 [2,5,6,4,1,3] => 2 [2,5,6,4,3,1] => 5 [2,6,1,3,4,5] => 2 [2,6,1,3,5,4] => 3 [2,6,1,4,3,5] => 3 [2,6,1,4,5,3] => 2 [2,6,1,5,3,4] => 2 [2,6,1,5,4,3] => 3 [2,6,3,1,4,5] => 5 [2,6,3,1,5,4] => 6 [2,6,3,4,1,5] => 2 [2,6,3,4,5,1] => 5 [2,6,3,5,1,4] => 1 [2,6,3,5,4,1] => 6 [2,6,4,1,3,5] => 4 [2,6,4,1,5,3] => 7 [2,6,4,3,1,5] => 3 [2,6,4,3,5,1] => 6 [2,6,4,5,1,3] => 2 [2,6,4,5,3,1] => 5 [2,6,5,1,3,4] => 5 [2,6,5,1,4,3] => 6 [2,6,5,3,1,4] => 4 [2,6,5,3,4,1] => 5 [2,6,5,4,1,3] => 3 [2,6,5,4,3,1] => 6 [3,1,2,4,5,6] => 3 [3,1,2,4,6,5] => 4 [3,1,2,5,4,6] => 4 [3,1,2,5,6,4] => 3 [3,1,2,6,4,5] => 3 [3,1,2,6,5,4] => 4 [3,1,4,2,5,6] => 6 [3,1,4,2,6,5] => 7 [3,1,4,5,2,6] => 3 [3,1,4,5,6,2] => 6 [3,1,4,6,2,5] => 2 [3,1,4,6,5,2] => 7 [3,1,5,2,4,6] => 5 [3,1,5,2,6,4] => 8 [3,1,5,4,2,6] => 4 [3,1,5,4,6,2] => 7 [3,1,5,6,2,4] => 3 [3,1,5,6,4,2] => 6 [3,1,6,2,4,5] => 6 [3,1,6,2,5,4] => 7 [3,1,6,4,2,5] => 5 [3,1,6,4,5,2] => 6 [3,1,6,5,2,4] => 4 [3,1,6,5,4,2] => 7 [3,2,1,4,5,6] => 4 [3,2,1,4,6,5] => 5 [3,2,1,5,4,6] => 5 [3,2,1,5,6,4] => 4 [3,2,1,6,4,5] => 4 [3,2,1,6,5,4] => 5 [3,2,4,1,5,6] => 5 [3,2,4,1,6,5] => 6 [3,2,4,5,1,6] => 4 [3,2,4,5,6,1] => 5 [3,2,4,6,1,5] => 3 [3,2,4,6,5,1] => 6 [3,2,5,1,4,6] => 4 [3,2,5,1,6,4] => 7 [3,2,5,4,1,6] => 5 [3,2,5,4,6,1] => 6 [3,2,5,6,1,4] => 4 [3,2,5,6,4,1] => 5 [3,2,6,1,4,5] => 5 [3,2,6,1,5,4] => 6 [3,2,6,4,1,5] => 6 [3,2,6,4,5,1] => 5 [3,2,6,5,1,4] => 5 [3,2,6,5,4,1] => 6 [3,4,1,2,5,6] => 3 [3,4,1,2,6,5] => 4 [3,4,1,5,2,6] => 4 [3,4,1,5,6,2] => 3 [3,4,1,6,2,5] => 3 [3,4,1,6,5,2] => 4 [3,4,2,1,5,6] => 4 [3,4,2,1,6,5] => 5 [3,4,2,5,1,6] => 3 [3,4,2,5,6,1] => 4 [3,4,2,6,1,5] => 2 [3,4,2,6,5,1] => 5 [3,4,5,1,2,6] => 3 [3,4,5,1,6,2] => 6 [3,4,5,2,1,6] => 4 [3,4,5,2,6,1] => 5 [3,4,5,6,1,2] => 3 [3,4,5,6,2,1] => 4 [3,4,6,1,2,5] => 4 [3,4,6,1,5,2] => 5 [3,4,6,2,1,5] => 5 [3,4,6,2,5,1] => 4 [3,4,6,5,1,2] => 4 [3,4,6,5,2,1] => 5 [3,5,1,2,4,6] => 4 [3,5,1,2,6,4] => 3 [3,5,1,4,2,6] => 3 [3,5,1,4,6,2] => 2 [3,5,1,6,2,4] => 2 [3,5,1,6,4,2] => 5 [3,5,2,1,4,6] => 5 [3,5,2,1,6,4] => 4 [3,5,2,4,1,6] => 2 [3,5,2,4,6,1] => 3 [3,5,2,6,1,4] => 1 [3,5,2,6,4,1] => 6 [3,5,4,1,2,6] => 4 [3,5,4,1,6,2] => 7 [3,5,4,2,1,6] => 5 [3,5,4,2,6,1] => 6 [3,5,4,6,1,2] => 4 [3,5,4,6,2,1] => 