***************************************************************************** * 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: St001043 ----------------------------------------------------------------------------- Collection: Perfect matchings ----------------------------------------------------------------------------- Description: The depth of the leaf closest to the root in the binary unordered tree associated with the perfect matching. The bijection between perfect matchings of $\{1,\dots,2n\}$ and trees with $n+1$ leaves is described in Example 5.2.6 of [1]. ----------------------------------------------------------------------------- References: [1] Stanley, R. P. Enumerative combinatorics. Vol. 2 [[MathSciNet:1676282]] ----------------------------------------------------------------------------- Code: def statistic(m): def aux(T): if len(T) == 0: return 0 return 1 + min(aux(T[0]), aux(T[1])) return aux(matching_to_tree(m)) def matching_to_tree(m): """ INPUT: - m, a PerfectMatching on {1,...,2n}. OUTPUT: a decreasingly labelled, unordered full binary tree with n+1 leaves. EXAMPLES:: sage: m = PerfectMatching([(1,4),(2,9),(3,10),(5,7),(6,8),(11,12)]) sage: ascii_art(matching_to_tree(m)) """ # the children of the smallest label are the largest remaining # element and its partner trees = [LabelledRootedTree([LabelledRootedTree([], label=i), LabelledRootedTree([], label=j)]) for i, j in m] max_label = m.size()//2+1 # last labelled node while len(trees) > 1: max_label += 1 # find tree with smallest child and both children smaller than max_label A = sorted([T for T in trees if max(T[0].label(), T[1].label()) < max_label], key = lambda T: min(T[0].label(), T[1].label()))[0] trees.remove(A) # give it's root node the new label A = LabelledRootedTree(A, label=max_label) # find tree with child having label max_label B = (T for T in trees if T[0].label() == max_label or T[1].label() == max_label).next() trees.remove(B) # replace B with [B[0], A] or [B[1], A] if B[0].label() == max_label: C = LabelledRootedTree([A, B[1]]) else: C = LabelledRootedTree([A, B[0]]) trees.append(C) return trees[0] ----------------------------------------------------------------------------- Statistic values: [(1,2)] => 1 [(1,2),(3,4)] => 1 [(1,3),(2,4)] => 1 [(1,4),(2,3)] => 1 [(1,2),(3,4),(5,6)] => 2 [(1,3),(2,4),(5,6)] => 2 [(1,4),(2,3),(5,6)] => 2 [(1,5),(2,3),(4,6)] => 1 [(1,6),(2,3),(4,5)] => 1 [(1,6),(2,4),(3,5)] => 1 [(1,5),(2,4),(3,6)] => 1 [(1,4),(2,5),(3,6)] => 1 [(1,3),(2,5),(4,6)] => 1 [(1,2),(3,5),(4,6)] => 1 [(1,2),(3,6),(4,5)] => 1 [(1,3),(2,6),(4,5)] => 1 [(1,4),(2,6),(3,5)] => 1 [(1,5),(2,6),(3,4)] => 1 [(1,6),(2,5),(3,4)] => 1 [(1,2),(3,4),(5,6),(7,8)] => 2 [(1,3),(2,4),(5,6),(7,8)] => 2 [(1,4),(2,3),(5,6),(7,8)] => 2 [(1,5),(2,3),(4,6),(7,8)] => 2 [(1,6),(2,3),(4,5),(7,8)] => 2 [(1,7),(2,3),(4,5),(6,8)] => 2 [(1,8),(2,3),(4,5),(6,7)] => 1 [(1,8),(2,4),(3,5),(6,7)] => 1 [(1,7),(2,4),(3,5),(6,8)] => 2 [(1,6),(2,4),(3,5),(7,8)] => 2 [(1,5),(2,4),(3,6),(7,8)] => 2 [(1,4),(2,5),(3,6),(7,8)] => 2 [(1,3),(2,5),(4,6),(7,8)] => 2 [(1,2),(3,5),(4,6),(7,8)] => 2 [(1,2),(3,6),(4,5),(7,8)] => 2 [(1,3),(2,6),(4,5),(7,8)] => 2 [(1,4),(2,6),(3,5),(7,8)] => 2 [(1,5),(2,6),(3,4),(7,8)] => 2 [(1,6),(2,5),(3,4),(7,8)] => 2 [(1,7),(2,5),(3,4),(6,8)] => 2 [(1,8),(2,5),(3,4),(6,7)] => 1 [(1,8),(2,6),(3,4),(5,7)] => 1 [(1,7),(2,6),(3,4),(5,8)] => 1 [(1,6),(2,7),(3,4),(5,8)] => 1 [(1,5),(2,7),(3,4),(6,8)] => 2 [(1,4),(2,7),(3,5),(6,8)] => 2 [(1,3),(2,7),(4,5),(6,8)] => 2 [(1,2),(3,7),(4,5),(6,8)] => 2 [(1,2),(3,8),(4,5),(6,7)] => 1 [(1,3),(2,8),(4,5),(6,7)] => 1 [(1,4),(2,8),(3,5),(6,7)] => 1 [(1,5),(2,8),(3,4),(6,7)] => 1 [(1,6),(2,8),(3,4),(5,7)] => 1 [(1,7),(2,8),(3,4),(5,6)] => 1 [(1,8),(2,7),(3,4),(5,6)] => 1 [(1,8),(2,7),(3,5),(4,6)] => 1 [(1,7),(2,8),(3,5),(4,6)] => 1 [(1,6),(2,8),(3,5),(4,7)] => 1 [(1,5),(2,8),(3,6),(4,7)] => 1 [(1,4),(2,8),(3,6),(5,7)] => 1 [(1,3),(2,8),(4,6),(5,7)] => 1 [(1,2),(3,8),(4,6),(5,7)] => 1 [(1,2),(3,7),(4,6),(5,8)] => 1 [(1,3),(2,7),(4,6),(5,8)] => 1 [(1,4),(2,7),(3,6),(5,8)] => 1 [(1,5),(2,7),(3,6),(4,8)] => 1 [(1,6),(2,7),(3,5),(4,8)] => 1 [(1,7),(2,6),(3,5),(4,8)] => 1 [(1,8),(2,6),(3,5),(4,7)] => 1 [(1,8),(2,5),(3,6),(4,7)] => 1 [(1,7),(2,5),(3,6),(4,8)] => 1 [(1,6),(2,5),(3,7),(4,8)] => 1 [(1,5),(2,6),(3,7),(4,8)] => 1 [(1,4),(2,6),(3,7),(5,8)] => 1 [(1,3),(2,6),(4,7),(5,8)] => 1 [(1,2),(3,6),(4,7),(5,8)] => 1 [(1,2),(3,5),(4,7),(6,8)] => 2 [(1,3),(2,5),(4,7),(6,8)] => 2 [(1,4),(2,5),(3,7),(6,8)] => 2 [(1,5),(2,4),(3,7),(6,8)] => 2 [(1,6),(2,4),(3,7),(5,8)] => 1 [(1,7),(2,4),(3,6),(5,8)] => 1 [(1,8),(2,4),(3,6),(5,7)] => 1 [(1,8),(2,3),(4,6),(5,7)] => 1 [(1,7),(2,3),(4,6),(5,8)] => 1 [(1,6),(2,3),(4,7),(5,8)] => 1 [(1,5),(2,3),(4,7),(6,8)] => 2 [(1,4),(2,3),(5,7),(6,8)] => 2 [(1,3),(2,4),(5,7),(6,8)] => 2 [(1,2),(3,4),(5,7),(6,8)] => 2 [(1,2),(3,4),(5,8),(6,7)] => 1 [(1,3),(2,4),(5,8),(6,7)] => 1 [(1,4),(2,3),(5,8),(6,7)] => 1 [(1,5),(2,3),(4,8),(6,7)] => 1 [(1,6),(2,3),(4,8),(5,7)] => 1 [(1,7),(2,3),(4,8),(5,6)] => 1 [(1,8),(2,3),(4,7),(5,6)] => 1 [(1,8),(2,4),(3,7),(5,6)] => 1 [(1,7),(2,4),(3,8),(5,6)] => 1 [(1,6),(2,4),(3,8),(5,7)] => 1 [(1,5),(2,4),(3,8),(6,7)] => 1 [(1,4),(2,5),(3,8),(6,7)] => 1 [(1,3),(2,5),(4,8),(6,7)] => 1 [(1,2),(3,5),(4,8),(6,7)] => 1 [(1,2),(3,6),(4,8),(5,7)] => 1 [(1,3),(2,6),(4,8),(5,7)] => 1 [(1,4),(2,6),(3,8),(5,7)] => 1 [(1,5),(2,6),(3,8),(4,7)] => 1 [(1,6),(2,5),(3,8),(4,7)] => 1 [(1,7),(2,5),(3,8),(4,6)] => 1 [(1,8),(2,5),(3,7),(4,6)] => 1 [(1,8),(2,6),(3,7),(4,5)] => 1 [(1,7),(2,6),(3,8),(4,5)] => 1 [(1,6),(2,7),(3,8),(4,5)] => 1 [(1,5),(2,7),(3,8),(4,6)] => 1 [(1,4),(2,7),(3,8),(5,6)] => 1 [(1,3),(2,7),(4,8),(5,6)] => 1 [(1,2),(3,7),(4,8),(5,6)] => 1 [(1,2),(3,8),(4,7),(5,6)] => 1 [(1,3),(2,8),(4,7),(5,6)] => 1 [(1,4),(2,8),(3,7),(5,6)] => 1 [(1,5),(2,8),(3,7),(4,6)] => 1 [(1,6),(2,8),(3,7),(4,5)] => 1 [(1,7),(2,8),(3,6),(4,5)] => 1 [(1,8),(2,7),(3,6),(4,5)] => 1 [(1,2),(3,4),(5,6),(7,8),(9,10)] => 2 [(1,3),(2,4),(5,6),(7,8),(9,10)] => 2 [(1,4),(2,3),(5,6),(7,8),(9,10)] => 