***************************************************************************** * 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: St000254 ----------------------------------------------------------------------------- Collection: Set partitions ----------------------------------------------------------------------------- Description: The nesting number of a set partition. This is the maximal number of chords in the standard representation of a set partition that mutually nest. ----------------------------------------------------------------------------- References: [1] Chen, W. Y. C., Deng, E. Y. P., Du, R. R. X., Stanley, R. P., Yan, C. H. Crossings and nestings of matchings and partitions [[MathSciNet:2272140]] [[arXiv:math/0501230]] ----------------------------------------------------------------------------- Code: def statistic(pi): return max([0] + [p[0] for p in to_vacillating(pi) if p != []]) def to_vacillating(pi): """Return the vacillating tableau associated to the set partition pi. INPUT: - pi, a set partition OUTPUT: - a vacillating tableau. EXAMPLES: sage: pi = SetPartition([[1,4,5,7], [2,6],[3]]) sage: to_vacillating(pi) [[], [], [1], [1], [1, 1], [1, 1], [1, 1], [1], [2], [1], [1, 1], [1], [1], [], []] """ T = [StandardTableau([])] perm = pi.to_permutation() mrep = perm.inverse() for j in range(pi.size(), 0, -1): prev = mrep(j) next = perm(j) if j == next: # singleton block T += [T[-1], T[-1]] elif next < j: # maximal element of a non-singleton block # do nothing, then insert prev T += [T[-1], T[-1].schensted_insert(prev)] elif prev > j: # minimal element of a non-singleton block # delete j then do nothing if max(T[-1].entries()) == j: new = T[-1].restrict(j-1) T += [new, new] else: print("ERROR") else: # transient # delete j then insert prev new = T[-1].restrict(j-1) T += [new, new.schensted_insert(prev)] return [t.shape() for t in T[::-1]] ----------------------------------------------------------------------------- Statistic values: {{1,2}} => 1 {{1},{2}} => 0 {{1,2,3}} => 1 {{1,2},{3}} => 1 {{1,3},{2}} => 1 {{1},{2,3}} => 1 {{1},{2},{3}} => 0 {{1,2,3,4}} => 1 {{1,2,3},{4}} => 1 {{1,2,4},{3}} => 1 {{1,2},{3,4}} => 1 {{1,2},{3},{4}} => 1 {{1,3,4},{2}} => 1 {{1,3},{2,4}} => 1 {{1,3},{2},{4}} => 1 {{1,4},{2,3}} => 2 {{1},{2,3,4}} => 1 {{1},{2,3},{4}} => 1 {{1,4},{2},{3}} => 1 {{1},{2,4},{3}} => 1 {{1},{2},{3,4}} => 1 {{1},{2},{3},{4}} => 0 {{1,2,3,4,5}} => 1 {{1,2,3,4},{5}} => 1 {{1,2,3,5},{4}} => 1 {{1,2,3},{4,5}} => 1 {{1,2,3},{4},{5}} => 1 {{1,2,4,5},{3}} => 1 {{1,2,4},{3,5}} => 1 {{1,2,4},{3},{5}} => 1 {{1,2,5},{3,4}} => 2 {{1,2},{3,4,5}} => 1 {{1,2},{3,4},{5}} => 1 {{1,2,5},{3},{4}} => 1 {{1,2},{3,5},{4}} => 1 {{1,2},{3},{4,5}} => 1 {{1,2},{3},{4},{5}} => 1 {{1,3,4,5},{2}} => 1 {{1,3,4},{2,5}} => 2 {{1,3,4},{2},{5}} => 1 {{1,3,5},{2,4}} => 1 {{1,3},{2,4,5}} => 1 {{1,3},{2,4},{5}} => 1 {{1,3,5},{2},{4}} => 1 {{1,3},{2,5},{4}} => 1 {{1,3},{2},{4,5}} => 1 {{1,3},{2},{4},{5}} => 1 {{1,4,5},{2,3}} => 2 {{1,4},{2,3,5}} => 2 {{1,4},{2,3},{5}} => 2 {{1,5},{2,3,4}} => 2 {{1},{2,3,4,5}} => 1 {{1},{2,3,4},{5}} => 1 {{1,5},{2,3},{4}} => 2 {{1},{2,3,5},{4}} => 1 {{1},{2,3},{4,5}} => 1 {{1},{2,3},{4},{5}} => 1 {{1,4,5},{2},{3}} => 1 {{1,4},{2,5},{3}} => 1 {{1,4},{2},{3,5}} => 1 {{1,4},{2},{3},{5}} => 1 {{1,5},{2,4},{3}} => 2 {{1},{2,4,5},{3}} => 1 {{1},{2,4},{3,5}} => 1 {{1},{2,4},{3},{5}} => 1 {{1,5},{2},{3,4}} => 2 {{1},{2,5},{3,4}} => 2 {{1},{2},{3,4,5}} => 1 {{1},{2},{3,4},{5}} => 1 {{1,5},{2},{3},{4}} => 1 {{1},{2,5},{3},{4}} => 1 {{1},{2},{3,5},{4}} => 1 {{1},{2},{3},{4,5}} => 1 {{1},{2},{3},{4},{5}} => 0 {{1,2,3,4,5,6}} => 1 {{1,2,3,4,5},{6}} => 1 {{1,2,3,4,6},{5}} => 1 {{1,2,3,4},{5,6}} => 1 {{1,2,3,4},{5},{6}} => 1 {{1,2,3,5,6},{4}} => 1 {{1,2,3,5},{4,6}} => 1 {{1,2,3,5},{4},{6}} => 1 {{1,2,3,6},{4,5}} => 2 {{1,2,3},{4,5,6}} => 1 {{1,2,3},{4,5},{6}} => 1 {{1,2,3,6},{4},{5}} => 1 {{1,2,3},{4,6},{5}} => 1 {{1,2,3},{4},{5,6}} => 1 {{1,2,3},{4},{5},{6}} => 1 {{1,2,4,5,6},{3}} => 1 {{1,2,4,5},{3,6}} => 2 {{1,2,4,5},{3},{6}} => 1 {{1,2,4,6},{3,5}} => 1 {{1,2,4},{3,5,6}} => 1 {{1,2,4},{3,5},{6}} => 1 {{1,2,4,6},{3},{5}} => 1 {{1,2,4},{3,6},{5}} => 1 {{1,2,4},{3},{5,6}} => 1 {{1,2,4},{3},{5},{6}} => 1 {{1,2,5,6},{3,4}} => 2 {{1,2,5},{3,4,6}} => 2 {{1,2,5},{3,4},{6}} => 2 {{1,2,6},{3,4,5}} => 2 {{1,2},{3,4,5,6}} => 1 {{1,2},{3,4,5},{6}} => 1 {{1,2,6},{3,4},{5}} => 2 {{1,2},{3,4,6},{5}} => 1 {{1,2},{3,4},{5,6}} => 