***************************************************************************** * 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: St001744 ----------------------------------------------------------------------------- Collection: Permutations ----------------------------------------------------------------------------- Description: The number of occurrences of the arrow pattern 1-2 with an arrow from 1 to 2 in a permutation. Let $\nu$ be a (partial) permutation of $[k]$ with $m$ letters together with dashes between some of its letters. An occurrence of $\nu$ in a permutation $\tau$ is a subsequence $\tau_{a_1},\dots,\tau_{a_m}$ such that $a_i + 1 = a_{i+1}$ whenever there is a dash between the $i$-th and the $(i+1)$-st letter of $\nu$, which is order isomorphic to $\nu$. Thus, $\nu$ is a vincular pattern, except that it is not required to be a permutation. An arrow pattern of size $k$ consists of such a generalized vincular pattern $\nu$ and arrows $b_1\to c_1, b_2\to c_2,\dots$, such that precisely the numbers $1,\dots,k$ appear in the vincular pattern and the arrows. Let $\Phi$ be the map [[Mp00087]]. Let $\tau$ be a permutation and $\sigma = \Phi(\tau)$. Then a subsequence $w = (x_{a_1},\dots,x_{a_m})$ of $\tau$ is an occurrence of the arrow pattern if $w$ is an occurrence of $\nu$, for each arrow $b\to c$ we have $\sigma(x_b) = x_c$ and $x_1 < x_2 < \dots < x_k$. ----------------------------------------------------------------------------- References: [1] Berman, Y., Tenner, B. E. Pattern-functions, statistics, and shallow permutations [[arXiv:2110.11146]] ----------------------------------------------------------------------------- Code: def vincular_occurrences_iterator(perm, pat, columns): perm = Permutation(perm) for pos in perm.pattern_positions(pat): if all(pos[i-1]+1 == pos[i] for i in columns): yield tuple(pos) from sage.combinat.permutation import to_standard def arrow_occurrences_iterator(perm, pat, columns, arrows): perm = Permutation(perm) s = set(pat + [p for p, _ in arrows] + [q for _, q in arrows]) k = max(s) assert min(s) == 1 and len(s) == k nu = to_standard(pat) sigma = perm.fundamental_transformation_inverse() for pos in vincular_occurrences_iterator(perm, nu, columns): x = [None]*k for i, a in enumerate(pos): x[pat[i]-1] = perm[a] for p, q in arrows: if x[p-1] is None and x[q-1] is None: raise ValueError("doesn't work for %s %s %s %s" % (perm, pat, columns, arrows)) if x[p-1] is None: x[p-1] = sigma.inverse()(x[q-1]) elif x[q-1] is None: x[q-1] = sigma(x[p-1]) if (all(x[i] < x[i+1] for i in range(len(x)-1)) and all(sigma(x[p-1]) == x[q-1] for p, q in arrows)): yield tuple(pos) def arrow_occurrences(perm, pat, columns, arrows): return list(arrow_occurrences_iterator(perm, pat, columns, arrows)) def statistic(pi): return len(arrow_occurrences(pi, [1,2], [1], [[1,2]])) ----------------------------------------------------------------------------- Statistic values: [1] => 0 [1,2] => 0 [2,1] => 0 [1,2,3] => 0 [1,3,2] => 0 [2,1,3] => 0 [2,3,1] => 0 [3,1,2] => 1 [3,2,1] => 0 [1,2,3,4] => 0 [1,2,4,3] => 0 [1,3,2,4] => 0 [1,3,4,2] => 0 [1,4,2,3] => 1 [1,4,3,2] => 0 [2,1,3,4] => 0 [2,1,4,3] => 0 [2,3,1,4] => 0 [2,3,4,1] => 0 [2,4,1,3] => 1 [2,4,3,1] => 