5 [3,5,6,1,2,4] => 3 [3,5,6,1,4,2] => 6 [3,5,6,2,1,4] => 4 [3,5,6,2,4,1] => 5 [3,5,6,4,1,2] => 3 [3,5,6,4,2,1] => 4 [3,6,1,2,4,5] => 3 [3,6,1,2,5,4] => 4 [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] => 4 [3,6,2,1,4,5] => 4 [3,6,2,1,5,4] => 5 [3,6,2,4,1,5] => 1 [3,6,2,4,5,1] => 4 [3,6,2,5,1,4] => 0 [3,6,2,5,4,1] => 5 [3,6,4,1,2,5] => 3 [3,6,4,1,5,2] => 8 [3,6,4,2,1,5] => 4 [3,6,4,2,5,1] => 7 [3,6,4,5,1,2] => 3 [3,6,4,5,2,1] => 4 [3,6,5,1,2,4] => 4 [3,6,5,1,4,2] => 7 [3,6,5,2,1,4] => 5 [3,6,5,2,4,1] => 6 [3,6,5,4,1,2] => 4 [3,6,5,4,2,1] => 5 [4,1,2,3,5,6] => 4 [4,1,2,3,6,5] => 5 [4,1,2,5,3,6] => 3 [4,1,2,5,6,3] => 4 [4,1,2,6,3,5] => 2 [4,1,2,6,5,3] => 5 [4,1,3,2,5,6] => 5 [4,1,3,2,6,5] => 6 [4,1,3,5,2,6] => 2 [4,1,3,5,6,2] => 5 [4,1,3,6,2,5] => 1 [4,1,3,6,5,2] => 6 [4,1,5,2,3,6] => 4 [4,1,5,2,6,3] => 9 [4,1,5,3,2,6] => 5 [4,1,5,3,6,2] => 8 [4,1,5,6,2,3] => 4 [4,1,5,6,3,2] => 5 [4,1,6,2,3,5] => 5 [4,1,6,2,5,3] => 8 [4,1,6,3,2,5] => 6 [4,1,6,3,5,2] => 7 [4,1,6,5,2,3] => 5 [4,1,6,5,3,2] => 6 [4,2,1,3,5,6] => 5 [4,2,1,3,6,5] => 6 [4,2,1,5,3,6] => 4 [4,2,1,5,6,3] => 5 [4,2,1,6,3,5] => 3 [4,2,1,6,5,3] => 6 [4,2,3,1,5,6] => 4 [4,2,3,1,6,5] => 5 [4,2,3,5,1,6] => 3 [4,2,3,5,6,1] => 4 [4,2,3,6,1,5] => 2 [4,2,3,6,5,1] => 5 [4,2,5,1,3,6] => 3 [4,2,5,1,6,3] => 8 [4,2,5,3,1,6] => 6 [4,2,5,3,6,1] => 7 [4,2,5,6,1,3] => 5 [4,2,5,6,3,1] => 4 [4,2,6,1,3,5] => 4 [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] => 4 [4,3,1,2,6,5] => 5 [4,3,1,5,2,6] => 5 [4,3,1,5,6,2] => 4 [4,3,1,6,2,5] => 4 [4,3,1,6,5,2] => 5 [4,3,2,1,5,6] => 5 [4,3,2,1,6,5] => 6 [4,3,2,5,1,6] => 4 [4,3,2,5,6,1] => 5 [4,3,2,6,1,5] => 3 [4,3,2,6,5,1] => 6 [4,3,5,1,2,6] => 4 [4,3,5,1,6,2] => 7 [4,3,5,2,1,6] => 5 [4,3,5,2,6,1] => 6 [4,3,5,6,1,2] => 4 [4,3,5,6,2,1] => 5 [4,3,6,1,2,5] => 5 [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] => 6 [4,5,1,2,3,6] => 3 [4,5,1,2,6,3] => 4 [4,5,1,3,2,6] => 4 [4,5,1,3,6,2] => 3 [4,5,1,6,2,3] => 3 [4,5,1,6,3,2] => 4 [4,5,2,1,3,6] => 4 [4,5,2,1,6,3] => 5 [4,5,2,3,1,6] => 3 [4,5,2,3,6,1] => 4 [4,5,2,6,1,3] => 2 [4,5,2,6,3,1] => 5 [4,5,3,1,2,6] => 3 [4,5,3,1,6,2] => 6 [4,5,3,2,1,6] => 4 [4,5,3,2,6,1] => 5 [4,5,3,6,1,2] => 3 [4,5,3,6,2,1] => 4 [4,5,6,1,2,3] => 