1 {{1,2},{3,4},{5},{6}} => 1 {{1,2,5,6},{3},{4}} => 1 {{1,2,5},{3,6},{4}} => 1 {{1,2,5},{3},{4,6}} => 1 {{1,2,5},{3},{4},{6}} => 1 {{1,2,6},{3,5},{4}} => 2 {{1,2},{3,5,6},{4}} => 1 {{1,2},{3,5},{4,6}} => 1 {{1,2},{3,5},{4},{6}} => 1 {{1,2,6},{3},{4,5}} => 2 {{1,2},{3,6},{4,5}} => 2 {{1,2},{3},{4,5,6}} => 1 {{1,2},{3},{4,5},{6}} => 1 {{1,2,6},{3},{4},{5}} => 1 {{1,2},{3,6},{4},{5}} => 1 {{1,2},{3},{4,6},{5}} => 1 {{1,2},{3},{4},{5,6}} => 1 {{1,2},{3},{4},{5},{6}} => 1 {{1,3,4,5,6},{2}} => 1 {{1,3,4,5},{2,6}} => 2 {{1,3,4,5},{2},{6}} => 1 {{1,3,4,6},{2,5}} => 2 {{1,3,4},{2,5,6}} => 2 {{1,3,4},{2,5},{6}} => 2 {{1,3,4,6},{2},{5}} => 1 {{1,3,4},{2,6},{5}} => 2 {{1,3,4},{2},{5,6}} => 1 {{1,3,4},{2},{5},{6}} => 1 {{1,3,5,6},{2,4}} => 1 {{1,3,5},{2,4,6}} => 1 {{1,3,5},{2,4},{6}} => 1 {{1,3,6},{2,4,5}} => 2 {{1,3},{2,4,5,6}} => 1 {{1,3},{2,4,5},{6}} => 1 {{1,3,6},{2,4},{5}} => 1 {{1,3},{2,4,6},{5}} => 1 {{1,3},{2,4},{5,6}} => 1 {{1,3},{2,4},{5},{6}} => 1 {{1,3,5,6},{2},{4}} => 1 {{1,3,5},{2,6},{4}} => 2 {{1,3,5},{2},{4,6}} => 1 {{1,3,5},{2},{4},{6}} => 1 {{1,3,6},{2,5},{4}} => 1 {{1,3},{2,5,6},{4}} => 1 {{1,3},{2,5},{4,6}} => 1 {{1,3},{2,5},{4},{6}} => 1 {{1,3,6},{2},{4,5}} => 2 {{1,3},{2,6},{4,5}} => 2 {{1,3},{2},{4,5,6}} => 1 {{1,3},{2},{4,5},{6}} => 1 {{1,3,6},{2},{4},{5}} => 1 {{1,3},{2,6},{4},{5}} => 1 {{1,3},{2},{4,6},{5}} => 1 {{1,3},{2},{4},{5,6}} => 1 {{1,3},{2},{4},{5},{6}} => 1 {{1,4,5,6},{2,3}} => 2 {{1,4,5},{2,3,6}} => 2 {{1,4,5},{2,3},{6}} => 2 {{1,4,6},{2,3,5}} => 2 {{1,4},{2,3,5,6}} => 2 {{1,4},{2,3,5},{6}} => 2 {{1,4,6},{2,3},{5}} => 2 {{1,4},{2,3,6},{5}} => 2 {{1,4},{2,3},{5,6}} => 2 {{1,4},{2,3},{5},{6}} => 2 {{1,5,6},{2,3,4}} => 2 {{1,5},{2,3,4,6}} => 2 {{1,5},{2,3,4},{6}} => 2 {{1,6},{2,3,4,5}} => 2 {{1},{2,3,4,5,6}} => 1 {{1},{2,3,4,5},{6}} => 1 {{1,6},{2,3,4},{5}} => 2 {{1},{2,3,4,6},{5}} => 1 {{1},{2,3,4},{5,6}} => 1 {{1},{2,3,4},{5},{6}} => 1 {{1,5,6},{2,3},{4}} => 2 {{1,5},{2,3,6},{4}} => 2 {{1,5},{2,3},{4,6}} => 2 {{1,5},{2,3},{4},{6}} => 2 {{1,6},{2,3,5},{4}} => 2 {{1},{2,3,5,6},{4}} => 1 {{1},{2,3,5},{4,6}} => 1 {{1},{2,3,5},{4},{6}} => 1 {{1,6},{2,3},{4,5}} => 2 {{1},{2,3,6},{4,5}} => 2 {{1},{2,3},{4,5,6}} => 1 {{1},{2,3},{4,5},{6}} => 1 {{1,6},{2,3},{4},{5}} => 2 {{1},{2,3,6},{4},{5}} => 1 {{1},{2,3},{4,6},{5}} => 1 {{1},{2,3},{4},{5,6}} => 1 {{1},{2,3},{4},{5},{6}} => 1 {{1,4,5,6},{2},{3}} => 1 {{1,4,5},{2,6},{3}} => 2 {{1,4,5},{2},{3,6}} => 2 {{1,4,5},{2},{3},{6}} => 1 {{1,4,6},{2,5},{3}} => 1 {{1,4},{2,5,6},{3}} => 1 {{1,4},{2,5},{3,6}} => 1 {{1,4},{2,5},{3},{6}} => 1 {{1,4,6},{2},{3,5}} => 1 {{1,4},{2,6},{3,5}} => 2 {{1,4},{2},{3,5,6}} => 1 {{1,4},{2},{3,5},{6}} => 1 {{1,4,6},{2},{3},{5}} => 1 {{1,4},{2,6},{3},{5}} => 1 {{1,4},{2},{3,6},{5}} => 1 {{1,4},{2},{3},{5,6}} => 1 {{1,4},{2},{3},{5},{6}} => 1 {{1,5,6},{2,4},{3}} => 2 {{1,5},{2,4,6},{3}} => 2 {{1,5},{2,4},{3,6}} => 2 {{1,5},{2,4},{3},{6}} => 2 {{1,6},{2,4,5},{3}} => 2 {{1},{2,4,5,6},{3}} => 1 {{1},{2,4,5},{3,6}} => 2 {{1},{2,4,5},{3},{6}} => 1 {{1,6},{2,4},{3,5}} => 2 {{1},{2,4,6},{3,5}} => 1 {{1},{2,4},{3,5,6}} => 1 {{1},{2,4},{3,5},{6}} => 1 {{1,6},{2,4},{3},{5}} => 2 {{1},{2,4,6},{3},{5}} => 1 {{1},{2,4},{3,6},{5}} => 1 {{1},{2,4},{3},{5,6}} => 1 {{1},{2,4},{3},{5},{6}} => 1 {{1,5,6},{2},{3,4}} => 2 {{1,5},{2,6},{3,4}} => 2 {{1,5},{2},{3,4,6}} => 2 {{1,5},{2},{3,4},{6}} => 2 {{1,6},{2,5},{3,4}} => 3 {{1},{2,5,6},{3,4}} => 2 {{1},{2,5},{3,4,6}} => 2 {{1},{2,5},{3,4},{6}} => 2 {{1,6},{2},{3,4,5}} => 2 {{1},{2,6},{3,4,5}} => 2 {{1},{2},{3,4,5,6}} => 1 {{1},{2},{3,4,5},{6}} => 1 {{1,6},{2},{3,4},{5}} => 2 {{1},{2,6},{3,4},{5}} => 2 {{1},{2},{3,4,6},{5}} => 1 {{1},{2},{3,4},{5,6}} => 1 {{1},{2},{3,4},{5},{6}} => 1 {{1,5,6},{2},{3},{4}} => 1 {{1,5},{2,6},{3},{4}} => 1 {{1,5},{2},{3,6},{4}} => 1 {{1,5},{2},{3},{4,6}} => 1 {{1,5},{2},{3},{4},{6}} => 1 {{1,6},{2,5},{3},{4}} => 2 {{1},{2,5,6},{3},{4}} => 1 {{1},{2,5},{3,6},{4}} => 1 {{1},{2,5},{3},{4,6}} => 1 {{1},{2,5},{3},{4},{6}} => 1 {{1,6},{2},{3,5},{4}} => 2 {{1},{2,6},{3,5},{4}} => 2 {{1},{2},{3,5,6},{4}} => 1 {{1},{2},{3,5},{4,6}} => 1 {{1},{2},{3,5},{4},{6}} => 1 {{1,6},{2},{3},{4,5}} => 2 {{1},{2,6},{3},{4,5}} => 2 {{1},{2},{3,6},{4,5}} => 2 {{1},{2},{3},{4,5,6}} => 1 {{1},{2},{3},{4,5},{6}} => 1 {{1,6},{2},{3},{4},{5}} => 1 {{1},{2,6},{3},{4},{5}} => 1 {{1},{2},{3,6},{4},{5}} => 1 {{1},{2},{3},{4,6},{5}} => 1 {{1},{2},{3},{4},{5,6}} => 1 {{1},{2},{3},{4},{5},{6}} => 