***************************************************************************** * 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: St001840 ----------------------------------------------------------------------------- Collection: Set partitions ----------------------------------------------------------------------------- Description: The number of descents of a set partition. The Mahonian representation of a set partition $\{B_1,\dots,B_k\}$ of $\{1,\dots,n\}$ is the restricted growth word $w_1\dots w_n\}$ obtained by sorting the blocks of the set partition according to their maximal element, and setting $w_i$ to the index of the block containing $i$. The word $w$ has a descent at position $i$ if $w_i > w_{i+1}$. ----------------------------------------------------------------------------- References: [1] Liu, S.-H. Mahonian and Euler-Mahonian statistics for set partitions [[arXiv:2202.02089]] ----------------------------------------------------------------------------- Code: def to_restricted_growth_word_blocks_max(self): w = [0] * self.size() for i, B in enumerate(sorted(self, key=lambda B: max(B))): for j in B: w[j-1] = i return w def statistic(p): w = to_restricted_growth_word_blocks_max(p) return sum(1 for i in range(len(w)-1) if w[i] > w[i+1]) ----------------------------------------------------------------------------- Statistic values: {{1}} => 0 {{1,2}} => 0 {{1},{2}} => 0 {{1,2,3}} => 0 {{1,2},{3}} => 0 {{1,3},{2}} => 1 {{1},{2,3}} => 0 {{1},{2},{3}} => 0 {{1,2,3,4}} => 0 {{1,2,3},{4}} => 0 {{1,2,4},{3}} => 1 {{1,2},{3,4}} => 0 {{1,2},{3},{4}} => 0 {{1,3,4},{2}} => 1 {{1,3},{2,4}} => 1 {{1,3},{2},{4}} => 1 {{1,4},{2,3}} => 1 {{1},{2,3,4}} => 0 {{1},{2,3},{4}} => 0 {{1,4},{2},{3}} => 1 {{1},{2,4},{3}} => 1 {{1},{2},{3,4}} => 0 {{1},{2},{3},{4}} => 0 {{1,2,3,4,5}} => 0 {{1,2,3,4},{5}} => 0 {{1,2,3,5},{4}} => 1 {{1,2,3},{4,5}} => 0 {{1,2,3},{4},{5}} => 0 {{1,2,4,5},{3}} => 1 {{1,2,4},{3,5}} => 1 {{1,2,4},{3},{5}} => 1 {{1,2,5},{3,4}} => 1 {{1,2},{3,4,5}} => 0 {{1,2},{3,4},{5}} => 0 {{1,2,5},{3},{4}} => 1 {{1,2},{3,5},{4}} => 1 {{1,2},{3},{4,5}} => 0 {{1,2},{3},{4},{5}} => 0 {{1,3,4,5},{2}} => 1 {{1,3,4},{2,5}} => 1 {{1,3,4},{2},{5}} => 1 {{1,3,5},{2,4}} => 2 {{1,3},{2,4,5}} => 1 {{1,3},{2,4},{5}} => 1 {{1,3,5},{2},{4}} => 2 {{1,3},{2,5},{4}} => 1 {{1,3},{2},{4,5}} => 1 {{1,3},{2},{4},{5}} => 1 {{1,4,5},{2,3}} => 1 {{1,4},{2,3,5}} => 1 {{1,4},{2,3},{5}} => 1 {{1,5},{2,3,4}} => 1 {{1},{2,3,4,5}} => 0 {{1},{2,3,4},{5}} => 0 {{1,5},{2,3},{4}} => 1 {{1},{2,3,5},{4}} => 1 {{1},{2,3},{4,5}} => 0 {{1},{2,3},{4},{5}} => 0 {{1,4,5},{2},{3}} => 1 {{1,4},{2,5},{3}} => 1 {{1,4},{2},{3,5}} => 2 {{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}} => 1 {{1},{2,5},{3,4}} => 1 {{1},{2},{3,4,5}} => 0 {{1},{2},{3,4},{5}} => 0 {{1,5},{2},{3},{4}} => 1 {{1},{2,5},{3},{4}} => 1 {{1},{2},{3,5},{4}} => 1 {{1},{2},{3},{4,5}} => 0 {{1},{2},{3},{4},{5}} => 0 {{1,2,3,4,5,6}} => 0 {{1,2,3,4,5},{6}} => 0 {{1,2,3,4,6},{5}} => 1 {{1,2,3,4},{5,6}} => 0 {{1,2,3,4},{5},{6}} => 0 {{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}} => 1 {{1,2,3},{4,5,6}} => 0 {{1,2,3},{4,5},{6}} => 0 {{1,2,3,6},{4},{5}} => 1 {{1,2,3},{4,6},{5}} => 1 {{1,2,3},{4},{5,6}} => 0 {{1,2,3},{4},{5},{6}} => 