***************************************************************************** * 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: St000562 ----------------------------------------------------------------------------- Collection: Set partitions ----------------------------------------------------------------------------- Description: The number of internal points of a set partition. An element $e$ is internal, if there are $f < e < g$ such that the blocks of $f$ and $g$ have larger minimal element than the block of $e$. See Section 5.5 of [1] ----------------------------------------------------------------------------- References: [1] Mansour, T. Combinatorics of set partitions [[MathSciNet:2953184]] ----------------------------------------------------------------------------- Code: def canonical_word(pi): """ Return the word with w_i being the index of the block of i, when pi is sorted according to minimal elements. EXAMPLES: sage: canonical_word([[1,3],[2,4,7],[5,6]]) 1212332 """ pi = SetPartition(pi).standardization() w = [None]*pi.size() for i, block in enumerate(sorted([sorted(b) for b in pi]), 1): for e in block: w[e-1] = i return Word(w) def statistic(pi): """e is internal, if there are f < e < g such that the blocks of f and g have larger minimal element than the block of e. sage: statistic([[1,4],[2,5,7],[3],[6]]) 2 sage: canonical_word([[1,5,9,12],[2,4,8],[3,7,11],[6,10]]) word: 123214321431 sage: statistic([[1,5,9,12],[2,4,8],[3,7,11],[6,10]]) 5 """ w = canonical_word(pi) count = 0 for (i, b) in enumerate(w): has_smaller = any(b < w[j] for j in range(i)) has_bigger = any(b < w[j] for j in range(i+1, len(w))) if has_smaller and has_bigger: count += 1 return count ----------------------------------------------------------------------------- Statistic values: {{1,2}} => 0 {{1},{2}} => 0 {{1,2,3}} => 0 {{1,2},{3}} => 0 {{1,3},{2}} => 0 {{1},{2,3}} => 0 {{1},{2},{3}} => 0 {{1,2,3,4}} => 0 {{1,2,3},{4}} => 0 {{1,2,4},{3}} => 0 {{1,2},{3,4}} => 0 {{1,2},{3},{4}} => 0 {{1,3,4},{2}} => 0 {{1,3},{2,4}} => 1 {{1,3},{2},{4}} => 1 {{1,4},{2,3}} => 0 {{1},{2,3,4}} => 0 {{1},{2,3},{4}} => 0 {{1,4},{2},{3}} => 0 {{1},{2,4},{3}} => 0 {{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}} => 0 {{1,2,3},{4,5}} => 0 {{1,2,3},{4},{5}} => 0 {{1,2,4,5},{3}} => 0 {{1,2,4},{3,5}} => 1 {{1,2,4},{3},{5}} => 1 {{1,2,5},{3,4}} => 0 {{1,2},{3,4,5}} => 0 {{1,2},{3,4},{5}} => 0 {{1,2,5},{3},{4}} => 0 {{1,2},{3,5},{4}} => 0 {{1,2},{3},{4,5}} => 0 {{1,2},{3},{4},{5}} => 0 {{1,3,4,5},{2}} => 0 {{1,3,4},{2,5}} => 2 {{1,3,4},{2},{5}} => 2 {{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}} => 0 {{1,4},{2,3,5}} => 1 {{1,4},{2,3},{5}} => 1 {{1,5},{2,3,4}} => 0 {{1},{2,3,4,5}} => 0 {{1},{2,3,4},{5}} => 0 {{1,5},{2,3},{4}} => 0 {{1},{2,3,5},{4}} => 0 {{1},{2,3},{4,5}} => 0 {{1},{2,3},{4},{5}} => 0 {{1,4,5},{2},{3}} => 0 {{1,4},{2,5},{3}} => 1 {{1,4},{2},{3,5}} => 1 {{1,4},{2},{3},{5}} => 1 {{1,5},{2,4},{3}} => 0 {{1},{2,4,5},{3}} => 0 {{1},{2,4},{3,5}} => 1 {{1},{2,4},{3},{5}} => 1 {{1,5},{2},{3,4}} => 0 {{1},{2,5},{3,4}} => 0 {{1},{2},{3,4,5}} => 0 {{1},{2},{3,4},{5}} => 0 {{1,5},{2},{3},{4}} => 0 {{1},{2,5},{3},{4}} => 0 {{1},{2},{3,5},{4}} => 0 {{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}} => 0 {{1,2,3,4},{5,6}} => 0 {{1,2,3,4},{5},{6}} => 0 {{1,2,3,5,6},{4}} => 0 {{1,2,3,5},{4,6}} => 1 {{1,2,3,5},{4},{6}} => 1 {{1,2,3,6},{4,5}} => 0 {{1,2,3},{4,5,6}} => 0 {{1,2,3},{4,5},{6}} => 0 {{1,2,3,6},{4},{5}} => 0 {{1,2,3},{4,6},{5}} => 0 {{1,2,3},{4},{5,6}} => 0 {{1,2,3},{4},{5},{6}} => 0 {{1,2,4,5,6},{3}} => 0 {{1,2,4,5},{3,6}} => 2 {{1,2,4,5},{3},{6}} => 2 {{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}} => 0 {{1,2,5},{3,4,6}} => 1 {{1,2,5},{3,4},{6}} => 1 {{1,2,6},{3,4,5}} => 0 {{1,2},{3,4,5,6}} => 0 {{1,2},{3,4,5},{6}} => 0 {{1,2,6},{3,4},{5}} => 0 {{1,2},{3,4,6},{5}} => 0 {{1,2},{3,4},{5,6}} => 0 {{1,2},{3,4},{5},{6}} => 0 {{1,2,5,6},{3},{4}} => 0 {{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}} => 0 {{1,2},{3,5,6},{4}} => 0 {{1,2},{3,5},{4,6}} => 1 {{1,2},{3,5},{4},{6}} => 1 {{1,2,6},{3},{4,5}} => 0 {{1,2},{3,6},{4,5}} => 0 {{1,2},{3},{4,5,6}} => 0 {{1,2},{3},{4,5},{6}} => 0 {{1,2,6},{3},{4},{5}} => 0 {{1,2},{3,6},{4},{5}} => 0 {{1,2},{3},{4,6},{5}} => 0 {{1,2},{3},{4},{5,6}} => 0 {{1,2},{3},{4},{5},{6}} => 0 {{1,3,4,5,6},{2}} => 0 {{1,3,4,5},{2,6}} => 3 {{1,3,4,5},{2},{6}} => 3 {{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}} => 2 {{1,3,4},{2,6},{5}} => 2 {{1,3,4},{2},{5,6}} => 2 {{1,3,4},{2},{5},{6}} => 2 {{1,3,5,6},{2,4}} => 1 {{1,3,5},{2,4,6}} => 2 {{1,3,5},{2,4},{6}} => 2 {{1,3,6},{2,4,5}} => 1 {{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}} => 2 {{1,3,5},{2},{4},{6}} => 2 {{1,3,6},{2,5},{4}} => 1 {{1,3},{2,5,6},{4}} => 1 {{1,3},{2,5},{4,6}} => 2 {{1,3},{2,5},{4},{6}} => 2 {{1,3,6},{2},{4,5}} => 1 {{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}} => 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}} => 0 {{1,4,5},{2,3,6}} => 2 {{1,4,5},{2,3},{6}} => 2 {{1,4,6},{2,3,5}} => 1 {{1,4},{2,3,5,6}} => 1 {{1,4},{2,3,5},{6}} => 1 {{1,4,6},{2,3},{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},{2,3,4}} => 0 {{1,5},{2,3,4,6}} => 1 {{1,5},{2,3,4},{6}} => 1 {{1,6},{2,3,4,5}} => 0 {{1},{2,3,4,5,6}} => 0 {{1},{2,3,4,5},{6}} => 0 {{1,6},{2,3,4},{5}} => 0 {{1},{2,3,4,6},{5}} => 0 {{1},{2,3,4},{5,6}} => 0 {{1},{2,3,4},{5},{6}} => 0 {{1,5,6},{2,3},{4}} => 0 {{1,5},{2,3,6},{4}} => 1 {{1,5},{2,3},{4,6}} => 1 {{1,5},{2,3},{4},{6}} => 1 {{1,6},{2,3,5},{4}} => 0 {{1},{2,3,5,6},{4}} => 0 {{1},{2,3,5},{4,6}} => 1 {{1},{2,3,5},{4},{6}} => 1 {{1,6},{2,3},{4,5}} => 0 {{1},{2,3,6},{4,5}} => 0 {{1},{2,3},{4,5,6}} => 0 {{1},{2,3},{4,5},{6}} => 0 {{1,6},{2,3},{4},{5}} => 0 {{1},{2,3,6},{4},{5}} => 0 {{1},{2,3},{4,6},{5}} => 0 {{1},{2,3},{4},{5,6}} => 0 {{1},{2,3},{4},{5},{6}} => 0 {{1,4,5,6},{2},{3}} => 0 {{1,4,5},{2,6},{3}} => 2 {{1,4,5},{2},{3,6}} => 2 {{1,4,5},{2},{3},{6}} => 2 {{1,4,6},{2,5},{3}} => 1 {{1,4},{2,5,6},{3}} => 1 {{1,4},{2,5},{3,6}} => 2 {{1,4},{2,5},{3},{6}} => 2 {{1,4,6},{2},{3,5}} => 1 {{1,4},{2,6},{3,5}} => 1 {{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}} => 0 {{1,5},{2,4,6},{3}} => 1 {{1,5},{2,4},{3,6}} => 2 {{1,5},{2,4},{3},{6}} => 2 {{1,6},{2,4,5},{3}} => 0 {{1},{2,4,5,6},{3}} => 0 {{1},{2,4,5},{3,6}} => 2 {{1},{2,4,5},{3},{6}} => 2 {{1,6},{2,4},{3,5}} => 1 {{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}} => 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 {{1,5,6},{2},{3,4}} => 0 {{1,5},{2,6},{3,4}} => 1 {{1,5},{2},{3,4,6}} => 1 {{1,5},{2},{3,4},{6}} => 1 {{1,6},{2,5},{3,4}} => 0 {{1},{2,5,6},{3,4}} => 0 {{1},{2,5},{3,4,6}} => 1 {{1},{2,5},{3,4},{6}} => 1 {{1,6},{2},{3,4,5}} => 0 {{1},{2,6},{3,4,5}} => 0 {{1},{2},{3,4,5,6}} => 0 {{1},{2},{3,4,5},{6}} => 0 {{1,6},{2},{3,4},{5}} => 0 {{1},{2,6},{3,4},{5}} => 0 {{1},{2},{3,4,6},{5}} => 0 {{1},{2},{3,4},{5,6}} => 0 {{1},{2},{3,4},{5},{6}} => 0 {{1,5,6},{2},{3},{4}} => 0 {{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}} => 0 {{1},{2,5,6},{3},{4}} => 0 {{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}} => 0 {{1},{2,6},{3,5},{4}} => 0 {{1},{2},{3,5,6},{4}} => 0 {{1},{2},{3,5},{4,6}} => 1 {{1},{2},{3,5},{4},{6}} => 1 {{1,6},{2},{3},{4,5}} => 0 {{1},{2,6},{3},{4,5}} => 0 {{1},{2},{3,6},{4,5}} => 0 {{1},{2},{3},{4,5,6}} => 0 {{1},{2},{3},{4,5},{6}} => 0 {{1,6},{2},{3},{4},{5}} => 0 {{1},{2,6},{3},{4},{5}} => 0 {{1},{2},{3,6},{4},{5}} => 0 {{1},{2},{3},{4,6},{5}} => 0 {{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}} => 0 {{1,2,3,4,5},{6,7}} => 0 {{1,2,3,4,5},{6},{7}} => 0 {{1,2,3,4,6,7},{5}} => 0 {{1,2,3,4,6},{5,7}} => 1 {{1,2,3,4,6},{5},{7}} => 1 {{1,2,3,4,7},{5,6}} => 0 {{1,2,3,4},{5,6,7}} => 0 {{1,2,3,4},{5,6},{7}} => 0 {{1,2,3,4,7},{5},{6}} => 0 {{1,2,3,4},{5,7},{6}} => 0 {{1,2,3,4},{5},{6,7}} => 0 {{1,2,3,4},{5},{6},{7}} => 0 {{1,2,3,5,6,7},{4}} => 0 {{1,2,3,5,6},{4,7}} => 2 {{1,2,3,5,6},{4},{7}} => 