0 {{1,2,3,4,5,6,7}} => 1 {{1,2,3,4,5,6},{7}} => 1 {{1,2,3,4,5,7},{6}} => 1 {{1,2,3,4,5},{6,7}} => 1 {{1,2,3,4,5},{6},{7}} => 1 {{1,2,3,4,6,7},{5}} => 1 {{1,2,3,4,6},{5,7}} => 1 {{1,2,3,4,6},{5},{7}} => 1 {{1,2,3,4,7},{5,6}} => 2 {{1,2,3,4},{5,6,7}} => 1 {{1,2,3,4},{5,6},{7}} => 1 {{1,2,3,4,7},{5},{6}} => 1 {{1,2,3,4},{5,7},{6}} => 1 {{1,2,3,4},{5},{6,7}} => 1 {{1,2,3,4},{5},{6},{7}} => 1 {{1,2,3,5,6,7},{4}} => 1 {{1,2,3,5,6},{4,7}} => 2 {{1,2,3,5,6},{4},{7}} => 1 {{1,2,3,5,7},{4,6}} => 1 {{1,2,3,5},{4,6,7}} => 1 {{1,2,3,5},{4,6},{7}} => 1 {{1,2,3,5,7},{4},{6}} => 1 {{1,2,3,5},{4,7},{6}} => 1 {{1,2,3,5},{4},{6,7}} => 1 {{1,2,3,5},{4},{6},{7}} => 1 {{1,2,3,6,7},{4,5}} => 2 {{1,2,3,6},{4,5,7}} => 2 {{1,2,3,6},{4,5},{7}} => 2 {{1,2,3,7},{4,5,6}} => 2 {{1,2,3},{4,5,6,7}} => 1 {{1,2,3},{4,5,6},{7}} => 1 {{1,2,3,7},{4,5},{6}} => 2 {{1,2,3},{4,5,7},{6}} => 1 {{1,2,3},{4,5},{6,7}} => 1 {{1,2,3},{4,5},{6},{7}} => 1 {{1,2,3,6,7},{4},{5}} => 1 {{1,2,3,6},{4,7},{5}} => 1 {{1,2,3,6},{4},{5,7}} => 1 {{1,2,3,6},{4},{5},{7}} => 1 {{1,2,3,7},{4,6},{5}} => 2 {{1,2,3},{4,6,7},{5}} => 1 {{1,2,3},{4,6},{5,7}} => 1 {{1,2,3},{4,6},{5},{7}} => 1 {{1,2,3,7},{4},{5,6}} => 2 {{1,2,3},{4,7},{5,6}} => 2 {{1,2,3},{4},{5,6,7}} => 1 {{1,2,3},{4},{5,6},{7}} => 1 {{1,2,3,7},{4},{5},{6}} => 1 {{1,2,3},{4,7},{5},{6}} => 1 {{1,2,3},{4},{5,7},{6}} => 1 {{1,2,3},{4},{5},{6,7}} => 1 {{1,2,3},{4},{5},{6},{7}} => 1 {{1,2,4,5,6,7},{3}} => 1 {{1,2,4,5,6},{3,7}} => 2 {{1,2,4,5,6},{3},{7}} => 1 {{1,2,4,5,7},{3,6}} => 2 {{1,2,4,5},{3,6,7}} => 2 {{1,2,4,5},{3,6},{7}} => 2 {{1,2,4,5,7},{3},{6}} => 1 {{1,2,4,5},{3,7},{6}} => 2 {{1,2,4,5},{3},{6,7}} => 1 {{1,2,4,5},{3},{6},{7}} => 1 {{1,2,4,6,7},{3,5}} => 1 {{1,2,4,6},{3,5,7}} => 1 {{1,2,4,6},{3,5},{7}} => 1 {{1,2,4,7},{3,5,6}} => 2 {{1,2,4},{3,5,6,7}} => 1 {{1,2,4},{3,5,6},{7}} => 1 {{1,2,4,7},{3,5},{6}} => 1 {{1,2,4},{3,5,7},{6}} => 1 {{1,2,4},{3,5},{6,7}} => 1 {{1,2,4},{3,5},{6},{7}} => 1 {{1,2,4,6,7},{3},{5}} => 1 {{1,2,4,6},{3,7},{5}} => 2 {{1,2,4,6},{3},{5,7}} => 1 {{1,2,4,6},{3},{5},{7}} => 1 {{1,2,4,7},{3,6},{5}} => 1 {{1,2,4},{3,6,7},{5}} => 1 {{1,2,4},{3,6},{5,7}} => 1 {{1,2,4},{3,6},{5},{7}} => 1 {{1,2,4,7},{3},{5,6}} => 2 {{1,2,4},{3,7},{5,6}} => 2 {{1,2,4},{3},{5,6,7}} => 1 {{1,2,4},{3},{5,6},{7}} => 1 {{1,2,4,7},{3},{5},{6}} => 1 {{1,2,4},{3,7},{5},{6}} => 1 {{1,2,4},{3},{5,7},{6}} => 1 {{1,2,4},{3},{5},{6,7}} => 1 {{1,2,4},{3},{5},{6},{7}} => 1 {{1,2,5,6,7},{3,4}} => 2 {{1,2,5,6},{3,4,7}} => 2 {{1,2,5,6},{3,4},{7}} => 2 {{1,2,5,7},{3,4,6}} => 2 {{1,2,5},{3,4,6,7}} => 2 {{1,2,5},{3,4,6},{7}} => 2 {{1,2,5,7},{3,4},{6}} => 2 {{1,2,5},{3,4,7},{6}} => 2 {{1,2,5},{3,4},{6,7}} => 2 {{1,2,5},{3,4},{6},{7}} => 2 {{1,2,6,7},{3,4,5}} => 2 {{1,2,6},{3,4,5,7}} => 2 {{1,2,6},{3,4,5},{7}} => 2 {{1,2,7},{3,4,5,6}} => 2 {{1,2},{3,4,5,6,7}} => 1 {{1,2},{3,4,5,6},{7}} => 1 {{1,2,7},{3,4,5},{6}} => 2 {{1,2},{3,4,5,7},{6}} => 1 {{1,2},{3,4,5},{6,7}} => 1 {{1,2},{3,4,5},{6},{7}} => 1 {{1,2,6,7},{3,4},{5}} => 2 {{1,2,6},{3,4,7},{5}} => 2 {{1,2,6},{3,4},{5,7}} => 2 {{1,2,6},{3,4},{5},{7}} => 2 {{1,2,7},{3,4,6},{5}} => 2 {{1,2},{3,4,6,7},{5}} => 1 {{1,2},{3,4,6},{5,7}} => 1 {{1,2},{3,4,6},{5},{7}} => 1 {{1,2,7},{3,4},{5,6}} => 2 {{1,2},{3,4,7},{5,6}} => 2 {{1,2},{3,4},{5,6,7}} => 1 {{1,2},{3,4},{5,6},{7}} => 1 {{1,2,7},{3,4},{5},{6}} => 2 {{1,2},{3,4,7},{5},{6}} => 1 {{1,2},{3,4},{5,7},{6}} => 1 {{1,2},{3,4},{5},{6,7}} => 1 {{1,2},{3,4},{5},{6},{7}} => 1 {{1,2,5,6,7},{3},{4}} => 1 {{1,2,5,6},{3,7},{4}} => 2 {{1,2,5,6},{3},{4,7}} => 2 {{1,2,5,6},{3},{4},{7}} => 1 {{1,2,5,7},{3,6},{4}} => 1 {{1,2,5},{3,6,7},{4}} => 1 {{1,2,5},{3,6},{4,7}} => 1 {{1,2,5},{3,6},{4},{7}} => 1 {{1,2,5,7},{3},{4,6}} => 1 {{1,2,5},{3,7},{4,6}} => 2 {{1,2,5},{3},{4,6,7}} => 1 {{1,2,5},{3},{4,6},{7}} => 1 {{1,2,5,7},{3},{4},{6}} => 1 {{1,2,5},{3,7},{4},{6}} => 1 {{1,2,5},{3},{4,7},{6}} => 1 {{1,2,5},{3},{4},{6,7}} => 1 {{1,2,5},{3},{4},{6},{7}} => 1 {{1,2,6,7},{3,5},{4}} => 2 {{1,2,6},{3,5,7},{4}} => 2 {{1,2,6},{3,5},{4,7}} => 2 {{1,2,6},{3,5},{4},{7}} => 2 {{1,2,7},{3,5,6},{4}} => 2 {{1,2},{3,5,6,7},{4}} => 1 {{1,2},{3,5,6},{4,7}} => 2 {{1,2},{3,5,6},{4},{7}} => 1 {{1,2,7},{3,5},{4,6}} => 2 {{1,2},{3,5,7},{4,6}} => 1 {{1,2},{3,5},{4,6,7}} => 1 {{1,2},{3,5},{4,6},{7}} => 1 {{1,2,7},{3,5},{4},{6}} => 2 {{1,2},{3,5,7},{4},{6}} => 1 {{1,2},{3,5},{4,7},{6}} => 1 {{1,2},{3,5},{4},{6,7}} => 1 {{1,2},{3,5},{4},{6},{7}} => 1 {{1,2,6,7},{3},{4,5}} => 2 {{1,2,6},{3,7},{4,5}} => 2 {{1,2,6},{3},{4,5,7}} => 2 {{1,2,6},{3},{4,5},{7}} => 2 {{1,2,7},{3,6},{4,5}} => 3 {{1,2},{3,6,7},{4,5}} => 2 {{1,2},{3,6},{4,5,7}} => 2 {{1,2},{3,6},{4,5},{7}} => 2 {{1,2,7},{3},{4,5,6}} => 2 {{1,2},{3,7},{4,5,6}} => 2 {{1,2},{3},{4,5,6,7}} => 1 {{1,2},{3},{4,5,6},{7}} => 1 {{1,2,7},{3},{4,5},{6}} => 2 {{1,2},{3,7},{4,5},{6}} => 2 {{1,2},{3},{4,5,7},{6}} => 1 {{1,2},{3},{4,5},{6,7}} => 1 {{1,2},{3},{4,5},{6},{7}} => 1 {{1,2,6,7},{3},{4},{5}} => 1 {{1,2,6},{3,7},{4},{5}} => 1 {{1,2,6},{3},{4,7},{5}} => 1 {{1,2,6},{3},{4},{5,7}} => 1 {{1,2,6},{3},{4},{5},{7}} => 1 {{1,2,7},{3,6},{4},{5}} => 2 {{1,2},{3,6,7},{4},{5}} => 1 {{1,2},{3,6},{4,7},{5}} => 1 {{1,2},{3,6},{4},{5,7}} => 1 {{1,2},{3,6},{4},{5},{7}} => 1 {{1,2,7},{3},{4,6},{5}} => 2 {{1,2},{3,7},{4,6},{5}} => 2 {{1,2},{3},{4,6,7},{5}} => 1 {{1,2},{3},{4,6},{5,7}} => 1 {{1,2},{3},{4,6},{5},{7}} => 1 {{1,2,7},{3},{4},{5,6}} => 2 {{1,2},{3,7},{4},{5,6}} => 2 {{1,2},{3},{4,7},{5,6}} => 2 {{1,2},{3},{4},{5,6,7}} => 1 {{1,2},{3},{4},{5,6},{7}} => 1 {{1,2,7},{3},{4},{5},{6}} => 1 {{1,2},{3,7},{4},{5},{6}} => 1 {{1,2},{3},{4,7},{5},{6}} => 1 {{1,2},{3},{4},{5,7},{6}} => 1 {{1,2},{3},{4},{5},{6,7}} => 1 {{1,2},{3},{4},{5},{6},{7}} => 1 {{1,3,4,5,6,7},{2}} => 1 {{1,3,4,5,6},{2,7}} => 2 {{1,3,4,5,6},{2},{7}} => 1 {{1,3,4,5,7},{2,6}} => 2 {{1,3,4,5},{2,6,7}} => 2 {{1,3,4,5},{2,6},{7}} => 2 {{1,3,4,5,7},{2},{6}} => 1 {{1,3,4,5},{2,7},{6}} => 2 {{1,3,4,5},{2},{6,7}} => 1 {{1,3,4,5},{2},{6},{7}} => 1 {{1,3,4,6,7},{2,5}} => 2 {{1,3,4,6},{2,5,7}} => 2 {{1,3,4,6},{2,5},{7}} => 2 {{1,3,4,7},{2,5,6}} => 2 {{1,3,4},{2,5,6,7}} => 2 {{1,3,4},{2,5,6},{7}} => 2 {{1,3,4,7},{2,5},{6}} => 2 {{1,3,4},{2,5,7},{6}} => 2 {{1,3,4},{2,5},{6,7}} => 2 {{1,3,4},{2,5},{6},{7}} => 2 {{1,3,4,6,7},{2},{5}} => 1 {{1,3,4,6},{2,7},{5}} => 2 {{1,3,4,6},{2},{5,7}} => 1 {{1,3,4,6},{2},{5},{7}} => 1 {{1,3,4,7},{2,6},{5}} => 2 {{1,3,4},{2,6,7},{5}} => 2 {{1,3,4},{2,6},{5,7}} => 2 {{1,3,4},{2,6},{5},{7}} => 2 {{1,3,4,7},{2},{5,6}} => 2 {{1,3,4},{2,7},{5,6}} => 2 {{1,3,4},{2},{5,6,7}} => 1 {{1,3,4},{2},{5,6},{7}} => 1 {{1,3,4,7},{2},{5},{6}} => 1 {{1,3,4},{2,7},{5},{6}} => 2 {{1,3,4},{2},{5,7},{6}} => 1 {{1,3,4},{2},{5},{6,7}} => 1 {{1,3,4},{2},{5},{6},{7}} => 1 {{1,3,5,6,7},{2,4}} => 1 {{1,3,5,6},{2,4,7}} => 2 {{1,3,5,6},{2,4},{7}} => 1 {{1,3,5,7},{2,4,6}} => 1 {{1,3,5},{2,4,6,7}} => 1 {{1,3,5},{2,4,6},{7}} => 1 {{1,3,5,7},{2,4},{6}} => 1 {{1,3,5},{2,4,7},{6}} => 1 {{1,3,5},{2,4},{6,7}} => 1 {{1,3,5},{2,4},{6},{7}} => 1 {{1,3,6,7},{2,4,5}} => 2 {{1,3,6},{2,4,5,7}} => 2 {{1,3,6},{2,4,5},{7}} => 2 {{1,3,7},{2,4,5,6}} => 2 {{1,3},{2,4,5,6,7}} => 1 {{1,3},{2,4,5,6},{7}} => 1 {{1,3,7},{2,4,5},{6}} => 2 {{1,3},{2,4,5,7},{6}} => 1 {{1,3},{2,4,5},{6,7}} => 1 {{1,3},{2,4,5},{6},{7}} => 1 {{1,3,6,7},{2,4},{5}} => 1 {{1,3,6},{2,4,7},{5}} => 1 {{1,3,6},{2,4},{5,7}} => 1 {{1,3,6},{2,4},{5},{7}} => 1 {{1,3,7},{2,4,6},{5}} => 2 {{1,3},{2,4,6,7},{5}} => 1 {{1,3},{2,4,6},{5,7}} => 1 {{1,3},{2,4,6},{5},{7}} => 1 {{1,3,7},{2,4},{5,6}} => 2 {{1,3},{2,4,7},{5,6}} => 2 {{1,3},{2,4},{5,6,7}} => 1 {{1,3},{2,4},{5,6},{7}} => 1 {{1,3,7},{2,4},{5},{6}} => 1 {{1,3},{2,4,7},{5},{6}} => 1 {{1,3},{2,4},{5,7},{6}} => 1 {{1,3},{2,4},{5},{6,7}} => 1 {{1,3},{2,4},{5},{6},{7}} => 1 {{1,3,5,6,7},{2},{4}} => 1 {{1,3,5,6},{2,7},{4}} => 2 {{1,3,5,6},{2},{4,7}} => 2 {{1,3,5,6},{2},{4},{7}} => 1 {{1,3,5,7},{2,6},{4}} => 2 {{1,3,5},{2,6,7},{4}} => 2 {{1,3,5},{2,6},{4,7}} => 2 {{1,3,5},{2,6},{4},{7}} => 2 {{1,3,5,7},{2},{4,6}} => 1 {{1,3,5},{2,7},{4,6}} => 2 {{1,3,5},{2},{4,6,7}} => 1 {{1,3,5},{2},{4,6},{7}} => 1 {{1,3,5,7},{2},{4},{6}} => 1 {{1,3,5},{2,7},{4},{6}} => 2 {{1,3,5},{2},{4,7},{6}} => 1 {{1,3,5},{2},{4},{6,7}} => 1 {{1,3,5},{2},{4},{6},{7}} => 1 {{1,3,6,7},{2,5},{4}} => 1 {{1,3,6},{2,5,7},{4}} => 1 {{1,3,6},{2,5},{4,7}} => 1 {{1,3,6},{2,5},{4},{7}} => 1 {{1,3,7},{2,5,6},{4}} => 2 {{1,3},{2,5,6,7},{4}} => 1 {{1,3},{2,5,6},{4,7}} => 2 {{1,3},{2,5,6},{4},{7}} => 1 {{1,3,7},{2,5},{4,6}} => 2 {{1,3},{2,5,7},{4,6}} => 1 {{1,3},{2,5},{4,6,7}} => 1 {{1,3},{2,5},{4,6},{7}} => 1 {{1,3,7},{2,5},{4},{6}} => 1 {{1,3},{2,5,7},{4},{6}} => 1 {{1,3},{2,5},{4,7},{6}} => 1 {{1,3},{2,5},{4},{6,7}} => 1 {{1,3},{2,5},{4},{6},{7}} => 1 {{1,3,6,7},{2},{4,5}} => 2 {{1,3,6},{2,7},{4,5}} => 3 {{1,3,6},{2},{4,5,7}} => 2 {{1,3,6},{2},{4,5},{7}} => 2 {{1,3,7},{2,6},{4,5}} => 2 {{1,3},{2,6,7},{4,5}} => 2 {{1,3},{2,6},{4,5,7}} => 2 {{1,3},{2,6},{4,5},{7}} => 2 {{1,3,7},{2},{4,5,6}} => 2 {{1,3},{2,7},{4,5,6}} => 2 {{1,3},{2},{4,5,6,7}} => 1 {{1,3},{2},{4,5,6},{7}} => 1 {{1,3,7},{2},{4,5},{6}} => 2 {{1,3},{2,7},{4,5},{6}} => 2 {{1,3},{2},{4,5,7},{6}} => 1 {{1,3},{2},{4,5},{6,7}} => 1 {{1,3},{2},{4,5},{6},{7}} => 1 {{1,3,6,7},{2},{4},{5}} => 1 {{1,3,6},{2,7},{4},{5}} => 2 {{1,3,6},{2},{4,7},{5}} => 1 {{1,3,6},{2},{4},{5,7}} => 1 {{1,3,6},{2},{4},{5},{7}} => 1 {{1,3,7},{2,6},{4},{5}} => 1 {{1,3},{2,6,7},{4},{5}} => 1 {{1,3},{2,6},{4,7},{5}} => 1 {{1,3},{2,6},{4},{5,7}} => 1 {{1,3},{2,6},{4},{5},{7}} => 1 {{1,3,7},{2},{4,6},{5}} => 2 {{1,3},{2,7},{4,6},{5}} => 2 {{1,3},{2},{4,6,7},{5}} => 1 {{1,3},{2},{4,6},{5,7}} => 1 {{1,3},{2},{4,6},{5},{7}} => 1 {{1,3,7},{2},{4},{5,6}} => 2 {{1,3},{2,7},{4},{5,6}} => 2 {{1,3},{2},{4,7},{5,6}} => 2 {{1,3},{2},{4},{5,6,7}} => 1 {{1,3},{2},{4},{5,6},{7}} => 1 {{1,3,7},{2},{4},{5},{6}} => 1 {{1,3},{2,7},{4},{5},{6}} => 1 {{1,3},{2},{4,7},{5},{6}} => 1 {{1,3},{2},{4},{5,7},{6}} => 1 {{1,3},{2},{4},{5},{6,7}} => 1 {{1,3},{2},{4},{5},{6},{7}} => 1 {{1,4,5,6,7},{2,3}} => 2 {{1,4,5,6},{2,3,7}} => 2 {{1,4,5,6},{2,3},{7}} => 2 {{1,4,5,7},{2,3,6}} => 2 {{1,4,5},{2,3,6,7}} => 2 {{1,4,5},{2,3,6},{7}} => 2 {{1,4,5,7},{2,3},{6}} => 2 {{1,4,5},{2,3,7},{6}} => 2 {{1,4,5},{2,3},{6,7}} => 2 {{1,4,5},{2,3},{6},{7}} => 2 {{1,4,6,7},{2,3,5}} => 2 {{1,4,6},{2,3,5,7}} => 2 {{1,4,6},{2,3,5},{7}} => 2 {{1,4,7},{2,3,5,6}} => 2 {{1,4},{2,3,5,6,7}} => 2 {{1,4},{2,3,5,6},{7}} => 2 {{1,4,7},{2,3,5},{6}} => 2 {{1,4},{2,3,5,7},{6}} => 2 {{1,4},{2,3,5},{6,7}} => 2 {{1,4},{2,3,5},{6},{7}} => 2 {{1,4,6,7},{2,3},{5}} => 2 {{1,4,6},{2,3,7},{5}} => 2 {{1,4,6},{2,3},{5,7}} => 2 {{1,4,6},{2,3},{5},{7}} => 2 {{1,4,7},{2,3,6},{5}} => 2 {{1,4},{2,3,6,7},{5}} => 2 {{1,4},{2,3,6},{5,7}} => 2 {{1,4},{2,3,6},{5},{7}} => 2 {{1,4,7},{2,3},{5,6}} => 2 {{1,4},{2,3,7},{5,6}} => 2 {{1,4},{2,3},{5,6,7}} => 2 {{1,4},{2,3},{5,6},{7}} => 2 {{1,4,7},{2,3},{5},{6}} => 2 {{1,4},{2,3,7},{5},{6}} => 2 {{1,4},{2,3},{5,7},{6}} => 2 {{1,4},{2,3},{5},{6,7}} => 2 {{1,4},{2,3},{5},{6},{7}} => 2 {{1,5,6,7},{2,3,4}} => 2 {{1,5,6},{2,3,4,7}} => 2 {{1,5,6},{2,3,4},{7}} => 2 {{1,5,7},{2,3,4,6}} => 2 {{1,5},{2,3,4,6,7}} => 2 {{1,5},{2,3,4,6},{7}} => 2 {{1,5,7},{2,3,4},{6}} => 2 {{1,5},{2,3,4,7},{6}} => 2 {{1,5},{2,3,4},{6,7}} => 2 {{1,5},{2,3,4},{6},{7}} => 2 {{1,6,7},{2,3,4,5}} => 2 {{1,6},{2,3,4,5,7}} => 2 {{1,6},{2,3,4,5},{7}} => 2 {{1,7},{2,3,4,5,6}} => 2 {{1},{2,3,4,5,6,7}} => 1 {{1},{2,3,4,5,6},{7}} => 1 {{1,7},{2,3,4,5},{6}} => 2 {{1},{2,3,4,5,7},{6}} => 1 {{1},{2,3,4,5},{6,7}} => 1 {{1},{2,3,4,5},{6},{7}} => 1 {{1,6,7},{2,3,4},{5}} => 2 {{1,6},{2,3,4,7},{5}} => 2 {{1,6},{2,3,4},{5,7}} => 2 {{1,6},{2,3,4},{5},{7}} => 2 {{1,7},{2,3,4,6},{5}} => 2 {{1},{2,3,4,6,7},{5}} => 1 {{1},{2,3,4,6},{5,7}} => 1 {{1},{2,3,4,6},{5},{7}} => 1 {{1,7},{2,3,4},{5,6}} => 2 {{1},{2,3,4,7},{5,6}} => 2 {{1},{2,3,4},{5,6,7}} => 1 {{1},{2,3,4},{5,6},{7}} => 1 {{1,7},{2,3,4},{5},{6}} => 2 {{1},{2,3,4,7},{5},{6}} => 1 {{1},{2,3,4},{5,7},{6}} => 1 {{1},{2,3,4},{5},{6,7}} => 1 {{1},{2,3,4},{5},{6},{7}} => 1 {{1,5,6,7},{2,3},{4}} => 2 {{1,5,6},{2,3,7},{4}} => 2 {{1,5,6},{2,3},{4,7}} => 2 {{1,5,6},{2,3},{4},{7}} => 2 {{1,5,7},{2,3,6},{4}} => 2 {{1,5},{2,3,6,7},{4}} => 2 {{1,5},{2,3,6},{4,7}} => 2 {{1,5},{2,3,6},{4},{7}} => 2 {{1,5,7},{2,3},{4,6}} => 2 {{1,5},{2,3,7},{4,6}} => 2 {{1,5},{2,3},{4,6,7}} => 2 {{1,5},{2,3},{4,6},{7}} => 2 {{1,5,7},{2,3},{4},{6}} => 2 {{1,5},{2,3,7},{4},{6}} => 2 {{1,5},{2,3},{4,7},{6}} => 2 {{1,5},{2,3},{4},{6,7}} => 2 {{1,5},{2,3},{4},{6},{7}} => 2 {{1,6,7},{2,3,5},{4}} => 2 {{1,6},{2,3,5,7},{4}} => 2 {{1,6},{2,3,5},{4,7}} => 2 {{1,6},{2,3,5},{4},{7}} => 2 {{1,7},{2,3,5,6},{4}} => 2 {{1},{2,3,5,6,7},{4}} => 1 {{1},{2,3,5,6},{4,7}} => 2 {{1},{2,3,5,6},{4},{7}} => 1 {{1,7},{2,3,5},{4,6}} => 2 {{1},{2,3,5,7},{4,6}} => 1 {{1},{2,3,5},{4,6,7}} => 1 {{1},{2,3,5},{4,6},{7}} => 1 {{1,7},{2,3,5},{4},{6}} => 2 {{1},{2,3,5,7},{4},{6}} => 1 {{1},{2,3,5},{4,7},{6}} => 1 {{1},{2,3,5},{4},{6,7}} => 1 {{1},{2,3,5},{4},{6},{7}} => 1 {{1,6,7},{2,3},{4,5}} => 2 {{1,6},{2,3,7},{4,5}} => 2 {{1,6},{2,3},{4,5,7}} => 2 {{1,6},{2,3},{4,5},{7}} => 2 {{1,7},{2,3,6},{4,5}} => 3 {{1},{2,3,6,7},{4,5}} => 2 {{1},{2,3,6},{4,5,7}} => 2 {{1},{2,3,6},{4,5},{7}} => 2 {{1,7},{2,3},{4,5,6}} => 2 {{1},{2,3,7},{4,5,6}} => 2 {{1},{2,3},{4,5,6,7}} => 1 {{1},{2,3},{4,5,6},{7}} => 1 {{1,7},{2,3},{4,5},{6}} => 2 {{1},{2,3,7},{4,5},{6}} => 