***************************************************************************** * 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: St001898 ----------------------------------------------------------------------------- Collection: Ordered set partitions ----------------------------------------------------------------------------- Description: The number of occurrences of an 132 pattern in an ordered set partition. An occurrence of a pattern $\pi\in\mathfrak S_k$ ordered set partition with blocks $B_1|\dots|B_\ell$ is a sequence of elements $e_1,\dots,e_k$ with $e_i\in B_{j_i}$ and $j_1 < \dots < j_k$ order-isomorphic to $\pi$. ----------------------------------------------------------------------------- References: [1] (service unreachable) [[MathSciNet:3245891]] ----------------------------------------------------------------------------- Code: from sage.combinat.permutation import to_standard def occurrences(p, pattern): """ Return elements in sequences of distinct blocks order isomorphic to `pattern`. """ o = [] for i, b in enumerate(p): q = p[i+1:] for e in b: o.extend(occurrences_aux(q, [e], pattern)) return o def occurrences_aux(p, prefix, pattern): """ Return all occurrences of the form `(prefix, suffix)` order isomorphic to `pattern`, where `suffix` are elements in sequences of distinct blocks of `p`. """ # TODO: we could do better, probably if len(pattern) == len(prefix): yield prefix else: pattern_prefix = to_standard(pattern[:len(prefix)+1]) for i, b in enumerate(p): q = p[i+1:] for e in b: new_prefix = prefix + [e] if to_standard(new_prefix) == pattern_prefix: yield from occurrences_aux(q, new_prefix, pattern) def statistic(p): return len(occurrences(p, [1,3,2])) ----------------------------------------------------------------------------- Statistic values: [{1}] => 0 [{1},{2}] => 0 [{2},{1}] => 0 [{1,2}] => 0 [{1},{2},{3}] => 0 [{1},{3},{2}] => 1 [{2},{1},{3}] => 0 [{3},{1},{2}] => 0 [{2},{3},{1}] => 0 [{3},{2},{1}] => 0 [{1},{2,3}] => 0 [{2},{1,3}] => 0 [{3},{1,2}] => 0 [{1,2},{3}] => 0 [{1,3},{2}] => 0 [{2,3},{1}] => 0 [{1,2,3}] => 0 [{1},{2},{3},{4}] => 0 [{1},{2},{4},{3}] => 2 [{1},{3},{2},{4}] => 1 [{1},{4},{2},{3}] => 2 [{1},{3},{4},{2}] => 2 [{1},{4},{3},{2}] => 3 [{2},{1},{3},{4}] => 0 [{2},{1},{4},{3}] => 2 [{3},{1},{2},{4}] => 0 [{4},{1},{2},{3}] => 0 [{3},{1},{4},{2}] => 1 [{4},{1},{3},{2}] => 1 [{2},{3},{1},{4}] => 0 [{2},{4},{1},{3}] => 1 [{3},{2},{1},{4}] => 0 [{4},{2},{1},{3}] => 0 [{3},{4},{1},{2}] => 0 [{4},{3},{1},{2}] => 0 [{2},{3},{4},{1}] => 0 [{2},{4},{3},{1}] => 1 [{3},{2},{4},{1}] => 0 [{4},{2},{3},{1}] => 0 [{3},{4},{2},{1}] => 0 [{4},{3},{2},{1}] => 0 [{1},{2},{3,4}] => 0 [{1},{3},{2,4}] => 1 [{1},{4},{2,3}] => 2 [{2},{1},{3,4}] => 0 [{3},{1},{2,4}] => 0 [{4},{1},{2,3}] => 0 [{2},{3},{1,4}] => 0 [{2},{4},{1,3}] => 1 [{3},{2},{1,4}] => 0 [{4},{2},{1,3}] => 0 [{3},{4},{1,2}] => 0 [{4},{3},{1,2}] => 0 [{1},{2,3},{4}] => 0 [{1},{2,4},{3}] => 1 [{1},{3,4},{2}] => 2 [{2},{1,3},{4}] => 0 [{2},{1,4},{3}] => 1 [{3},{1,2},{4}] => 0 [{4},{1,2},{3}] => 0 [{3},{1,4},{2}] => 0 [{4},{1,3},{2}] => 0 [{2},{3,4},{1}] => 0 [{3},{2,4},{1}] => 0 [{4},{2,3},{1}] => 0 [{1},{2,3,4}] => 0 [{2},{1,3,4}] => 0 [{3},{1,2,4}] => 0 [{4},{1,2,3}] => 0 [{1,2},{3},{4}] => 0 [{1,2},{4},{3}] => 2 [{1,3},{2},{4}] => 0 [{1,4},{2},{3}] => 0 [{1,3},{4},{2}] => 1 [{1,4},{3},{2}] => 1 [{2,3},{1},{4}] => 0 [{2,4},{1},{3}] => 0 [{3,4},{1},{2}] => 0 [{2,3},{4},{1}] => 0 [{2,4},{3},{1}] => 0 [{3,4},{2},{1}] => 0 [{1,2},{3,4}] => 0 [{1,3},{2,4}] => 0 [{1,4},{2,3}] => 0 [{2,3},{1,4}] => 0 [{2,4},{1,3}] => 0 [{3,4},{1,2}] => 0 [{1,2,3},{4}] => 0 [{1,2,4},{3}] => 0 [{1,3,4},{2}] => 0 [{2,3,4},{1}] => 0 [{1,2,3,4}] => 0 [{1},{2},{3},{4},{5}] => 0 [{1},{2},{3},{5},{4}] => 3 [{1},{2},{4},{3},{5}] => 2 [{1},{2},{5},{3},{4}] => 4 [{1},{2},{4},{5},{3}] => 4 [{1},{2},{5},{4},{3}] => 6 [{1},{3},{2},{4},{5}] => 1 [{1},{3},{2},{5},{4}] => 4 [{1},{4},{2},{3},{5}] => 2 [{1},{5},{2},{3},{4}] => 3 [{1},{4},{2},{5},{3}] => 4 [{1},{5},{2},{4},{3}] => 5 [{1},{3},{4},{2},{5}] => 2 [{1},{3},{5},{2},{4}] => 4 [{1},{4},{3},{2},{5}] => 3 [{1},{5},{3},{2},{4}] => 4 [{1},{4},{5},{2},{3}] => 4 [{1},{5},{4},{2},{3}] => 5 [{1},{3},{4},{5},{2}] => 3 [{1},{3},{5},{4},{2}] => 5 [{1},{4},{3},{5},{2}] => 4 [{1},{5},{3},{4},{2}] => 5 [{1},{4},{5},{3},{2}] => 5 [{1},{5},{4},{3},{2}] => 6 [{2},{1},{3},{4},{5}] => 