2 [(1,5),(2,3),(4,6),(7,8),(9,10)] => 2 [(1,6),(2,3),(4,5),(7,8),(9,10)] => 2 [(1,7),(2,3),(4,5),(6,8),(9,10)] => 2 [(1,8),(2,3),(4,5),(6,7),(9,10)] => 2 [(1,9),(2,3),(4,5),(6,7),(8,10)] => 2 [(1,10),(2,3),(4,5),(6,7),(8,9)] => 1 [(1,10),(2,4),(3,5),(6,7),(8,9)] => 1 [(1,9),(2,4),(3,5),(6,7),(8,10)] => 2 [(1,8),(2,4),(3,5),(6,7),(9,10)] => 2 [(1,7),(2,4),(3,5),(6,8),(9,10)] => 2 [(1,6),(2,4),(3,5),(7,8),(9,10)] => 2 [(1,5),(2,4),(3,6),(7,8),(9,10)] => 2 [(1,4),(2,5),(3,6),(7,8),(9,10)] => 2 [(1,3),(2,5),(4,6),(7,8),(9,10)] => 2 [(1,2),(3,5),(4,6),(7,8),(9,10)] => 2 [(1,2),(3,6),(4,5),(7,8),(9,10)] => 2 [(1,3),(2,6),(4,5),(7,8),(9,10)] => 2 [(1,4),(2,6),(3,5),(7,8),(9,10)] => 2 [(1,5),(2,6),(3,4),(7,8),(9,10)] => 2 [(1,6),(2,5),(3,4),(7,8),(9,10)] => 2 [(1,7),(2,5),(3,4),(6,8),(9,10)] => 2 [(1,8),(2,5),(3,4),(6,7),(9,10)] => 2 [(1,9),(2,5),(3,4),(6,7),(8,10)] => 2 [(1,10),(2,5),(3,4),(6,7),(8,9)] => 1 [(1,10),(2,6),(3,4),(5,7),(8,9)] => 1 [(1,9),(2,6),(3,4),(5,7),(8,10)] => 2 [(1,8),(2,6),(3,4),(5,7),(9,10)] => 2 [(1,7),(2,6),(3,4),(5,8),(9,10)] => 2 [(1,6),(2,7),(3,4),(5,8),(9,10)] => 2 [(1,5),(2,7),(3,4),(6,8),(9,10)] => 2 [(1,4),(2,7),(3,5),(6,8),(9,10)] => 2 [(1,3),(2,7),(4,5),(6,8),(9,10)] => 2 [(1,2),(3,7),(4,5),(6,8),(9,10)] => 2 [(1,2),(3,8),(4,5),(6,7),(9,10)] => 2 [(1,3),(2,8),(4,5),(6,7),(9,10)] => 2 [(1,4),(2,8),(3,5),(6,7),(9,10)] => 2 [(1,5),(2,8),(3,4),(6,7),(9,10)] => 2 [(1,6),(2,8),(3,4),(5,7),(9,10)] => 2 [(1,7),(2,8),(3,4),(5,6),(9,10)] => 2 [(1,8),(2,7),(3,4),(5,6),(9,10)] => 2 [(1,9),(2,7),(3,4),(5,6),(8,10)] => 2 [(1,10),(2,7),(3,4),(5,6),(8,9)] => 1 [(1,10),(2,8),(3,4),(5,6),(7,9)] => 1 [(1,9),(2,8),(3,4),(5,6),(7,10)] => 2 [(1,8),(2,9),(3,4),(5,6),(7,10)] => 2 [(1,7),(2,9),(3,4),(5,6),(8,10)] => 2 [(1,6),(2,9),(3,4),(5,7),(8,10)] => 2 [(1,5),(2,9),(3,4),(6,7),(8,10)] => 2 [(1,4),(2,9),(3,5),(6,7),(8,10)] => 2 [(1,3),(2,9),(4,5),(6,7),(8,10)] => 2 [(1,2),(3,9),(4,5),(6,7),(8,10)] => 2 [(1,2),(3,10),(4,5),(6,7),(8,9)] => 1 [(1,3),(2,10),(4,5),(6,7),(8,9)] => 1 [(1,4),(2,10),(3,5),(6,7),(8,9)] => 1 [(1,5),(2,10),(3,4),(6,7),(8,9)] => 1 [(1,6),(2,10),(3,4),(5,7),(8,9)] => 1 [(1,7),(2,10),(3,4),(5,6),(8,9)] => 1 [(1,8),(2,10),(3,4),(5,6),(7,9)] => 1 [(1,9),(2,10),(3,4),(5,6),(7,8)] => 1 [(1,10),(2,9),(3,4),(5,6),(7,8)] => 1 [(1,10),(2,9),(3,5),(4,6),(7,8)] => 1 [(1,9),(2,10),(3,5),(4,6),(7,8)] => 1 [(1,8),(2,10),(3,5),(4,6),(7,9)] => 1 [(1,7),(2,10),(3,5),(4,6),(8,9)] => 1 [(1,6),(2,10),(3,5),(4,7),(8,9)] => 1 [(1,5),(2,10),(3,6),(4,7),(8,9)] => 1 [(1,4),(2,10),(3,6),(5,7),(8,9)] => 1 [(1,3),(2,10),(4,6),(5,7),(8,9)] => 1 [(1,2),(3,10),(4,6),(5,7),(8,9)] => 1 [(1,2),(3,9),(4,6),(5,7),(8,10)] => 2 [(1,3),(2,9),(4,6),(5,7),(8,10)] => 2 [(1,4),(2,9),(3,6),(5,7),(8,10)] => 2 [(1,5),(2,9),(3,6),(4,7),(8,10)] => 2 [(1,6),(2,9),(3,5),(4,7),(8,10)] => 2 [(1,7),(2,9),(3,5),(4,6),(8,10)] => 2 [(1,8),(2,9),(3,5),(4,6),(7,10)] => 2 [(1,9),(2,8),(3,5),(4,6),(7,10)] => 2 [(1,10),(2,8),(3,5),(4,6),(7,9)] => 1 [(1,10),(2,7),(3,5),(4,6),(8,9)] => 1 [(1,9),(2,7),(3,5),(4,6),(8,10)] => 2 [(1,8),(2,7),(3,5),(4,6),(9,10)] => 2 [(1,7),(2,8),(3,5),(4,6),(9,10)] => 2 [(1,6),(2,8),(3,5),(4,7),(9,10)] => 2 [(1,5),(2,8),(3,6),(4,7),(9,10)] => 2 [(1,4),(2,8),(3,6),(5,7),(9,10)] => 2 [(1,3),(2,8),(4,6),(5,7),(9,10)] => 2 [(1,2),(3,8),(4,6),(5,7),(9,10)] => 2 [(1,2),(3,7),(4,6),(5,8),(9,10)] => 2 [(1,3),(2,7),(4,6),(5,8),(9,10)] => 2 [(1,4),(2,7),(3,6),(5,8),(9,10)] => 2 [(1,5),(2,7),(3,6),(4,8),(9,10)] => 2 [(1,6),(2,7),(3,5),(4,8),(9,10)] => 2 [(1,7),(2,6),(3,5),(4,8),(9,10)] => 2 [(1,8),(2,6),(3,5),(4,7),(9,10)] => 2 [(1,9),(2,6),(3,5),(4,7),(8,10)] => 2 [(1,10),(2,6),(3,5),(4,7),(8,9)] => 1 [(1,10),(2,5),(3,6),(4,7),(8,9)] => 1 [(1,9),(2,5),(3,6),(4,7),(8,10)] => 2 [(1,8),(2,5),(3,6),(4,7),(9,10)] => 2 [(1,7),(2,5),(3,6),(4,8),(9,10)] => 2 [(1,6),(2,5),(3,7),(4,8),(9,10)] => 2 [(1,5),(2,6),(3,7),(4,8),(9,10)] => 2 [(1,4),(2,6),(3,7),(5,8),(9,10)] => 2 [(1,3),(2,6),(4,7),(5,8),(9,10)] => 2 [(1,2),(3,6),(4,7),(5,8),(9,10)] => 2 [(1,2),(3,5),(4,7),(6,8),(9,10)] => 2 [(1,3),(2,5),(4,7),(6,8),(9,10)] => 2 [(1,4),(2,5),(3,7),(6,8),(9,10)] => 2 [(1,5),(2,4),(3,7),(6,8),(9,10)] => 2 [(1,6),(2,4),(3,7),(5,8),(9,10)] => 2 [(1,7),(2,4),(3,6),(5,8),(9,10)] => 2 [(1,8),(2,4),(3,6),(5,7),(9,10)] => 2 [(1,9),(2,4),(3,6),(5,7),(8,10)] => 2 [(1,10),(2,4),(3,6),(5,7),(8,9)] => 1 [(1,10),(2,3),(4,6),(5,7),(8,9)] => 1 [(1,9),(2,3),(4,6),(5,7),(8,10)] => 2 [(1,8),(2,3),(4,6),(5,7),(9,10)] => 2 [(1,7),(2,3),(4,6),(5,8),(9,10)] => 2 [(1,6),(2,3),(4,7),(5,8),(9,10)] => 2 [(1,5),(2,3),(4,7),(6,8),(9,10)] => 2 [(1,4),(2,3),(5,7),(6,8),(9,10)] => 2 [(1,3),(2,4),(5,7),(6,8),(9,10)] => 2 [(1,2),(3,4),(5,7),(6,8),(9,10)] => 2 [(1,2),(3,4),(5,8),(6,7),(9,10)] => 2 [(1,3),(2,4),(5,8),(6,7),(9,10)] => 2 [(1,4),(2,3),(5,8),(6,7),(9,10)] => 2 [(1,5),(2,3),(4,8),(6,7),(9,10)] => 2 [(1,6),(2,3),(4,8),(5,7),(9,10)] => 2 [(1,7),(2,3),(4,8),(5,6),(9,10)] => 2 [(1,8),(2,3),(4,7),(5,6),(9,10)] => 2 [(1,9),(2,3),(4,7),(5,6),(8,10)] => 2 [(1,10),(2,3),(4,7),(5,6),(8,9)] => 1 [(1,10),(2,4),(3,7),(5,6),(8,9)] => 1 [(1,9),(2,4),(3,7),(5,6),(8,10)] => 2 [(1,8),(2,4),(3,7),(5,6),(9,10)] => 2 [(1,7),(2,4),(3,8),(5,6),(9,10)] => 2 [(1,6),(2,4),(3,8),(5,7),(9,10)] => 2 [(1,5),(2,4),(3,8),(6,7),(9,10)] => 2 [(1,4),(2,5),(3,8),(6,7),(9,10)] => 2 [(1,3),(2,5),(4,8),(6,7),(9,10)] => 2 [(1,2),(3,5),(4,8),(6,7),(9,10)] => 2 [(1,2),(3,6),(4,8),(5,7),(9,10)] => 2 [(1,3),(2,6),(4,8),(5,7),(9,10)] => 2 [(1,4),(2,6),(3,8),(5,7),(9,10)] => 2 [(1,5),(2,6),(3,8),(4,7),(9,10)] => 2 [(1,6),(2,5),(3,8),(4,7),(9,10)] => 2 [(1,7),(2,5),(3,8),(4,6),(9,10)] => 2 [(1,8),(2,5),(3,7),(4,6),(9,10)] => 2 [(1,9),(2,5),(3,7),(4,6),(8,10)] => 2 [(1,10),(2,5),(3,7),(4,6),(8,9)] => 1 [(1,10),(2,6),(3,7),(4,5),(8,9)] => 1 [(1,9),(2,6),(3,7),(4,5),(8,10)] => 2 [(1,8),(2,6),(3,7),(4,5),(9,10)] => 2 [(1,7),(2,6),(3,8),(4,5),(9,10)] => 2 [(1,6),(2,7),(3,8),(4,5),(9,10)] => 2 [(1,5),(2,7),(3,8),(4,6),(9,10)] => 2 [(1,4),(2,7),(3,8),(5,6),(9,10)] => 2 [(1,3),(2,7),(4,8),(5,6),(9,10)] => 2 [(1,2),(3,7),(4,8),(5,6),(9,10)] => 2 [(1,2),(3,8),(4,7),(5,6),(9,10)] => 2 [(1,3),(2,8),(4,7),(5,6),(9,10)] => 2 [(1,4),(2,8),(3,7),(5,6),(9,10)] => 2 [(1,5),(2,8),(3,7),(4,6),(9,10)] => 2 [(1,6),(2,8),(3,7),(4,5),(9,10)] => 2 [(1,7),(2,8),(3,6),(4,5),(9,10)] => 2 [(1,8),(2,7),(3,6),(4,5),(9,10)] => 2 [(1,9),(2,7),(3,6),(4,5),(8,10)] => 2 [(1,10),(2,7),(3,6),(4,5),(8,9)] => 1 [(1,10),(2,8),(3,6),(4,5),(7,9)] => 1 [(1,9),(2,8),(3,6),(4,5),(7,10)] => 2 [(1,8),(2,9),(3,6),(4,5),(7,10)] => 2 [(1,7),(2,9),(3,6),(4,5),(8,10)] => 2 [(1,6),(2,9),(3,7),(4,5),(8,10)] => 2 [(1,5),(2,9),(3,7),(4,6),(8,10)] => 2 [(1,4),(2,9),(3,7),(5,6),(8,10)] => 2 [(1,3),(2,9),(4,7),(5,6),(8,10)] => 2 [(1,2),(3,9),(4,7),(5,6),(8,10)] => 2 [(1,2),(3,10),(4,7),(5,6),(8,9)] => 1 [(1,3),(2,10),(4,7),(5,6),(8,9)] => 1 [(1,4),(2,10),(3,7),(5,6),(8,9)] => 1 [(1,5),(2,10),(3,7),(4,6),(8,9)] => 1 [(1,6),(2,10),(3,7),(4,5),(8,9)] => 1 [(1,7),(2,10),(3,6),(4,5),(8,9)] => 1 [(1,8),(2,10),(3,6),(4,5),(7,9)] => 1 [(1,9),(2,10),(3,6),(4,5),(7,8)] => 1 [(1,10),(2,9),(3,6),(4,5),(7,8)] => 1 [(1,10),(2,9),(3,7),(4,5),(6,8)] => 1 [(1,9),(2,10),(3,7),(4,5),(6,8)] => 1 [(1,8),(2,10),(3,7),(4,5),(6,9)] => 1 [(1,7),(2,10),(3,8),(4,5),(6,9)] => 1 [(1,6),(2,10),(3,8),(4,5),(7,9)] => 1 [(1,5),(2,10),(3,8),(4,6),(7,9)] => 1 [(1,4),(2,10),(3,8),(5,6),(7,9)] => 1 [(1,3),(2,10),(4,8),(5,6),(7,9)] => 1 [(1,2),(3,10),(4,8),(5,6),(7,9)] => 1 [(1,2),(3,9),(4,8),(5,6),(7,10)] => 2 [(1,3),(2,9),(4,8),(5,6),(7,10)] => 2 [(1,4),(2,9),(3,8),(5,6),(7,10)] => 2 [(1,5),(2,9),(3,8),(4,6),(7,10)] => 2 [(1,6),(2,9),(3,8),(4,5),(7,10)] => 2 [(1,7),(2,9),(3,8),(4,5),(6,10)] => 1 [(1,8),(2,9),(3,7),(4,5),(6,10)] => 1 [(1,9),(2,8),(3,7),(4,5),(6,10)] => 1 [(1,10),(2,8),(3,7),(4,5),(6,9)] => 1 [(1,10),(2,7),(3,8),(4,5),(6,9)] => 1 [(1,9),(2,7),(3,8),(4,5),(6,10)] => 1 [(1,8),(2,7),(3,9),(4,5),(6,10)] => 1 [(1,7),(2,8),(3,9),(4,5),(6,10)] => 1 [(1,6),(2,8),(3,9),(4,5),(7,10)] => 2 [(1,5),(2,8),(3,9),(4,6),(7,10)] => 2 [(1,4),(2,8),(3,9),(5,6),(7,10)] => 2 [(1,3),(2,8),(4,9),(5,6),(7,10)] => 2 [(1,2),(3,8),(4,9),(5,6),(7,10)] => 2 [(1,2),(3,7),(4,9),(5,6),(8,10)] => 2 [(1,3),(2,7),(4,9),(5,6),(8,10)] => 2 [(1,4),(2,7),(3,9),(5,6),(8,10)] => 2 [(1,5),(2,7),(3,9),(4,6),(8,10)] => 2 [(1,6),(2,7),(3,9),(4,5),(8,10)] => 2 [(1,7),(2,6),(3,9),(4,5),(8,10)] => 2 [(1,8),(2,6),(3,9),(4,5),(7,10)] => 2 [(1,9),(2,6),(3,8),(4,5),(7,10)] => 2 [(1,10),(2,6),(3,8),(4,5),(7,9)] => 1 [(1,10),(2,5),(3,8),(4,6),(7,9)] => 1 [(1,9),(2,5),(3,8),(4,6),(7,10)] => 2 [(1,8),(2,5),(3,9),(4,6),(7,10)] => 2 [(1,7),(2,5),(3,9),(4,6),(8,10)] => 2 [(1,6),(2,5),(3,9),(4,7),(8,10)] => 2 [(1,5),(2,6),(3,9),(4,7),(8,10)] => 2 [(1,4),(2,6),(3,9),(5,7),(8,10)] => 2 [(1,3),(2,6),(4,9),(5,7),(8,10)] => 2 [(1,2),(3,6),(4,9),(5,7),(8,10)] => 2 [(1,2),(3,5),(4,9),(6,7),(8,10)] => 2 [(1,3),(2,5),(4,9),(6,7),(8,10)] => 2 [(1,4),(2,5),(3,9),(6,7),(8,10)] => 2 [(1,5),(2,4),(3,9),(6,7),(8,10)] => 2 [(1,6),(2,4),(3,9),(5,7),(8,10)] => 2 [(1,7),(2,4),(3,9),(5,6),(8,10)] => 2 [(1,8),(2,4),(3,9),(5,6),(7,10)] => 2 [(1,9),(2,4),(3,8),(5,6),(7,10)] => 2 [(1,10),(2,4),(3,8),(5,6),(7,9)] => 1 [(1,10),(2,3),(4,8),(5,6),(7,9)] => 1 [(1,9),(2,3),(4,8),(5,6),(7,10)] => 2 [(1,8),(2,3),(4,9),(5,6),(7,10)] => 2 [(1,7),(2,3),(4,9),(5,6),(8,10)] => 2 [(1,6),(2,3),(4,9),(5,7),(8,10)] => 2 [(1,5),(2,3),(4,9),(6,7),(8,10)] => 2 [(1,4),(2,3),(5,9),(6,7),(8,10)] => 2 [(1,3),(2,4),(5,9),(6,7),(8,10)] => 2 [(1,2),(3,4),(5,9),(6,7),(8,10)] => 2 [(1,2),(3,4),(5,10),(6,7),(8,9)] => 1 [(1,3),(2,4),(5,10),(6,7),(8,9)] => 1 [(1,4),(2,3),(5,10),(6,7),(8,9)] => 1 [(1,5),(2,3),(4,10),(6,7),(8,9)] => 1 [(1,6),(2,3),(4,10),(5,7),(8,9)] => 1 [(1,7),(2,3),(4,10),(5,6),(8,9)] => 1 [(1,8),(2,3),(4,10),(5,6),(7,9)] => 1 [(1,9),(2,3),(4,10),(5,6),(7,8)] => 1 [(1,10),(2,3),(4,9),(5,6),(7,8)] => 1 [(1,10),(2,4),(3,9),(5,6),(7,8)] => 1 [(1,9),(2,4),(3,10),(5,6),(7,8)] => 1 [(1,8),(2,4),(3,10),(5,6),(7,9)] => 1 [(1,7),(2,4),(3,10),(5,6),(8,9)] => 1 [(1,6),(2,4),(3,10),(5,7),(8,9)] => 1 [(1,5),(2,4),(3,10),(6,7),(8,9)] => 1 [(1,4),(2,5),(3,10),(6,7),(8,9)] => 1 [(1,3),(2,5),(4,10),(6,7),(8,9)] => 1 [(1,2),(3,5),(4,10),(6,7),(8,9)] => 1 [(1,2),(3,6),(4,10),(5,7),(8,9)] => 1 [(1,3),(2,6),(4,10),(5,7),(8,9)] => 1 [(1,4),(2,6),(3,10),(5,7),(8,9)] => 1 [(1,5),(2,6),(3,10),(4,7),(8,9)] => 1 [(1,6),(2,5),(3,10),(4,7),(8,9)] => 1 [(1,7),(2,5),(3,10),(4,6),(8,9)] => 1 [(1,8),(2,5),(3,10),(4,6),(7,9)] => 1 [(1,9),(2,5),(3,10),(4,6),(7,8)] => 1 [(1,10),(2,5),(3,9),(4,6),(7,8)] => 1 [(1,10),(2,6),(3,9),(4,5),(7,8)] => 1 [(1,9),(2,6),(3,10),(4,5),(7,8)] => 1 [(1,8),(2,6),(3,10),(4,5),(7,9)] => 1 [(1,7),(2,6),(3,10),(4,5),(8,9)] => 1 [(1,6),(2,7),(3,10),(4,5),(8,9)] => 1 [(1,5),(2,7),(3,10),(4,6),(8,9)] => 1 [(1,4),(2,7),(3,10),(5,6),(8,9)] => 1 [(1,3),(2,7),(4,10),(5,6),(8,9)] => 1 [(1,2),(3,7),(4,10),(5,6),(8,9)] => 1 [(1,2),(3,8),(4,10),(5,6),(7,9)] => 1 [(1,3),(2,8),(4,10),(5,6),(7,9)] => 1 [(1,4),(2,8),(3,10),(5,6),(7,9)] => 1 [(1,5),(2,8),(3,10),(4,6),(7,9)] => 1 [(1,6),(2,8),(3,10),(4,5),(7,9)] => 1 [(1,7),(2,8),(3,10),(4,5),(6,9)] => 1 [(1,8),(2,7),(3,10),(4,5),(6,9)] => 1 [(1,9),(2,7),(3,10),(4,5),(6,8)] => 1 [(1,10),(2,7),(3,9),(4,5),(6,8)] => 1 [(1,10),(2,8),(3,9),(4,5),(6,7)] => 1 [(1,9),(2,8),(3,10),(4,5),(6,7)] => 1 [(1,8),(2,9),(3,10),(4,5),(6,7)] => 1 [(1,7),(2,9),(3,10),(4,5),(6,8)] => 1 [(1,6),(2,9),(3,10),(4,5),(7,8)] => 1 [(1,5),(2,9),(3,10),(4,6),(7,8)] => 1 [(1,4),(2,9),(3,10),(5,6),(7,8)] => 1 [(1,3),(2,9),(4,10),(5,6),(7,8)] => 1 [(1,2),(3,9),(4,10),(5,6),(7,8)] => 1 [(1,2),(3,10),(4,9),(5,6),(7,8)] => 1 [(1,3),(2,10),(4,9),(5,6),(7,8)] => 1 [(1,4),(2,10),(3,9),(5,6),(7,8)] => 1 [(1,5),(2,10),(3,9),(4,6),(7,8)] => 1 [(1,6),(2,10),(3,9),(4,5),(7,8)] => 1 [(1,7),(2,10),(3,9),(4,5),(6,8)] => 1 [(1,8),(2,10),(3,9),(4,5),(6,7)] => 1 [(1,9),(2,10),(3,8),(4,5),(6,7)] => 1 [(1,10),(2,9),(3,8),(4,5),(6,7)] => 1 [(1,10),(2,9),(3,8),(4,6),(5,7)] => 1 [(1,9),(2,10),(3,8),(4,6),(5,7)] => 1 [(1,8),(2,10),(3,9),(4,6),(5,7)] => 1 [(1,7),(2,10),(3,9),(4,6),(5,8)] => 1 [(1,6),(2,10),(3,9),(4,7),(5,8)] => 