4 [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] => 5 [4,6,1,2,3,5] => 2 [4,6,1,2,5,3] => 5 [4,6,1,3,2,5] => 3 [4,6,1,3,5,2] => 4 [4,6,1,5,2,3] => 2 [4,6,1,5,3,2] => 3 [4,6,2,1,3,5] => 3 [4,6,2,1,5,3] => 6 [4,6,2,3,1,5] => 2 [4,6,2,3,5,1] => 5 [4,6,2,5,1,3] => 1 [4,6,2,5,3,1] => 4 [4,6,3,1,2,5] => 2 [4,6,3,1,5,2] => 7 [4,6,3,2,1,5] => 3 [4,6,3,2,5,1] => 6 [4,6,3,5,1,2] => 2 [4,6,3,5,2,1] => 3 [4,6,5,1,2,3] => 5 [4,6,5,1,3,2] => 6 [4,6,5,2,1,3] => 6 [4,6,5,2,3,1] => 5 [4,6,5,3,1,2] => 5 [4,6,5,3,2,1] => 6 [5,1,2,3,4,6] => 3 [5,1,2,3,6,4] => 6 [5,1,2,4,3,6] => 4 [5,1,2,4,6,3] => 5 [5,1,2,6,3,4] => 3 [5,1,2,6,4,3] => 4 [5,1,3,2,4,6] => 4 [5,1,3,2,6,4] => 7 [5,1,3,4,2,6] => 3 [5,1,3,4,6,2] => 6 [5,1,3,6,2,4] => 2 [5,1,3,6,4,2] => 5 [5,1,4,2,3,6] => 3 [5,1,4,2,6,3] => 8 [5,1,4,3,2,6] => 4 [5,1,4,3,6,2] => 7 [5,1,4,6,2,3] => 3 [5,1,4,6,3,2] => 4 [5,1,6,2,3,4] => 6 [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] => 7 [5,2,1,3,4,6] => 4 [5,2,1,3,6,4] => 7 [5,2,1,4,3,6] => 5 [5,2,1,4,6,3] => 6 [5,2,1,6,3,4] => 4 [5,2,1,6,4,3] => 5 [5,2,3,1,4,6] => 3 [5,2,3,1,6,4] => 6 [5,2,3,4,1,6] => 4 [5,2,3,4,6,1] => 5 [5,2,3,6,1,4] => 3 [5,2,3,6,4,1] => 4 [5,2,4,1,3,6] => 2 [5,2,4,1,6,3] => 7 [5,2,4,3,1,6] => 5 [5,2,4,3,6,1] => 6 [5,2,4,6,1,3] => 4 [5,2,4,6,3,1] => 3 [5,2,6,1,3,4] => 5 [5,2,6,1,4,3] => 6 [5,2,6,3,1,4] => 8 [5,2,6,3,4,1] => 5 [5,2,6,4,1,3] => 7 [5,2,6,4,3,1] => 6 [5,3,1,2,4,6] => 3 [5,3,1,2,6,4] => 6 [5,3,1,4,2,6] => 6 [5,3,1,4,6,2] => 5 [5,3,1,6,2,4] => 5 [5,3,1,6,4,2] => 4 [5,3,2,1,4,6] => 4 [5,3,2,1,6,4] => 7 [5,3,2,4,1,6] => 5 [5,3,2,4,6,1] => 6 [5,3,2,6,1,4] => 4 [5,3,2,6,4,1] => 5 [5,3,4,1,2,6] => 3 [5,3,4,1,6,2] => 6 [5,3,4,2,1,6] => 4 [5,3,4,2,6,1] => 5 [5,3,4,6,1,2] => 3 [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] => 7 [5,3,6,2,4,1] => 4 [5,3,6,4,1,2] => 6 [5,3,6,4,2,1] => 7 [5,4,1,2,3,6] => 4 [5,4,1,2,6,3] => 5 [5,4,1,3,2,6] => 5 [5,4,1,3,6,2] => 4 [5,4,1,6,2,3] => 4 [5,4,1,6,3,2] => 5 [5,4,2,1,3,6] => 5 [5,4,2,1,6,3] => 6 [5,4,2,3,1,6] => 4 [5,4,2,3,6,1] => 5 [5,4,2,6,1,3] => 3 [5,4,2,6,3,1] => 6 [5,4,3,1,2,6] => 4 [5,4,3,1,6,2] => 7 [5,4,3,2,1,6] => 5 [5,4,3,2,6,1] => 6 [5,4,3,6,1,2] => 4 [5,4,3,6,2,1] => 5 [5,4,6,1,2,3] => 