0 {{1,2,4,5,6},{3}} => 1 {{1,2,4,5},{3,6}} => 1 {{1,2,4,5},{3},{6}} => 1 {{1,2,4,6},{3,5}} => 2 {{1,2,4},{3,5,6}} => 1 {{1,2,4},{3,5},{6}} => 1 {{1,2,4,6},{3},{5}} => 2 {{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}} => 1 {{1,2,5},{3,4,6}} => 1 {{1,2,5},{3,4},{6}} => 1 {{1,2,6},{3,4,5}} => 1 {{1,2},{3,4,5,6}} => 0 {{1,2},{3,4,5},{6}} => 0 {{1,2,6},{3,4},{5}} => 1 {{1,2},{3,4,6},{5}} => 1 {{1,2},{3,4},{5,6}} => 0 {{1,2},{3,4},{5},{6}} => 0 {{1,2,5,6},{3},{4}} => 1 {{1,2,5},{3,6},{4}} => 1 {{1,2,5},{3},{4,6}} => 2 {{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}} => 1 {{1,2},{3,6},{4,5}} => 1 {{1,2},{3},{4,5,6}} => 0 {{1,2},{3},{4,5},{6}} => 0 {{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}} => 0 {{1,2},{3},{4},{5},{6}} => 0 {{1,3,4,5,6},{2}} => 1 {{1,3,4,5},{2,6}} => 1 {{1,3,4,5},{2},{6}} => 1 {{1,3,4,6},{2,5}} => 2 {{1,3,4},{2,5,6}} => 1 {{1,3,4},{2,5},{6}} => 1 {{1,3,4,6},{2},{5}} => 2 {{1,3,4},{2,6},{5}} => 1 {{1,3,4},{2},{5,6}} => 1 {{1,3,4},{2},{5},{6}} => 1 {{1,3,5,6},{2,4}} => 2 {{1,3,5},{2,4,6}} => 2 {{1,3,5},{2,4},{6}} => 2 {{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}} => 2 {{1,3},{2,4,6},{5}} => 2 {{1,3},{2,4},{5,6}} => 1 {{1,3},{2,4},{5},{6}} => 1 {{1,3,5,6},{2},{4}} => 2 {{1,3,5},{2,6},{4}} => 2 {{1,3,5},{2},{4,6}} => 2 {{1,3,5},{2},{4},{6}} => 2 {{1,3,6},{2,5},{4}} => 2 {{1,3},{2,5,6},{4}} => 1 {{1,3},{2,5},{4,6}} => 2 {{1,3},{2,5},{4},{6}} => 1 {{1,3,6},{2},{4,5}} => 2 {{1,3},{2,6},{4,5}} => 1 {{1,3},{2},{4,5,6}} => 1 {{1,3},{2},{4,5},{6}} => 1 {{1,3,6},{2},{4},{5}} => 2 {{1,3},{2,6},{4},{5}} => 1 {{1,3},{2},{4,6},{5}} => 2 {{1,3},{2},{4},{5,6}} => 1 {{1,3},{2},{4},{5},{6}} => 1 {{1,4,5,6},{2,3}} => 1 {{1,4,5},{2,3,6}} => 1 {{1,4,5},{2,3},{6}} => 1 {{1,4,6},{2,3,5}} => 2 {{1,4},{2,3,5,6}} => 1 {{1,4},{2,3,5},{6}} => 1 {{1,4,6},{2,3},{5}} => 2 {{1,4},{2,3,6},{5}} => 1 {{1,4},{2,3},{5,6}} => 1 {{1,4},{2,3},{5},{6}} => 1 {{1,5,6},{2,3,4}} => 1 {{1,5},{2,3,4,6}} => 1 {{1,5},{2,3,4},{6}} => 1 {{1,6},{2,3,4,5}} => 1 {{1},{2,3,4,5,6}} => 0 {{1},{2,3,4,5},{6}} => 0 {{1,6},{2,3,4},{5}} => 1 {{1},{2,3,4,6},{5}} => 1 {{1},{2,3,4},{5,6}} => 0 {{1},{2,3,4},{5},{6}} => 0 {{1,5,6},{2,3},{4}} => 1 {{1,5},{2,3,6},{4}} => 1 {{1,5},{2,3},{4,6}} => 2 {{1,5},{2,3},{4},{6}} => 1 {{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}} => 1 {{1},{2,3,6},{4,5}} => 1 {{1},{2,3},{4,5,6}} => 0 {{1},{2,3},{4,5},{6}} => 0 {{1,6},{2,3},{4},{5}} => 1 {{1},{2,3,6},{4},{5}} => 1 {{1},{2,3},{4,6},{5}} => 1 {{1},{2,3},{4},{5,6}} => 0 {{1},{2,3},{4},{5},{6}} => 0 {{1,4,5,6},{2},{3}} => 1 {{1,4,5},{2,6},{3}} => 1 {{1,4,5},{2},{3,6}} => 2 {{1,4,5},{2},{3},{6}} => 1 {{1,4,6},{2,5},{3}} => 3 {{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}} => 2 {{1,4},{2,6},{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},{2,6},{3},{5}} => 1 {{1,4},{2},{3,6},{5}} => 2 {{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}} => 1 {{1},{2,4,5},{3},{6}} => 1 {{1,6},{2,4},{3,5}} => 2 {{1},{2,4,6},{3,5}} => 2 {{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}} => 2 {{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}} => 1 {{1,5},{2,6},{3,4}} => 1 {{1,5},{2},{3,4,6}} => 2 {{1,5},{2},{3,4},{6}} => 1 {{1,6},{2,5},{3,4}} => 2 {{1},{2,5,6},{3,4}} => 