1 [(1,5),(2,10),(3,9),(4,7),(6,8)] => 1 [(1,4),(2,10),(3,9),(5,7),(6,8)] => 1 [(1,3),(2,10),(4,9),(5,7),(6,8)] => 1 [(1,2),(3,10),(4,9),(5,7),(6,8)] => 1 [(1,2),(3,9),(4,10),(5,7),(6,8)] => 1 [(1,3),(2,9),(4,10),(5,7),(6,8)] => 1 [(1,4),(2,9),(3,10),(5,7),(6,8)] => 1 [(1,5),(2,9),(3,10),(4,7),(6,8)] => 1 [(1,6),(2,9),(3,10),(4,7),(5,8)] => 1 [(1,7),(2,9),(3,10),(4,6),(5,8)] => 1 [(1,8),(2,9),(3,10),(4,6),(5,7)] => 1 [(1,9),(2,8),(3,10),(4,6),(5,7)] => 1 [(1,10),(2,8),(3,9),(4,6),(5,7)] => 1 [(1,10),(2,7),(3,9),(4,6),(5,8)] => 1 [(1,9),(2,7),(3,10),(4,6),(5,8)] => 1 [(1,8),(2,7),(3,10),(4,6),(5,9)] => 1 [(1,7),(2,8),(3,10),(4,6),(5,9)] => 1 [(1,6),(2,8),(3,10),(4,7),(5,9)] => 1 [(1,5),(2,8),(3,10),(4,7),(6,9)] => 1 [(1,4),(2,8),(3,10),(5,7),(6,9)] => 1 [(1,3),(2,8),(4,10),(5,7),(6,9)] => 1 [(1,2),(3,8),(4,10),(5,7),(6,9)] => 1 [(1,2),(3,7),(4,10),(5,8),(6,9)] => 1 [(1,3),(2,7),(4,10),(5,8),(6,9)] => 1 [(1,4),(2,7),(3,10),(5,8),(6,9)] => 1 [(1,5),(2,7),(3,10),(4,8),(6,9)] => 1 [(1,6),(2,7),(3,10),(4,8),(5,9)] => 1 [(1,7),(2,6),(3,10),(4,8),(5,9)] => 1 [(1,8),(2,6),(3,10),(4,7),(5,9)] => 1 [(1,9),(2,6),(3,10),(4,7),(5,8)] => 1 [(1,10),(2,6),(3,9),(4,7),(5,8)] => 1 [(1,10),(2,5),(3,9),(4,7),(6,8)] => 1 [(1,9),(2,5),(3,10),(4,7),(6,8)] => 1 [(1,8),(2,5),(3,10),(4,7),(6,9)] => 1 [(1,7),(2,5),(3,10),(4,8),(6,9)] => 1 [(1,6),(2,5),(3,10),(4,8),(7,9)] => 1 [(1,5),(2,6),(3,10),(4,8),(7,9)] => 1 [(1,4),(2,6),(3,10),(5,8),(7,9)] => 1 [(1,3),(2,6),(4,10),(5,8),(7,9)] => 1 [(1,2),(3,6),(4,10),(5,8),(7,9)] => 1 [(1,2),(3,5),(4,10),(6,8),(7,9)] => 1 [(1,3),(2,5),(4,10),(6,8),(7,9)] => 1 [(1,4),(2,5),(3,10),(6,8),(7,9)] => 1 [(1,5),(2,4),(3,10),(6,8),(7,9)] => 1 [(1,6),(2,4),(3,10),(5,8),(7,9)] => 1 [(1,7),(2,4),(3,10),(5,8),(6,9)] => 1 [(1,8),(2,4),(3,10),(5,7),(6,9)] => 1 [(1,9),(2,4),(3,10),(5,7),(6,8)] => 1 [(1,10),(2,4),(3,9),(5,7),(6,8)] => 1 [(1,10),(2,3),(4,9),(5,7),(6,8)] => 1 [(1,9),(2,3),(4,10),(5,7),(6,8)] => 1 [(1,8),(2,3),(4,10),(5,7),(6,9)] => 1 [(1,7),(2,3),(4,10),(5,8),(6,9)] => 1 [(1,6),(2,3),(4,10),(5,8),(7,9)] => 1 [(1,5),(2,3),(4,10),(6,8),(7,9)] => 1 [(1,4),(2,3),(5,10),(6,8),(7,9)] => 1 [(1,3),(2,4),(5,10),(6,8),(7,9)] => 1 [(1,2),(3,4),(5,10),(6,8),(7,9)] => 1 [(1,2),(3,4),(5,9),(6,8),(7,10)] => 2 [(1,3),(2,4),(5,9),(6,8),(7,10)] => 2 [(1,4),(2,3),(5,9),(6,8),(7,10)] => 2 [(1,5),(2,3),(4,9),(6,8),(7,10)] => 2 [(1,6),(2,3),(4,9),(5,8),(7,10)] => 2 [(1,7),(2,3),(4,9),(5,8),(6,10)] => 1 [(1,8),(2,3),(4,9),(5,7),(6,10)] => 1 [(1,9),(2,3),(4,8),(5,7),(6,10)] => 1 [(1,10),(2,3),(4,8),(5,7),(6,9)] => 1 [(1,10),(2,4),(3,8),(5,7),(6,9)] => 1 [(1,9),(2,4),(3,8),(5,7),(6,10)] => 1 [(1,8),(2,4),(3,9),(5,7),(6,10)] => 1 [(1,7),(2,4),(3,9),(5,8),(6,10)] => 1 [(1,6),(2,4),(3,9),(5,8),(7,10)] => 2 [(1,5),(2,4),(3,9),(6,8),(7,10)] => 2 [(1,4),(2,5),(3,9),(6,8),(7,10)] => 2 [(1,3),(2,5),(4,9),(6,8),(7,10)] => 2 [(1,2),(3,5),(4,9),(6,8),(7,10)] => 2 [(1,2),(3,6),(4,9),(5,8),(7,10)] => 2 [(1,3),(2,6),(4,9),(5,8),(7,10)] => 2 [(1,4),(2,6),(3,9),(5,8),(7,10)] => 2 [(1,5),(2,6),(3,9),(4,8),(7,10)] => 2 [(1,6),(2,5),(3,9),(4,8),(7,10)] => 2 [(1,7),(2,5),(3,9),(4,8),(6,10)] => 1 [(1,8),(2,5),(3,9),(4,7),(6,10)] => 1 [(1,9),(2,5),(3,8),(4,7),(6,10)] => 1 [(1,10),(2,5),(3,8),(4,7),(6,9)] => 1 [(1,10),(2,6),(3,8),(4,7),(5,9)] => 1 [(1,9),(2,6),(3,8),(4,7),(5,10)] => 1 [(1,8),(2,6),(3,9),(4,7),(5,10)] => 1 [(1,7),(2,6),(3,9),(4,8),(5,10)] => 1 [(1,6),(2,7),(3,9),(4,8),(5,10)] => 1 [(1,5),(2,7),(3,9),(4,8),(6,10)] => 1 [(1,4),(2,7),(3,9),(5,8),(6,10)] => 1 [(1,3),(2,7),(4,9),(5,8),(6,10)] => 1 [(1,2),(3,7),(4,9),(5,8),(6,10)] => 1 [(1,2),(3,8),(4,9),(5,7),(6,10)] => 1 [(1,3),(2,8),(4,9),(5,7),(6,10)] => 1 [(1,4),(2,8),(3,9),(5,7),(6,10)] => 1 [(1,5),(2,8),(3,9),(4,7),(6,10)] => 1 [(1,6),(2,8),(3,9),(4,7),(5,10)] => 1 [(1,7),(2,8),(3,9),(4,6),(5,10)] => 1 [(1,8),(2,7),(3,9),(4,6),(5,10)] => 1 [(1,9),(2,7),(3,8),(4,6),(5,10)] => 1 [(1,10),(2,7),(3,8),(4,6),(5,9)] => 1 [(1,10),(2,8),(3,7),(4,6),(5,9)] => 1 [(1,9),(2,8),(3,7),(4,6),(5,10)] => 1 [(1,8),(2,9),(3,7),(4,6),(5,10)] => 1 [(1,7),(2,9),(3,8),(4,6),(5,10)] => 1 [(1,6),(2,9),(3,8),(4,7),(5,10)] => 1 [(1,5),(2,9),(3,8),(4,7),(6,10)] => 1 [(1,4),(2,9),(3,8),(5,7),(6,10)] => 1 [(1,3),(2,9),(4,8),(5,7),(6,10)] => 1 [(1,2),(3,9),(4,8),(5,7),(6,10)] => 1 [(1,2),(3,10),(4,8),(5,7),(6,9)] => 1 [(1,3),(2,10),(4,8),(5,7),(6,9)] => 1 [(1,4),(2,10),(3,8),(5,7),(6,9)] => 1 [(1,5),(2,10),(3,8),(4,7),(6,9)] => 1 [(1,6),(2,10),(3,8),(4,7),(5,9)] => 1 [(1,7),(2,10),(3,8),(4,6),(5,9)] => 1 [(1,8),(2,10),(3,7),(4,6),(5,9)] => 1 [(1,9),(2,10),(3,7),(4,6),(5,8)] => 1 [(1,10),(2,9),(3,7),(4,6),(5,8)] => 1 [(1,10),(2,9),(3,6),(4,7),(5,8)] => 1 [(1,9),(2,10),(3,6),(4,7),(5,8)] => 1 [(1,8),(2,10),(3,6),(4,7),(5,9)] => 1 [(1,7),(2,10),(3,6),(4,8),(5,9)] => 1 [(1,6),(2,10),(3,7),(4,8),(5,9)] => 1 [(1,5),(2,10),(3,7),(4,8),(6,9)] => 1 [(1,4),(2,10),(3,7),(5,8),(6,9)] => 1 [(1,3),(2,10),(4,7),(5,8),(6,9)] => 1 [(1,2),(3,10),(4,7),(5,8),(6,9)] => 1 [(1,2),(3,9),(4,7),(5,8),(6,10)] => 1 [(1,3),(2,9),(4,7),(5,8),(6,10)] => 1 [(1,4),(2,9),(3,7),(5,8),(6,10)] => 1 [(1,5),(2,9),(3,7),(4,8),(6,10)] => 1 [(1,6),(2,9),(3,7),(4,8),(5,10)] => 1 [(1,7),(2,9),(3,6),(4,8),(5,10)] => 1 [(1,8),(2,9),(3,6),(4,7),(5,10)] => 1 [(1,9),(2,8),(3,6),(4,7),(5,10)] => 1 [(1,10),(2,8),(3,6),(4,7),(5,9)] => 1 [(1,10),(2,7),(3,6),(4,8),(5,9)] => 1 [(1,9),(2,7),(3,6),(4,8),(5,10)] => 1 [(1,8),(2,7),(3,6),(4,9),(5,10)] => 1 [(1,7),(2,8),(3,6),(4,9),(5,10)] => 1 [(1,6),(2,8),(3,7),(4,9),(5,10)] => 1 [(1,5),(2,8),(3,7),(4,9),(6,10)] => 1 [(1,4),(2,8),(3,7),(5,9),(6,10)] => 1 [(1,3),(2,8),(4,7),(5,9),(6,10)] => 1 [(1,2),(3,8),(4,7),(5,9),(6,10)] => 1 [(1,2),(3,7),(4,8),(5,9),(6,10)] => 1 [(1,3),(2,7),(4,8),(5,9),(6,10)] => 1 [(1,4),(2,7),(3,8),(5,9),(6,10)] => 1 [(1,5),(2,7),(3,8),(4,9),(6,10)] => 1 [(1,6),(2,7),(3,8),(4,9),(5,10)] => 1 [(1,7),(2,6),(3,8),(4,9),(5,10)] => 1 [(1,8),(2,6),(3,7),(4,9),(5,10)] => 1 [(1,9),(2,6),(3,7),(4,8),(5,10)] => 1 [(1,10),(2,6),(3,7),(4,8),(5,9)] => 1 [(1,10),(2,5),(3,7),(4,8),(6,9)] => 1 [(1,9),(2,5),(3,7),(4,8),(6,10)] => 1 [(1,8),(2,5),(3,7),(4,9),(6,10)] => 1 [(1,7),(2,5),(3,8),(4,9),(6,10)] => 1 [(1,6),(2,5),(3,8),(4,9),(7,10)] => 2 [(1,5),(2,6),(3,8),(4,9),(7,10)] => 2 [(1,4),(2,6),(3,8),(5,9),(7,10)] => 2 [(1,3),(2,6),(4,8),(5,9),(7,10)] => 2 [(1,2),(3,6),(4,8),(5,9),(7,10)] => 2 [(1,2),(3,5),(4,8),(6,9),(7,10)] => 2 [(1,3),(2,5),(4,8),(6,9),(7,10)] => 2 [(1,4),(2,5),(3,8),(6,9),(7,10)] => 2 [(1,5),(2,4),(3,8),(6,9),(7,10)] => 2 [(1,6),(2,4),(3,8),(5,9),(7,10)] => 2 [(1,7),(2,4),(3,8),(5,9),(6,10)] => 1 [(1,8),(2,4),(3,7),(5,9),(6,10)] => 1 [(1,9),(2,4),(3,7),(5,8),(6,10)] => 1 [(1,10),(2,4),(3,7),(5,8),(6,9)] => 1 [(1,10),(2,3),(4,7),(5,8),(6,9)] => 1 [(1,9),(2,3),(4,7),(5,8),(6,10)] => 1 [(1,8),(2,3),(4,7),(5,9),(6,10)] => 1 [(1,7),(2,3),(4,8),(5,9),(6,10)] => 1 [(1,6),(2,3),(4,8),(5,9),(7,10)] => 2 [(1,5),(2,3),(4,8),(6,9),(7,10)] => 2 [(1,4),(2,3),(5,8),(6,9),(7,10)] => 2 [(1,3),(2,4),(5,8),(6,9),(7,10)] => 2 [(1,2),(3,4),(5,8),(6,9),(7,10)] => 2 [(1,2),(3,4),(5,7),(6,9),(8,10)] => 2 [(1,3),(2,4),(5,7),(6,9),(8,10)] => 2 [(1,4),(2,3),(5,7),(6,9),(8,10)] => 2 [(1,5),(2,3),(4,7),(6,9),(8,10)] => 2 [(1,6),(2,3),(4,7),(5,9),(8,10)] => 2 [(1,7),(2,3),(4,6),(5,9),(8,10)] => 2 [(1,8),(2,3),(4,6),(5,9),(7,10)] => 2 [(1,9),(2,3),(4,6),(5,8),(7,10)] => 2 [(1,10),(2,3),(4,6),(5,8),(7,9)] => 1 [(1,10),(2,4),(3,6),(5,8),(7,9)] => 1 [(1,9),(2,4),(3,6),(5,8),(7,10)] => 2 [(1,8),(2,4),(3,6),(5,9),(7,10)] => 2 [(1,7),(2,4),(3,6),(5,9),(8,10)] => 2 [(1,6),(2,4),(3,7),(5,9),(8,10)] => 2 [(1,5),(2,4),(3,7),(6,9),(8,10)] => 2 [(1,4),(2,5),(3,7),(6,9),(8,10)] => 2 [(1,3),(2,5),(4,7),(6,9),(8,10)] => 2 [(1,2),(3,5),(4,7),(6,9),(8,10)] => 2 [(1,2),(3,6),(4,7),(5,9),(8,10)] => 2 [(1,3),(2,6),(4,7),(5,9),(8,10)] => 2 [(1,4),(2,6),(3,7),(5,9),(8,10)] => 2 [(1,5),(2,6),(3,7),(4,9),(8,10)] => 2 [(1,6),(2,5),(3,7),(4,9),(8,10)] => 2 [(1,7),(2,5),(3,6),(4,9),(8,10)] => 2 [(1,8),(2,5),(3,6),(4,9),(7,10)] => 2 [(1,9),(2,5),(3,6),(4,8),(7,10)] => 2 [(1,10),(2,5),(3,6),(4,8),(7,9)] => 1 [(1,10),(2,6),(3,5),(4,8),(7,9)] => 1 [(1,9),(2,6),(3,5),(4,8),(7,10)] => 2 [(1,8),(2,6),(3,5),(4,9),(7,10)] => 2 [(1,7),(2,6),(3,5),(4,9),(8,10)] => 2 [(1,6),(2,7),(3,5),(4,9),(8,10)] => 2 [(1,5),(2,7),(3,6),(4,9),(8,10)] => 2 [(1,4),(2,7),(3,6),(5,9),(8,10)] => 2 [(1,3),(2,7),(4,6),(5,9),(8,10)] => 2 [(1,2),(3,7),(4,6),(5,9),(8,10)] => 2 [(1,2),(3,8),(4,6),(5,9),(7,10)] => 2 [(1,3),(2,8),(4,6),(5,9),(7,10)] => 2 [(1,4),(2,8),(3,6),(5,9),(7,10)] => 2 [(1,5),(2,8),(3,6),(4,9),(7,10)] => 2 [(1,6),(2,8),(3,5),(4,9),(7,10)] => 2 [(1,7),(2,8),(3,5),(4,9),(6,10)] => 1 [(1,8),(2,7),(3,5),(4,9),(6,10)] => 1 [(1,9),(2,7),(3,5),(4,8),(6,10)] => 1 [(1,10),(2,7),(3,5),(4,8),(6,9)] => 1 [(1,10),(2,8),(3,5),(4,7),(6,9)] => 1 [(1,9),(2,8),(3,5),(4,7),(6,10)] => 1 [(1,8),(2,9),(3,5),(4,7),(6,10)] => 1 [(1,7),(2,9),(3,5),(4,8),(6,10)] => 1 [(1,6),(2,9),(3,5),(4,8),(7,10)] => 2 [(1,5),(2,9),(3,6),(4,8),(7,10)] => 2 [(1,4),(2,9),(3,6),(5,8),(7,10)] => 2 [(1,3),(2,9),(4,6),(5,8),(7,10)] => 2 [(1,2),(3,9),(4,6),(5,8),(7,10)] => 2 [(1,2),(3,10),(4,6),(5,8),(7,9)] => 1 [(1,3),(2,10),(4,6),(5,8),(7,9)] => 1 [(1,4),(2,10),(3,6),(5,8),(7,9)] => 1 [(1,5),(2,10),(3,6),(4,8),(7,9)] => 1 [(1,6),(2,10),(3,5),(4,8),(7,9)] => 1 [(1,7),(2,10),(3,5),(4,8),(6,9)] => 1 [(1,8),(2,10),(3,5),(4,7),(6,9)] => 1 [(1,9),(2,10),(3,5),(4,7),(6,8)] => 1 [(1,10),(2,9),(3,5),(4,7),(6,8)] => 1 [(1,10),(2,9),(3,4),(5,7),(6,8)] => 1 [(1,9),(2,10),(3,4),(5,7),(6,8)] => 1 [(1,8),(2,10),(3,4),(5,7),(6,9)] => 1 [(1,7),(2,10),(3,4),(5,8),(6,9)] => 1 [(1,6),(2,10),(3,4),(5,8),(7,9)] => 1 [(1,5),(2,10),(3,4),(6,8),(7,9)] => 1 [(1,4),(2,10),(3,5),(6,8),(7,9)] => 1 [(1,3),(2,10),(4,5),(6,8),(7,9)] => 1 [(1,2),(3,10),(4,5),(6,8),(7,9)] => 1 [(1,2),(3,9),(4,5),(6,8),(7,10)] => 2 [(1,3),(2,9),(4,5),(6,8),(7,10)] => 2 [(1,4),(2,9),(3,5),(6,8),(7,10)] => 2 [(1,5),(2,9),(3,4),(6,8),(7,10)] => 2 [(1,6),(2,9),(3,4),(5,8),(7,10)] => 2 [(1,7),(2,9),(3,4),(5,8),(6,10)] => 1 [(1,8),(2,9),(3,4),(5,7),(6,10)] => 1 [(1,9),(2,8),(3,4),(5,7),(6,10)] => 1 [(1,10),(2,8),(3,4),(5,7),(6,9)] => 1 [(1,10),(2,7),(3,4),(5,8),(6,9)] => 1 [(1,9),(2,7),(3,4),(5,8),(6,10)] => 1 [(1,8),(2,7),(3,4),(5,9),(6,10)] => 1 [(1,7),(2,8),(3,4),(5,9),(6,10)] => 1 [(1,6),(2,8),(3,4),(5,9),(7,10)] => 2 [(1,5),(2,8),(3,4),(6,9),(7,10)] => 2 [(1,4),(2,8),(3,5),(6,9),(7,10)] => 2 [(1,3),(2,8),(4,5),(6,9),(7,10)] => 2 [(1,2),(3,8),(4,5),(6,9),(7,10)] => 2 [(1,2),(3,7),(4,5),(6,9),(8,10)] => 2 [(1,3),(2,7),(4,5),(6,9),(8,10)] => 2 [(1,4),(2,7),(3,5),(6,9),(8,10)] => 2 [(1,5),(2,7),(3,4),(6,9),(8,10)] => 2 [(1,6),(2,7),(3,4),(5,9),(8,10)] => 2 [(1,7),(2,6),(3,4),(5,9),(8,10)] => 2 [(1,8),(2,6),(3,4),(5,9),(7,10)] => 2 [(1,9),(2,6),(3,4),(5,8),(7,10)] => 2 [(1,10),(2,6),(3,4),(5,8),(7,9)] => 1 [(1,10),(2,5),(3,4),(6,8),(7,9)] => 1 [(1,9),(2,5),(3,4),(6,8),(7,10)] => 2 [(1,8),(2,5),(3,4),(6,9),(7,10)] => 2 [(1,7),(2,5),(3,4),(6,9),(8,10)] => 2 [(1,6),(2,5),(3,4),(7,9),(8,10)] => 2 [(1,5),(2,6),(3,4),(7,9),(8,10)] => 2 [(1,4),(2,6),(3,5),(7,9),(8,10)] => 2 [(1,3),(2,6),(4,5),(7,9),(8,10)] => 2 [(1,2),(3,6),(4,5),(7,9),(8,10)] => 2 [(1,2),(3,5),(4,6),(7,9),(8,10)] => 2 [(1,3),(2,5),(4,6),(7,9),(8,10)] => 2 [(1,4),(2,5),(3,6),(7,9),(8,10)] => 2 [(1,5),(2,4),(3,6),(7,9),(8,10)] => 2 [(1,6),(2,4),(3,5),(7,9),(8,10)] => 2 [(1,7),(2,4),(3,5),(6,9),(8,10)] => 2 [(1,8),(2,4),(3,5),(6,9),(7,10)] => 2 [(1,9),(2,4),(3,5),(6,8),(7,10)] => 2 [(1,10),(2,4),(3,5),(6,8),(7,9)] => 1 [(1,10),(2,3),(4,5),(6,8),(7,9)] => 1 [(1,9),(2,3),(4,5),(6,8),(7,10)] => 2 [(1,8),(2,3),(4,5),(6,9),(7,10)] => 2 [(1,7),(2,3),(4,5),(6,9),(8,10)] => 2 [(1,6),(2,3),(4,5),(7,9),(8,10)] => 2 [(1,5),(2,3),(4,6),(7,9),(8,10)] => 2 [(1,4),(2,3),(5,6),(7,9),(8,10)] => 2 [(1,3),(2,4),(5,6),(7,9),(8,10)] => 2 [(1,2),(3,4),(5,6),(7,9),(8,10)] => 2 [(1,2),(3,4),(5,6),(7,10),(8,9)] => 2 [(1,3),(2,4),(5,6),(7,10),(8,9)] => 2 [(1,4),(2,3),(5,6),(7,10),(8,9)] => 2 [(1,5),(2,3),(4,6),(7,10),(8,9)] => 2 [(1,6),(2,3),(4,5),(7,10),(8,9)] => 2 [(1,7),(2,3),(4,5),(6,10),(8,9)] => 1 [(1,8),(2,3),(4,5),(6,10),(7,9)] => 