0 [3,1,2,4] => 1 [3,1,4,2] => 0 [3,2,1,4] => 0 [3,2,4,1] => 0 [3,4,1,2] => 1 [3,4,2,1] => 0 [4,1,2,3] => 2 [4,1,3,2] => 1 [4,2,1,3] => 1 [4,2,3,1] => 1 [4,3,1,2] => 1 [4,3,2,1] => 0 [1,2,3,4,5] => 0 [1,2,3,5,4] => 0 [1,2,4,3,5] => 0 [1,2,4,5,3] => 0 [1,2,5,3,4] => 1 [1,2,5,4,3] => 0 [1,3,2,4,5] => 0 [1,3,2,5,4] => 0 [1,3,4,2,5] => 0 [1,3,4,5,2] => 0 [1,3,5,2,4] => 1 [1,3,5,4,2] => 0 [1,4,2,3,5] => 1 [1,4,2,5,3] => 0 [1,4,3,2,5] => 0 [1,4,3,5,2] => 0 [1,4,5,2,3] => 1 [1,4,5,3,2] => 0 [1,5,2,3,4] => 2 [1,5,2,4,3] => 1 [1,5,3,2,4] => 1 [1,5,3,4,2] => 1 [1,5,4,2,3] => 1 [1,5,4,3,2] => 0 [2,1,3,4,5] => 0 [2,1,3,5,4] => 0 [2,1,4,3,5] => 0 [2,1,4,5,3] => 0 [2,1,5,3,4] => 1 [2,1,5,4,3] => 0 [2,3,1,4,5] => 0 [2,3,1,5,4] => 0 [2,3,4,1,5] => 0 [2,3,4,5,1] => 0 [2,3,5,1,4] => 1 [2,3,5,4,1] => 0 [2,4,1,3,5] => 1 [2,4,1,5,3] => 0 [2,4,3,1,5] => 0 [2,4,3,5,1] => 0 [2,4,5,1,3] => 1 [2,4,5,3,1] => 0 [2,5,1,3,4] => 2 [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] => 0 [3,1,2,4,5] => 1 [3,1,2,5,4] => 1 [3,1,4,2,5] => 0 [3,1,4,5,2] => 0 [3,1,5,2,4] => 1 [3,1,5,4,2] => 0 [3,2,1,4,5] => 0 [3,2,1,5,4] => 0 [3,2,4,1,5] => 0 [3,2,4,5,1] => 0 [3,2,5,1,4] => 1 [3,2,5,4,1] => 0 [3,4,1,2,5] => 1 [3,4,1,5,2] => 0 [3,4,2,1,5] => 0 [3,4,2,5,1] => 0 [3,4,5,1,2] => 1 [3,4,5,2,1] => 0 [3,5,1,2,4] => 2 [3,5,1,4,2] => 1 [3,5,2,1,4] => 1 [3,5,2,4,1] => 1 [3,5,4,1,2] => 1 [3,5,4,2,1] => 0 [4,1,2,3,5] => 2 [4,1,2,5,3] => 1 [4,1,3,2,5] => 1 [4,1,3,5,2] => 1 [4,1,5,2,3] => 1 [4,1,5,3,2] => 0 [4,2,1,3,5] => 1 [4,2,1,5,3] => 0 [4,2,3,1,5] => 1 [4,2,3,5,1] => 1 [4,2,5,1,3] => 1 [4,2,5,3,1] => 0 [4,3,1,2,5] => 1 [4,3,1,5,2] => 0 [4,3,2,1,5] => 0 [4,3,2,5,1] => 0 [4,3,5,1,2] => 1 [4,3,5,2,1] => 0 [4,5,1,2,3] => 2 [4,5,1,3,2] => 1 [4,5,2,1,3] => 1 [4,5,2,3,1] => 1 [4,5,3,1,2] => 1 [4,5,3,2,1] => 0 [5,1,2,3,4] => 3 [5,1,2,4,3] => 2 [5,1,3,2,4] => 2 [5,1,3,4,2] => 2 [5,1,4,2,3] => 2 [5,1,4,3,2] => 1 [5,2,1,3,4] => 2 [5,2,1,4,3] => 1 [5,2,3,1,4] => 2 [5,2,3,4,1] => 2 [5,2,4,1,3] => 2 [5,2,4,3,1] => 1 [5,3,1,2,4] => 2 [5,3,1,4,2] => 1 [5,3,2,1,4] => 1 [5,3,2,4,1] => 1 [5,3,4,1,2] => 2 [5,3,4,2,1] => 1 [5,4,1,2,3] => 2 [5,4,1,3,2] => 1 [5,4,2,1,3] => 1 [5,4,2,3,1] => 1 [5,4,3,1,2] => 1 [5,4,3,2,1] => 0 [1,2,3,4,5,6] => 0 [1,2,3,4,6,5] => 0 [1,2,3,5,4,6] => 0 [1,2,3,5,6,4] => 0 [1,2,3,6,4,5] => 1 [1,2,3,6,5,4] => 0 [1,2,4,3,5,6] => 0 [1,2,4,3,6,5] => 0 [1,2,4,5,3,6] => 0 [1,2,4,5,6,3] => 0 [1,2,4,6,3,5] => 1 [1,2,4,6,5,3] => 0 [1,2,5,3,4,6] => 1 [1,2,5,3,6,4] => 0 [1,2,5,4,3,6] => 0 [1,2,5,4,6,3] => 0 [1,2,5,6,3,4] => 1 [1,2,5,6,4,3] => 0 [1,2,6,3,4,5] => 2 [1,2,6,3,5,4] => 1 [1,2,6,4,3,5] => 1 [1,2,6,4,5,3] => 1 [1,2,6,5,3,4] => 1 [1,2,6,5,4,3] => 0 [1,3,2,4,5,6] => 0 [1,3,2,4,6,5] => 0 [1,3,2,5,4,6] => 0 [1,3,2,5,6,4] => 0 [1,3,2,6,4,5] => 1 [1,3,2,6,5,4] => 0 [1,3,4,2,5,6] => 0 [1,3,4,2,6,5] => 0 [1,3,4,5,2,6] => 0 [1,3,4,5,6,2] => 0 [1,3,4,6,2,5] => 1 [1,3,4,6,5,2] => 0 [1,3,5,2,4,6] => 1 [1,3,5,2,6,4] => 0 [1,3,5,4,2,6] => 0 [1,3,5,4,6,2] => 0 [1,3,5,6,2,4] => 1 [1,3,5,6,4,2] => 0 [1,3,6,2,4,5] => 2 [1,3,6,2,5,4] => 1 [1,3,6,4,2,5] => 1 [1,3,6,4,5,2] => 1 [1,3,6,5,2,4] => 1 [1,3,6,5,4,2] => 0 [1,4,2,3,5,6] => 1 [1,4,2,3,6,5] => 1 [1,4,2,5,3,6] => 0 [1,4,2,5,6,3] => 0 [1,4,2,6,3,5] => 1 [1,4,2,6,5,3] => 