2 {{1},{2,3},{4,5,7},{6}} => 1 {{1},{2,3},{4,5},{6,7}} => 1 {{1},{2,3},{4,5},{6},{7}} => 1 {{1,6,7},{2,3},{4},{5}} => 2 {{1,6},{2,3,7},{4},{5}} => 2 {{1,6},{2,3},{4,7},{5}} => 2 {{1,6},{2,3},{4},{5,7}} => 2 {{1,6},{2,3},{4},{5},{7}} => 2 {{1,7},{2,3,6},{4},{5}} => 2 {{1},{2,3,6,7},{4},{5}} => 1 {{1},{2,3,6},{4,7},{5}} => 1 {{1},{2,3,6},{4},{5,7}} => 1 {{1},{2,3,6},{4},{5},{7}} => 1 {{1,7},{2,3},{4,6},{5}} => 2 {{1},{2,3,7},{4,6},{5}} => 2 {{1},{2,3},{4,6,7},{5}} => 1 {{1},{2,3},{4,6},{5,7}} => 1 {{1},{2,3},{4,6},{5},{7}} => 1 {{1,7},{2,3},{4},{5,6}} => 2 {{1},{2,3,7},{4},{5,6}} => 2 {{1},{2,3},{4,7},{5,6}} => 2 {{1},{2,3},{4},{5,6,7}} => 1 {{1},{2,3},{4},{5,6},{7}} => 1 {{1,7},{2,3},{4},{5},{6}} => 2 {{1},{2,3,7},{4},{5},{6}} => 1 {{1},{2,3},{4,7},{5},{6}} => 1 {{1},{2,3},{4},{5,7},{6}} => 1 {{1},{2,3},{4},{5},{6,7}} => 1 {{1},{2,3},{4},{5},{6},{7}} => 1 {{1,4,5,6,7},{2},{3}} => 1 {{1,4,5,6},{2,7},{3}} => 2 {{1,4,5,6},{2},{3,7}} => 2 {{1,4,5,6},{2},{3},{7}} => 1 {{1,4,5,7},{2,6},{3}} => 2 {{1,4,5},{2,6,7},{3}} => 2 {{1,4,5},{2,6},{3,7}} => 2 {{1,4,5},{2,6},{3},{7}} => 2 {{1,4,5,7},{2},{3,6}} => 2 {{1,4,5},{2,7},{3,6}} => 3 {{1,4,5},{2},{3,6,7}} => 2 {{1,4,5},{2},{3,6},{7}} => 2 {{1,4,5,7},{2},{3},{6}} => 1 {{1,4,5},{2,7},{3},{6}} => 2 {{1,4,5},{2},{3,7},{6}} => 2 {{1,4,5},{2},{3},{6,7}} => 1 {{1,4,5},{2},{3},{6},{7}} => 1 {{1,4,6,7},{2,5},{3}} => 1 {{1,4,6},{2,5,7},{3}} => 1 {{1,4,6},{2,5},{3,7}} => 2 {{1,4,6},{2,5},{3},{7}} => 1 {{1,4,7},{2,5,6},{3}} => 2 {{1,4},{2,5,6,7},{3}} => 1 {{1,4},{2,5,6},{3,7}} => 2 {{1,4},{2,5,6},{3},{7}} => 1 {{1,4,7},{2,5},{3,6}} => 1 {{1,4},{2,5,7},{3,6}} => 1 {{1,4},{2,5},{3,6,7}} => 1 {{1,4},{2,5},{3,6},{7}} => 1 {{1,4,7},{2,5},{3},{6}} => 1 {{1,4},{2,5,7},{3},{6}} => 1 {{1,4},{2,5},{3,7},{6}} => 1 {{1,4},{2,5},{3},{6,7}} => 1 {{1,4},{2,5},{3},{6},{7}} => 1 {{1,4,6,7},{2},{3,5}} => 1 {{1,4,6},{2,7},{3,5}} => 2 {{1,4,6},{2},{3,5,7}} => 1 {{1,4,6},{2},{3,5},{7}} => 1 {{1,4,7},{2,6},{3,5}} => 2 {{1,4},{2,6,7},{3,5}} => 2 {{1,4},{2,6},{3,5,7}} => 2 {{1,4},{2,6},{3,5},{7}} => 2 {{1,4,7},{2},{3,5,6}} => 2 {{1,4},{2,7},{3,5,6}} => 2 {{1,4},{2},{3,5,6,7}} => 1 {{1,4},{2},{3,5,6},{7}} => 1 {{1,4,7},{2},{3,5},{6}} => 1 {{1,4},{2,7},{3,5},{6}} => 2 {{1,4},{2},{3,5,7},{6}} => 1 {{1,4},{2},{3,5},{6,7}} => 1 {{1,4},{2},{3,5},{6},{7}} => 1 {{1,4,6,7},{2},{3},{5}} => 1 {{1,4,6},{2,7},{3},{5}} => 2 {{1,4,6},{2},{3,7},{5}} => 2 {{1,4,6},{2},{3},{5,7}} => 1 {{1,4,6},{2},{3},{5},{7}} => 1 {{1,4,7},{2,6},{3},{5}} => 1 {{1,4},{2,6,7},{3},{5}} => 1 {{1,4},{2,6},{3,7},{5}} => 1 {{1,4},{2,6},{3},{5,7}} => 1 {{1,4},{2,6},{3},{5},{7}} => 1 {{1,4,7},{2},{3,6},{5}} => 1 {{1,4},{2,7},{3,6},{5}} => 2 {{1,4},{2},{3,6,7},{5}} => 1 {{1,4},{2},{3,6},{5,7}} => 1 {{1,4},{2},{3,6},{5},{7}} => 1 {{1,4,7},{2},{3},{5,6}} => 2 {{1,4},{2,7},{3},{5,6}} => 2 {{1,4},{2},{3,7},{5,6}} => 2 {{1,4},{2},{3},{5,6,7}} => 1 {{1,4},{2},{3},{5,6},{7}} => 1 {{1,4,7},{2},{3},{5},{6}} => 1 {{1,4},{2,7},{3},{5},{6}} => 1 {{1,4},{2},{3,7},{5},{6}} => 1 {{1,4},{2},{3},{5,7},{6}} => 1 {{1,4},{2},{3},{5},{6,7}} => 1 {{1,4},{2},{3},{5},{6},{7}} => 1 {{1,5,6,7},{2,4},{3}} => 2 {{1,5,6},{2,4,7},{3}} => 2 {{1,5,6},{2,4},{3,7}} => 2 {{1,5,6},{2,4},{3},{7}} => 2 {{1,5,7},{2,4,6},{3}} => 2 {{1,5},{2,4,6,7},{3}} => 2 {{1,5},{2,4,6},{3,7}} => 2 {{1,5},{2,4,6},{3},{7}} => 2 {{1,5,7},{2,4},{3,6}} => 2 {{1,5},{2,4,7},{3,6}} => 2 {{1,5},{2,4},{3,6,7}} => 2 {{1,5},{2,4},{3,6},{7}} => 2 {{1,5,7},{2,4},{3},{6}} => 2 {{1,5},{2,4,7},{3},{6}} => 2 {{1,5},{2,4},{3,7},{6}} => 2 {{1,5},{2,4},{3},{6,7}} => 2 {{1,5},{2,4},{3},{6},{7}} => 2 {{1,6,7},{2,4,5},{3}} => 2 {{1,6},{2,4,5,7},{3}} => 2 {{1,6},{2,4,5},{3,7}} => 2 {{1,6},{2,4,5},{3},{7}} => 2 {{1,7},{2,4,5,6},{3}} => 2 {{1},{2,4,5,6,7},{3}} => 1 {{1},{2,4,5,6},{3,7}} => 2 {{1},{2,4,5,6},{3},{7}} => 1 {{1,7},{2,4,5},{3,6}} => 3 {{1},{2,4,5,7},{3,6}} => 2 {{1},{2,4,5},{3,6,7}} => 2 {{1},{2,4,5},{3,6},{7}} => 2 {{1,7},{2,4,5},{3},{6}} => 2 {{1},{2,4,5,7},{3},{6}} => 1 {{1},{2,4,5},{3,7},{6}} => 2 {{1},{2,4,5},{3},{6,7}} => 1 {{1},{2,4,5},{3},{6},{7}} => 1 {{1,6,7},{2,4},{3,5}} => 2 {{1,6},{2,4,7},{3,5}} => 2 {{1,6},{2,4},{3,5,7}} => 2 {{1,6},{2,4},{3,5},{7}} => 2 {{1,7},{2,4,6},{3,5}} => 2 {{1},{2,4,6,7},{3,5}} => 1 {{1},{2,4,6},{3,5,7}} => 1 {{1},{2,4,6},{3,5},{7}} => 1 {{1,7},{2,4},{3,5,6}} => 2 {{1},{2,4,7},{3,5,6}} => 2 {{1},{2,4},{3,5,6,7}} => 1 {{1},{2,4},{3,5,6},{7}} => 1 {{1,7},{2,4},{3,5},{6}} => 2 {{1},{2,4,7},{3,5},{6}} => 1 {{1},{2,4},{3,5,7},{6}} => 1 {{1},{2,4},{3,5},{6,7}} => 1 {{1},{2,4},{3,5},{6},{7}} => 1 {{1,6,7},{2,4},{3},{5}} => 2 {{1,6},{2,4,7},{3},{5}} => 2 {{1,6},{2,4},{3,7},{5}} => 2 {{1,6},{2,4},{3},{5,7}} => 2 {{1,6},{2,4},{3},{5},{7}} => 2 {{1,7},{2,4,6},{3},{5}} => 2 {{1},{2,4,6,7},{3},{5}} => 1 {{1},{2,4,6},{3,7},{5}} => 2 {{1},{2,4,6},{3},{5,7}} => 1 {{1},{2,4,6},{3},{5},{7}} => 1 {{1,7},{2,4},{3,6},{5}} => 2 {{1},{2,4,7},{3,6},{5}} => 1 {{1},{2,4},{3,6,7},{5}} => 1 {{1},{2,4},{3,6},{5,7}} => 1 {{1},{2,4},{3,6},{5},{7}} => 1 {{1,7},{2,4},{3},{5,6}} => 2 {{1},{2,4,7},{3},{5,6}} => 2 {{1},{2,4},{3,7},{5,6}} => 2 {{1},{2,4},{3},{5,6,7}} => 1 {{1},{2,4},{3},{5,6},{7}} => 1 {{1,7},{2,4},{3},{5},{6}} => 2 {{1},{2,4,7},{3},{5},{6}} => 1 {{1},{2,4},{3,7},{5},{6}} => 1 {{1},{2,4},{3},{5,7},{6}} => 1 {{1},{2,4},{3},{5},{6,7}} => 1 {{1},{2,4},{3},{5},{6},{7}} => 1 {{1,5,6,7},{2},{3,4}} => 2 {{1,5,6},{2,7},{3,4}} => 2 {{1,5,6},{2},{3,4,7}} => 2 {{1,5,6},{2},{3,4},{7}} => 2 {{1,5,7},{2,6},{3,4}} => 2 {{1,5},{2,6,7},{3,4}} => 2 {{1,5},{2,6},{3,4,7}} => 2 {{1,5},{2,6},{3,4},{7}} => 2 {{1,5,7},{2},{3,4,6}} => 2 {{1,5},{2,7},{3,4,6}} => 2 {{1,5},{2},{3,4,6,7}} => 2 {{1,5},{2},{3,4,6},{7}} => 2 {{1,5,7},{2},{3,4},{6}} => 2 {{1,5},{2,7},{3,4},{6}} => 2 {{1,5},{2},{3,4,7},{6}} => 2 {{1,5},{2},{3,4},{6,7}} => 2 {{1,5},{2},{3,4},{6},{7}} => 2 {{1,6,7},{2,5},{3,4}} => 3 {{1,6},{2,5,7},{3,4}} => 3 {{1,6},{2,5},{3,4,7}} => 3 {{1,6},{2,5},{3,4},{7}} => 3 {{1,7},{2,5,6},{3,4}} => 3 {{1},{2,5,6,7},{3,4}} => 2 {{1},{2,5,6},{3,4,7}} => 2 {{1},{2,5,6},{3,4},{7}} => 2 {{1,7},{2,5},{3,4,6}} => 3 {{1},{2,5,7},{3,4,6}} => 2 {{1},{2,5},{3,4,6,7}} => 2 {{1},{2,5},{3,4,6},{7}} => 2 {{1,7},{2,5},{3,4},{6}} => 3 {{1},{2,5,7},{3,4},{6}} => 2 {{1},{2,5},{3,4,7},{6}} => 2 {{1},{2,5},{3,4},{6,7}} => 2 {{1},{2,5},{3,4},{6},{7}} => 2 {{1,6,7},{2},{3,4,5}} => 2 {{1,6},{2,7},{3,4,5}} => 2 {{1,6},{2},{3,4,5,7}} => 2 {{1,6},{2},{3,4,5},{7}} => 2 {{1,7},{2,6},{3,4,5}} => 3 {{1},{2,6,7},{3,4,5}} => 2 {{1},{2,6},{3,4,5,7}} => 2 {{1},{2,6},{3,4,5},{7}} => 2 {{1,7},{2},{3,4,5,6}} => 2 {{1},{2,7},{3,4,5,6}} => 2 {{1},{2},{3,4,5,6,7}} => 1 {{1},{2},{3,4,5,6},{7}} => 1 {{1,7},{2},{3,4,5},{6}} => 2 {{1},{2,7},{3,4,5},{6}} => 2 {{1},{2},{3,4,5,7},{6}} => 1 {{1},{2},{3,4,5},{6,7}} => 1 {{1},{2},{3,4,5},{6},{7}} => 1 {{1,6,7},{2},{3,4},{5}} => 2 {{1,6},{2,7},{3,4},{5}} => 2 {{1,6},{2},{3,4,7},{5}} => 2 {{1,6},{2},{3,4},{5,7}} => 2 {{1,6},{2},{3,4},{5},{7}} => 2 {{1,7},{2,6},{3,4},{5}} => 3 {{1},{2,6,7},{3,4},{5}} => 2 {{1},{2,6},{3,4,7},{5}} => 2 {{1},{2,6},{3,4},{5,7}} => 2 {{1},{2,6},{3,4},{5},{7}} => 2 {{1,7},{2},{3,4,6},{5}} => 2 {{1},{2,7},{3,4,6},{5}} => 2 {{1},{2},{3,4,6,7},{5}} => 1 {{1},{2},{3,4,6},{5,7}} => 1 {{1},{2},{3,4,6},{5},{7}} => 1 {{1,7},{2},{3,4},{5,6}} => 2 {{1},{2,7},{3,4},{5,6}} => 2 {{1},{2},{3,4,7},{5,6}} => 2 {{1},{2},{3,4},{5,6,7}} => 1 {{1},{2},{3,4},{5,6},{7}} => 1 {{1,7},{2},{3,4},{5},{6}} => 2 {{1},{2,7},{3,4},{5},{6}} => 2 {{1},{2},{3,4,7},{5},{6}} => 1 {{1},{2},{3,4},{5,7},{6}} => 1 {{1},{2},{3,4},{5},{6,7}} => 1 {{1},{2},{3,4},{5},{6},{7}} => 1 {{1,5,6,7},{2},{3},{4}} => 1 {{1,5,6},{2,7},{3},{4}} => 2 {{1,5,6},{2},{3,7},{4}} => 2 {{1,5,6},{2},{3},{4,7}} => 2 {{1,5,6},{2},{3},{4},{7}} => 1 {{1,5,7},{2,6},{3},{4}} => 1 {{1,5},{2,6,7},{3},{4}} => 1 {{1,5},{2,6},{3,7},{4}} => 1 {{1,5},{2,6},{3},{4,7}} => 1 {{1,5},{2,6},{3},{4},{7}} => 1 {{1,5,7},{2},{3,6},{4}} => 1 {{1,5},{2,7},{3,6},{4}} => 2 {{1,5},{2},{3,6,7},{4}} => 1 {{1,5},{2},{3,6},{4,7}} => 1 {{1,5},{2},{3,6},{4},{7}} => 1 {{1,5,7},{2},{3},{4,6}} => 1 {{1,5},{2,7},{3},{4,6}} => 2 {{1,5},{2},{3,7},{4,6}} => 2 {{1,5},{2},{3},{4,6,7}} => 1 {{1,5},{2},{3},{4,6},{7}} => 1 {{1,5,7},{2},{3},{4},{6}} => 1 {{1,5},{2,7},{3},{4},{6}} => 1 {{1,5},{2},{3,7},{4},{6}} => 1 {{1,5},{2},{3},{4,7},{6}} => 1 {{1,5},{2},{3},{4},{6,7}} => 1 {{1,5},{2},{3},{4},{6},{7}} => 1 {{1,6,7},{2,5},{3},{4}} => 2 {{1,6},{2,5,7},{3},{4}} => 2 {{1,6},{2,5},{3,7},{4}} => 2 {{1,6},{2,5},{3},{4,7}} => 2 {{1,6},{2,5},{3},{4},{7}} => 2 {{1,7},{2,5,6},{3},{4}} => 2 {{1},{2,5,6,7},{3},{4}} => 1 {{1},{2,5,6},{3,7},{4}} => 2 {{1},{2,5,6},{3},{4,7}} => 2 {{1},{2,5,6},{3},{4},{7}} => 1 {{1,7},{2,5},{3,6},{4}} => 2 {{1},{2,5,7},{3,6},{4}} => 1 {{1},{2,5},{3,6,7},{4}} => 1 {{1},{2,5},{3,6},{4,7}} => 1 {{1},{2,5},{3,6},{4},{7}} => 1 {{1,7},{2,5},{3},{4,6}} => 2 {{1},{2,5,7},{3},{4,6}} => 1 {{1},{2,5},{3,7},{4,6}} => 