0 [{2},{1},{3},{5},{4}] => 3 [{2},{1},{4},{3},{5}] => 2 [{2},{1},{5},{3},{4}] => 4 [{2},{1},{4},{5},{3}] => 4 [{2},{1},{5},{4},{3}] => 6 [{3},{1},{2},{4},{5}] => 0 [{3},{1},{2},{5},{4}] => 3 [{4},{1},{2},{3},{5}] => 0 [{5},{1},{2},{3},{4}] => 0 [{4},{1},{2},{5},{3}] => 2 [{5},{1},{2},{4},{3}] => 2 [{3},{1},{4},{2},{5}] => 1 [{3},{1},{5},{2},{4}] => 3 [{4},{1},{3},{2},{5}] => 1 [{5},{1},{3},{2},{4}] => 1 [{4},{1},{5},{2},{3}] => 2 [{5},{1},{4},{2},{3}] => 2 [{3},{1},{4},{5},{2}] => 2 [{3},{1},{5},{4},{2}] => 4 [{4},{1},{3},{5},{2}] => 2 [{5},{1},{3},{4},{2}] => 2 [{4},{1},{5},{3},{2}] => 3 [{5},{1},{4},{3},{2}] => 3 [{2},{3},{1},{4},{5}] => 0 [{2},{3},{1},{5},{4}] => 3 [{2},{4},{1},{3},{5}] => 1 [{2},{5},{1},{3},{4}] => 2 [{2},{4},{1},{5},{3}] => 3 [{2},{5},{1},{4},{3}] => 4 [{3},{2},{1},{4},{5}] => 0 [{3},{2},{1},{5},{4}] => 3 [{4},{2},{1},{3},{5}] => 0 [{5},{2},{1},{3},{4}] => 0 [{4},{2},{1},{5},{3}] => 2 [{5},{2},{1},{4},{3}] => 2 [{3},{4},{1},{2},{5}] => 0 [{3},{5},{1},{2},{4}] => 1 [{4},{3},{1},{2},{5}] => 0 [{5},{3},{1},{2},{4}] => 0 [{4},{5},{1},{2},{3}] => 0 [{5},{4},{1},{2},{3}] => 0 [{3},{4},{1},{5},{2}] => 1 [{3},{5},{1},{4},{2}] => 2 [{4},{3},{1},{5},{2}] => 1 [{5},{3},{1},{4},{2}] => 1 [{4},{5},{1},{3},{2}] => 1 [{5},{4},{1},{3},{2}] => 1 [{2},{3},{4},{1},{5}] => 0 [{2},{3},{5},{1},{4}] => 2 [{2},{4},{3},{1},{5}] => 1 [{2},{5},{3},{1},{4}] => 2 [{2},{4},{5},{1},{3}] => 2 [{2},{5},{4},{1},{3}] => 3 [{3},{2},{4},{1},{5}] => 0 [{3},{2},{5},{1},{4}] => 2 [{4},{2},{3},{1},{5}] => 0 [{5},{2},{3},{1},{4}] => 0 [{4},{2},{5},{1},{3}] => 1 [{5},{2},{4},{1},{3}] => 1 [{3},{4},{2},{1},{5}] => 0 [{3},{5},{2},{1},{4}] => 1 [{4},{3},{2},{1},{5}] => 0 [{5},{3},{2},{1},{4}] => 0 [{4},{5},{2},{1},{3}] => 0 [{5},{4},{2},{1},{3}] => 0 [{3},{4},{5},{1},{2}] => 0 [{3},{5},{4},{1},{2}] => 1 [{4},{3},{5},{1},{2}] => 0 [{5},{3},{4},{1},{2}] => 0 [{4},{5},{3},{1},{2}] => 0 [{5},{4},{3},{1},{2}] => 0 [{2},{3},{4},{5},{1}] => 0 [{2},{3},{5},{4},{1}] => 2 [{2},{4},{3},{5},{1}] => 1 [{2},{5},{3},{4},{1}] => 2 [{2},{4},{5},{3},{1}] => 2 [{2},{5},{4},{3},{1}] => 3 [{3},{2},{4},{5},{1}] => 0 [{3},{2},{5},{4},{1}] => 2 [{4},{2},{3},{5},{1}] => 0 [{5},{2},{3},{4},{1}] => 0 [{4},{2},{5},{3},{1}] => 1 [{5},{2},{4},{3},{1}] => 1 [{3},{4},{2},{5},{1}] => 0 [{3},{5},{2},{4},{1}] => 1 [{4},{3},{2},{5},{1}] => 0 [{5},{3},{2},{4},{1}] => 0 [{4},{5},{2},{3},{1}] => 0 [{5},{4},{2},{3},{1}] => 0 [{3},{4},{5},{2},{1}] => 0 [{3},{5},{4},{2},{1}] => 1 [{4},{3},{5},{2},{1}] => 0 [{5},{3},{4},{2},{1}] => 0 [{4},{5},{3},{2},{1}] => 0 [{5},{4},{3},{2},{1}] => 0 [{1},{2},{3},{4,5}] => 0 [{1},{2},{4},{3,5}] => 2 [{1},{2},{5},{3,4}] => 4 [{1},{3},{2},{4,5}] => 1 [{1},{4},{2},{3,5}] => 2 [{1},{5},{2},{3,4}] => 3 [{1},{3},{4},{2,5}] => 2 [{1},{3},{5},{2,4}] => 4 [{1},{4},{3},{2,5}] => 3 [{1},{5},{3},{2,4}] => 4 [{1},{4},{5},{2,3}] => 4 [{1},{5},{4},{2,3}] => 5 [{2},{1},{3},{4,5}] => 0 [{2},{1},{4},{3,5}] => 2 [{2},{1},{5},{3,4}] => 4 [{3},{1},{2},{4,5}] => 0 [{4},{1},{2},{3,5}] => 0 [{5},{1},{2},{3,4}] => 0 [{3},{1},{4},{2,5}] => 1 [{3},{1},{5},{2,4}] => 3 [{4},{1},{3},{2,5}] => 1 [{5},{1},{3},{2,4}] => 1 [{4},{1},{5},{2,3}] => 2 [{5},{1},{4},{2,3}] => 2 [{2},{3},{1},{4,5}] => 0 [{2},{4},{1},{3,5}] => 1 [{2},{5},{1},{3,4}] => 2 [{3},{2},{1},{4,5}] => 0 [{4},{2},{1},{3,5}] => 0 [{5},{2},{1},{3,4}] => 0 [{3},{4},{1},{2,5}] => 0 [{3},{5},{1},{2,4}] => 1 [{4},{3},{1},{2,5}] => 0 [{5},{3},{1},{2,4}] => 0 [{4},{5},{1},{2,3}] => 0 [{5},{4},{1},{2,3}] => 0 [{2},{3},{4},{1,5}] => 0 [{2},{3},{5},{1,4}] => 2 [{2},{4},{3},{1,5}] => 1 [{2},{5},{3},{1,4}] => 2 [{2},{4},{5},{1,3}] => 2 [{2},{5},{4},{1,3}] => 3 [{3},{2},{4},{1,5}] => 0 [{3},{2},{5},{1,4}] => 2 [{4},{2},{3},{1,5}] => 0 [{5},{2},{3},{1,4}] => 0 [{4},{2},{5},{1,3}] => 1 [{5},{2},{4},{1,3}] => 1 [{3},{4},{2},{1,5}] => 0 [{3},{5},{2},{1,4}] => 1 [{4},{3},{2},{1,5}] => 0 [{5},{3},{2},{1,4}] => 0 [{4},{5},{2},{1,3}] => 0 [{5},{4},{2},{1,3}] => 0 [{3},{4},{5},{1,2}] => 0 [{3},{5},{4},{1,2}] => 1 [{4},{3},{5},{1,2}] => 0 [{5},{3},{4},{1,2}] => 0 [{4},{5},{3},{1,2}] => 0 [{5},{4},{3},{1,2}] => 0 [{1},{2},{3,4},{5}] => 0 [{1},{2},{3,5},{4}] => 2 [{1},{2},{4,5},{3}] => 4 [{1},{3},{2,4},{5}] => 1 [{1},{3},{2,5},{4}] => 3 [{1},{4},{2,3},{5}] => 2 [{1},{5},{2,3},{4}] => 3 [{1},{4},{2,5},{3}] => 3 [{1},{5},{2,4},{3}] => 4 [{1},{3},{4,5},{2}] => 3 [{1},{4},{3,5},{2}] => 4 [{1},{5},{3,4},{2}] => 5 [{2},{1},{3,4},{5}] => 0 [{2},{1},{3,5},{4}] => 2 [{2},{1},{4,5},{3}] => 4 [{3},{1},{2,4},{5}] => 0 [{3},{1},{2,5},{4}] => 2 [{4},{1},{2,3},{5}] => 0 [{5},{1},{2,3},{4}] => 0 [{4},{1},{2,5},{3}] => 1 [{5},{1},{2,4},{3}] => 1 [{3},{1},{4,5},{2}] => 2 [{4},{1},{3,5},{2}] => 2 [{5},{1},{3,4},{2}] => 2 [{2},{3},{1,4},{5}] => 0 [{2},{3},{1,5},{4}] => 2 [{2},{4},{1,3},{5}] => 1 [{2},{5},{1,3},{4}] => 2 [{2},{4},{1,5},{3}] => 2 [{2},{5},{1,4},{3}] => 3 [{3},{2},{1,4},{5}] => 0 [{3},{2},{1,5},{4}] => 2 [{4},{2},{1,3},{5}] => 0 [{5},{2},{1,3},{4}] => 0 [{4},{2},{1,5},{3}] => 1 [{5},{2},{1,4},{3}] => 1 [{3},{4},{1,2},{5}] => 0 [{3},{5},{1,2},{4}] => 1 [{4},{3},{1,2},{5}] => 0 [{5},{3},{1,2},{4}] => 0 [{4},{5},{1,2},{3}] => 0 [{5},{4},{1,2},{3}] => 0 [{3},{4},{1,5},{2}] => 0 [{3},{5},{1,4},{2}] => 1 [{4},{3},{1,5},{2}] => 0 [{5},{3},{1,4},{2}] => 0 [{4},{5},{1,3},{2}] => 0 [{5},{4},{1,3},{2}] => 0 [{2},{3},{4,5},{1}] => 0 [{2},{4},{3,5},{1}] => 1 [{2},{5},{3,4},{1}] => 2 [{3},{2},{4,5},{1}] => 0 [{4},{2},{3,5},{1}] => 0 [{5},{2},{3,4},{1}] => 0 [{3},{4},{2,5},{1}] => 0 [{3},{5},{2,4},{1}] => 1 [{4},{3},{2,5},{1}] => 0 [{5},{3},{2,4},{1}] => 0 [{4},{5},{2,3},{1}] => 0 [{5},{4},{2,3},{1}] => 0 [{1},{2},{3,4,5}] => 0 [{1},{3},{2,4,5}] => 1 [{1},{4},{2,3,5}] => 2 [{1},{5},{2,3,4}] => 3 [{2},{1},{3,4,5}] => 0 [{3},{1},{2,4,5}] => 0 [{4},{1},{2,3,5}] => 0 [{5},{1},{2,3,4}] => 0 [{2},{3},{1,4,5}] => 0 [{2},{4},{1,3,5}] => 1 [{2},{5},{1,3,4}] => 2 [{3},{2},{1,4,5}] => 0 [{4},{2},{1,3,5}] => 0 [{5},{2},{1,3,4}] => 0 [{3},{4},{1,2,5}] => 0 [{3},{5},{1,2,4}] => 1 [{4},{3},{1,2,5}] => 0 [{5},{3},{1,2,4}] => 0 [{4},{5},{1,2,3}] => 0 [{5},{4},{1,2,3}] => 0 [{1},{2,3},{4},{5}] => 0 [{1},{2,3},{5},{4}] => 3 [{1},{2,4},{3},{5}] => 1 [{1},{2,5},{3},{4}] => 2 [{1},{2,4},{5},{3}] => 3 [{1},{2,5},{4},{3}] => 4 [{1},{3,4},{2},{5}] => 2 [{1},{3,5},{2},{4}] => 3 [{1},{4,5},{2},{3}] => 4 [{1},{3,4},{5},{2}] => 3 [{1},{3,5},{4},{2}] => 4 [{1},{4,5},{3},{2}] => 5 [{2},{1,3},{4},{5}] => 0 [{2},{1,3},{5},{4}] => 3 [{2},{1,4},{3},{5}] => 1 [{2},{1,5},{3},{4}] => 2 [{2},{1,4},{5},{3}] => 3 [{2},{1,5},{4},{3}] => 4 [{3},{1,2},{4},{5}] => 0 [{3},{1,2},{5},{4}] => 3 [{4},{1,2},{3},{5}] => 0 [{5},{1,2},{3},{4}] => 0 [{4},{1,2},{5},{3}] => 2 [{5},{1,2},{4},{3}] => 2 [{3},{1,4},{2},{5}] => 0 [{3},{1,5},{2},{4}] => 1 [{4},{1,3},{2},{5}] => 0 [{5},{1,3},{2},{4}] => 0 [{4},{1,5},{2},{3}] => 0 [{5},{1,4},{2},{3}] => 0 [{3},{1,4},{5},{2}] => 1 [{3},{1,5},{4},{2}] => 2 [{4},{1,3},{5},{2}] => 1 [{5},{1,3},{4},{2}] => 1 [{4},{1,5},{3},{2}] => 1 [{5},{1,4},{3},{2}] => 1 [{2},{3,4},{1},{5}] => 0 [{2},{3,5},{1},{4}] => 1 [{2},{4,5},{1},{3}] => 2 [{3},{2,4},{1},{5}] => 0 [{3},{2,5},{1},{4}] => 1 [{4},{2,3},{1},{5}] => 0 [{5},{2,3},{1},{4}] => 0 [{4},{2,5},{1},{3}] => 0 [{5},{2,4},{1},{3}] => 0 [{3},{4,5},{1},{2}] => 0 [{4},{3,5},{1},{2}] => 0 [{5},{3,4},{1},{2}] => 0 [{2},{3,4},{5},{1}] => 0 [{2},{3,5},{4},{1}] => 1 [{2},{4,5},{3},{1}] => 2 [{3},{2,4},{5},{1}] => 0 [{3},{2,5},{4},{1}] => 1 [{4},{2,3},{5},{1}] => 0 [{5},{2,3},{4},{1}] => 0 [{4},{2,5},{3},{1}] => 0 [{5},{2,4},{3},{1}] => 0 [{3},{4,5},{2},{1}] => 0 [{4},{3,5},{2},{1}] => 0 [{5},{3,4},{2},{1}] => 0 [{1},{2,3},{4,5}] => 0 [{1},{2,4},{3,5}] => 1 [{1},{2,5},{3,4}] => 2 [{1},{3,4},{2,5}] => 2 [{1},{3,5},{2,4}] => 3 [{1},{4,5},{2,3}] => 4 [{2},{1,3},{4,5}] => 0 [{2},{1,4},{3,5}] => 1 [{2},{1,5},{3,4}] => 2 [{3},{1,2},{4,5}] => 0 [{4},{1,2},{3,5}] => 0 [{5},{1,2},{3,4}] => 0 [{3},{1,4},{2,5}] => 0 [{3},{1,5},{2,4}] => 1 [{4},{1,3},{2,5}] => 0 [{5},{1,3},{2,4}] => 0 [{4},{1,5},{2,3}] => 0 [{5},{1,4},{2,3}] => 0 [{2},{3,4},{1,5}] => 0 [{2},{3,5},{1,4}] => 1 [{2},{4,5},{1,3}] => 2 [{3},{2,4},{1,5}] => 0 [{3},{2,5},{1,4}] => 1 [{4},{2,3},{1,5}] => 0 [{5},{2,3},{1,4}] => 0 [{4},{2,5},{1,3}] => 0 [{5},{2,4},{1,3}] => 0 [{3},{4,5},{1,2}] => 0 [{4},{3,5},{1,2}] => 0 [{5},{3,4},{1,2}] => 0 [{1},{2,3,4},{5}] => 0 [{1},{2,3,5},{4}] => 1 [{1},{2,4,5},{3}] => 2 [{1},{3,4,5},{2}] => 3 [{2},{1,3,4},{5}] => 0 [{2},{1,3,5},{4}] => 1 [{2},{1,4,5},{3}] => 2 [{3},{1,2,4},{5}] => 0 [{3},{1,2,5},{4}] => 1 [{4},{1,2,3},{5}] => 0 [{5},{1,2,3},{4}] => 0 [{4},{1,2,5},{3}] => 0 [{5},{1,2,4},{3}] => 0 [{3},{1,4,5},{2}] => 0 [{4},{1,3,5},{2}] => 0 [{5},{1,3,4},{2}] => 0 [{2},{3,4,5},{1}] => 0 [{3},{2,4,5},{1}] => 0 [{4},{2,3,5},{1}] => 0 [{5},{2,3,4},{1}] => 0 [{1},{2,3,4,5}] => 0 [{2},{1,3,4,5}] => 0 [{3},{1,2,4,5}] => 0 [{4},{1,2,3,5}] => 0 [{5},{1,2,3,4}] => 0 [{1,2},{3},{4},{5}] => 0 [{1,2},{3},{5},{4}] => 3 [{1,2},{4},{3},{5}] => 2 [{1,2},{5},{3},{4}] => 4 [{1,2},{4},{5},{3}] => 4 [{1,2},{5},{4},{3}] => 6 [{1,3},{2},{4},{5}] => 0 [{1,3},{2},{5},{4}] => 3 [{1,4},{2},{3},{5}] => 0 [{1,5},{2},{3},{4}] => 0 [{1,4},{2},{5},{3}] => 2 [{1,5},{2},{4},{3}] => 2 [{1,3},{4},{2},{5}] => 1 [{1,3},{5},{2},{4}] => 3 [{1,4},{3},{2},{5}] => 1 [{1,5},{3},{2},{4}] => 1 [{1,4},{5},{2},{3}] => 2 [{1,5},{4},{2},{3}] => 2 [{1,3},{4},{5},{2}] => 2 [{1,3},{5},{4},{2}] => 4 [{1,4},{3},{5},{2}] => 2 [{1,5},{3},{4},{2}] => 2 [{1,4},{5},{3},{2}] => 3 [{1,5},{4},{3},{2}] => 3 [{2,3},{1},{4},{5}] => 0 [{2,3},{1},{5},{4}] => 3 [{2,4},{1},{3},{5}] => 0 [{2,5},{1},{3},{4}] => 0 [{2,4},{1},{5},{3}] => 2 [{2,5},{1},{4},{3}] => 2 [{3,4},{1},{2},{5}] => 0 [{3,5},{1},{2},{4}] => 0 [{4,5},{1},{2},{3}] => 0 [{3,4},{1},{5},{2}] => 1 [{3,5},{1},{4},{2}] => 1 [{4,5},{1},{3},{2}] => 1 [{2,3},{4},{1},{5}] => 0 [{2,3},{5},{1},{4}] => 2 [{2,4},{3},{1},{5}] => 0 [{2,5},{3},{1},{4}] => 0 [{2,4},{5},{1},{3}] => 1 [{2,5},{4},{1},{3}] => 1 [{3,4},{2},{1},{5}] => 0 [{3,5},{2},{1},{4}] => 0 [{4,5},{2},{1},{3}] => 0 [{3,4},{5},{1},{2}] => 0 [{3,5},{4},{1},{2}] => 0 [{4,5},{3},{1},{2}] => 0 [{2,3},{4},{5},{1}] => 0 [{2,3},{5},{4},{1}] => 2 [{2,4},{3},{5},{1}] => 0 [{2,5},{3},{4},{1}] => 0 [{2,4},{5},{3},{1}] => 1 [{2,5},{4},{3},{1}] => 1 [{3,4},{2},{5},{1}] => 0 [{3,5},{2},{4},{1}] => 0 [{4,5},{2},{3},{1}] => 0 [{3,4},{5},{2},{1}] => 0 [{3,5},{4},{2},{1}] => 0 [{4,5},{3},{2},{1}] => 0 [{1,2},{3},{4,5}] => 0 [{1,2},{4},{3,5}] => 2 [{1,2},{5},{3,4}] => 4 [{1,3},{2},{4,5}] => 0 [{1,4},{2},{3,5}] => 0 [{1,5},{2},{3,4}] => 0 [{1,3},{4},{2,5}] => 1 [{1,3},{5},{2,4}] => 3 [{1,4},{3},{2,5}] => 1 [{1,5},{3},{2,4}] => 1 [{1,4},{5},{2,3}] => 2 [{1,5},{4},{2,3}] => 2 [{2,3},{1},{4,5}] => 0 [{2,4},{1},{3,5}] => 0 [{2,5},{1},{3,4}] => 0 [{3,4},{1},{2,5}] => 0 [{3,5},{1},{2,4}] => 0 [{4,5},{1},{2,3}] => 0 [{2,3},{4},{1,5}] => 0 [{2,3},{5},{1,4}] => 2 [{2,4},{3},{1,5}] => 0 [{2,5},{3},{1,4}] => 0 [{2,4},{5},{1,3}] => 1 [{2,5},{4},{1,3}] => 1 [{3,4},{2},{1,5}] => 0 [{3,5},{2},{1,4}] => 0 [{4,5},{2},{1,3}] => 0 [{3,4},{5},{1,2}] => 0 [{3,5},{4},{1,2}] => 0 [{4,5},{3},{1,2}] => 0 [{1,2},{3,4},{5}] => 0 [{1,2},{3,5},{4}] => 2 [{1,2},{4,5},{3}] => 4 [{1,3},{2,4},{5}] => 0 [{1,3},{2,5},{4}] => 2 [{1,4},{2,3},{5}] => 0 [{1,5},{2,3},{4}] => 0 [{1,4},{2,5},{3}] => 1 [{1,5},{2,4},{3}] => 1 [{1,3},{4,5},{2}] => 2 [{1,4},{3,5},{2}] => 2 [{1,5},{3,4},{2}] => 2 [{2,3},{1,4},{5}] => 0 [{2,3},{1,5},{4}] => 2 [{2,4},{1,3},{5}] => 0 [{2,5},{1,3},{4}] => 0 [{2,4},{1,5},{3}] => 1 [{2,5},{1,4},{3}] => 1 [{3,4},{1,2},{5}] => 0 [{3,5},{1,2},{4}] => 0 [{4,5},{1,2},{3}] => 0 [{3,4},{1,5},{2}] => 0 [{3,5},{1,4},{2}] => 0 [{4,5},{1,3},{2}] => 0 [{2,3},{4,5},{1}] => 0 [{2,4},{3,5},{1}] => 0 [{2,5},{3,4},{1}] => 0 [{3,4},{2,5},{1}] => 0 [{3,5},{2,4},{1}] => 0 [{4,5},{2,3},{1}] => 0 [{1,2},{3,4,5}] => 0 [{1,3},{2,4,5}] => 0 [{1,4},{2,3,5}] => 0 [{1,5},{2,3,4}] => 0 [{2,3},{1,4,5}] => 0 [{2,4},{1,3,5}] => 0 [{2,5},{1,3,4}] => 0 [{3,4},{1,2,5}] => 0 [{3,5},{1,2,4}] => 0 [{4,5},{1,2,3}] => 0 [{1,2,3},{4},{5}] => 0 [{1,2,3},{5},{4}] => 3 [{1,2,4},{3},{5}] => 0 [{1,2,5},{3},{4}] => 0 [{1,2,4},{5},{3}] => 2 [{1,2,5},{4},{3}] => 2 [{1,3,4},{2},{5}] => 0 [{1,3,5},{2},{4}] => 0 [{1,4,5},{2},{3}] => 0 [{1,3,4},{5},{2}] => 1 [{1,3,5},{4},{2}] => 1 [{1,4,5},{3},{2}] => 1 [{2,3,4},{1},{5}] => 0 [{2,3,5},{1},{4}] => 0 [{2,4,5},{1},{3}] => 0 [{3,4,5},{1},{2}] => 0 [{2,3,4},{5},{1}] => 0 [{2,3,5},{4},{1}] => 0 [{2,4,5},{3},{1}] => 0 [{3,4,5},{2},{1}] => 0 [{1,2,3},{4,5}] => 0 [{1,2,4},{3,5}] => 0 [{1,2,5},{3,4}] => 0 [{1,3,4},{2,5}] => 0 [{1,3,5},{2,4}] => 0 [{1,4,5},{2,3}] => 0 [{2,3,4},{1,5}] => 0 [{2,3,5},{1,4}] => 0 [{2,4,5},{1,3}] => 0 [{3,4,5},{1,2}] => 0 [{1,2,3,4},{5}] => 0 [{1,2,3,5},{4}] => 0 [{1,2,4,5},{3}] => 0 [{1,3,4,5},{2}] => 0 [{2,3,4,5},{1}] => 0 [{1,2,3,4,5}] => 0 [{1},{2},{3},{4},{5},{6}] => 0 [{1},{2},{3},{4},{6},{5}] => 4 [{1},{2},{3},{5},{4},{6}] => 3 [{1},{2},{3},{6},{4},{5}] => 6 [{1},{2},{3},{5},{6},{4}] => 6 [{1},{2},{3},{6},{5},{4}] => 9 [{1},{2},{4},{3},{5},{6}] => 2 [{1},{2},{4},{3},{6},{5}] => 6 [{1},{2},{5},{3},{4},{6}] => 4 [{1},{2},{6},{3},{4},{5}] => 6 [{1},{2},{5},{3},{6},{4}] => 7 [{1},{2},{6},{3},{5},{4}] => 9 [{1},{2},{4},{5},{3},{6}] => 4 [{1},{2},{4},{6},{3},{5}] => 7 [{1},{2},{5},{4},{3},{6}] => 6 [{1},{2},{6},{4},{3},{5}] => 8 [{1},{2},{5},{6},{3},{4}] => 8 [{1},{2},{6},{5},{3},{4}] => 10 [{1},{2},{4},{5},{6},{3}] => 6 [{1},{2},{4},{6},{5},{3}] => 9 [{1},{2},{5},{4},{6},{3}] => 8 [{1},{2},{6},{4},{5},{3}] => 10 [{1},{2},{5},{6},{4},{3}] => 10 [{1},{2},{6},{5},{4},{3}] => 12 [{1},{3},{2},{4},{5},{6}] => 1 [{1},{3},{2},{4},{6},{5}] => 5 [{1},{3},{2},{5},{4},{6}] => 4 [{1},{3},{2},{6},{4},{5}] => 7 [{1},{3},{2},{5},{6},{4}] => 7 [{1},{3},{2},{6},{5},{4}] => 10 [{1},{4},{2},{3},{5},{6}] => 2 [{1},{4},{2},{3},{6},{5}] => 6 [{1},{5},{2},{3},{4},{6}] => 3 [{1},{6},{2},{3},{4},{5}] => 4 [{1},{5},{2},{3},{6},{4}] => 6 [{1},{6},{2},{3},{5},{4}] => 7 [{1},{4},{2},{5},{3},{6}] => 4 [{1},{4},{2},{6},{3},{5}] => 7 [{1},{5},{2},{4},{3},{6}] => 5 [{1},{6},{2},{4},{3},{5}] => 6 [{1},{5},{2},{6},{3},{4}] => 7 [{1},{6},{2},{5},{3},{4}] => 8 [{1},{4},{2},{5},{6},{3}] => 6 [{1},{4},{2},{6},{5},{3}] => 9 [{1},{5},{2},{4},{6},{3}] => 7 [{1},{6},{2},{4},{5},{3}] => 8 [{1},{5},{2},{6},{4},{3}] => 9 [{1},{6},{2},{5},{4},{3}] => 10 [{1},{3},{4},{2},{5},{6}] => 2 [{1},{3},{4},{2},{6},{5}] => 6 [{1},{3},{5},{2},{4},{6}] => 4 [{1},{3},{6},{2},{4},{5}] => 6 [{1},{3},{5},{2},{6},{4}] => 7 [{1},{3},{6},{2},{5},{4}] => 9 [{1},{4},{3},{2},{5},{6}] => 3 [{1},{4},{3},{2},{6},{5}] => 7 [{1},{5},{3},{2},{4},{6}] => 4 [{1},{6},{3},{2},{4},{5}] => 5 [{1},{5},{3},{2},{6},{4}] => 7 [{1},{6},{3},{2},{5},{4}] => 8 [{1},{4},{5},{2},{3},{6}] => 4 [{1},{4},{6},{2},{3},{5}] => 6 [{1},{5},{4},{2},{3},{6}] => 5 [{1},{6},{4},{2},{3},{5}] => 6 [{1},{5},{6},{2},{3},{4}] => 6 [{1},{6},{5},{2},{3},{4}] => 7 [{1},{4},{5},{2},{6},{3}] => 6 [{1},{4},{6},{2},{5},{3}] => 8 [{1},{5},{4},{2},{6},{3}] => 7 [{1},{6},{4},{2},{5},{3}] => 8 [{1},{5},{6},{2},{4},{3}] => 8 [{1},{6},{5},{2},{4},{3}] => 9 [{1},{3},{4},{5},{2},{6}] => 3 [{1},{3},{4},{6},{2},{5}] => 6 [{1},{3},{5},{4},{2},{6}] => 5 [{1},{3},{6},{4},{2},{5}] => 7 [{1},{3},{5},{6},{2},{4}] => 7 [{1},{3},{6},{5},{2},{4}] => 9 [{1},{4},{3},{5},{2},{6}] => 4 [{1},{4},{3},{6},{2},{5}] => 7 [{1},{5},{3},{4},{2},{6}] => 5 [{1},{6},{3},{4},{2},{5}] => 6 [{1},{5},{3},{6},{2},{4}] => 7 [{1},{6},{3},{5},{2},{4}] => 8 [{1},{4},{5},{3},{2},{6}] => 5 [{1},{4},{6},{3},{2},{5}] => 7 [{1},{5},{4},{3},{2},{6}] => 6 [{1},{6},{4},{3},{2},{5}] => 7 [{1},{5},{6},{3},{2},{4}] => 7 [{1},{6},{5},{3},{2},{4}] => 8 [{1},{4},{5},{6},{2},{3}] => 6 [{1},{4},{6},{5},{2},{3}] => 8 [{1},{5},{4},{6},{2},{3}] => 7 [{1},{6},{4},{5},{2},{3}] => 8 [{1},{5},{6},{4},{2},{3}] => 8 [{1},{6},{5},{4},{2},{3}] => 9 [{1},{3},{4},{5},{6},{2}] => 4 [{1},{3},{4},{6},{5},{2}] => 7 [{1},{3},{5},{4},{6},{2}] => 6 [{1},{3},{6},{4},{5},{2}] => 8 [{1},{3},{5},{6},{4},{2}] => 8 [{1},{3},{6},{5},{4},{2}] => 10 [{1},{4},{3},{5},{6},{2}] => 5 [{1},{4},{3},{6},{5},{2}] => 8 [{1},{5},{3},{4},{6},{2}] => 6 [{1},{6},{3},{4},{5},{2}] => 7 [{1},{5},{3},{6},{4},{2}] => 8 [{1},{6},{3},{5},{4},{2}] => 9 [{1},{4},{5},{3},{6},{2}] => 6 [{1},{4},{6},{3},{5},{2}] => 8 [{1},{5},{4},{3},{6},{2}] => 7 [{1},{6},{4},{3},{5},{2}] => 8 [{1},{5},{6},{3},{4},{2}] => 8 [{1},{6},{5},{3},{4},{2}] => 9 [{1},{4},{5},{6},{3},{2}] => 7 [{1},{4},{6},{5},{3},{2}] => 9 [{1},{5},{4},{6},{3},{2}] => 8 [{1},{6},{4},{5},{3},{2}] => 9 [{1},{5},{6},{4},{3},{2}] => 9 [{1},{6},{5},{4},{3},{2}] => 10 [{2},{1},{3},{4},{5},{6}] => 0 [{2},{1},{3},{4},{6},{5}] => 4 [{2},{1},{3},{5},{4},{6}] => 3 [{2},{1},{3},{6},{4},{5}] => 6 [{2},{1},{3},{5},{6},{4}] => 6 [{2},{1},{3},{6},{5},{4}] => 9 [{2},{1},{4},{3},{5},{6}] => 2 [{2},{1},{4},{3},{6},{5}] => 6 [{2},{1},{5},{3},{4},{6}] => 4 [{2},{1},{6},{3},{4},{5}] => 6 [{2},{1},{5},{3},{6},{4}] => 7 [{2},{1},{6},{3},{5},{4}] => 9 [{2},{1},{4},{5},{3},{6}] => 4 [{2},{1},{4},{6},{3},{5}] => 7 [{2},{1},{5},{4},{3},{6}] => 6 [{2},{1},{6},{4},{3},{5}] => 8 [{2},{1},{5},{6},{3},{4}] => 8 [{2},{1},{6},{5},{3},{4}] => 10 [{2},{1},{4},{5},{6},{3}] => 6 [{2},{1},{4},{6},{5},{3}] => 9 [{2},{1},{5},{4},{6},{3}] => 8 [{2},{1},{6},{4},{5},{3}] => 10 [{2},{1},{5},{6},{4},{3}] => 10 [{2},{1},{6},{5},{4},{3}] => 12 [{3},{1},{2},{4},{5},{6}] => 0 [{3},{1},{2},{4},{6},{5}] => 4 [{3},{1},{2},{5},{4},{6}] => 3 [{3},{1},{2},{6},{4},{5}] => 6 [{3},{1},{2},{5},{6},{4}] => 6 [{3},{1},{2},{6},{5},{4}] => 9 [{4},{1},{2},{3},{5},{6}] => 0 [{4},{1},{2},{3},{6},{5}] => 4 [{5},{1},{2},{3},{4},{6}] => 0 [{6},{1},{2},{3},{4},{5}] => 0 [{5},{1},{2},{3},{6},{4}] => 3 [{6},{1},{2},{3},{5},{4}] => 3 [{4},{1},{2},{5},{3},{6}] => 2 [{4},{1},{2},{6},{3},{5}] => 5 [{5},{1},{2},{4},{3},{6}] => 2 [{6},{1},{2},{4},{3},{5}] => 2 [{5},{1},{2},{6},{3},{4}] => 4 [{6},{1},{2},{5},{3},{4}] => 4 [{4},{1},{2},{5},{6},{3}] => 4 [{4},{1},{2},{6},{5},{3}] => 7 [{5},{1},{2},{4},{6},{3}] => 4 [{6},{1},{2},{4},{5},{3}] => 4 [{5},{1},{2},{6},{4},{3}] => 6 [{6},{1},{2},{5},{4},{3}] => 6 [{3},{1},{4},{2},{5},{6}] => 1 [{3},{1},{4},{2},{6},{5}] => 5 [{3},{1},{5},{2},{4},{6}] => 3 [{3},{1},{6},{2},{4},{5}] => 5 [{3},{1},{5},{2},{6},{4}] => 6 [{3},{1},{6},{2},{5},{4}] => 8 [{4},{1},{3},{2},{5},{6}] => 1 [{4},{1},{3},{2},{6},{5}] => 5 [{5},{1},{3},{2},{4},{6}] => 1 [{6},{1},{3},{2},{4},{5}] => 1 [{5},{1},{3},{2},{6},{4}] => 4 [{6},{1},{3},{2},{5},{4}] => 4 [{4},{1},{5},{2},{3},{6}] => 2 [{4},{1},{6},{2},{3},{5}] => 4 [{5},{1},{4},{2},{3},{6}] => 2 [{6},{1},{4},{2},{3},{5}] => 2 [{5},{1},{6},{2},{3},{4}] => 3 [{6},{1},{5},{2},{3},{4}] => 3 [{4},{1},{5},{2},{6},{3}] => 4 [{4},{1},{6},{2},{5},{3}] => 6 [{5},{1},{4},{2},{6},{3}] => 4 [{6},{1},{4},{2},{5},{3}] => 4 [{5},{1},{6},{2},{4},{3}] => 5 [{6},{1},{5},{2},{4},{3}] => 5 [{3},{1},{4},{5},{2},{6}] => 2 [{3},{1},{4},{6},{2},{5}] => 5 [{3},{1},{5},{4},{2},{6}] => 4 [{3},{1},{6},{4},{2},{5}] => 6 [{3},{1},{5},{6},{2},{4}] => 6 [{3},{1},{6},{5},{2},{4}] => 8 [{4},{1},{3},{5},{2},{6}] => 2 [{4},{1},{3},{6},{2},{5}] => 5 [{5},{1},{3},{4},{2},{6}] => 2 [{6},{1},{3},{4},{2},{5}] => 2 [{5},{1},{3},{6},{2},{4}] => 4 [{6},{1},{3},{5},{2},{4}] => 4 [{4},{1},{5},{3},{2},{6}] => 3 [{4},{1},{6},{3},{2},{5}] => 5 [{5},{1},{4},{3},{2},{6}] => 3 [{6},{1},{4},{3},{2},{5}] => 3 [{5},{1},{6},{3},{2},{4}] => 4 [{6},{1},{5},{3},{2},{4}] => 4 [{4},{1},{5},{6},{2},{3}] => 4 [{4},{1},{6},{5},{2},{3}] => 6 [{5},{1},{4},{6},{2},{3}] => 4 [{6},{1},{4},{5},{2},{3}] => 4 [{5},{1},{6},{4},{2},{3}] => 5 [{6},{1},{5},{4},{2},{3}] => 5 [{3},{1},{4},{5},{6},{2}] => 3 [{3},{1},{4},{6},{5},{2}] => 6 [{3},{1},{5},{4},{6},{2}] => 5 [{3},{1},{6},{4},{5},{2}] => 7 [{3},{1},{5},{6},{4},{2}] => 7 [{3},{1},{6},{5},{4},{2}] => 9 [{4},{1},{3},{5},{6},{2}] => 3 [{4},{1},{3},{6},{5},{2}] => 6 [{5},{1},{3},{4},{6},{2}] => 3 [{6},{1},{3},{4},{5},{2}] => 3 [{5},{1},{3},{6},{4},{2}] => 5 [{6},{1},{3},{5},{4},{2}] => 5 [{4},{1},{5},{3},{6},{2}] => 4 [{4},{1},{6},{3},{5},{2}] => 6 [{5},{1},{4},{3},{6},{2}] => 4 [{6},{1},{4},{3},{5},{2}] => 4 [{5},{1},{6},{3},{4},{2}] => 5 [{6},{1},{5},{3},{4},{2}] => 5 [{4},{1},{5},{6},{3},{2}] => 5 [{4},{1},{6},{5},{3},{2}] => 7 [{5},{1},{4},{6},{3},{2}] => 5 [{6},{1},{4},{5},{3},{2}] => 5 [{5},{1},{6},{4},{3},{2}] => 6 [{6},{1},{5},{4},{3},{2}] => 6 [{2},{3},{1},{4},{5},{6}] => 0 [{2},{3},{1},{4},{6},{5}] => 4 [{2},{3},{1},{5},{4},{6}] => 3 [{2},{3},{1},{6},{4},{5}] => 6 [{2},{3},{1},{5},{6},{4}] => 6 [{2},{3},{1},{6},{5},{4}] => 9 [{2},{4},{1},{3},{5},{6}] => 1 [{2},{4},{1},{3},{6},{5}] => 5 [{2},{5},{1},{3},{4},{6}] => 2 [{2},{6},{1},{3},{4},{5}] => 3 [{2},{5},{1},{3},{6},{4}] => 5 [{2},{6},{1},{3},{5},{4}] => 6 [{2},{4},{1},{5},{3},{6}] => 3 [{2},{4},{1},{6},{3},{5}] => 6 [{2},{5},{1},{4},{3},{6}] => 4 [{2},{6},{1},{4},{3},{5}] => 5 [{2},{5},{1},{6},{3},{4}] => 6 [{2},{6},{1},{5},{3},{4}] => 7 [{2},{4},{1},{5},{6},{3}] => 5 [{2},{4},{1},{6},{5},{3}] => 8 [{2},{5},{1},{4},{6},{3}] => 6 [{2},{6},{1},{4},{5},{3}] => 7 [{2},{5},{1},{6},{4},{3}] => 8 [{2},{6},{1},{5},{4},{3}] => 9 [{3},{2},{1},{4},{5},{6}] => 0 [{3},{2},{1},{4},{6},{5}] => 4 [{3},{2},{1},{5},{4},{6}] => 3 [{3},{2},{1},{6},{4},{5}] => 6 [{3},{2},{1},{5},{6},{4}] => 6 [{3},{2},{1},{6},{5},{4}] => 9 [{4},{2},{1},{3},{5},{6}] => 0 [{4},{2},{1},{3},{6},{5}] => 4 [{5},{2},{1},{3},{4},{6}] => 0 [{6},{2},{1},{3},{4},{5}] => 0 [{5},{2},{1},{3},{6},{4}] => 3 [{6},{2},{1},{3},{5},{4}] => 3 [{4},{2},{1},{5},{3},{6}] => 2 [{4},{2},{1},{6},{3},{5}] => 5 [{5},{2},{1},{4},{3},{6}] => 2 [{6},{2},{1},{4},{3},{5}] => 2 [{5},{2},{1},{6},{3},{4}] => 4 [{6},{2},{1},{5},{3},{4}] => 4 [{4},{2},{1},{5},{6},{3}] => 4 [{4},{2},{1},{6},{5},{3}] => 7 [{5},{2},{1},{4},{6},{3}] => 4 [{6},{2},{1},{4},{5},{3}] => 4 [{5},{2},{1},{6},{4},{3}] => 6 [{6},{2},{1},{5},{4},{3}] => 6 [{3},{4},{1},{2},{5},{6}] => 0 [{3},{4},{1},{2},{6},{5}] => 4 [{3},{5},{1},{2},{4},{6}] => 1 [{3},{6},{1},{2},{4},{5}] => 2 [{3},{5},{1},{2},{6},{4}] => 