0 [1,4,3,2,5,6] => 0 [1,4,3,2,6,5] => 0 [1,4,3,5,2,6] => 0 [1,4,3,5,6,2] => 0 [1,4,3,6,2,5] => 1 [1,4,3,6,5,2] => 0 [1,4,5,2,3,6] => 1 [1,4,5,2,6,3] => 0 [1,4,5,3,2,6] => 0 [1,4,5,3,6,2] => 0 [1,4,5,6,2,3] => 1 [1,4,5,6,3,2] => 0 [1,4,6,2,3,5] => 2 [1,4,6,2,5,3] => 1 [1,4,6,3,2,5] => 1 [1,4,6,3,5,2] => 1 [1,4,6,5,2,3] => 1 [1,4,6,5,3,2] => 0 [1,5,2,3,4,6] => 2 [1,5,2,3,6,4] => 1 [1,5,2,4,3,6] => 1 [1,5,2,4,6,3] => 1 [1,5,2,6,3,4] => 1 [1,5,2,6,4,3] => 0 [1,5,3,2,4,6] => 1 [1,5,3,2,6,4] => 0 [1,5,3,4,2,6] => 1 [1,5,3,4,6,2] => 1 [1,5,3,6,2,4] => 1 [1,5,3,6,4,2] => 0 [1,5,4,2,3,6] => 1 [1,5,4,2,6,3] => 0 [1,5,4,3,2,6] => 0 [1,5,4,3,6,2] => 0 [1,5,4,6,2,3] => 1 [1,5,4,6,3,2] => 0 [1,5,6,2,3,4] => 2 [1,5,6,2,4,3] => 1 [1,5,6,3,2,4] => 1 [1,5,6,3,4,2] => 1 [1,5,6,4,2,3] => 1 [1,5,6,4,3,2] => 0 [1,6,2,3,4,5] => 3 [1,6,2,3,5,4] => 2 [1,6,2,4,3,5] => 2 [1,6,2,4,5,3] => 2 [1,6,2,5,3,4] => 2 [1,6,2,5,4,3] => 1 [1,6,3,2,4,5] => 2 [1,6,3,2,5,4] => 1 [1,6,3,4,2,5] => 2 [1,6,3,4,5,2] => 2 [1,6,3,5,2,4] => 2 [1,6,3,5,4,2] => 1 [1,6,4,2,3,5] => 2 [1,6,4,2,5,3] => 1 [1,6,4,3,2,5] => 1 [1,6,4,3,5,2] => 1 [1,6,4,5,2,3] => 2 [1,6,4,5,3,2] => 1 [1,6,5,2,3,4] => 2 [1,6,5,2,4,3] => 1 [1,6,5,3,2,4] => 1 [1,6,5,3,4,2] => 1 [1,6,5,4,2,3] => 1 [1,6,5,4,3,2] => 0 [2,1,3,4,5,6] => 0 [2,1,3,4,6,5] => 0 [2,1,3,5,4,6] => 0 [2,1,3,5,6,4] => 0 [2,1,3,6,4,5] => 1 [2,1,3,6,5,4] => 0 [2,1,4,3,5,6] => 0 [2,1,4,3,6,5] => 0 [2,1,4,5,3,6] => 0 [2,1,4,5,6,3] => 0 [2,1,4,6,3,5] => 1 [2,1,4,6,5,3] => 0 [2,1,5,3,4,6] => 1 [2,1,5,3,6,4] => 0 [2,1,5,4,3,6] => 0 [2,1,5,4,6,3] => 0 [2,1,5,6,3,4] => 1 [2,1,5,6,4,3] => 0 [2,1,6,3,4,5] => 2 [2,1,6,3,5,4] => 1 [2,1,6,4,3,5] => 1 [2,1,6,4,5,3] => 1 [2,1,6,5,3,4] => 1 [2,1,6,5,4,3] => 0 [2,3,1,4,5,6] => 0 [2,3,1,4,6,5] => 0 [2,3,1,5,4,6] => 0 [2,3,1,5,6,4] => 0 [2,3,1,6,4,5] => 1 [2,3,1,6,5,4] => 0 [2,3,4,1,5,6] => 0 [2,3,4,1,6,5] => 0 [2,3,4,5,1,6] => 0 [2,3,4,5,6,1] => 0 [2,3,4,6,1,5] => 1 [2,3,4,6,5,1] => 0 [2,3,5,1,4,6] => 1 [2,3,5,1,6,4] => 0 [2,3,5,4,1,6] => 0 [2,3,5,4,6,1] => 0 [2,3,5,6,1,4] => 1 [2,3,5,6,4,1] => 0 [2,3,6,1,4,5] => 2 [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] => 0 [2,4,1,3,5,6] => 1 [2,4,1,3,6,5] => 1 [2,4,1,5,3,6] => 0 [2,4,1,5,6,3] => 0 [2,4,1,6,3,5] => 1 [2,4,1,6,5,3] => 0 [2,4,3,1,5,6] => 0 [2,4,3,1,6,5] => 0 [2,4,3,5,1,6] => 0 [2,4,3,5,6,1] => 0 [2,4,3,6,1,5] => 1 [2,4,3,6,5,1] => 0 [2,4,5,1,3,6] => 1 [2,4,5,1,6,3] => 0 [2,4,5,3,1,6] => 0 [2,4,5,3,6,1] => 0 [2,4,5,6,1,3] => 1 [2,4,5,6,3,1] => 0 [2,4,6,1,3,5] => 2 [2,4,6,1,5,3] => 1 [2,4,6,3,1,5] => 1 [2,4,6,3,5,1] => 1 [2,4,6,5,1,3] => 1 [2,4,6,5,3,1] => 0 [2,5,1,3,4,6] => 2 [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] => 1 [2,5,1,6,4,3] => 0 [2,5,3,1,4,6] => 1 [2,5,3,1,6,4] => 0 [2,5,3,4,1,6] => 1 [2,5,3,4,6,1] => 1 [2,5,3,6,1,4] => 1 [2,5,3,6,4,1] => 0 [2,5,4,1,3,6] => 1 [2,5,4,1,6,3] => 0 [2,5,4,3,1,6] => 0 [2,5,4,3,6,1] => 0 [2,5,4,6,1,3] => 1 [2,5,4,6,3,1] => 0 [2,5,6,1,3,4] => 2 [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] => 1 [2,5,6,4,3,1] => 0 [2,6,1,3,4,5] => 3 [2,6,1,3,5,4] => 2 [2,6,1,4,3,5] => 2 [2,6,1,4,5,3] => 2 [2,6,1,5,3,4] => 2 [2,6,1,5,4,3] => 1 [2,6,3,1,4,5] => 2 [2,6,3,1,5,4] => 1 [2,6,3,4,1,5] => 2 [2,6,3,4,5,1] => 2 [2,6,3,5,1,4] => 2 [2,6,3,5,4,1] => 1 [2,6,4,1,3,5] => 2 [2,6,4,1,5,3] => 1 [2,6,4,3,1,5] => 1 [2,6,4,3,5,1] => 1 [2,6,4,5,1,3] => 2 [2,6,4,5,3,1] => 1 [2,6,5,1,3,4] => 2 [2,6,5,1,4,3] => 1 [2,6,5,3,1,4] => 1 [2,6,5,3,4,1] => 1 [2,6,5,4,1,3] => 1 [2,6,5,4,3,1] => 0 [3,1,2,4,5,6] => 1 [3,1,2,4,6,5] => 1 [3,1,2,5,4,6] => 1 [3,1,2,5,6,4] => 1 [3,1,2,6,4,5] => 2 [3,1,2,6,5,4] => 1 [3,1,4,2,5,6] => 0 [3,1,4,2,6,5] => 0 [3,1,4,5,2,6] => 0 [3,1,4,5,6,2] => 0 [3,1,4,6,2,5] => 1 [3,1,4,6,5,2] => 0 [3,1,5,2,4,6] => 1 [3,1,5,2,6,4] => 0 [3,1,5,4,2,6] => 0 [3,1,5,4,6,2] => 0 [3,1,5,6,2,4] => 1 [3,1,5,6,4,2] => 0 [3,1,6,2,4,5] => 2 [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] => 0 [3,2,1,4,5,6] => 0 [3,2,1,4,6,5] => 0 [3,2,1,5,4,6] => 0 [3,2,1,5,6,4] => 0 [3,2,1,6,4,5] => 1 [3,2,1,6,5,4] => 0 [3,2,4,1,5,6] => 0 [3,2,4,1,6,5] => 0 [3,2,4,5,1,6] => 0 [3,2,4,5,6,1] => 0 [3,2,4,6,1,5] => 1 [3,2,4,6,5,1] => 0 [3,2,5,1,4,6] => 1 [3,2,5,1,6,4] => 0 [3,2,5,4,1,6] => 0 [3,2,5,4,6,1] => 0 [3,2,5,6,1,4] => 1 [3,2,5,6,4,1] => 0 [3,2,6,1,4,5] => 2 [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] => 0 [3,4,1,2,5,6] => 1 [3,4,1,2,6,5] => 1 [3,4,1,5,2,6] => 0 [3,4,1,5,6,2] => 0 [3,4,1,6,2,5] => 1 [3,4,1,6,5,2] => 0 [3,4,2,1,5,6] => 0 [3,4,2,1,6,5] => 0 [3,4,2,5,1,6] => 0 [3,4,2,5,6,1] => 0 [3,4,2,6,1,5] => 1 [3,4,2,6,5,1] => 0 [3,4,5,1,2,6] => 1 [3,4,5,1,6,2] => 0 [3,4,5,2,1,6] => 0 [3,4,5,2,6,1] => 0 [3,4,5,6,1,2] => 1 [3,4,5,6,2,1] => 0 [3,4,6,1,2,5] => 2 [3,4,6,1,5,2] => 1 [3,4,6,2,1,5] => 1 [3,4,6,2,5,1] => 1 [3,4,6,5,1,2] => 1 [3,4,6,5,2,1] => 0 [3,5,1,2,4,6] => 2 [3,5,1,2,6,4] => 1 [3,5,1,4,2,6] => 1 [3,5,1,4,6,2] => 1 [3,5,1,6,2,4] => 1 [3,5,1,6,4,2] => 0 [3,5,2,1,4,6] => 1 [3,5,2,1,6,4] => 0 [3,5,2,4,1,6] => 1 [3,5,2,4,6,1] => 1 [3,5,2,6,1,4] => 1 [3,5,2,6,4,1] => 0 [3,5,4,1,2,6] => 1 [3,5,4,1,6,2] => 0 [3,5,4,2,1,6] => 0 [3,5,4,2,6,1] => 0 [3,5,4,6,1,2] => 1 [3,5,4,6,2,1] => 0 [3,5,6,1,2,4] => 2 [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] => 1 [3,5,6,4,2,1] => 0 [3,6,1,2,4,5] => 3 [3,6,1,2,5,4] => 2 [3,6,1,4,2,5] => 2 [3,6,1,4,5,2] => 2 [3,6,1,5,2,4] => 2 [3,6,1,5,4,2] => 1 [3,6,2,1,4,5] => 2 [3,6,2,1,5,4] => 1 [3,6,2,4,1,5] => 2 [3,6,2,4,5,1] => 2 [3,6,2,5,1,4] => 2 [3,6,2,5,4,1] => 1 [3,6,4,1,2,5] => 2 [3,6,4,1,5,2] => 1 [3,6,4,2,1,5] => 1 [3,6,4,2,5,1] => 1 [3,6,4,5,1,2] => 2 [3,6,4,5,2,1] => 1 [3,6,5,1,2,4] => 2 [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] => 1 [3,6,5,4,2,1] => 0 [4,1,2,3,5,6] => 2 [4,1,2,3,6,5] => 2 [4,1,2,5,3,6] => 1 [4,1,2,5,6,3] => 1 [4,1,2,6,3,5] => 2 [4,1,2,6,5,3] => 1 [4,1,3,2,5,6] => 1 [4,1,3,2,6,5] => 1 [4,1,3,5,2,6] => 1 [4,1,3,5,6,2] => 1 [4,1,3,6,2,5] => 2 [4,1,3,6,5,2] => 1 [4,1,5,2,3,6] => 1 [4,1,5,2,6,3] => 0 [4,1,5,3,2,6] => 0 [4,1,5,3,6,2] => 0 [4,1,5,6,2,3] => 1 [4,1,5,6,3,2] => 0 [4,1,6,2,3,5] => 2 [4,1,6,2,5,3] => 1 [4,1,6,3,2,5] => 1 [4,1,6,3,5,2] => 1 [4,1,6,5,2,3] => 1 [4,1,6,5,3,2] => 0 [4,2,1,3,5,6] => 1 [4,2,1,3,6,5] => 1 [4,2,1,5,3,6] => 0 [4,2,1,5,6,3] => 0 [4,2,1,6,3,5] => 1 [4,2,1,6,5,3] => 0 [4,2,3,1,5,6] => 1 [4,2,3,1,6,5] => 1 [4,2,3,5,1,6] => 1 [4,2,3,5,6,1] => 1 [4,2,3,6,1,5] => 2 [4,2,3,6,5,1] => 1 [4,2,5,1,3,6] => 1 [4,2,5,1,6,3] => 0 [4,2,5,3,1,6] => 0 [4,2,5,3,6,1] => 0 [4,2,5,6,1,3] => 1 [4,2,5,6,3,1] => 0 [4,2,6,1,3,5] => 2 [4,2,6,1,5,3] => 1 [4,2,6,3,1,5] => 1 [4,2,6,3,5,1] => 1 [4,2,6,5,1,3] => 1 [4,2,6,5,3,1] => 0 [4,3,1,2,5,6] => 1 [4,3,1,2,6,5] => 1 [4,3,1,5,2,6] => 0 [4,3,1,5,6,2] => 0 [4,3,1,6,2,5] => 1 [4,3,1,6,5,2] => 0 [4,3,2,1,5,6] => 0 [4,3,2,1,6,5] => 0 [4,3,2,5,1,6] => 0 [4,3,2,5,6,1] => 0 [4,3,2,6,1,5] => 1 [4,3,2,6,5,1] => 0 [4,3,5,1,2,6] => 1 [4,3,5,1,6,2] => 0 [4,3,5,2,1,6] => 0 [4,3,5,2,6,1] => 0 [4,3,5,6,1,2] => 1 [4,3,5,6,2,1] => 0 [4,3,6,1,2,5] => 2 [4,3,6,1,5,2] => 1 [4,3,6,2,1,5] => 1 [4,3,6,2,5,1] => 1 [4,3,6,5,1,2] => 1 [4,3,6,5,2,1] => 0 [4,5,1,2,3,6] => 2 [4,5,1,2,6,3] => 1 [4,5,1,3,2,6] => 1 [4,5,1,3,6,2] => 1 [4,5,1,6,2,3] => 1 [4,5,1,6,3,2] => 0 [4,5,2,1,3,6] => 1 [4,5,2,1,6,3] => 0 [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] => 0 [4,5,3,1,2,6] => 1 [4,5,3,1,6,2] => 0 [4,5,3,2,1,6] => 0 [4,5,3,2,6,1] => 0 [4,5,3,6,1,2] => 1 [4,5,3,6,2,1] => 0 [4,5,6,1,2,3] => 2 [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] => 0 [4,6,1,2,3,5] => 3 [4,6,1,2,5,3] => 2 [4,6,1,3,2,5] => 2 [4,6,1,3,5,2] => 2 [4,6,1,5,2,3] => 2 [4,6,1,5,3,2] => 1 [4,6,2,1,3,5] => 2 [4,6,2,1,5,3] => 1 [4,6,2,3,1,5] => 2 [4,6,2,3,5,1] => 2 [4,6,2,5,1,3] => 2 [4,6,2,5,3,1] => 1 [4,6,3,1,2,5] => 2 [4,6,3,1,5,2] => 1 [4,6,3,2,1,5] => 1 [4,6,3,2,5,1] => 1 [4,6,3,5,1,2] => 2 [4,6,3,5,2,1] => 1 [4,6,5,1,2,3] => 2 [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] => 0 [5,1,2,3,4,6] => 3 [5,1,2,3,6,4] => 2 [5,1,2,4,3,6] => 2 [5,1,2,4,6,3] => 2 [5,1,2,6,3,4] => 2 [5,1,2,6,4,3] => 1 [5,1,3,2,4,6] => 2 [5,1,3,2,6,4] => 1 [5,1,3,4,2,6] => 2 [5,1,3,4,6,2] => 2 [5,1,3,6,2,4] => 2 [5,1,3,6,4,2] => 1 [5,1,4,2,3,6] => 2 [5,1,4,2,6,3] => 1 [5,1,4,3,2,6] => 1 [5,1,4,3,6,2] => 1 [5,1,4,6,2,3] => 2 [5,1,4,6,3,2] => 1 [5,1,6,2,3,4] => 2 [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] => 1 [5,1,6,4,3,2] => 0 [5,2,1,3,4,6] => 2 [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] => 1 [5,2,1,6,4,3] => 0 [5,2,3,1,4,6] => 2 [5,2,3,1,6,4] => 1 [5,2,3,4,1,6] => 2 [5,2,3,4,6,1] => 2 [5,2,3,6,1,4] => 2 [5,2,3,6,4,1] => 1 [5,2,4,1,3,6] => 2 [5,2,4,1,6,3] => 1 [5,2,4,3,1,6] => 1 [5,2,4,3,6,1] => 1 [5,2,4,6,1,3] => 2 [5,2,4,6,3,1] => 1 [5,2,6,1,3,4] => 2 [5,2,6,1,4,3] => 1 [5,2,6,3,1,4] => 1 [5,2,6,3,4,1] => 1 [5,2,6,4,1,3] => 1 [5,2,6,4,3,1] => 0 [5,3,1,2,4,6] => 2 [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] => 1 [5,3,1,6,4,2] => 0 [5,3,2,1,4,6] => 1 [5,3,2,1,6,4] => 0 [5,3,2,4,1,6] => 1 [5,3,2,4,6,1] => 1 [5,3,2,6,1,4] => 1 [5,3,2,6,4,1] => 0 [5,3,4,1,2,6] => 2 [5,3,4,1,6,2] => 1 [5,3,4,2,1,6] => 1 [5,3,4,2,6,1] => 1 [5,3,4,6,1,2] => 2 [5,3,4,6,2,1] => 1 [5,3,6,1,2,4] => 2 [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] => 1 [5,3,6,4,2,1] => 0 [5,4,1,2,3,6] => 2 [5,4,1,2,6,3] => 1 [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] => 0 [5,4,2,1,3,6] => 1 [5,4,2,1,6,3] => 0 [5,4,2,3,1,6] => 1 [5,4,2,3,6,1] => 1 [5,4,2,6,1,3] => 1 [5,4,2,6,3,1] => 0 [5,4,3,1,2,6] => 1 [5,4,3,1,6,2] => 0 [5,4,3,2,1,6] => 0 [5,4,3,2,6,1] => 0 [5,4,3,6,1,2] => 1 [5,4,3,6,2,1] => 0 [5,4,6,1,2,3] => 2 [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] => 0 [5,6,1,2,3,4] => 3 [5,6,1,2,4,3] => 2 [5,6,1,3,2,4] => 2 [5,6,1,3,4,2] => 2 [5,6,1,4,2,3] => 2 [5,6,1,4,3,2] => 