1 {{1},{2,5},{3,4,6}} => 1 {{1},{2,5},{3,4},{6}} => 1 {{1,6},{2},{3,4,5}} => 1 {{1},{2,6},{3,4,5}} => 1 {{1},{2},{3,4,5,6}} => 0 {{1},{2},{3,4,5},{6}} => 0 {{1,6},{2},{3,4},{5}} => 1 {{1},{2,6},{3,4},{5}} => 1 {{1},{2},{3,4,6},{5}} => 1 {{1},{2},{3,4},{5,6}} => 0 {{1},{2},{3,4},{5},{6}} => 0 {{1,5,6},{2},{3},{4}} => 1 {{1,5},{2,6},{3},{4}} => 1 {{1,5},{2},{3,6},{4}} => 2 {{1,5},{2},{3},{4,6}} => 2 {{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}} => 2 {{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}} => 1 {{1},{2,6},{3},{4,5}} => 1 {{1},{2},{3,6},{4,5}} => 1 {{1},{2},{3},{4,5,6}} => 0 {{1},{2},{3},{4,5},{6}} => 0 {{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}} => 0 {{1},{2},{3},{4},{5},{6}} => 0 {{1,2,3,4,5,6,7}} => 0 {{1,2,3,4,5,6},{7}} => 0 {{1,2,3,4,5,7},{6}} => 1 {{1,2,3,4,5},{6,7}} => 0 {{1,2,3,4,5},{6},{7}} => 0 {{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}} => 1 {{1,2,3,4},{5,6,7}} => 0 {{1,2,3,4},{5,6},{7}} => 0 {{1,2,3,4,7},{5},{6}} => 1 {{1,2,3,4},{5,7},{6}} => 1 {{1,2,3,4},{5},{6,7}} => 0 {{1,2,3,4},{5},{6},{7}} => 0 {{1,2,3,5,6,7},{4}} => 1 {{1,2,3,5,6},{4,7}} => 1 {{1,2,3,5,6},{4},{7}} => 1 {{1,2,3,5,7},{4,6}} => 2 {{1,2,3,5},{4,6,7}} => 1 {{1,2,3,5},{4,6},{7}} => 1 {{1,2,3,5,7},{4},{6}} => 2 {{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}} => 1 {{1,2,3,6},{4,5,7}} => 1 {{1,2,3,6},{4,5},{7}} => 1 {{1,2,3,7},{4,5,6}} => 1 {{1,2,3},{4,5,6,7}} => 0 {{1,2,3},{4,5,6},{7}} => 0 {{1,2,3,7},{4,5},{6}} => 1 {{1,2,3},{4,5,7},{6}} => 1 {{1,2,3},{4,5},{6,7}} => 0 {{1,2,3},{4,5},{6},{7}} => 0 {{1,2,3,6,7},{4},{5}} => 1 {{1,2,3,6},{4,7},{5}} => 1 {{1,2,3,6},{4},{5,7}} => 2 {{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}} => 1 {{1,2,3},{4,7},{5,6}} => 1 {{1,2,3},{4},{5,6,7}} => 0 {{1,2,3},{4},{5,6},{7}} => 0 {{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}} => 0 {{1,2,3},{4},{5},{6},{7}} => 0 {{1,2,4,5,6,7},{3}} => 1 {{1,2,4,5,6},{3,7}} => 1 {{1,2,4,5,6},{3},{7}} => 1 {{1,2,4,5,7},{3,6}} => 2 {{1,2,4,5},{3,6,7}} => 1 {{1,2,4,5},{3,6},{7}} => 1 {{1,2,4,5,7},{3},{6}} => 2 {{1,2,4,5},{3,7},{6}} => 1 {{1,2,4,5},{3},{6,7}} => 1 {{1,2,4,5},{3},{6},{7}} => 1 {{1,2,4,6,7},{3,5}} => 2 {{1,2,4,6},{3,5,7}} => 2 {{1,2,4,6},{3,5},{7}} => 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 {{1,2,4,7},{3,5},{6}} => 2 {{1,2,4},{3,5,7},{6}} => 2 {{1,2,4},{3,5},{6,7}} => 1 {{1,2,4},{3,5},{6},{7}} => 1 {{1,2,4,6,7},{3},{5}} => 2 {{1,2,4,6},{3,7},{5}} => 2 {{1,2,4,6},{3},{5,7}} => 2 {{1,2,4,6},{3},{5},{7}} => 2 {{1,2,4,7},{3,6},{5}} => 2 {{1,2,4},{3,6,7},{5}} => 1 {{1,2,4},{3,6},{5,7}} => 2 {{1,2,4},{3,6},{5},{7}} => 1 {{1,2,4,7},{3},{5,6}} => 2 {{1,2,4},{3,7},{5,6}} => 1 {{1,2,4},{3},{5,6,7}} => 1 {{1,2,4},{3},{5,6},{7}} => 1 {{1,2,4,7},{3},{5},{6}} => 2 {{1,2,4},{3,7},{5},{6}} => 1 {{1,2,4},{3},{5,7},{6}} => 2 {{1,2,4},{3},{5},{6,7}} => 1 {{1,2,4},{3},{5},{6},{7}} => 1 {{1,2,5,6,7},{3,4}} => 1 {{1,2,5,6},{3,4,7}} => 1 {{1,2,5,6},{3,4},{7}} => 1 {{1,2,5,7},{3,4,6}} => 2 {{1,2,5},{3,4,6,7}} => 1 {{1,2,5},{3,4,6},{7}} => 1 {{1,2,5,7},{3,4},{6}} => 2 {{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},{3,4,5}} => 1 {{1,2,6},{3,4,5,7}} => 1 {{1,2,6},{3,4,5},{7}} => 1 {{1,2,7},{3,4,5,6}} => 1 {{1,2},{3,4,5,6,7}} => 