5 [5,4,6,1,3,2] => 6 [5,4,6,2,1,3] => 6 [5,4,6,2,3,1] => 5 [5,4,6,3,1,2] => 5 [5,4,6,3,2,1] => 6 [5,6,1,2,3,4] => 3 [5,6,1,2,4,3] => 4 [5,6,1,3,2,4] => 4 [5,6,1,3,4,2] => 3 [5,6,1,4,2,3] => 3 [5,6,1,4,3,2] => 4 [5,6,2,1,3,4] => 4 [5,6,2,1,4,3] => 5 [5,6,2,3,1,4] => 3 [5,6,2,3,4,1] => 4 [5,6,2,4,1,3] => 2 [5,6,2,4,3,1] => 5 [5,6,3,1,2,4] => 3 [5,6,3,1,4,2] => 6 [5,6,3,2,1,4] => 4 [5,6,3,2,4,1] => 5 [5,6,3,4,1,2] => 3 [5,6,3,4,2,1] => 4 [5,6,4,1,2,3] => 4 [5,6,4,1,3,2] => 5 [5,6,4,2,1,3] => 5 [5,6,4,2,3,1] => 4 [5,6,4,3,1,2] => 4 [5,6,4,3,2,1] => 5 [6,1,2,3,4,5] => 4 [6,1,2,3,5,4] => 5 [6,1,2,4,3,5] => 5 [6,1,2,4,5,3] => 4 [6,1,2,5,3,4] => 4 [6,1,2,5,4,3] => 5 [6,1,3,2,4,5] => 5 [6,1,3,2,5,4] => 6 [6,1,3,4,2,5] => 4 [6,1,3,4,5,2] => 5 [6,1,3,5,2,4] => 3 [6,1,3,5,4,2] => 6 [6,1,4,2,3,5] => 4 [6,1,4,2,5,3] => 7 [6,1,4,3,2,5] => 5 [6,1,4,3,5,2] => 6 [6,1,4,5,2,3] => 4 [6,1,4,5,3,2] => 5 [6,1,5,2,3,4] => 5 [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] => 6 [6,2,1,3,4,5] => 5 [6,2,1,3,5,4] => 6 [6,2,1,4,3,5] => 6 [6,2,1,4,5,3] => 5 [6,2,1,5,3,4] => 5 [6,2,1,5,4,3] => 6 [6,2,3,1,4,5] => 4 [6,2,3,1,5,4] => 5 [6,2,3,4,1,5] => 5 [6,2,3,4,5,1] => 4 [6,2,3,5,1,4] => 4 [6,2,3,5,4,1] => 5 [6,2,4,1,3,5] => 3 [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] => 4 [6,2,5,1,4,3] => 5 [6,2,5,3,1,4] => 7 [6,2,5,3,4,1] => 4 [6,2,5,4,1,3] => 6 [6,2,5,4,3,1] => 5 [6,3,1,2,4,5] => 4 [6,3,1,2,5,4] => 5 [6,3,1,4,2,5] => 7 [6,3,1,4,5,2] => 4 [6,3,1,5,2,4] => 6 [6,3,1,5,4,2] => 5 [6,3,2,1,4,5] => 5 [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] => 6 [6,3,4,1,2,5] => 4 [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] => 5 [6,3,5,1,2,4] => 5 [6,3,5,1,4,2] => 4 [6,3,5,2,1,4] => 6 [6,3,5,2,4,1] => 3 [6,3,5,4,1,2] => 5 [6,3,5,4,2,1] => 6 [6,4,1,2,3,5] => 5 [6,4,1,2,5,3] => 4 [6,4,1,3,2,5] => 6 [6,4,1,3,5,2] => 3 [6,4,1,5,2,3] => 5 [6,4,1,5,3,2] => 6 [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] => 7 [6,4,3,1,2,5] => 5 [6,4,3,1,5,2] => 6 [6,4,3,2,1,5] => 6 [6,4,3,2,5,1] => 5 [6,4,3,5,1,2] => 5 [6,4,3,5,2,1] => 6 [6,4,5,1,2,3] => 4 [6,4,5,1,3,2] => 5 [6,4,5,2,1,3] => 5 [6,4,5,2,3,1] => 4 [6,4,5,3,1,2] => 4 [6,4,5,3,2,1] => 5 [6,5,1,2,3,4] => 4 [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] => 5 [6,5,2,1,3,4] => 5 [6,5,2,1,4,3] => 6 [6,5,2,3,1,4] => 4 [6,5,2,3,4,1] => 5 [6,5,2,4,1,3] => 3 [6,5,2,4,3,1] => 6 [6,5,3,1,2,4] => 4 [6,5,3,1,4,2] => 7 [6,5,3,2,1,4] => 5 [6,5,3,2,4,1] => 6 [6,5,3,4,1,2] => 4 [6,5,3,4,2,1] => 5 [6,5,4,1,2,3] => 5 [6,5,4,1,3,2] => 6 [6,5,4,2,1,3] => 6 [6,5,4,2,3,1] => 5 [6,5,4,3,1,2] => 5 [6,5,4,3,2,1] => 6 [1,2,3,4,5,6,7] => 3 [1,2,3,4,5,7,6] => 4 [1,2,3,4,6,5,7] => 4 [1,2,3,4,6,7,5] => 3 [1,2,3,4,7,5,6] => 3 [1,2,3,4,7,6,5] => 4 [1,2,3,5,4,6,7] => 4 [1,2,3,5,4,7,6] => 5 [1,2,3,5,6,4,7] => 3 [1,2,3,5,6,7,4] => 4 [1,2,3,5,7,4,6] => 2 [1,2,3,5,7,6,4] => 5 [1,2,3,6,4,5,7] => 3 [1,2,3,6,4,7,5] => 6 [1,2,3,6,5,4,7] => 4 [1,2,3,6,5,7,4] => 5 [1,2,3,6,7,4,5] => 3 [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] => 4 [1,2,3,7,6,4,5] => 4 [1,2,3,7,6,5,4] => 5 [1,2,4,3,5,6,7] => 4 [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] => 3 [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] => 2 [1,2,4,6,3,7,5] => 5 [1,2,4,6,5,3,7] => 5 [1,2,4,6,5,7,3] => 4 [1,2,4,6,7,3,5] => 4 [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] => 6 [1,2,4,7,5,6,3] => 3 [1,2,4,7,6,3,5] => 5 [1,2,4,7,6,5,3] => 4 [1,2,5,3,4,6,7] => 3 [1,2,5,3,4,7,6] => 4 [1,2,5,3,6,4,7] => 6 [1,2,5,3,6,7,4] => 3 [1,2,5,3,7,4,6] => 5 [1,2,5,3,7,6,4] => 4 [1,2,5,4,3,6,7] => 4 [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] => 3 [1,2,5,6,3,7,4] => 4 [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] => 4 [1,2,5,7,3,4,6] => 4 [1,2,5,7,3,6,4] => 3 [1,2,5,7,4,3,6] => 5 [1,2,5,7,4,6,3] => 2 [1,2,5,7,6,3,4] => 4 [1,2,5,7,6,4,3] => 5 [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] => 2 [1,2,6,3,7,4,5] => 4 [1,2,6,3,7,5,4] => 5 [1,2,6,4,3,5,7] => 5 [1,2,6,4,3,7,5] => 4 [1,2,6,4,5,3,7] => 4 [1,2,6,4,5,7,3] => 3 [1,2,6,4,7,3,5] => 3 [1,2,6,4,7,5,3] => 6 [1,2,6,5,3,4,7] => 4 [1,2,6,5,3,7,4] => 5 [1,2,6,5,4,3,7] => 5 [1,2,6,5,4,7,3] => 4 [1,2,6,5,7,3,4] => 4 [1,2,6,5,7,4,3] => 5 [1,2,6,7,3,4,5] => 3 [1,2,6,7,3,5,4] => 4 [1,2,6,7,4,3,5] => 4 [1,2,6,7,4,5,3] => 3 [1,2,6,7,5,3,4] => 3 [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] => 3 [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] => 