1 [(1,9),(2,3),(4,5),(6,10),(7,8)] => 1 [(1,10),(2,3),(4,5),(6,9),(7,8)] => 1 [(1,10),(2,4),(3,5),(6,9),(7,8)] => 1 [(1,9),(2,4),(3,5),(6,10),(7,8)] => 1 [(1,8),(2,4),(3,5),(6,10),(7,9)] => 1 [(1,7),(2,4),(3,5),(6,10),(8,9)] => 1 [(1,6),(2,4),(3,5),(7,10),(8,9)] => 2 [(1,5),(2,4),(3,6),(7,10),(8,9)] => 2 [(1,4),(2,5),(3,6),(7,10),(8,9)] => 2 [(1,3),(2,5),(4,6),(7,10),(8,9)] => 2 [(1,2),(3,5),(4,6),(7,10),(8,9)] => 2 [(1,2),(3,6),(4,5),(7,10),(8,9)] => 2 [(1,3),(2,6),(4,5),(7,10),(8,9)] => 2 [(1,4),(2,6),(3,5),(7,10),(8,9)] => 2 [(1,5),(2,6),(3,4),(7,10),(8,9)] => 2 [(1,6),(2,5),(3,4),(7,10),(8,9)] => 2 [(1,7),(2,5),(3,4),(6,10),(8,9)] => 1 [(1,8),(2,5),(3,4),(6,10),(7,9)] => 1 [(1,9),(2,5),(3,4),(6,10),(7,8)] => 1 [(1,10),(2,5),(3,4),(6,9),(7,8)] => 1 [(1,10),(2,6),(3,4),(5,9),(7,8)] => 1 [(1,9),(2,6),(3,4),(5,10),(7,8)] => 1 [(1,8),(2,6),(3,4),(5,10),(7,9)] => 1 [(1,7),(2,6),(3,4),(5,10),(8,9)] => 1 [(1,6),(2,7),(3,4),(5,10),(8,9)] => 1 [(1,5),(2,7),(3,4),(6,10),(8,9)] => 1 [(1,4),(2,7),(3,5),(6,10),(8,9)] => 1 [(1,3),(2,7),(4,5),(6,10),(8,9)] => 1 [(1,2),(3,7),(4,5),(6,10),(8,9)] => 1 [(1,2),(3,8),(4,5),(6,10),(7,9)] => 1 [(1,3),(2,8),(4,5),(6,10),(7,9)] => 1 [(1,4),(2,8),(3,5),(6,10),(7,9)] => 1 [(1,5),(2,8),(3,4),(6,10),(7,9)] => 1 [(1,6),(2,8),(3,4),(5,10),(7,9)] => 1 [(1,7),(2,8),(3,4),(5,10),(6,9)] => 1 [(1,8),(2,7),(3,4),(5,10),(6,9)] => 1 [(1,9),(2,7),(3,4),(5,10),(6,8)] => 1 [(1,10),(2,7),(3,4),(5,9),(6,8)] => 1 [(1,10),(2,8),(3,4),(5,9),(6,7)] => 1 [(1,9),(2,8),(3,4),(5,10),(6,7)] => 1 [(1,8),(2,9),(3,4),(5,10),(6,7)] => 1 [(1,7),(2,9),(3,4),(5,10),(6,8)] => 1 [(1,6),(2,9),(3,4),(5,10),(7,8)] => 1 [(1,5),(2,9),(3,4),(6,10),(7,8)] => 1 [(1,4),(2,9),(3,5),(6,10),(7,8)] => 1 [(1,3),(2,9),(4,5),(6,10),(7,8)] => 1 [(1,2),(3,9),(4,5),(6,10),(7,8)] => 1 [(1,2),(3,10),(4,5),(6,9),(7,8)] => 1 [(1,3),(2,10),(4,5),(6,9),(7,8)] => 1 [(1,4),(2,10),(3,5),(6,9),(7,8)] => 1 [(1,5),(2,10),(3,4),(6,9),(7,8)] => 1 [(1,6),(2,10),(3,4),(5,9),(7,8)] => 1 [(1,7),(2,10),(3,4),(5,9),(6,8)] => 1 [(1,8),(2,10),(3,4),(5,9),(6,7)] => 1 [(1,9),(2,10),(3,4),(5,8),(6,7)] => 1 [(1,10),(2,9),(3,4),(5,8),(6,7)] => 1 [(1,10),(2,9),(3,5),(4,8),(6,7)] => 1 [(1,9),(2,10),(3,5),(4,8),(6,7)] => 1 [(1,8),(2,10),(3,5),(4,9),(6,7)] => 1 [(1,7),(2,10),(3,5),(4,9),(6,8)] => 1 [(1,6),(2,10),(3,5),(4,9),(7,8)] => 1 [(1,5),(2,10),(3,6),(4,9),(7,8)] => 1 [(1,4),(2,10),(3,6),(5,9),(7,8)] => 1 [(1,3),(2,10),(4,6),(5,9),(7,8)] => 1 [(1,2),(3,10),(4,6),(5,9),(7,8)] => 1 [(1,2),(3,9),(4,6),(5,10),(7,8)] => 1 [(1,3),(2,9),(4,6),(5,10),(7,8)] => 1 [(1,4),(2,9),(3,6),(5,10),(7,8)] => 1 [(1,5),(2,9),(3,6),(4,10),(7,8)] => 1 [(1,6),(2,9),(3,5),(4,10),(7,8)] => 1 [(1,7),(2,9),(3,5),(4,10),(6,8)] => 1 [(1,8),(2,9),(3,5),(4,10),(6,7)] => 1 [(1,9),(2,8),(3,5),(4,10),(6,7)] => 1 [(1,10),(2,8),(3,5),(4,9),(6,7)] => 1 [(1,10),(2,7),(3,5),(4,9),(6,8)] => 1 [(1,9),(2,7),(3,5),(4,10),(6,8)] => 1 [(1,8),(2,7),(3,5),(4,10),(6,9)] => 1 [(1,7),(2,8),(3,5),(4,10),(6,9)] => 1 [(1,6),(2,8),(3,5),(4,10),(7,9)] => 1 [(1,5),(2,8),(3,6),(4,10),(7,9)] => 1 [(1,4),(2,8),(3,6),(5,10),(7,9)] => 1 [(1,3),(2,8),(4,6),(5,10),(7,9)] => 1 [(1,2),(3,8),(4,6),(5,10),(7,9)] => 1 [(1,2),(3,7),(4,6),(5,10),(8,9)] => 1 [(1,3),(2,7),(4,6),(5,10),(8,9)] => 1 [(1,4),(2,7),(3,6),(5,10),(8,9)] => 1 [(1,5),(2,7),(3,6),(4,10),(8,9)] => 1 [(1,6),(2,7),(3,5),(4,10),(8,9)] => 1 [(1,7),(2,6),(3,5),(4,10),(8,9)] => 1 [(1,8),(2,6),(3,5),(4,10),(7,9)] => 1 [(1,9),(2,6),(3,5),(4,10),(7,8)] => 1 [(1,10),(2,6),(3,5),(4,9),(7,8)] => 1 [(1,10),(2,5),(3,6),(4,9),(7,8)] => 1 [(1,9),(2,5),(3,6),(4,10),(7,8)] => 1 [(1,8),(2,5),(3,6),(4,10),(7,9)] => 1 [(1,7),(2,5),(3,6),(4,10),(8,9)] => 1 [(1,6),(2,5),(3,7),(4,10),(8,9)] => 1 [(1,5),(2,6),(3,7),(4,10),(8,9)] => 1 [(1,4),(2,6),(3,7),(5,10),(8,9)] => 1 [(1,3),(2,6),(4,7),(5,10),(8,9)] => 1 [(1,2),(3,6),(4,7),(5,10),(8,9)] => 1 [(1,2),(3,5),(4,7),(6,10),(8,9)] => 1 [(1,3),(2,5),(4,7),(6,10),(8,9)] => 1 [(1,4),(2,5),(3,7),(6,10),(8,9)] => 1 [(1,5),(2,4),(3,7),(6,10),(8,9)] => 1 [(1,6),(2,4),(3,7),(5,10),(8,9)] => 1 [(1,7),(2,4),(3,6),(5,10),(8,9)] => 1 [(1,8),(2,4),(3,6),(5,10),(7,9)] => 1 [(1,9),(2,4),(3,6),(5,10),(7,8)] => 1 [(1,10),(2,4),(3,6),(5,9),(7,8)] => 1 [(1,10),(2,3),(4,6),(5,9),(7,8)] => 1 [(1,9),(2,3),(4,6),(5,10),(7,8)] => 1 [(1,8),(2,3),(4,6),(5,10),(7,9)] => 1 [(1,7),(2,3),(4,6),(5,10),(8,9)] => 1 [(1,6),(2,3),(4,7),(5,10),(8,9)] => 1 [(1,5),(2,3),(4,7),(6,10),(8,9)] => 1 [(1,4),(2,3),(5,7),(6,10),(8,9)] => 1 [(1,3),(2,4),(5,7),(6,10),(8,9)] => 1 [(1,2),(3,4),(5,7),(6,10),(8,9)] => 1 [(1,2),(3,4),(5,8),(6,10),(7,9)] => 1 [(1,3),(2,4),(5,8),(6,10),(7,9)] => 1 [(1,4),(2,3),(5,8),(6,10),(7,9)] => 1 [(1,5),(2,3),(4,8),(6,10),(7,9)] => 1 [(1,6),(2,3),(4,8),(5,10),(7,9)] => 1 [(1,7),(2,3),(4,8),(5,10),(6,9)] => 1 [(1,8),(2,3),(4,7),(5,10),(6,9)] => 1 [(1,9),(2,3),(4,7),(5,10),(6,8)] => 1 [(1,10),(2,3),(4,7),(5,9),(6,8)] => 1 [(1,10),(2,4),(3,7),(5,9),(6,8)] => 1 [(1,9),(2,4),(3,7),(5,10),(6,8)] => 1 [(1,8),(2,4),(3,7),(5,10),(6,9)] => 1 [(1,7),(2,4),(3,8),(5,10),(6,9)] => 1 [(1,6),(2,4),(3,8),(5,10),(7,9)] => 1 [(1,5),(2,4),(3,8),(6,10),(7,9)] => 1 [(1,4),(2,5),(3,8),(6,10),(7,9)] => 1 [(1,3),(2,5),(4,8),(6,10),(7,9)] => 1 [(1,2),(3,5),(4,8),(6,10),(7,9)] => 1 [(1,2),(3,6),(4,8),(5,10),(7,9)] => 1 [(1,3),(2,6),(4,8),(5,10),(7,9)] => 1 [(1,4),(2,6),(3,8),(5,10),(7,9)] => 1 [(1,5),(2,6),(3,8),(4,10),(7,9)] => 1 [(1,6),(2,5),(3,8),(4,10),(7,9)] => 1 [(1,7),(2,5),(3,8),(4,10),(6,9)] => 1 [(1,8),(2,5),(3,7),(4,10),(6,9)] => 1 [(1,9),(2,5),(3,7),(4,10),(6,8)] => 1 [(1,10),(2,5),(3,7),(4,9),(6,8)] => 1 [(1,10),(2,6),(3,7),(4,9),(5,8)] => 1 [(1,9),(2,6),(3,7),(4,10),(5,8)] => 1 [(1,8),(2,6),(3,7),(4,10),(5,9)] => 1 [(1,7),(2,6),(3,8),(4,10),(5,9)] => 1 [(1,6),(2,7),(3,8),(4,10),(5,9)] => 1 [(1,5),(2,7),(3,8),(4,10),(6,9)] => 1 [(1,4),(2,7),(3,8),(5,10),(6,9)] => 1 [(1,3),(2,7),(4,8),(5,10),(6,9)] => 1 [(1,2),(3,7),(4,8),(5,10),(6,9)] => 1 [(1,2),(3,8),(4,7),(5,10),(6,9)] => 1 [(1,3),(2,8),(4,7),(5,10),(6,9)] => 1 [(1,4),(2,8),(3,7),(5,10),(6,9)] => 1 [(1,5),(2,8),(3,7),(4,10),(6,9)] => 1 [(1,6),(2,8),(3,7),(4,10),(5,9)] => 1 [(1,7),(2,8),(3,6),(4,10),(5,9)] => 1 [(1,8),(2,7),(3,6),(4,10),(5,9)] => 1 [(1,9),(2,7),(3,6),(4,10),(5,8)] => 1 [(1,10),(2,7),(3,6),(4,9),(5,8)] => 1 [(1,10),(2,8),(3,6),(4,9),(5,7)] => 1 [(1,9),(2,8),(3,6),(4,10),(5,7)] => 1 [(1,8),(2,9),(3,6),(4,10),(5,7)] => 1 [(1,7),(2,9),(3,6),(4,10),(5,8)] => 1 [(1,6),(2,9),(3,7),(4,10),(5,8)] => 1 [(1,5),(2,9),(3,7),(4,10),(6,8)] => 1 [(1,4),(2,9),(3,7),(5,10),(6,8)] => 1 [(1,3),(2,9),(4,7),(5,10),(6,8)] => 1 [(1,2),(3,9),(4,7),(5,10),(6,8)] => 1 [(1,2),(3,10),(4,7),(5,9),(6,8)] => 1 [(1,3),(2,10),(4,7),(5,9),(6,8)] => 1 [(1,4),(2,10),(3,7),(5,9),(6,8)] => 1 [(1,5),(2,10),(3,7),(4,9),(6,8)] => 1 [(1,6),(2,10),(3,7),(4,9),(5,8)] => 1 [(1,7),(2,10),(3,6),(4,9),(5,8)] => 1 [(1,8),(2,10),(3,6),(4,9),(5,7)] => 1 [(1,9),(2,10),(3,6),(4,8),(5,7)] => 1 [(1,10),(2,9),(3,6),(4,8),(5,7)] => 1 [(1,10),(2,9),(3,7),(4,8),(5,6)] => 1 [(1,9),(2,10),(3,7),(4,8),(5,6)] => 1 [(1,8),(2,10),(3,7),(4,9),(5,6)] => 1 [(1,7),(2,10),(3,8),(4,9),(5,6)] => 1 [(1,6),(2,10),(3,8),(4,9),(5,7)] => 1 [(1,5),(2,10),(3,8),(4,9),(6,7)] => 1 [(1,4),(2,10),(3,8),(5,9),(6,7)] => 1 [(1,3),(2,10),(4,8),(5,9),(6,7)] => 1 [(1,2),(3,10),(4,8),(5,9),(6,7)] => 1 [(1,2),(3,9),(4,8),(5,10),(6,7)] => 1 [(1,3),(2,9),(4,8),(5,10),(6,7)] => 1 [(1,4),(2,9),(3,8),(5,10),(6,7)] => 1 [(1,5),(2,9),(3,8),(4,10),(6,7)] => 1 [(1,6),(2,9),(3,8),(4,10),(5,7)] => 1 [(1,7),(2,9),(3,8),(4,10),(5,6)] => 1 [(1,8),(2,9),(3,7),(4,10),(5,6)] => 1 [(1,9),(2,8),(3,7),(4,10),(5,6)] => 1 [(1,10),(2,8),(3,7),(4,9),(5,6)] => 1 [(1,10),(2,7),(3,8),(4,9),(5,6)] => 1 [(1,9),(2,7),(3,8),(4,10),(5,6)] => 1 [(1,8),(2,7),(3,9),(4,10),(5,6)] => 1 [(1,7),(2,8),(3,9),(4,10),(5,6)] => 1 [(1,6),(2,8),(3,9),(4,10),(5,7)] => 1 [(1,5),(2,8),(3,9),(4,10),(6,7)] => 1 [(1,4),(2,8),(3,9),(5,10),(6,7)] => 1 [(1,3),(2,8),(4,9),(5,10),(6,7)] => 1 [(1,2),(3,8),(4,9),(5,10),(6,7)] => 1 [(1,2),(3,7),(4,9),(5,10),(6,8)] => 1 [(1,3),(2,7),(4,9),(5,10),(6,8)] => 1 [(1,4),(2,7),(3,9),(5,10),(6,8)] => 1 [(1,5),(2,7),(3,9),(4,10),(6,8)] => 1 [(1,6),(2,7),(3,9),(4,10),(5,8)] => 1 [(1,7),(2,6),(3,9),(4,10),(5,8)] => 1 [(1,8),(2,6),(3,9),(4,10),(5,7)] => 1 [(1,9),(2,6),(3,8),(4,10),(5,7)] => 1 [(1,10),(2,6),(3,8),(4,9),(5,7)] => 1 [(1,10),(2,5),(3,8),(4,9),(6,7)] => 1 [(1,9),(2,5),(3,8),(4,10),(6,7)] => 1 [(1,8),(2,5),(3,9),(4,10),(6,7)] => 1 [(1,7),(2,5),(3,9),(4,10),(6,8)] => 1 [(1,6),(2,5),(3,9),(4,10),(7,8)] => 1 [(1,5),(2,6),(3,9),(4,10),(7,8)] => 1 [(1,4),(2,6),(3,9),(5,10),(7,8)] => 1 [(1,3),(2,6),(4,9),(5,10),(7,8)] => 1 [(1,2),(3,6),(4,9),(5,10),(7,8)] => 1 [(1,2),(3,5),(4,9),(6,10),(7,8)] => 1 [(1,3),(2,5),(4,9),(6,10),(7,8)] => 1 [(1,4),(2,5),(3,9),(6,10),(7,8)] => 1 [(1,5),(2,4),(3,9),(6,10),(7,8)] => 1 [(1,6),(2,4),(3,9),(5,10),(7,8)] => 1 [(1,7),(2,4),(3,9),(5,10),(6,8)] => 1 [(1,8),(2,4),(3,9),(5,10),(6,7)] => 1 [(1,9),(2,4),(3,8),(5,10),(6,7)] => 1 [(1,10),(2,4),(3,8),(5,9),(6,7)] => 1 [(1,10),(2,3),(4,8),(5,9),(6,7)] => 1 [(1,9),(2,3),(4,8),(5,10),(6,7)] => 1 [(1,8),(2,3),(4,9),(5,10),(6,7)] => 1 [(1,7),(2,3),(4,9),(5,10),(6,8)] => 1 [(1,6),(2,3),(4,9),(5,10),(7,8)] => 1 [(1,5),(2,3),(4,9),(6,10),(7,8)] => 1 [(1,4),(2,3),(5,9),(6,10),(7,8)] => 1 [(1,3),(2,4),(5,9),(6,10),(7,8)] => 1 [(1,2),(3,4),(5,9),(6,10),(7,8)] => 1 [(1,2),(3,4),(5,10),(6,9),(7,8)] => 1 [(1,3),(2,4),(5,10),(6,9),(7,8)] => 1 [(1,4),(2,3),(5,10),(6,9),(7,8)] => 1 [(1,5),(2,3),(4,10),(6,9),(7,8)] => 1 [(1,6),(2,3),(4,10),(5,9),(7,8)] => 1 [(1,7),(2,3),(4,10),(5,9),(6,8)] => 1 [(1,8),(2,3),(4,10),(5,9),(6,7)] => 1 [(1,9),(2,3),(4,10),(5,8),(6,7)] => 1 [(1,10),(2,3),(4,9),(5,8),(6,7)] => 1 [(1,10),(2,4),(3,9),(5,8),(6,7)] => 1 [(1,9),(2,4),(3,10),(5,8),(6,7)] => 1 [(1,8),(2,4),(3,10),(5,9),(6,7)] => 1 [(1,7),(2,4),(3,10),(5,9),(6,8)] => 1 [(1,6),(2,4),(3,10),(5,9),(7,8)] => 1 [(1,5),(2,4),(3,10),(6,9),(7,8)] => 1 [(1,4),(2,5),(3,10),(6,9),(7,8)] => 1 [(1,3),(2,5),(4,10),(6,9),(7,8)] => 1 [(1,2),(3,5),(4,10),(6,9),(7,8)] => 1 [(1,2),(3,6),(4,10),(5,9),(7,8)] => 1 [(1,3),(2,6),(4,10),(5,9),(7,8)] => 1 [(1,4),(2,6),(3,10),(5,9),(7,8)] => 1 [(1,5),(2,6),(3,10),(4,9),(7,8)] => 1 [(1,6),(2,5),(3,10),(4,9),(7,8)] => 1 [(1,7),(2,5),(3,10),(4,9),(6,8)] => 1 [(1,8),(2,5),(3,10),(4,9),(6,7)] => 1 [(1,9),(2,5),(3,10),(4,8),(6,7)] => 1 [(1,10),(2,5),(3,9),(4,8),(6,7)] => 1 [(1,10),(2,6),(3,9),(4,8),(5,7)] => 1 [(1,9),(2,6),(3,10),(4,8),(5,7)] => 1 [(1,8),(2,6),(3,10),(4,9),(5,7)] => 1 [(1,7),(2,6),(3,10),(4,9),(5,8)] => 1 [(1,6),(2,7),(3,10),(4,9),(5,8)] => 1 [(1,5),(2,7),(3,10),(4,9),(6,8)] => 1 [(1,4),(2,7),(3,10),(5,9),(6,8)] => 1 [(1,3),(2,7),(4,10),(5,9),(6,8)] => 1 [(1,2),(3,7),(4,10),(5,9),(6,8)] => 1 [(1,2),(3,8),(4,10),(5,9),(6,7)] => 1 [(1,3),(2,8),(4,10),(5,9),(6,7)] => 1 [(1,4),(2,8),(3,10),(5,9),(6,7)] => 1 [(1,5),(2,8),(3,10),(4,9),(6,7)] => 1 [(1,6),(2,8),(3,10),(4,9),(5,7)] => 1 [(1,7),(2,8),(3,10),(4,9),(5,6)] => 1 [(1,8),(2,7),(3,10),(4,9),(5,6)] => 1 [(1,9),(2,7),(3,10),(4,8),(5,6)] => 1 [(1,10),(2,7),(3,9),(4,8),(5,6)] => 1 [(1,10),(2,8),(3,9),(4,7),(5,6)] => 1 [(1,9),(2,8),(3,10),(4,7),(5,6)] => 1 [(1,8),(2,9),(3,10),(4,7),(5,6)] => 1 [(1,7),(2,9),(3,10),(4,8),(5,6)] => 1 [(1,6),(2,9),(3,10),(4,8),(5,7)] => 1 [(1,5),(2,9),(3,10),(4,8),(6,7)] => 1 [(1,4),(2,9),(3,10),(5,8),(6,7)] => 1 [(1,3),(2,9),(4,10),(5,8),(6,7)] => 1 [(1,2),(3,9),(4,10),(5,8),(6,7)] => 1 [(1,2),(3,10),(4,9),(5,8),(6,7)] => 1 [(1,3),(2,10),(4,9),(5,8),(6,7)] => 1 [(1,4),(2,10),(3,9),(5,8),(6,7)] => 1 [(1,5),(2,10),(3,9),(4,8),(6,7)] => 1 [(1,6),(2,10),(3,9),(4,8),(5,7)] => 1 [(1,7),(2,10),(3,9),(4,8),(5,6)] => 1 [(1,8),(2,10),(3,9),(4,7),(5,6)] => 1 [(1,9),(2,10),(3,8),(4,7),(5,6)] => 1 [(1,10),(2,9),(3,8),(4,7),(5,6)] => 1 [(1,2),(3,4),(5,8),(6,7),(9,10),(11,12)] => 2 [(1,2),(3,4),(5,8),(6,7),(9,12),(10,11)] => 2 [(1,2),(3,4),(5,10),(6,7),(8,9),(11,12)] => 2 [(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)] => 1 [(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)] => 1 [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)] => 2 [(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)] => 2 [(1,2),(3,4),(5,10),(6,9),(7,8),(11,12)] => 2 [(1,2),(3,4),(5,12),(6,9),(7,8),(10,11)] => 1 [(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)] => 1 [(1,2),(3,4),(5,6),(7,10),(8,9),(11,12)] => 2 [(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)] => 1 [(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)] => 1 [(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)] => 1 [(1,2),(3,4),(5,6),(7,8),(9,11),(10,12)] => 2 [(1,2),(3,4),(5,6),(7,9),(8,10),(11,12)] => 2 [(1,2),(3,4),(5,6),(7,9),(8,11),(10,12)] => 2 [(1,2),(3,4),(5,6),(7,10),(8,11),(9,12)] => 2 [(1,2),(3,4),(5,7),(6,8),(9,10),(11,12)] => 2 [(1,2),(3,4),(5,7),(6,8),(9,11),(10,12)] => 2 [(1,2),(3,4),(5,7),(6,9),(8,10),(11,12)] => 2 [(1,2),(3,4),(5,7),(6,9),(8,11),(10,12)] => 2 [(1,2),(3,4),(5,7),(6,10),(8,11),(9,12)] => 2 [(1,2),(3,4),(5,8),(6,9),(7,10),(11,12)] => 2 [(1,2),(3,4),(5,8),(6,9),(7,11),(10,12)] => 2 [(1,2),(3,4),(5,8),(6,10),(7,11),(9,12)] => 2 [(1,2),(3,4),(5,9),(6,10),(7,11),(8,12)] => 2 [(1,2),(3,5),(4,6),(7,8),(9,10),(11,12)] => 2 [(1,2),(3,5),(4,6),(7,8),(9,11),(10,12)] => 2 [(1,2),(3,5),(4,6),(7,9),(8,10),(11,12)] => 2 [(1,2),(3,5),(4,6),(7,9),(8,11),(10,12)] => 2 [(1,2),(3,5),(4,6),(7,10),(8,11),(9,12)] => 2 [(1,2),(3,5),(4,7),(6,8),(9,10),(11,12)] => 2 [(1,2),(3,5),(4,7),(6,8),(9,11),(10,12)] => 2 [(1,2),(3,5),(4,7),(6,9),(8,10),(11,12)] => 2 [(1,2),(3,5),(4,7),(6,9),(8,11),(10,12)] => 2 [(1,2),(3,5),(4,7),(6,10),(8,11),(9,12)] => 2 [(1,2),(3,4),(5,6),(7,9),(8,12),(10,11)] => 2 [(1,2),(3,4),(5,6),(7,10),(8,12),(9,11)] => 2 [(1,2),(3,4),(5,6),(7,11),(8,9),(10,12)] => 2 [(1,2),(3,4),(5,6),(7,11),(8,10),(9,12)] => 2 [(1,2),(3,4),(5,6),(7,11),(8,12),(9,10)] => 2 [(1,2),(3,4),(5,6),(7,12),(8,10),(9,11)] => 1 [(1,2),(3,4),(5,7),(6,8),(9,12),(10,11)] => 2 [(1,2),(3,4),(5,7),(6,9),(8,12),(10,11)] => 2 [(1,2),(3,4),(5,7),(6,10),(8,9),(11,12)] => 2 [(1,2),(3,4),(5,7),(6,10),(8,12),(9,11)] => 2 [(1,2),(3,4),(5,7),(6,11),(8,9),(10,12)] => 2 [(1,2),(3,4),(5,7),(6,11),(8,10),(9,12)] => 2 [(1,2),(3,4),(5,7),(6,11),(8,12),(9,10)] => 2 [(1,2),(3,4),(5,7),(6,12),(8,9),(10,11)] => 1 [(1,2),(3,4),(5,7),(6,12),(8,10),(9,11)] => 1 [(1,2),(3,4),(5,7),(6,12),(8,11),(9,10)] => 1 [(1,2),(3,4),(5,8),(6,7),(9,11),(10,12)] => 2 [(1,2),(3,4),(5,8),(6,9),(7,12),(10,11)] => 1 [(1,2),(3,4),(5,8),(6,10),(7,12),(9,11)] => 1 [(1,2),(3,4),(5,8),(6,10),(7,9),(11,12)] => 2 [(1,2),(3,4),(5,8),(6,11),(7,12),(9,10)] => 1 [(1,2),(3,4),(5,8),(6,11),(7,10),(9,12)] => 2 [(1,2),(3,4),(5,8),(6,11),(7,9),(10,12)] => 2 [(1,2),(3,4),(5,8),(6,12),(7,11),(9,10)] => 1 [(1,2),(3,4),(5,8),(6,12),(7,10),(9,11)] => 1 [(1,2),(3,4),(5,8),(6,12),(7,9),(10,11)] => 1 [(1,2),(3,4),(5,9),(6,7),(8,10),(11,12)] => 2 [(1,2),(3,4),(5,9),(6,7),(8,11),(10,12)] => 2 [(1,2),(3,4),(5,9),(6,7),(8,12),(10,11)] => 2 [(1,2),(3,4),(5,9),(6,8),(7,12),(10,11)] => 1 [(1,2),(3,4),(5,9),(6,8),(7,11),(10,12)] => 2 [(1,2),(3,4),(5,9),(6,8),(7,10),(11,12)] => 2 [(1,2),(3,4),(5,9),(6,10),(7,12),(8,11)] => 1 [(1,2),(3,4),(5,9),(6,10),(7,8),(11,12)] => 2 [(1,2),(3,4),(5,9),(6,11),(7,12),(8,10)] => 1 [(1,2),(3,4),(5,9),(6,11),(7,10),(8,12)] => 2 [(1,2),(3,4),(5,9),(6,11),(7,8),(10,12)] => 2 [(1,2),(3,4),(5,9),(6,12),(7,11),(8,10)] => 1 [(1,2),(3,4),(5,9),(6,12),(7,10),(8,11)] => 1 [(1,2),(3,4),(5,9),(6,12),(7,8),(10,11)] => 1 [(1,2),(3,4),(5,10),(6,7),(8,11),(9,12)] => 2 [(1,2),(3,4),(5,10),(6,7),(8,12),(9,11)] => 2 [(1,2),(3,4),(5,10),(6,8),(7,12),(9,11)] => 1 [(1,2),(3,4),(5,10),(6,8),(7,11),(9,12)] => 2 [(1,2),(3,4),(5,10),(6,8),(7,9),(11,12)] => 2 [(1,2),(3,4),(5,10),(6,9),(7,12),(8,11)] => 1 [(1,2),(3,4),(5,10),(6,9),(7,11),(8,12)] => 2 [(1,2),(3,4),(5,10),(6,11),(7,12),(8,9)] => 1 [(1,2),(3,4),(5,10),(6,11),(7,9),(8,12)] => 2 [(1,2),(3,4),(5,10),(6,11),(7,8),(9,12)] => 2 [(1,2),(3,4),(5,10),(6,12),(7,11),(8,9)] => 1 [(1,2),(3,4),(5,10),(6,12),(7,9),(8,11)] => 1 [(1,2),(3,4),(5,10),(6,12),(7,8),(9,11)] => 1 [(1,2),(3,4),(5,11),(6,7),(8,9),(10,12)] => 2 [(1,2),(3,4),(5,11),(6,7),(8,10),(9,12)] => 2 [(1,2),(3,4),(5,11),(6,7),(8,12),(9,10)] => 2 [(1,2),(3,4),(5,11),(6,8),(7,12),(9,10)] => 1 [(1,2),(3,4),(5,11),(6,8),(7,10),(9,12)] => 2 [(1,2),(3,4),(5,11),(6,8),(7,9),(10,12)] => 2 [(1,2),(3,4),(5,11),(6,9),(7,12),(8,10)] => 1 [(1,2),(3,4),(5,11),(6,9),(7,10),(8,12)] => 2 [(1,2),(3,4),(5,11),(6,9),(7,8),(10,12)] => 2 [(1,2),(3,4),(5,11),(6,10),(7,12),(8,9)] => 1 [(1,2),(3,4),(5,11),(6,10),(7,9),(8,12)] => 2 [(1,2),(3,4),(5,11),(6,10),(7,8),(9,12)] => 2 [(1,2),(3,4),(5,11),(6,12),(7,10),(8,9)] => 1 [(1,2),(3,4),(5,11),(6,12),(7,9),(8,10)] => 1 [(1,2),(3,4),(5,11),(6,12),(7,8),(9,10)] => 1 [(1,2),(3,4),(5,12),(6,7),(8,10),(9,11)] => 1 [(1,2),(3,4),(5,12),(6,8),(7,11),(9,10)] => 1 [(1,2),(3,4),(5,12),(6,8),(7,10),(9,11)] => 1 [(1,2),(3,4),(5,12),(6,8),(7,9),(10,11)] => 1 [(1,2),(3,4),(5,12),(6,9),(7,11),(8,10)] => 1 [(1,2),(3,4),(5,12),(6,9),(7,10),(8,11)] => 1 [(1,2),(3,4),(5,12),(6,10),(7,11),(8,9)] => 1 [(1,2),(3,4),(5,12),(6,10),(7,9),(8,11)] => 1 [(1,2),(3,4),(5,12),(6,10),(7,8),(9,11)] => 1 [(1,2),(3,4),(5,12),(6,11),(7,9),(8,10)] => 1 [(1,2),(3,5),(4,6),(7,8),(9,12),(10,11)] => 2 [(1,2),(3,5),(4,6),(7,9),(8,12),(10,11)] => 2 [(1,2),(3,5),(4,6),(7,10),(8,9),(11,12)] => 2 [(1,2),(3,5),(4,6),(7,10),(8,12),(9,11)] => 2 [(1,2),(3,5),(4,6),(7,11),(8,9),(10,12)] => 2 [(1,2),(3,5),(4,6),(7,11),(8,10),(9,12)] => 2 [(1,2),(3,5),(4,6),(7,11),(8,12),(9,10)] => 2 [(1,2),(3,5),(4,6),(7,12),(8,9),(10,11)] => 1 [(1,2),(3,5),(4,6),(7,12),(8,10),(9,11)] => 1 [(1,2),(3,5),(4,6),(7,12),(8,11),(9,10)] => 1 [(1,2),(3,5),(4,7),(6,8),(9,12),(10,11)] => 2 [(1,2),(3,5),(4,7),(6,9),(8,12),(10,11)] => 2 [(1,2),(3,5),(4,7),(6,10),(8,9),(11,12)] => 2 [(1,2),(3,5),(4,7),(6,10),(8,12),(9,11)] => 2 [(1,2),(3,5),(4,7),(6,11),(8,9),(10,12)] => 2 [(1,2),(3,5),(4,7),(6,11),(8,10),(9,12)] => 2 ----------------------------------------------------------------------------- Created: Nov 08, 2017 at 21:41 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Nov 12, 2017 at 17:25 by Martin Rubey