4 [{3},{6},{1},{2},{5},{4}] => 5 [{4},{3},{1},{2},{5},{6}] => 0 [{4},{3},{1},{2},{6},{5}] => 4 [{5},{3},{1},{2},{4},{6}] => 0 [{6},{3},{1},{2},{4},{5}] => 0 [{5},{3},{1},{2},{6},{4}] => 3 [{6},{3},{1},{2},{5},{4}] => 3 [{4},{5},{1},{2},{3},{6}] => 0 [{4},{6},{1},{2},{3},{5}] => 1 [{5},{4},{1},{2},{3},{6}] => 0 [{6},{4},{1},{2},{3},{5}] => 0 [{5},{6},{1},{2},{3},{4}] => 0 [{6},{5},{1},{2},{3},{4}] => 0 [{4},{5},{1},{2},{6},{3}] => 2 [{4},{6},{1},{2},{5},{3}] => 3 [{5},{4},{1},{2},{6},{3}] => 2 [{6},{4},{1},{2},{5},{3}] => 2 [{5},{6},{1},{2},{4},{3}] => 2 [{6},{5},{1},{2},{4},{3}] => 2 [{3},{4},{1},{5},{2},{6}] => 1 [{3},{4},{1},{6},{2},{5}] => 4 [{3},{5},{1},{4},{2},{6}] => 2 [{3},{6},{1},{4},{2},{5}] => 3 [{3},{5},{1},{6},{2},{4}] => 4 [{3},{6},{1},{5},{2},{4}] => 5 [{4},{3},{1},{5},{2},{6}] => 1 [{4},{3},{1},{6},{2},{5}] => 4 [{5},{3},{1},{4},{2},{6}] => 1 [{6},{3},{1},{4},{2},{5}] => 1 [{5},{3},{1},{6},{2},{4}] => 3 [{6},{3},{1},{5},{2},{4}] => 3 [{4},{5},{1},{3},{2},{6}] => 1 [{4},{6},{1},{3},{2},{5}] => 2 [{5},{4},{1},{3},{2},{6}] => 1 [{6},{4},{1},{3},{2},{5}] => 1 [{5},{6},{1},{3},{2},{4}] => 1 [{6},{5},{1},{3},{2},{4}] => 1 [{4},{5},{1},{6},{2},{3}] => 2 [{4},{6},{1},{5},{2},{3}] => 3 [{5},{4},{1},{6},{2},{3}] => 2 [{6},{4},{1},{5},{2},{3}] => 2 [{5},{6},{1},{4},{2},{3}] => 2 [{6},{5},{1},{4},{2},{3}] => 2 [{3},{4},{1},{5},{6},{2}] => 2 [{3},{4},{1},{6},{5},{2}] => 5 [{3},{5},{1},{4},{6},{2}] => 3 [{3},{6},{1},{4},{5},{2}] => 4 [{3},{5},{1},{6},{4},{2}] => 5 [{3},{6},{1},{5},{4},{2}] => 6 [{4},{3},{1},{5},{6},{2}] => 2 [{4},{3},{1},{6},{5},{2}] => 5 [{5},{3},{1},{4},{6},{2}] => 2 [{6},{3},{1},{4},{5},{2}] => 2 [{5},{3},{1},{6},{4},{2}] => 4 [{6},{3},{1},{5},{4},{2}] => 4 [{4},{5},{1},{3},{6},{2}] => 2 [{4},{6},{1},{3},{5},{2}] => 3 [{5},{4},{1},{3},{6},{2}] => 2 [{6},{4},{1},{3},{5},{2}] => 2 [{5},{6},{1},{3},{4},{2}] => 2 [{6},{5},{1},{3},{4},{2}] => 2 [{4},{5},{1},{6},{3},{2}] => 3 [{4},{6},{1},{5},{3},{2}] => 4 [{5},{4},{1},{6},{3},{2}] => 3 [{6},{4},{1},{5},{3},{2}] => 3 [{5},{6},{1},{4},{3},{2}] => 3 [{6},{5},{1},{4},{3},{2}] => 3 [{2},{3},{4},{1},{5},{6}] => 0 [{2},{3},{4},{1},{6},{5}] => 4 [{2},{3},{5},{1},{4},{6}] => 2 [{2},{3},{6},{1},{4},{5}] => 4 [{2},{3},{5},{1},{6},{4}] => 5 [{2},{3},{6},{1},{5},{4}] => 7 [{2},{4},{3},{1},{5},{6}] => 1 [{2},{4},{3},{1},{6},{5}] => 5 [{2},{5},{3},{1},{4},{6}] => 2 [{2},{6},{3},{1},{4},{5}] => 3 [{2},{5},{3},{1},{6},{4}] => 5 [{2},{6},{3},{1},{5},{4}] => 6 [{2},{4},{5},{1},{3},{6}] => 2 [{2},{4},{6},{1},{3},{5}] => 4 [{2},{5},{4},{1},{3},{6}] => 3 [{2},{6},{4},{1},{3},{5}] => 4 [{2},{5},{6},{1},{3},{4}] => 4 [{2},{6},{5},{1},{3},{4}] => 5 [{2},{4},{5},{1},{6},{3}] => 4 [{2},{4},{6},{1},{5},{3}] => 6 [{2},{5},{4},{1},{6},{3}] => 5 [{2},{6},{4},{1},{5},{3}] => 6 [{2},{5},{6},{1},{4},{3}] => 6 [{2},{6},{5},{1},{4},{3}] => 7 [{3},{2},{4},{1},{5},{6}] => 0 [{3},{2},{4},{1},{6},{5}] => 4 [{3},{2},{5},{1},{4},{6}] => 2 [{3},{2},{6},{1},{4},{5}] => 4 [{3},{2},{5},{1},{6},{4}] => 5 [{3},{2},{6},{1},{5},{4}] => 7 [{4},{2},{3},{1},{5},{6}] => 0 [{4},{2},{3},{1},{6},{5}] => 4 [{5},{2},{3},{1},{4},{6}] => 0 [{6},{2},{3},{1},{4},{5}] => 0 [{5},{2},{3},{1},{6},{4}] => 3 [{6},{2},{3},{1},{5},{4}] => 3 [{4},{2},{5},{1},{3},{6}] => 1 [{4},{2},{6},{1},{3},{5}] => 3 [{5},{2},{4},{1},{3},{6}] => 1 [{6},{2},{4},{1},{3},{5}] => 1 [{5},{2},{6},{1},{3},{4}] => 2 [{6},{2},{5},{1},{3},{4}] => 2 [{4},{2},{5},{1},{6},{3}] => 3 [{4},{2},{6},{1},{5},{3}] => 5 [{5},{2},{4},{1},{6},{3}] => 3 [{6},{2},{4},{1},{5},{3}] => 3 [{5},{2},{6},{1},{4},{3}] => 4 [{6},{2},{5},{1},{4},{3}] => 4 [{3},{4},{2},{1},{5},{6}] => 0 [{3},{4},{2},{1},{6},{5}] => 4 [{3},{5},{2},{1},{4},{6}] => 1 [{3},{6},{2},{1},{4},{5}] => 2 [{3},{5},{2},{1},{6},{4}] => 4 [{3},{6},{2},{1},{5},{4}] => 5 [{4},{3},{2},{1},{5},{6}] => 0 [{4},{3},{2},{1},{6},{5}] => 4 [{5},{3},{2},{1},{4},{6}] => 0 [{6},{3},{2},{1},{4},{5}] => 0 [{5},{3},{2},{1},{6},{4}] => 3 [{6},{3},{2},{1},{5},{4}] => 3 [{4},{5},{2},{1},{3},{6}] => 0 [{4},{6},{2},{1},{3},{5}] => 1 [{5},{4},{2},{1},{3},{6}] => 0 [{6},{4},{2},{1},{3},{5}] => 0 [{5},{6},{2},{1},{3},{4}] => 0 [{6},{5},{2},{1},{3},{4}] => 0 [{4},{5},{2},{1},{6},{3}] => 2 [{4},{6},{2},{1},{5},{3}] => 3 [{5},{4},{2},{1},{6},{3}] => 2 [{6},{4},{2},{1},{5},{3}] => 2 [{5},{6},{2},{1},{4},{3}] => 2 [{6},{5},{2},{1},{4},{3}] => 2 [{3},{4},{5},{1},{2},{6}] => 0 [{3},{4},{6},{1},{2},{5}] => 2 [{3},{5},{4},{1},{2},{6}] => 1 [{3},{6},{4},{1},{2},{5}] => 2 [{3},{5},{6},{1},{2},{4}] => 2 [{3},{6},{5},{1},{2},{4}] => 3 [{4},{3},{5},{1},{2},{6}] => 0 [{4},{3},{6},{1},{2},{5}] => 2 [{5},{3},{4},{1},{2},{6}] => 0 [{6},{3},{4},{1},{2},{5}] => 0 [{5},{3},{6},{1},{2},{4}] => 1 [{6},{3},{5},{1},{2},{4}] => 1 [{4},{5},{3},{1},{2},{6}] => 0 [{4},{6},{3},{1},{2},{5}] => 1 [{5},{4},{3},{1},{2},{6}] => 0 [{6},{4},{3},{1},{2},{5}] => 0 [{5},{6},{3},{1},{2},{4}] => 0 [{6},{5},{3},{1},{2},{4}] => 0 [{4},{5},{6},{1},{2},{3}] => 0 [{4},{6},{5},{1},{2},{3}] => 1 [{5},{4},{6},{1},{2},{3}] => 0 [{6},{4},{5},{1},{2},{3}] => 0 [{5},{6},{4},{1},{2},{3}] => 0 [{6},{5},{4},{1},{2},{3}] => 0 [{3},{4},{5},{1},{6},{2}] => 1 [{3},{4},{6},{1},{5},{2}] => 3 [{3},{5},{4},{1},{6},{2}] => 2 [{3},{6},{4},{1},{5},{2}] => 3 [{3},{5},{6},{1},{4},{2}] => 3 [{3},{6},{5},{1},{4},{2}] => 4 [{4},{3},{5},{1},{6},{2}] => 1 [{4},{3},{6},{1},{5},{2}] => 3 [{5},{3},{4},{1},{6},{2}] => 1 [{6},{3},{4},{1},{5},{2}] => 1 [{5},{3},{6},{1},{4},{2}] => 2 [{6},{3},{5},{1},{4},{2}] => 2 [{4},{5},{3},{1},{6},{2}] => 1 [{4},{6},{3},{1},{5},{2}] => 2 [{5},{4},{3},{1},{6},{2}] => 1 [{6},{4},{3},{1},{5},{2}] => 1 [{5},{6},{3},{1},{4},{2}] => 1 [{6},{5},{3},{1},{4},{2}] => 1 [{4},{5},{6},{1},{3},{2}] => 1 [{4},{6},{5},{1},{3},{2}] => 2 [{5},{4},{6},{1},{3},{2}] => 1 [{6},{4},{5},{1},{3},{2}] => 1 [{5},{6},{4},{1},{3},{2}] => 1 [{6},{5},{4},{1},{3},{2}] => 1 [{2},{3},{4},{5},{1},{6}] => 0 [{2},{3},{4},{6},{1},{5}] => 3 [{2},{3},{5},{4},{1},{6}] => 2 [{2},{3},{6},{4},{1},{5}] => 4 [{2},{3},{5},{6},{1},{4}] => 4 [{2},{3},{6},{5},{1},{4}] => 6 [{2},{4},{3},{5},{1},{6}] => 1 [{2},{4},{3},{6},{1},{5}] => 4 [{2},{5},{3},{4},{1},{6}] => 2 [{2},{6},{3},{4},{1},{5}] => 3 [{2},{5},{3},{6},{1},{4}] => 4 [{2},{6},{3},{5},{1},{4}] => 5 [{2},{4},{5},{3},{1},{6}] => 2 [{2},{4},{6},{3},{1},{5}] => 4 [{2},{5},{4},{3},{1},{6}] => 3 [{2},{6},{4},{3},{1},{5}] => 4 [{2},{5},{6},{3},{1},{4}] => 4 [{2},{6},{5},{3},{1},{4}] => 5 [{2},{4},{5},{6},{1},{3}] => 3 [{2},{4},{6},{5},{1},{3}] => 5 [{2},{5},{4},{6},{1},{3}] => 4 [{2},{6},{4},{5},{1},{3}] => 5 [{2},{5},{6},{4},{1},{3}] => 5 [{2},{6},{5},{4},{1},{3}] => 6 [{3},{2},{4},{5},{1},{6}] => 0 [{3},{2},{4},{6},{1},{5}] => 3 [{3},{2},{5},{4},{1},{6}] => 2 [{3},{2},{6},{4},{1},{5}] => 4 [{3},{2},{5},{6},{1},{4}] => 4 [{3},{2},{6},{5},{1},{4}] => 6 [{4},{2},{3},{5},{1},{6}] => 0 [{4},{2},{3},{6},{1},{5}] => 3 [{5},{2},{3},{4},{1},{6}] => 0 [{6},{2},{3},{4},{1},{5}] => 0 [{5},{2},{3},{6},{1},{4}] => 2 [{6},{2},{3},{5},{1},{4}] => 2 [{4},{2},{5},{3},{1},{6}] => 1 [{4},{2},{6},{3},{1},{5}] => 3 [{5},{2},{4},{3},{1},{6}] => 1 [{6},{2},{4},{3},{1},{5}] => 1 [{5},{2},{6},{3},{1},{4}] => 2 [{6},{2},{5},{3},{1},{4}] => 2 [{4},{2},{5},{6},{1},{3}] => 2 [{4},{2},{6},{5},{1},{3}] => 4 [{5},{2},{4},{6},{1},{3}] => 2 [{6},{2},{4},{5},{1},{3}] => 2 [{5},{2},{6},{4},{1},{3}] => 3 [{6},{2},{5},{4},{1},{3}] => 3 [{3},{4},{2},{5},{1},{6}] => 0 [{3},{4},{2},{6},{1},{5}] => 3 [{3},{5},{2},{4},{1},{6}] => 1 [{3},{6},{2},{4},{1},{5}] => 2 [{3},{5},{2},{6},{1},{4}] => 3 [{3},{6},{2},{5},{1},{4}] => 4 [{4},{3},{2},{5},{1},{6}] => 0 [{4},{3},{2},{6},{1},{5}] => 3 [{5},{3},{2},{4},{1},{6}] => 0 [{6},{3},{2},{4},{1},{5}] => 0 [{5},{3},{2},{6},{1},{4}] => 2 [{6},{3},{2},{5},{1},{4}] => 2 [{4},{5},{2},{3},{1},{6}] => 0 [{4},{6},{2},{3},{1},{5}] => 1 [{5},{4},{2},{3},{1},{6}] => 0 [{6},{4},{2},{3},{1},{5}] => 0 [{5},{6},{2},{3},{1},{4}] => 0 [{6},{5},{2},{3},{1},{4}] => 0 [{4},{5},{2},{6},{1},{3}] => 1 [{4},{6},{2},{5},{1},{3}] => 2 [{5},{4},{2},{6},{1},{3}] => 1 [{6},{4},{2},{5},{1},{3}] => 1 [{5},{6},{2},{4},{1},{3}] => 1 [{6},{5},{2},{4},{1},{3}] => 1 [{3},{4},{5},{2},{1},{6}] => 0 [{3},{4},{6},{2},{1},{5}] => 2 [{3},{5},{4},{2},{1},{6}] => 1 [{3},{6},{4},{2},{1},{5}] => 2 [{3},{5},{6},{2},{1},{4}] => 2 [{3},{6},{5},{2},{1},{4}] => 3 [{4},{3},{5},{2},{1},{6}] => 0 [{4},{3},{6},{2},{1},{5}] => 2 [{5},{3},{4},{2},{1},{6}] => 0 [{6},{3},{4},{2},{1},{5}] => 0 [{5},{3},{6},{2},{1},{4}] => 1 [{6},{3},{5},{2},{1},{4}] => 1 [{4},{5},{3},{2},{1},{6}] => 0 [{4},{6},{3},{2},{1},{5}] => 1 [{5},{4},{3},{2},{1},{6}] => 0 ----------------------------------------------------------------------------- Created: May 25, 2023 at 11:08 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: May 25, 2023 at 11:08 by Martin Rubey