1 [5,6,2,1,3,4] => 2 [5,6,2,1,4,3] => 1 [5,6,2,3,1,4] => 2 [5,6,2,3,4,1] => 2 [5,6,2,4,1,3] => 2 [5,6,2,4,3,1] => 1 [5,6,3,1,2,4] => 2 [5,6,3,1,4,2] => 1 [5,6,3,2,1,4] => 1 [5,6,3,2,4,1] => 1 [5,6,3,4,1,2] => 2 [5,6,3,4,2,1] => 1 [5,6,4,1,2,3] => 2 [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] => 1 [5,6,4,3,2,1] => 0 [6,1,2,3,4,5] => 4 [6,1,2,3,5,4] => 3 [6,1,2,4,3,5] => 3 [6,1,2,4,5,3] => 3 [6,1,2,5,3,4] => 3 [6,1,2,5,4,3] => 2 [6,1,3,2,4,5] => 3 [6,1,3,2,5,4] => 2 [6,1,3,4,2,5] => 3 [6,1,3,4,5,2] => 3 [6,1,3,5,2,4] => 3 [6,1,3,5,4,2] => 2 [6,1,4,2,3,5] => 3 [6,1,4,2,5,3] => 2 [6,1,4,3,2,5] => 2 [6,1,4,3,5,2] => 2 [6,1,4,5,2,3] => 3 [6,1,4,5,3,2] => 2 [6,1,5,2,3,4] => 3 [6,1,5,2,4,3] => 2 [6,1,5,3,2,4] => 2 [6,1,5,3,4,2] => 2 [6,1,5,4,2,3] => 2 [6,1,5,4,3,2] => 1 [6,2,1,3,4,5] => 3 [6,2,1,3,5,4] => 2 [6,2,1,4,3,5] => 2 [6,2,1,4,5,3] => 2 [6,2,1,5,3,4] => 2 [6,2,1,5,4,3] => 1 [6,2,3,1,4,5] => 3 [6,2,3,1,5,4] => 2 [6,2,3,4,1,5] => 3 [6,2,3,4,5,1] => 3 [6,2,3,5,1,4] => 3 [6,2,3,5,4,1] => 2 [6,2,4,1,3,5] => 3 [6,2,4,1,5,3] => 2 [6,2,4,3,1,5] => 2 [6,2,4,3,5,1] => 2 [6,2,4,5,1,3] => 3 [6,2,4,5,3,1] => 2 [6,2,5,1,3,4] => 3 [6,2,5,1,4,3] => 2 [6,2,5,3,1,4] => 2 [6,2,5,3,4,1] => 2 [6,2,5,4,1,3] => 2 [6,2,5,4,3,1] => 1 [6,3,1,2,4,5] => 3 [6,3,1,2,5,4] => 2 [6,3,1,4,2,5] => 2 [6,3,1,4,5,2] => 2 [6,3,1,5,2,4] => 2 [6,3,1,5,4,2] => 1 [6,3,2,1,4,5] => 2 [6,3,2,1,5,4] => 1 [6,3,2,4,1,5] => 2 [6,3,2,4,5,1] => 2 [6,3,2,5,1,4] => 2 [6,3,2,5,4,1] => 1 [6,3,4,1,2,5] => 3 [6,3,4,1,5,2] => 2 [6,3,4,2,1,5] => 2 [6,3,4,2,5,1] => 2 [6,3,4,5,1,2] => 3 [6,3,4,5,2,1] => 2 [6,3,5,1,2,4] => 3 [6,3,5,1,4,2] => 2 [6,3,5,2,1,4] => 2 [6,3,5,2,4,1] => 2 [6,3,5,4,1,2] => 2 [6,3,5,4,2,1] => 1 [6,4,1,2,3,5] => 3 [6,4,1,2,5,3] => 2 [6,4,1,3,2,5] => 2 [6,4,1,3,5,2] => 2 [6,4,1,5,2,3] => 2 [6,4,1,5,3,2] => 1 [6,4,2,1,3,5] => 2 [6,4,2,1,5,3] => 1 [6,4,2,3,1,5] => 2 [6,4,2,3,5,1] => 2 [6,4,2,5,1,3] => 2 [6,4,2,5,3,1] => 1 [6,4,3,1,2,5] => 2 [6,4,3,1,5,2] => 1 [6,4,3,2,1,5] => 1 [6,4,3,2,5,1] => 1 [6,4,3,5,1,2] => 2 [6,4,3,5,2,1] => 1 [6,4,5,1,2,3] => 3 [6,4,5,1,3,2] => 2 [6,4,5,2,1,3] => 2 [6,4,5,2,3,1] => 2 [6,4,5,3,1,2] => 2 [6,4,5,3,2,1] => 1 [6,5,1,2,3,4] => 3 [6,5,1,2,4,3] => 2 [6,5,1,3,2,4] => 2 [6,5,1,3,4,2] => 2 [6,5,1,4,2,3] => 2 [6,5,1,4,3,2] => 1 [6,5,2,1,3,4] => 2 [6,5,2,1,4,3] => 1 [6,5,2,3,1,4] => 2 [6,5,2,3,4,1] => 2 [6,5,2,4,1,3] => 2 [6,5,2,4,3,1] => 1 [6,5,3,1,2,4] => 2 [6,5,3,1,4,2] => 1 [6,5,3,2,1,4] => 1 [6,5,3,2,4,1] => 1 [6,5,3,4,1,2] => 2 [6,5,3,4,2,1] => 1 [6,5,4,1,2,3] => 2 [6,5,4,1,3,2] => 1 [6,5,4,2,1,3] => 1 [6,5,4,2,3,1] => 1 [6,5,4,3,1,2] => 1 [6,5,4,3,2,1] => 0 [1,2,3,4,5,6,7] => 0 [1,2,3,4,5,7,6] => 0 [1,2,3,4,6,5,7] => 0 [1,2,3,4,6,7,5] => 0 [1,2,3,4,7,5,6] => 1 [1,2,3,4,7,6,5] => 0 [1,2,3,5,4,6,7] => 0 [1,2,3,5,4,7,6] => 0 [1,2,3,5,6,4,7] => 0 [1,2,3,5,6,7,4] => 0 [1,2,3,5,7,4,6] => 1 [1,2,3,5,7,6,4] => 0 [1,2,3,6,4,5,7] => 1 [1,2,3,6,4,7,5] => 0 [1,2,3,6,5,4,7] => 0 [1,2,3,6,5,7,4] => 0 [1,2,3,6,7,4,5] => 1 [1,2,3,6,7,5,4] => 0 [1,2,3,7,4,5,6] => 2 [1,2,3,7,4,6,5] => 1 [1,2,3,7,5,4,6] => 1 [1,2,3,7,5,6,4] => 1 [1,2,3,7,6,4,5] => 1 [1,2,3,7,6,5,4] => 0 [1,2,4,3,5,6,7] => 0 [1,2,4,3,5,7,6] => 0 [1,2,4,3,6,5,7] => 0 [1,2,4,3,6,7,5] => 0 [1,2,4,3,7,5,6] => 1 [1,2,4,3,7,6,5] => 0 [1,2,4,5,3,6,7] => 0 [1,2,4,5,3,7,6] => 0 [1,2,4,5,6,3,7] => 0 [1,2,4,5,6,7,3] => 0 [1,2,4,5,7,3,6] => 1 [1,2,4,5,7,6,3] => 0 [1,2,4,6,3,5,7] => 1 [1,2,4,6,3,7,5] => 0 [1,2,4,6,5,3,7] => 0 [1,2,4,6,5,7,3] => 0 [1,2,4,6,7,3,5] => 1 [1,2,4,6,7,5,3] => 0 [1,2,4,7,3,5,6] => 2 [1,2,4,7,3,6,5] => 1 [1,2,4,7,5,3,6] => 1 [1,2,4,7,5,6,3] => 1 [1,2,4,7,6,3,5] => 1 [1,2,4,7,6,5,3] => 0 [1,2,5,3,4,6,7] => 1 [1,2,5,3,4,7,6] => 1 [1,2,5,3,6,4,7] => 0 [1,2,5,3,6,7,4] => 0 [1,2,5,3,7,4,6] => 1 [1,2,5,3,7,6,4] => 0 [1,2,5,4,3,6,7] => 0 [1,2,5,4,3,7,6] => 0 [1,2,5,4,6,3,7] => 0 [1,2,5,4,6,7,3] => 0 [1,2,5,4,7,3,6] => 1 [1,2,5,4,7,6,3] => 0 [1,2,5,6,3,4,7] => 1 [1,2,5,6,3,7,4] => 0 [1,2,5,6,4,3,7] => 0 [1,2,5,6,4,7,3] => 0 [1,2,5,6,7,3,4] => 1 [1,2,5,6,7,4,3] => 0 [1,2,5,7,3,4,6] => 2 [1,2,5,7,3,6,4] => 1 [1,2,5,7,4,3,6] => 1 [1,2,5,7,4,6,3] => 1 [1,2,5,7,6,3,4] => 1 [1,2,5,7,6,4,3] => 0 [1,2,6,3,4,5,7] => 2 [1,2,6,3,4,7,5] => 1 [1,2,6,3,5,4,7] => 1 [1,2,6,3,5,7,4] => 1 [1,2,6,3,7,4,5] => 1 [1,2,6,3,7,5,4] => 0 [1,2,6,4,3,5,7] => 1 [1,2,6,4,3,7,5] => 0 [1,2,6,4,5,3,7] => 1 [1,2,6,4,5,7,3] => 1 [1,2,6,4,7,3,5] => 1 [1,2,6,4,7,5,3] => 0 [1,2,6,5,3,4,7] => 1 [1,2,6,5,3,7,4] => 0 [1,2,6,5,4,3,7] => 0 [1,2,6,5,4,7,3] => 0 [1,2,6,5,7,3,4] => 1 [1,2,6,5,7,4,3] => 0 [1,2,6,7,3,4,5] => 2 [1,2,6,7,3,5,4] => 1 [1,2,6,7,4,3,5] => 1 [1,2,6,7,4,5,3] => 1 [1,2,6,7,5,3,4] => 1 [1,2,6,7,5,4,3] => 0 [1,2,7,3,4,5,6] => 3 [1,2,7,3,4,6,5] => 2 [1,2,7,3,5,4,6] => 2 [1,2,7,3,5,6,4] => 2 [1,2,7,3,6,4,5] => 2 [1,2,7,3,6,5,4] => 1 [1,2,7,4,3,5,6] => 2 [1,2,7,4,3,6,5] => 1 [1,2,7,4,5,3,6] => 2 [1,2,7,4,5,6,3] => 2 [1,2,7,4,6,3,5] => 2 [1,2,7,4,6,5,3] => 1 [1,2,7,5,3,4,6] => 2 [1,2,7,5,3,6,4] => 1 [1,2,7,5,4,3,6] => 1 [1,2,7,5,4,6,3] => 1 [1,2,7,5,6,3,4] => 2 [1,2,7,5,6,4,3] => 1 [1,2,7,6,3,4,5] => 2 [1,2,7,6,3,5,4] => 1 [1,2,7,6,4,3,5] => 1 [1,2,7,6,4,5,3] => 1 [1,2,7,6,5,3,4] => 1 [1,2,7,6,5,4,3] => 0 [1,3,2,4,5,6,7] => 0 [1,3,2,4,5,7,6] => 0 [1,3,2,4,6,5,7] => 0 [1,3,2,4,6,7,5] => 0 [1,3,2,4,7,5,6] => 1 [1,3,2,4,7,6,5] => 0 [1,3,2,5,4,6,7] => 0 [1,3,2,5,4,7,6] => 0 [1,3,2,5,6,4,7] => 0 [1,3,2,5,6,7,4] => 0 [1,3,2,5,7,4,6] => 1 [1,3,2,5,7,6,4] => 0 [1,3,2,6,4,5,7] => 1 [1,3,2,6,4,7,5] => 0 [1,3,2,6,5,4,7] => 0 [1,3,2,6,5,7,4] => 0 [1,3,2,6,7,4,5] => 1 [1,3,2,6,7,5,4] => 0 [1,3,2,7,4,5,6] => 2 [1,3,2,7,4,6,5] => 1 [1,3,2,7,5,4,6] => 1 [1,3,2,7,5,6,4] => 1 [1,3,2,7,6,4,5] => 1 [1,3,2,7,6,5,4] => 0 [1,3,4,2,5,6,7] => 0 [1,3,4,2,5,7,6] => 0 [1,3,4,2,6,5,7] => 0 [1,3,4,2,6,7,5] => 0 [1,3,4,2,7,5,6] => 1 [1,3,4,2,7,6,5] => 0 [1,3,4,5,2,6,7] => 0 [1,3,4,5,2,7,6] => 0 [1,3,4,5,6,2,7] => 0 [1,3,4,5,6,7,2] => 0 [1,3,4,5,7,2,6] => 1 [1,3,4,5,7,6,2] => 0 [1,3,4,6,2,5,7] => 1 [1,3,4,6,2,7,5] => 0 [1,3,4,6,5,2,7] => 0 [1,3,4,6,5,7,2] => 0 [1,3,4,6,7,2,5] => 1 [1,3,4,6,7,5,2] => 0 [1,3,4,7,2,5,6] => 2 [1,3,4,7,2,6,5] => 1 [1,3,4,7,5,2,6] => 1 [1,3,4,7,5,6,2] => 1 [1,3,4,7,6,2,5] => 1 [1,3,4,7,6,5,2] => 0 [1,3,5,2,4,6,7] => 1 [1,3,5,2,4,7,6] => 1 [1,3,5,2,6,4,7] => 0 [1,3,5,2,6,7,4] => 0 [1,3,5,2,7,4,6] => 1 [1,3,5,2,7,6,4] => 0 [1,3,5,4,2,6,7] => 0 [1,3,5,4,2,7,6] => 0 [1,3,5,4,6,2,7] => 0 [1,3,5,4,6,7,2] => 0 [1,3,5,4,7,2,6] => 1 [1,3,5,4,7,6,2] => 0 [1,3,5,6,2,4,7] => 1 [1,3,5,6,2,7,4] => 0 [1,3,5,6,4,2,7] => 