0 {{1,2},{3,4,5,6},{7}} => 0 {{1,2,7},{3,4,5},{6}} => 1 {{1,2},{3,4,5,7},{6}} => 1 {{1,2},{3,4,5},{6,7}} => 0 {{1,2},{3,4,5},{6},{7}} => 0 {{1,2,6,7},{3,4},{5}} => 1 {{1,2,6},{3,4,7},{5}} => 1 {{1,2,6},{3,4},{5,7}} => 2 {{1,2,6},{3,4},{5},{7}} => 1 {{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}} => 1 {{1,2},{3,4,7},{5,6}} => 1 {{1,2},{3,4},{5,6,7}} => 0 {{1,2},{3,4},{5,6},{7}} => 0 {{1,2,7},{3,4},{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}} => 0 {{1,2},{3,4},{5},{6},{7}} => 0 {{1,2,5,6,7},{3},{4}} => 1 {{1,2,5,6},{3,7},{4}} => 1 {{1,2,5,6},{3},{4,7}} => 2 {{1,2,5,6},{3},{4},{7}} => 1 {{1,2,5,7},{3,6},{4}} => 3 {{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}} => 2 {{1,2,5},{3,7},{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},{3,7},{4},{6}} => 1 {{1,2,5},{3},{4,7},{6}} => 2 {{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}} => 1 {{1,2},{3,5,6},{4},{7}} => 1 {{1,2,7},{3,5},{4,6}} => 2 {{1,2},{3,5,7},{4,6}} => 2 {{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}} => 2 {{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}} => 1 {{1,2,6},{3,7},{4,5}} => 1 {{1,2,6},{3},{4,5,7}} => 2 {{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},{4,5,7}} => 1 {{1,2},{3,6},{4,5},{7}} => 1 {{1,2,7},{3},{4,5,6}} => 1 {{1,2},{3,7},{4,5,6}} => 1 {{1,2},{3},{4,5,6,7}} => 0 {{1,2},{3},{4,5,6},{7}} => 0 {{1,2,7},{3},{4,5},{6}} => 1 {{1,2},{3,7},{4,5},{6}} => 1 {{1,2},{3},{4,5,7},{6}} => 1 {{1,2},{3},{4,5},{6,7}} => 0 {{1,2},{3},{4,5},{6},{7}} => 0 {{1,2,6,7},{3},{4},{5}} => 1 {{1,2,6},{3,7},{4},{5}} => 1 {{1,2,6},{3},{4,7},{5}} => 2 {{1,2,6},{3},{4},{5,7}} => 2 {{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}} => 2 {{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}} => 1 {{1,2},{3,7},{4},{5,6}} => 1 {{1,2},{3},{4,7},{5,6}} => 1 {{1,2},{3},{4},{5,6,7}} => 0 {{1,2},{3},{4},{5,6},{7}} => 0 {{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}} => 0 {{1,2},{3},{4},{5},{6},{7}} => 0 {{1,3,4,5,6,7},{2}} => 1 {{1,3,4,5,6},{2,7}} => 1 {{1,3,4,5,6},{2},{7}} => 1 {{1,3,4,5,7},{2,6}} => 2 {{1,3,4,5},{2,6,7}} => 1 {{1,3,4,5},{2,6},{7}} => 1 {{1,3,4,5,7},{2},{6}} => 2 {{1,3,4,5},{2,7},{6}} => 1 {{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}} => 1 {{1,3,4},{2,5,6},{7}} => 1 {{1,3,4,7},{2,5},{6}} => 2 {{1,3,4},{2,5,7},{6}} => 2 {{1,3,4},{2,5},{6,7}} => 1 {{1,3,4},{2,5},{6},{7}} => 1 {{1,3,4,6,7},{2},{5}} => 2 {{1,3,4,6},{2,7},{5}} => 2 {{1,3,4,6},{2},{5,7}} => 2 {{1,3,4,6},{2},{5},{7}} => 2 {{1,3,4,7},{2,6},{5}} => 2 {{1,3,4},{2,6,7},{5}} => 1 {{1,3,4},{2,6},{5,7}} => 2 {{1,3,4},{2,6},{5},{7}} => 1 {{1,3,4,7},{2},{5,6}} => 2 {{1,3,4},{2,7},{5,6}} => 1 {{1,3,4},{2},{5,6,7}} => 1 {{1,3,4},{2},{5,6},{7}} => 1 {{1,3,4,7},{2},{5},{6}} => 2 {{1,3,4},{2,7},{5},{6}} => 1 {{1,3,4},{2},{5,7},{6}} => 2 {{1,3,4},{2},{5},{6,7}} => 1 {{1,3,4},{2},{5},{6},{7}} => 1 {{1,3,5,6,7},{2,4}} => 2 {{1,3,5,6},{2,4,7}} => 2 {{1,3,5,6},{2,4},{7}} => 2 {{1,3,5,7},{2,4,6}} => 3 {{1,3,5},{2,4,6,7}} => 2 {{1,3,5},{2,4,6},{7}} => 2 {{1,3,5,7},{2,4},{6}} => 3 {{1,3,5},{2,4,7},{6}} => 2 {{1,3,5},{2,4},{6,7}} => 2 {{1,3,5},{2,4},{6},{7}} => 2 {{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}} => 2 {{1,3},{2,4,5},{6,7}} => 1 {{1,3},{2,4,5},{6},{7}} => 