3 [1,2,7,4,5,6,3] => 4 [1,2,7,4,6,3,5] => 2 [1,2,7,4,6,5,3] => 5 [1,2,7,5,3,4,6] => 3 [1,2,7,5,3,6,4] => 6 [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] => 4 [1,2,7,6,3,5,4] => 5 [1,2,7,6,4,3,5] => 5 [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] => 4 [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] => 6 [1,3,2,5,6,4,7] => 4 [1,3,2,5,6,7,4] => 5 [1,3,2,5,7,4,6] => 3 [1,3,2,5,7,6,4] => 6 [1,3,2,6,4,5,7] => 4 [1,3,2,6,4,7,5] => 7 [1,3,2,6,5,4,7] => 5 [1,3,2,6,5,7,4] => 6 [1,3,2,6,7,4,5] => 4 [1,3,2,6,7,5,4] => 5 [1,3,2,7,4,5,6] => 5 [1,3,2,7,4,6,5] => 6 [1,3,2,7,5,4,6] => 6 [1,3,2,7,5,6,4] => 5 [1,3,2,7,6,4,5] => 5 [1,3,2,7,6,5,4] => 6 [1,3,4,2,5,6,7] => 3 [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] => 5 [1,3,4,5,6,2,7] => 3 [1,3,4,5,6,7,2] => 4 [1,3,4,5,7,2,6] => 2 [1,3,4,5,7,6,2] => 5 [1,3,4,6,2,5,7] => 3 [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] => 3 [1,3,4,6,7,5,2] => 4 [1,3,4,7,2,5,6] => 4 [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] => 4 [1,3,4,7,6,5,2] => 5 [1,3,5,2,4,6,7] => 2 [1,3,5,2,4,7,6] => 3 [1,3,5,2,6,4,7] => 5 [1,3,5,2,6,7,4] => 2 [1,3,5,2,7,4,6] => 4 [1,3,5,2,7,6,4] => 3 [1,3,5,4,2,6,7] => 5 [1,3,5,4,2,7,6] => 6 [1,3,5,4,6,2,7] => 4 [1,3,5,4,6,7,2] => 5 [1,3,5,4,7,2,6] => 3 [1,3,5,4,7,6,2] => 6 [1,3,5,6,2,4,7] => 4 [1,3,5,6,2,7,4] => 5 [1,3,5,6,4,2,7] => 3 [1,3,5,6,4,7,2] => 4 [1,3,5,6,7,2,4] => 2 [1,3,5,6,7,4,2] => 5 [1,3,5,7,2,4,6] => 5 [1,3,5,7,2,6,4] => 4 [1,3,5,7,4,2,6] => 4 [1,3,5,7,4,6,2] => 3 [1,3,5,7,6,2,4] => 3 [1,3,5,7,6,4,2] => 6 [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] => 1 [1,3,6,2,7,4,5] => 3 [1,3,6,2,7,5,4] => 4 [1,3,6,4,2,5,7] => 6 [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] => 2 [1,3,6,4,7,5,2] => 7 [1,3,6,5,2,4,7] => 5 [1,3,6,5,2,7,4] => 6 [1,3,6,5,4,2,7] => 4 [1,3,6,5,4,7,2] => 5 [1,3,6,5,7,2,4] => 3 [1,3,6,5,7,4,2] => 6 [1,3,6,7,2,4,5] => 4 [1,3,6,7,2,5,4] => 5 [1,3,6,7,4,2,5] => 3 [1,3,6,7,4,5,2] => 4 [1,3,6,7,5,2,4] => 2 [1,3,6,7,5,4,2] => 5 [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] => 2 [1,3,7,2,6,4,5] => 2 [1,3,7,2,6,5,4] => 3 [1,3,7,4,2,5,6] => 5 [1,3,7,4,2,6,5] => 6 [1,3,7,4,5,2,6] => 2 [1,3,7,4,5,6,2] => 