2 {{1},{2,5},{3},{4,6,7}} => 1 {{1},{2,5},{3},{4,6},{7}} => 1 {{1,7},{2,5},{3},{4},{6}} => 2 {{1},{2,5,7},{3},{4},{6}} => 1 {{1},{2,5},{3,7},{4},{6}} => 1 {{1},{2,5},{3},{4,7},{6}} => 1 {{1},{2,5},{3},{4},{6,7}} => 1 {{1},{2,5},{3},{4},{6},{7}} => 1 {{1,6,7},{2},{3,5},{4}} => 2 {{1,6},{2,7},{3,5},{4}} => 2 {{1,6},{2},{3,5,7},{4}} => 2 {{1,6},{2},{3,5},{4,7}} => 2 {{1,6},{2},{3,5},{4},{7}} => 2 {{1,7},{2,6},{3,5},{4}} => 3 {{1},{2,6,7},{3,5},{4}} => 2 {{1},{2,6},{3,5,7},{4}} => 2 {{1},{2,6},{3,5},{4,7}} => 2 {{1},{2,6},{3,5},{4},{7}} => 2 {{1,7},{2},{3,5,6},{4}} => 2 {{1},{2,7},{3,5,6},{4}} => 2 {{1},{2},{3,5,6,7},{4}} => 1 {{1},{2},{3,5,6},{4,7}} => 2 {{1},{2},{3,5,6},{4},{7}} => 1 {{1,7},{2},{3,5},{4,6}} => 2 {{1},{2,7},{3,5},{4,6}} => 2 {{1},{2},{3,5,7},{4,6}} => 1 {{1},{2},{3,5},{4,6,7}} => 1 {{1},{2},{3,5},{4,6},{7}} => 1 {{1,7},{2},{3,5},{4},{6}} => 2 {{1},{2,7},{3,5},{4},{6}} => 2 {{1},{2},{3,5,7},{4},{6}} => 1 {{1},{2},{3,5},{4,7},{6}} => 1 {{1},{2},{3,5},{4},{6,7}} => 1 {{1},{2},{3,5},{4},{6},{7}} => 1 {{1,6,7},{2},{3},{4,5}} => 2 {{1,6},{2,7},{3},{4,5}} => 2 {{1,6},{2},{3,7},{4,5}} => 2 {{1,6},{2},{3},{4,5,7}} => 2 {{1,6},{2},{3},{4,5},{7}} => 2 {{1,7},{2,6},{3},{4,5}} => 3 {{1},{2,6,7},{3},{4,5}} => 2 {{1},{2,6},{3,7},{4,5}} => 2 {{1},{2,6},{3},{4,5,7}} => 2 {{1},{2,6},{3},{4,5},{7}} => 2 {{1,7},{2},{3,6},{4,5}} => 3 {{1},{2,7},{3,6},{4,5}} => 3 {{1},{2},{3,6,7},{4,5}} => 2 {{1},{2},{3,6},{4,5,7}} => 2 {{1},{2},{3,6},{4,5},{7}} => 2 {{1,7},{2},{3},{4,5,6}} => 2 {{1},{2,7},{3},{4,5,6}} => 2 {{1},{2},{3,7},{4,5,6}} => 2 {{1},{2},{3},{4,5,6,7}} => 1 {{1},{2},{3},{4,5,6},{7}} => 1 {{1,7},{2},{3},{4,5},{6}} => 2 {{1},{2,7},{3},{4,5},{6}} => 2 {{1},{2},{3,7},{4,5},{6}} => 2 {{1},{2},{3},{4,5,7},{6}} => 1 {{1},{2},{3},{4,5},{6,7}} => 1 {{1},{2},{3},{4,5},{6},{7}} => 1 {{1,6,7},{2},{3},{4},{5}} => 1 {{1,6},{2,7},{3},{4},{5}} => 1 {{1,6},{2},{3,7},{4},{5}} => 1 {{1,6},{2},{3},{4,7},{5}} => 1 {{1,6},{2},{3},{4},{5,7}} => 1 {{1,6},{2},{3},{4},{5},{7}} => 1 {{1,7},{2,6},{3},{4},{5}} => 2 {{1},{2,6,7},{3},{4},{5}} => 1 {{1},{2,6},{3,7},{4},{5}} => 1 {{1},{2,6},{3},{4,7},{5}} => 1 {{1},{2,6},{3},{4},{5,7}} => 1 {{1},{2,6},{3},{4},{5},{7}} => 1 {{1,7},{2},{3,6},{4},{5}} => 2 {{1},{2,7},{3,6},{4},{5}} => 2 {{1},{2},{3,6,7},{4},{5}} => 1 {{1},{2},{3,6},{4,7},{5}} => 1 {{1},{2},{3,6},{4},{5,7}} => 1 {{1},{2},{3,6},{4},{5},{7}} => 1 {{1,7},{2},{3},{4,6},{5}} => 2 {{1},{2,7},{3},{4,6},{5}} => 2 {{1},{2},{3,7},{4,6},{5}} => 2 {{1},{2},{3},{4,6,7},{5}} => 1 {{1},{2},{3},{4,6},{5,7}} => 1 {{1},{2},{3},{4,6},{5},{7}} => 1 {{1,7},{2},{3},{4},{5,6}} => 2 {{1},{2,7},{3},{4},{5,6}} => 2 {{1},{2},{3,7},{4},{5,6}} => 2 {{1},{2},{3},{4,7},{5,6}} => 2 {{1},{2},{3},{4},{5,6,7}} => 1 {{1},{2},{3},{4},{5,6},{7}} => 1 {{1,7},{2},{3},{4},{5},{6}} => 1 {{1},{2,7},{3},{4},{5},{6}} => 1 {{1},{2},{3,7},{4},{5},{6}} => 1 {{1},{2},{3},{4,7},{5},{6}} => 1 {{1},{2},{3},{4},{5,7},{6}} => 1 {{1},{2},{3},{4},{5},{6,7}} => 1 {{1},{2},{3},{4},{5},{6},{7}} => 0 {{1},{2},{3,4,5,6,7,8}} => 1 {{1},{2,4,5,6,7,8},{3}} => 1 {{1},{2,3,5,6,7,8},{4}} => 1 {{1},{2,3,4,6,7,8},{5}} => 1 {{1},{2,3,4,5,7,8},{6}} => 1 {{1},{2,3,4,5,6,7},{8}} => 1 {{1},{2,3,4,5,6,8},{7}} => 1 {{1},{2,3,4,5,6,7,8}} => 1 {{1,2},{3,4,5,6,7,8}} => 1 {{1,4,5,6,7,8},{2},{3}} => 1 {{1,3,5,6,7,8},{2},{4}} => 1 {{1,3,4,5,6,7,8},{2}} => 1 {{1,4,5,6,7,8},{2,3}} => 2 {{1,2,4,5,6,7,8},{3}} => 1 {{1,2,5,6,7,8},{3,4}} => 2 {{1,2,3,5,6,7,8},{4}} => 1 {{1,2,3,6,7,8},{4,5}} => 2 {{1,2,3,4,6,7,8},{5}} => 1 {{1,2,3,4,5,6},{7,8}} => 1 {{1,2,3,4,7,8},{5,6}} => 2 {{1,2,3,4,5,7,8},{6}} => 1 {{1,2,3,4,5,6,7},{8}} => 1 {{1,8},{2,3,4,5,6,7}} => 2 {{1,2,3,4,5,8},{6,7}} => 2 {{1,2,3,4,5,6,8},{7}} => 1 {{1,2,3,4,5,6,7,8}} => 1 {{1,3,5,6,7,8},{2,4}} => 1 {{1,3,4,6,7,8},{2,5}} => 2 {{1,2,4,6,7,8},{3,5}} => 1 {{1,3,4,5,7,8},{2,6}} => 2 {{1,2,4,5,7,8},{3,6}} => 2 {{1,2,3,5,7,8},{4,6}} => 1 {{1,3,4,5,6,8},{2,7}} => 2 {{1,2,4,5,6,8},{3,7}} => 2 {{1,2,3,5,6,8},{4,7}} => 2 {{1,2,3,4,6,8},{5,7}} => 1 {{1,3,4,5,6,7},{2,8}} => 2 {{1,2,4,5,6,7},{3,8}} => 2 {{1,2,3,5,6,7},{4,8}} => 2 {{1,2,3,4,6,7},{5,8}} => 2 {{1,2,3,4,5,7},{6,8}} => 1 {{1,3},{2,4,5,6,7,8}} => 1 {{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 ----------------------------------------------------------------------------- Created: Jun 06, 2015 at 00:23 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: May 27, 2021 at 11:25 by Martin Rubey