1 {{1,3,6,7},{2,4},{5}} => 2 {{1,3,6},{2,4,7},{5}} => 2 {{1,3,6},{2,4},{5,7}} => 3 {{1,3,6},{2,4},{5},{7}} => 2 {{1,3,7},{2,4,6},{5}} => 3 {{1,3},{2,4,6,7},{5}} => 2 {{1,3},{2,4,6},{5,7}} => 2 {{1,3},{2,4,6},{5},{7}} => 2 {{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}} => 2 {{1,3},{2,4,7},{5},{6}} => 2 {{1,3},{2,4},{5,7},{6}} => 2 {{1,3},{2,4},{5},{6,7}} => 1 {{1,3},{2,4},{5},{6},{7}} => 1 {{1,3,5,6,7},{2},{4}} => 2 {{1,3,5,6},{2,7},{4}} => 2 {{1,3,5,6},{2},{4,7}} => 2 {{1,3,5,6},{2},{4},{7}} => 2 {{1,3,5,7},{2,6},{4}} => 3 {{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}} => 3 {{1,3,5},{2,7},{4,6}} => 2 {{1,3,5},{2},{4,6,7}} => 2 {{1,3,5},{2},{4,6},{7}} => 2 {{1,3,5,7},{2},{4},{6}} => 3 {{1,3,5},{2,7},{4},{6}} => 2 {{1,3,5},{2},{4,7},{6}} => 2 {{1,3,5},{2},{4},{6,7}} => 2 {{1,3,5},{2},{4},{6},{7}} => 2 {{1,3,6,7},{2,5},{4}} => 2 {{1,3,6},{2,5,7},{4}} => 3 {{1,3,6},{2,5},{4,7}} => 2 {{1,3,6},{2,5},{4},{7}} => 2 {{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}} => 3 {{1,3},{2,5,7},{4,6}} => 2 {{1,3},{2,5},{4,6,7}} => 2 {{1,3},{2,5},{4,6},{7}} => 2 {{1,3,7},{2,5},{4},{6}} => 2 {{1,3},{2,5,7},{4},{6}} => 2 {{1,3},{2,5},{4,7},{6}} => 2 {{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}} => 2 {{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}} => 1 {{1,3},{2,6},{4,5,7}} => 2 {{1,3},{2,6},{4,5},{7}} => 1 {{1,3,7},{2},{4,5,6}} => 2 {{1,3},{2,7},{4,5,6}} => 1 {{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}} => 1 {{1,3},{2},{4,5,7},{6}} => 2 {{1,3},{2},{4,5},{6,7}} => 1 {{1,3},{2},{4,5},{6},{7}} => 1 {{1,3,6,7},{2},{4},{5}} => 2 {{1,3,6},{2,7},{4},{5}} => 2 {{1,3,6},{2},{4,7},{5}} => 2 {{1,3,6},{2},{4},{5,7}} => 3 {{1,3,6},{2},{4},{5},{7}} => 2 {{1,3,7},{2,6},{4},{5}} => 2 {{1,3},{2,6,7},{4},{5}} => 1 {{1,3},{2,6},{4,7},{5}} => 2 {{1,3},{2,6},{4},{5,7}} => 2 {{1,3},{2,6},{4},{5},{7}} => 1 {{1,3,7},{2},{4,6},{5}} => 3 {{1,3},{2,7},{4,6},{5}} => 2 {{1,3},{2},{4,6,7},{5}} => 2 {{1,3},{2},{4,6},{5,7}} => 2 {{1,3},{2},{4,6},{5},{7}} => 2 {{1,3,7},{2},{4},{5,6}} => 2 {{1,3},{2,7},{4},{5,6}} => 1 {{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}} => 2 {{1,3},{2,7},{4},{5},{6}} => 1 {{1,3},{2},{4,7},{5},{6}} => 2 {{1,3},{2},{4},{5,7},{6}} => 2 {{1,3},{2},{4},{5},{6,7}} => 1 {{1,3},{2},{4},{5},{6},{7}} => 1 {{1,4,5,6,7},{2,3}} => 1 {{1,4,5,6},{2,3,7}} => 1 {{1,4,5,6},{2,3},{7}} => 1 {{1,4,5,7},{2,3,6}} => 2 {{1,4,5},{2,3,6,7}} => 1 {{1,4,5},{2,3,6},{7}} => 1 {{1,4,5,7},{2,3},{6}} => 2 {{1,4,5},{2,3,7},{6}} => 1 {{1,4,5},{2,3},{6,7}} => 1 {{1,4,5},{2,3},{6},{7}} => 1 {{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}} => 1 {{1,4},{2,3,5,6},{7}} => 1 {{1,4,7},{2,3,5},{6}} => 2 {{1,4},{2,3,5,7},{6}} => 2 {{1,4},{2,3,5},{6,7}} => 1 {{1,4},{2,3,5},{6},{7}} => 1 {{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}} => 1 {{1,4},{2,3,6},{5,7}} => 2 {{1,4},{2,3,6},{5},{7}} => 1 {{1,4,7},{2,3},{5,6}} => 2 {{1,4},{2,3,7},{5,6}} => 1 {{1,4},{2,3},{5,6,7}} => 1 {{1,4},{2,3},{5,6},{7}} => 1 {{1,4,7},{2,3},{5},{6}} => 2 {{1,4},{2,3,7},{5},{6}} => 1 {{1,4},{2,3},{5,7},{6}} => 2 {{1,4},{2,3},{5},{6,7}} => 1 {{1,4},{2,3},{5},{6},{7}} => 1 {{1,5,6,7},{2,3,4}} => 1 {{1,5,6},{2,3,4,7}} => 1 {{1,5,6},{2,3,4},{7}} => 1 {{1,5,7},{2,3,4,6}} => 