0 [1,3,5,6,4,7,2] => 0 [1,3,5,6,7,2,4] => 1 [1,3,5,6,7,4,2] => 0 [1,3,5,7,2,4,6] => 2 [1,3,5,7,2,6,4] => 1 [1,3,5,7,4,2,6] => 1 [1,3,5,7,4,6,2] => 1 [1,3,5,7,6,2,4] => 1 [1,3,5,7,6,4,2] => 0 [1,3,6,2,4,5,7] => 2 [1,3,6,2,4,7,5] => 1 [1,3,6,2,5,4,7] => 1 [1,3,6,2,5,7,4] => 1 [1,3,6,2,7,4,5] => 1 [1,3,6,2,7,5,4] => 0 [1,3,6,4,2,5,7] => 1 [1,3,6,4,2,7,5] => 0 [1,3,6,4,5,2,7] => 1 [1,3,6,4,5,7,2] => 1 [1,3,6,4,7,2,5] => 1 [1,3,6,4,7,5,2] => 0 [1,3,6,5,2,4,7] => 1 [1,3,6,5,2,7,4] => 0 [1,3,6,5,4,2,7] => 0 [1,3,6,5,4,7,2] => 0 [1,3,6,5,7,2,4] => 1 [1,3,6,5,7,4,2] => 0 [1,3,6,7,2,4,5] => 2 [1,3,6,7,2,5,4] => 1 [1,3,6,7,4,2,5] => 1 [1,3,6,7,4,5,2] => 1 [1,3,6,7,5,2,4] => 1 [1,3,6,7,5,4,2] => 0 [1,3,7,2,4,5,6] => 3 [1,3,7,2,4,6,5] => 2 [1,3,7,2,5,4,6] => 2 [1,3,7,2,5,6,4] => 2 [1,3,7,2,6,4,5] => 2 [1,3,7,2,6,5,4] => 1 [1,3,7,4,2,5,6] => 2 [1,3,7,4,2,6,5] => 1 [1,3,7,4,5,2,6] => 2 [1,3,7,4,5,6,2] => 2 [1,3,7,4,6,2,5] => 2 [1,3,7,4,6,5,2] => 1 [1,3,7,5,2,4,6] => 2 [1,3,7,5,2,6,4] => 1 [1,3,7,5,4,2,6] => 1 [1,3,7,5,4,6,2] => 1 [1,3,7,5,6,2,4] => 2 [1,3,7,5,6,4,2] => 1 [1,3,7,6,2,4,5] => 2 [1,3,7,6,2,5,4] => 1 [1,3,7,6,4,2,5] => 1 [1,3,7,6,4,5,2] => 1 [1,3,7,6,5,2,4] => 1 [1,3,7,6,5,4,2] => 0 [1,4,2,3,5,6,7] => 1 [1,4,2,3,5,7,6] => 1 [1,4,2,3,6,5,7] => 1 [1,4,2,3,6,7,5] => 1 [1,4,2,3,7,5,6] => 2 [1,4,2,3,7,6,5] => 1 [1,4,2,5,3,6,7] => 0 [1,4,2,5,3,7,6] => 0 [1,4,2,5,6,3,7] => 0 [1,4,2,5,6,7,3] => 0 [1,4,2,5,7,3,6] => 1 [1,4,2,5,7,6,3] => 0 [1,4,2,6,3,5,7] => 1 [1,4,2,6,3,7,5] => 0 [1,4,2,6,5,3,7] => 0 [1,4,2,6,5,7,3] => 0 [1,4,2,6,7,3,5] => 1 [1,4,2,6,7,5,3] => 0 [1,4,2,7,3,5,6] => 2 [1,4,2,7,3,6,5] => 1 [1,4,2,7,5,3,6] => 1 [1,4,2,7,5,6,3] => 1 [1,4,2,7,6,3,5] => 1 [1,4,2,7,6,5,3] => 0 [1,4,3,2,5,6,7] => 0 [1,4,3,2,5,7,6] => 0 [1,4,3,2,6,5,7] => 0 [1,4,3,2,6,7,5] => 0 [1,4,3,2,7,5,6] => 1 [1,4,3,2,7,6,5] => 0 [1,4,3,5,2,6,7] => 0 [1,4,3,5,2,7,6] => 0 [1,4,3,5,6,2,7] => 0 [1,4,3,5,6,7,2] => 0 [1,4,3,5,7,2,6] => 1 [1,4,3,5,7,6,2] => 0 [1,4,3,6,2,5,7] => 1 [1,4,3,6,2,7,5] => 0 [1,4,3,6,5,2,7] => 0 [1,4,3,6,5,7,2] => 0 [1,4,3,6,7,2,5] => 1 [1,4,3,6,7,5,2] => 0 [1,4,3,7,2,5,6] => 2 [1,4,3,7,2,6,5] => 1 [1,4,3,7,5,2,6] => 1 [1,4,3,7,5,6,2] => 1 [1,4,3,7,6,2,5] => 1 [1,4,3,7,6,5,2] => 0 [1,4,5,2,3,6,7] => 1 [1,4,5,2,3,7,6] => 1 [1,4,5,2,6,3,7] => 0 [1,4,5,2,6,7,3] => 0 [1,4,5,2,7,3,6] => 1 [1,4,5,2,7,6,3] => 0 [1,4,5,3,2,6,7] => 0 [1,4,5,3,2,7,6] => 0 [1,4,5,3,6,2,7] => 0 [1,4,5,3,6,7,2] => 0 [1,4,5,3,7,2,6] => 1 [1,4,5,3,7,6,2] => 0 [1,4,5,6,2,3,7] => 1 [1,4,5,6,2,7,3] => 0 [1,4,5,6,3,2,7] => 0 [1,4,5,6,3,7,2] => 0 [1,4,5,6,7,2,3] => 1 [1,4,5,6,7,3,2] => 0 [1,4,5,7,2,3,6] => 2 [1,4,5,7,2,6,3] => 1 [1,4,5,7,3,2,6] => 1 [1,4,5,7,3,6,2] => 1 [1,4,5,7,6,2,3] => 1 [1,4,5,7,6,3,2] => 0 [1,4,6,2,3,5,7] => 2 [1,4,6,2,3,7,5] => 1 [1,4,6,2,5,3,7] => 1 [1,4,6,2,5,7,3] => 1 [1,4,6,2,7,3,5] => 1 [1,4,6,2,7,5,3] => 0 [1,4,6,3,2,5,7] => 1 [1,4,6,3,2,7,5] => 0 [1,4,6,3,5,2,7] => 1 [1,4,6,3,5,7,2] => 1 [1,4,6,3,7,2,5] => 1 [1,4,6,3,7,5,2] => 0 [1,4,6,5,2,3,7] => 1 [1,4,6,5,2,7,3] => 0 [1,4,6,5,3,2,7] => 0 ----------------------------------------------------------------------------- Created: Oct 23, 2021 at 00:29 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Oct 23, 2021 at 00:29 by Martin Rubey