5 [1,3,7,4,6,2,5] => 1 [1,3,7,4,6,5,2] => 6 [1,3,7,5,2,4,6] => 4 [1,3,7,5,2,6,4] => 7 [1,3,7,5,4,2,6] => 3 [1,3,7,5,4,6,2] => 6 [1,3,7,5,6,2,4] => 2 [1,3,7,5,6,4,2] => 5 [1,3,7,6,2,4,5] => 5 [1,3,7,6,2,5,4] => 6 [1,3,7,6,4,2,5] => 4 [1,3,7,6,4,5,2] => 5 [1,3,7,6,5,2,4] => 3 [1,3,7,6,5,4,2] => 6 [1,4,2,3,5,6,7] => 3 [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] => 6 [1,4,2,5,3,7,6] => 7 [1,4,2,5,6,3,7] => 3 [1,4,2,5,6,7,3] => 6 [1,4,2,5,7,3,6] => 2 [1,4,2,5,7,6,3] => 7 [1,4,2,6,3,5,7] => 5 [1,4,2,6,3,7,5] => 8 [1,4,2,6,5,3,7] => 4 [1,4,2,6,5,7,3] => 7 [1,4,2,6,7,3,5] => 3 [1,4,2,6,7,5,3] => 6 [1,4,2,7,3,5,6] => 6 [1,4,2,7,3,6,5] => 7 [1,4,2,7,5,3,6] => 5 [1,4,2,7,5,6,3] => 6 [1,4,2,7,6,3,5] => 4 [1,4,2,7,6,5,3] => 7 [1,4,3,2,5,6,7] => 4 [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] => 6 [1,4,3,5,6,2,7] => 4 [1,4,3,5,6,7,2] => 5 [1,4,3,5,7,2,6] => 3 [1,4,3,5,7,6,2] => 6 [1,4,3,6,2,5,7] => 4 [1,4,3,6,2,7,5] => 7 [1,4,3,6,5,2,7] => 5 [1,4,3,6,5,7,2] => 6 [1,4,3,6,7,2,5] => 4 [1,4,3,6,7,5,2] => 5 [1,4,3,7,2,5,6] => 5 [1,4,3,7,2,6,5] => 6 [1,4,3,7,5,2,6] => 6 [1,4,3,7,5,6,2] => 5 [1,4,3,7,6,2,5] => 5 [1,4,3,7,6,5,2] => 6 [1,4,5,2,3,6,7] => 3 [1,4,5,2,3,7,6] => 4 [1,4,5,2,6,3,7] => 4 [1,4,5,2,6,7,3] => 3 [1,4,5,2,7,3,6] => 3 [1,4,5,2,7,6,3] => 4 [1,4,5,3,2,6,7] => 4 [1,4,5,3,2,7,6] => 5 [1,4,5,3,6,2,7] => 3 [1,4,5,3,6,7,2] => 4 [1,4,5,3,7,2,6] => 2 [1,4,5,3,7,6,2] => 5 [1,4,5,6,2,3,7] => 3 [1,4,5,6,2,7,3] => 6 [1,4,5,6,3,2,7] => 4 [1,4,5,6,3,7,2] => 5 [1,4,5,6,7,2,3] => 3 [1,4,5,6,7,3,2] => 4 [1,4,5,7,2,3,6] => 4 [1,4,5,7,2,6,3] => 5 [1,4,5,7,3,2,6] => 5 [1,4,5,7,3,6,2] => 4 [1,4,5,7,6,2,3] => 4 [1,4,5,7,6,3,2] => 5 [1,4,6,2,3,5,7] => 4 [1,4,6,2,3,7,5] => 3 [1,4,6,2,5,3,7] => 3 [1,4,6,2,5,7,3] => 2 [1,4,6,2,7,3,5] => 2 [1,4,6,2,7,5,3] => 5 [1,4,6,3,2,5,7] => 5 [1,4,6,3,2,7,5] => 4 [1,4,6,3,5,2,7] => 2 [1,4,6,3,5,7,2] => 3 [1,4,6,3,7,2,5] => 1 [1,4,6,3,7,5,2] => 6 [1,4,6,5,2,3,7] => 4 [1,4,6,5,2,7,3] => 7 [1,4,6,5,3,2,7] => 5 [1,4,6,5,3,7,2] => 6 ----------------------------------------------------------------------------- Created: Dec 30, 2016 at 14:38 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Dec 30, 2016 at 14:38 by Martin Rubey