2 {{1,5},{2,3,4,6,7}} => 1 {{1,5},{2,3,4,6},{7}} => 1 {{1,5,7},{2,3,4},{6}} => 2 {{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},{2,3,4,5}} => 1 {{1,6},{2,3,4,5,7}} => 1 {{1,6},{2,3,4,5},{7}} => 1 {{1,7},{2,3,4,5,6}} => 1 {{1},{2,3,4,5,6,7}} => 0 {{1},{2,3,4,5,6},{7}} => 0 {{1,7},{2,3,4,5},{6}} => 1 {{1},{2,3,4,5,7},{6}} => 1 {{1},{2,3,4,5},{6,7}} => 0 {{1},{2,3,4,5},{6},{7}} => 0 {{1,6,7},{2,3,4},{5}} => 1 {{1,6},{2,3,4,7},{5}} => 1 {{1,6},{2,3,4},{5,7}} => 2 {{1,6},{2,3,4},{5},{7}} => 1 {{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}} => 1 {{1},{2,3,4,7},{5,6}} => 1 {{1},{2,3,4},{5,6,7}} => 0 {{1},{2,3,4},{5,6},{7}} => 0 {{1,7},{2,3,4},{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}} => 0 {{1},{2,3,4},{5},{6},{7}} => 0 {{1,5,6,7},{2,3},{4}} => 1 {{1,5,6},{2,3,7},{4}} => 1 {{1,5,6},{2,3},{4,7}} => 2 {{1,5,6},{2,3},{4},{7}} => 1 {{1,5,7},{2,3,6},{4}} => 3 {{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}} => 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}} => 1 {{1,5},{2,3},{4,7},{6}} => 2 {{1,5},{2,3},{4},{6,7}} => 1 {{1,5},{2,3},{4},{6},{7}} => 1 {{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}} => 1 {{1},{2,3,5,6},{4},{7}} => 1 {{1,7},{2,3,5},{4,6}} => 2 {{1},{2,3,5,7},{4,6}} => 2 {{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}} => 2 {{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}} => 1 {{1,6},{2,3,7},{4,5}} => 1 {{1,6},{2,3},{4,5,7}} => 2 {{1,6},{2,3},{4,5},{7}} => 1 {{1,7},{2,3,6},{4,5}} => 2 {{1},{2,3,6,7},{4,5}} => 1 {{1},{2,3,6},{4,5,7}} => 1 {{1},{2,3,6},{4,5},{7}} => 1 {{1,7},{2,3},{4,5,6}} => 1 {{1},{2,3,7},{4,5,6}} => 1 {{1},{2,3},{4,5,6,7}} => 0 {{1},{2,3},{4,5,6},{7}} => 0 {{1,7},{2,3},{4,5},{6}} => 1 {{1},{2,3,7},{4,5},{6}} => 1 {{1},{2,3},{4,5,7},{6}} => 1 {{1},{2,3},{4,5},{6,7}} => 0 {{1},{2,3},{4,5},{6},{7}} => 0 {{1,6,7},{2,3},{4},{5}} => 1 {{1,6},{2,3,7},{4},{5}} => 1 {{1,6},{2,3},{4,7},{5}} => 2 {{1,6},{2,3},{4},{5,7}} => 2 {{1,6},{2,3},{4},{5},{7}} => 1 {{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}} => 2 {{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}} => 1 {{1},{2,3,7},{4},{5,6}} => 1 {{1},{2,3},{4,7},{5,6}} => 1 {{1},{2,3},{4},{5,6,7}} => 0 {{1},{2,3},{4},{5,6},{7}} => 0 {{1,7},{2,3},{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}} => 0 {{1},{2,3},{4},{5},{6},{7}} => 0 {{1,4,5,6,7},{2},{3}} => 1 {{1,4,5,6},{2,7},{3}} => 1 {{1,4,5,6},{2},{3,7}} => 2 {{1,4,5,6},{2},{3},{7}} => 1 {{1,4,5,7},{2,6},{3}} => 3 {{1,4,5},{2,6,7},{3}} => 1 {{1,4,5},{2,6},{3,7}} => 1 {{1,4,5},{2,6},{3},{7}} => 1 {{1,4,5,7},{2},{3,6}} => 2 {{1,4,5},{2,7},{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},{2,7},{3},{6}} => 1 {{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}} => 3 {{1,4,6},{2,5,7},{3}} => 2 {{1,4,6},{2,5},{3,7}} => 3 {{1,4,6},{2,5},{3},{7}} => 3 {{1,4,7},{2,5,6},{3}} => 3 {{1,4},{2,5,6,7},{3}} => 1 {{1,4},{2,5,6},{3,7}} => 1 {{1,4},{2,5,6},{3},{7}} => 1 {{1,4,7},{2,5},{3,6}} => 2 {{1,4},{2,5,7},{3,6}} => 3 {{1,4},{2,5},{3,6,7}} => 1 {{1,4},{2,5},{3,6},{7}} => 1 {{1,4,7},{2,5},{3},{6}} => 3 {{1,4},{2,5,7},{3},{6}} => 2 {{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}} => 2 {{1,4,6},{2,7},{3,5}} => 2 {{1,4,6},{2},{3,5,7}} => 3 {{1,4,6},{2},{3,5},{7}} => 2 {{1,4,7},{2,6},{3,5}} => 3 {{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}} => 2 {{1,4},{2},{3,5,6},{7}} => 2 {{1,4,7},{2},{3,5},{6}} => 2 {{1,4},{2,7},{3,5},{6}} => 2 {{1,4},{2},{3,5,7},{6}} => 3 {{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},{2,7},{3},{5}} => 2 {{1,4,6},{2},{3,7},{5}} => 3 {{1,4,6},{2},{3},{5,7}} => 2 {{1,4,6},{2},{3},{5},{7}} => 2 {{1,4,7},{2,6},{3},{5}} => 3 {{1,4},{2,6,7},{3},{5}} => 1 {{1,4},{2,6},{3,7},{5}} => 1 {{1,4},{2,6},{3},{5,7}} => 2 {{1,4},{2,6},{3},{5},{7}} => 1 {{1,4,7},{2},{3,6},{5}} => 2 {{1,4},{2,7},{3,6},{5}} => 2 {{1,4},{2},{3,6,7},{5}} => 2 {{1,4},{2},{3,6},{5,7}} => 3 {{1,4},{2},{3,6},{5},{7}} => 2 {{1,4,7},{2},{3},{5,6}} => 2 {{1,4},{2,7},{3},{5,6}} => 1 {{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}} => 2 {{1,4},{2,7},{3},{5},{6}} => 1 {{1,4},{2},{3,7},{5},{6}} => 2 {{1,4},{2},{3},{5,7},{6}} => 2 {{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}} => 3 {{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}} => 3 {{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}} => 3 {{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}} => 1 {{1},{2,4,5,6},{3},{7}} => 1 {{1,7},{2,4,5},{3,6}} => 2 {{1},{2,4,5,7},{3,6}} => 2 {{1},{2,4,5},{3,6,7}} => 1 {{1},{2,4,5},{3,6},{7}} => 1 {{1,7},{2,4,5},{3},{6}} => 2 {{1},{2,4,5,7},{3},{6}} => 2 {{1},{2,4,5},{3,7},{6}} => 1 {{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}} => 3 {{1,6},{2,4},{3,5},{7}} => 2 {{1,7},{2,4,6},{3,5}} => 3 {{1},{2,4,6,7},{3,5}} => 2 {{1},{2,4,6},{3,5,7}} => 2 {{1},{2,4,6},{3,5},{7}} => 2 {{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}} => 2 {{1},{2,4},{3,5,7},{6}} => 2 {{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}} => 3 {{1,6},{2,4},{3},{5},{7}} => 2 {{1,7},{2,4,6},{3},{5}} => 3 {{1},{2,4,6,7},{3},{5}} => 2 {{1},{2,4,6},{3,7},{5}} => 2 {{1},{2,4,6},{3},{5,7}} => 2 {{1},{2,4,6},{3},{5},{7}} => 2 {{1,7},{2,4},{3,6},{5}} => 2 {{1},{2,4,7},{3,6},{5}} => 2 {{1},{2,4},{3,6,7},{5}} => 1 {{1},{2,4},{3,6},{5,7}} => 2 {{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}} => 1 {{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}} => 2 {{1},{2,4},{3,7},{5},{6}} => 1 {{1},{2,4},{3},{5,7},{6}} => 2 {{1},{2,4},{3},{5},{6,7}} => 1 {{1},{2,4},{3},{5},{6},{7}} => 1 {{1,5,6,7},{2},{3,4}} => 1 {{1,5,6},{2,7},{3,4}} => 1 {{1,5,6},{2},{3,4,7}} => 2 {{1,5,6},{2},{3,4},{7}} => 1 {{1,5,7},{2,6},{3,4}} => 3 {{1,5},{2,6,7},{3,4}} => 1 {{1,5},{2,6},{3,4,7}} => 1 {{1,5},{2,6},{3,4},{7}} => 1 {{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}} => 1 {{1,5},{2},{3,4,7},{6}} => 2 {{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},{3,4,7}} => 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},{3,4,7}} => 1 {{1},{2,5,6},{3,4},{7}} => 1 {{1,7},{2,5},{3,4,6}} => 2 {{1},{2,5,7},{3,4,6}} => 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}} => 2 {{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},{3,4,5}} => 1 {{1,6},{2,7},{3,4,5}} => 1 {{1,6},{2},{3,4,5,7}} => 2 {{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},{3,4,5,7}} => 1 {{1},{2,6},{3,4,5},{7}} => 1 {{1,7},{2},{3,4,5,6}} => 1 {{1},{2,7},{3,4,5,6}} => 1 {{1},{2},{3,4,5,6,7}} => 0 {{1},{2},{3,4,5,6},{7}} => 0 {{1,7},{2},{3,4,5},{6}} => 1 {{1},{2,7},{3,4,5},{6}} => 1 {{1},{2},{3,4,5,7},{6}} => 1 {{1},{2},{3,4,5},{6,7}} => 0 {{1},{2},{3,4,5},{6},{7}} => 0 {{1,6,7},{2},{3,4},{5}} => 1 {{1,6},{2,7},{3,4},{5}} => 1 {{1,6},{2},{3,4,7},{5}} => 2 {{1,6},{2},{3,4},{5,7}} => 2 {{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},{3,4,7},{5}} => 1 {{1},{2,6},{3,4},{5,7}} => 2 {{1},{2,6},{3,4},{5},{7}} => 1 {{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}} => 1 {{1},{2,7},{3,4},{5,6}} => 1 {{1},{2},{3,4,7},{5,6}} => 1 {{1},{2},{3,4},{5,6,7}} => 0 {{1},{2},{3,4},{5,6},{7}} => 0 {{1,7},{2},{3,4},{5},{6}} => 1 {{1},{2,7},{3,4},{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}} => 0 {{1},{2},{3,4},{5},{6},{7}} => 0 {{1,5,6,7},{2},{3},{4}} => 1 {{1,5,6},{2,7},{3},{4}} => 1 {{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}} => 3 {{1,5},{2,6,7},{3},{4}} => 1 {{1,5},{2,6},{3,7},{4}} => 1 {{1,5},{2,6},{3},{4,7}} => 2 {{1,5},{2,6},{3},{4},{7}} => 1 {{1,5,7},{2},{3,6},{4}} => 3 {{1,5},{2,7},{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},{2,7},{3},{4,6}} => 2 {{1,5},{2},{3,7},{4,6}} => 3 {{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}} => 1 {{1,5},{2},{3,7},{4},{6}} => 2 {{1,5},{2},{3},{4,7},{6}} => 2 {{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}} => 3 {{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}} => 1 {{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}} => 3 {{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}} => 3 {{1},{2,5,7},{3},{4,6}} => 2 {{1},{2,5},{3,7},{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}} => 2 {{1},{2,5,7},{3},{4},{6}} => 2 {{1},{2,5},{3,7},{4},{6}} => 1 {{1},{2,5},{3},{4,7},{6}} => 2 {{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}} => 3 {{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}} => 1 {{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}} => 2 {{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}} => 2 {{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}} => 1 {{1,6},{2,7},{3},{4,5}} => 1 {{1,6},{2},{3,7},{4,5}} => 2 {{1,6},{2},{3},{4,5,7}} => 2 {{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},{4,5,7}} => 2 {{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},{4,5,7}} => 1 {{1},{2},{3,6},{4,5},{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},{4,5,6,7}} => 0 {{1},{2},{3},{4,5,6},{7}} => 0 {{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},{4,5,7},{6}} => 1 {{1},{2},{3},{4,5},{6,7}} => 0 {{1},{2},{3},{4,5},{6},{7}} => 0 {{1,6,7},{2},{3},{4},{5}} => 1 {{1,6},{2,7},{3},{4},{5}} => 1 {{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}} => 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}} => 2 {{1},{2,6},{3},{4},{5,7}} => 2 {{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}} => 2 {{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}} => 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},{5,6,7}} => 0 {{1},{2},{3},{4},{5,6},{7}} => 0 {{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}} => 0 {{1},{2},{3},{4},{5},{6},{7}} => 0 ----------------------------------------------------------------------------- Created: Oct 06, 2022 at 15:16 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Oct 06, 2022 at 15:16 by Martin Rubey