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 {{1,2,3,5,7},{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}} => 0 {{1,2,3,6},{4,5,7}} => 1 {{1,2,3,6},{4,5},{7}} => 1 {{1,2,3,7},{4,5,6}} => 0 {{1,2,3},{4,5,6,7}} => 0 {{1,2,3},{4,5,6},{7}} => 0 {{1,2,3,7},{4,5},{6}} => 0 {{1,2,3},{4,5,7},{6}} => 0 {{1,2,3},{4,5},{6,7}} => 0 {{1,2,3},{4,5},{6},{7}} => 0 {{1,2,3,6,7},{4},{5}} => 0 {{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}} => 0 {{1,2,3},{4,6,7},{5}} => 0 {{1,2,3},{4,6},{5,7}} => 1 {{1,2,3},{4,6},{5},{7}} => 1 {{1,2,3,7},{4},{5,6}} => 0 {{1,2,3},{4,7},{5,6}} => 0 {{1,2,3},{4},{5,6,7}} => 0 {{1,2,3},{4},{5,6},{7}} => 0 {{1,2,3,7},{4},{5},{6}} => 0 {{1,2,3},{4,7},{5},{6}} => 0 {{1,2,3},{4},{5,7},{6}} => 0 {{1,2,3},{4},{5},{6,7}} => 0 {{1,2,3},{4},{5},{6},{7}} => 0 {{1,2,4,5,6,7},{3}} => 0 {{1,2,4,5,6},{3,7}} => 3 {{1,2,4,5,6},{3},{7}} => 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 {{1,2,4,5,7},{3},{6}} => 2 {{1,2,4,5},{3,7},{6}} => 2 {{1,2,4,5},{3},{6,7}} => 2 {{1,2,4,5},{3},{6},{7}} => 2 {{1,2,4,6,7},{3,5}} => 1 {{1,2,4,6},{3,5,7}} => 2 {{1,2,4,6},{3,5},{7}} => 2 {{1,2,4,7},{3,5,6}} => 1 {{1,2,4},{3,5,6,7}} => 1 {{1,2,4},{3,5,6},{7}} => 1 {{1,2,4,7},{3,5},{6}} => 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}} => 2 {{1,2,4,6},{3},{5},{7}} => 2 {{1,2,4,7},{3,6},{5}} => 1 {{1,2,4},{3,6,7},{5}} => 1 {{1,2,4},{3,6},{5,7}} => 2 {{1,2,4},{3,6},{5},{7}} => 2 {{1,2,4,7},{3},{5,6}} => 1 {{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}} => 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}} => 0 {{1,2,5,6},{3,4,7}} => 2 {{1,2,5,6},{3,4},{7}} => 2 {{1,2,5,7},{3,4,6}} => 1 {{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},{3,4,7},{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}} => 0 {{1,2,6},{3,4,5,7}} => 1 {{1,2,6},{3,4,5},{7}} => 1 {{1,2,7},{3,4,5,6}} => 0 {{1,2},{3,4,5,6,7}} => 0 {{1,2},{3,4,5,6},{7}} => 0 {{1,2,7},{3,4,5},{6}} => 0 {{1,2},{3,4,5,7},{6}} => 0 {{1,2},{3,4,5},{6,7}} => 0 {{1,2},{3,4,5},{6},{7}} => 0 {{1,2,6,7},{3,4},{5}} => 0 {{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},{3,4,6},{5}} => 0 {{1,2},{3,4,6,7},{5}} => 0 {{1,2},{3,4,6},{5,7}} => 1 {{1,2},{3,4,6},{5},{7}} => 1 {{1,2,7},{3,4},{5,6}} => 0 {{1,2},{3,4,7},{5,6}} => 0 {{1,2},{3,4},{5,6,7}} => 0 {{1,2},{3,4},{5,6},{7}} => 0 {{1,2,7},{3,4},{5},{6}} => 0 {{1,2},{3,4,7},{5},{6}} => 0 {{1,2},{3,4},{5,7},{6}} => 0 {{1,2},{3,4},{5},{6,7}} => 0 {{1,2},{3,4},{5},{6},{7}} => 0 {{1,2,5,6,7},{3},{4}} => 0 {{1,2,5,6},{3,7},{4}} => 2 {{1,2,5,6},{3},{4,7}} => 2 {{1,2,5,6},{3},{4},{7}} => 2 {{1,2,5,7},{3,6},{4}} => 1 {{1,2,5},{3,6,7},{4}} => 1 {{1,2,5},{3,6},{4,7}} => 2 {{1,2,5},{3,6},{4},{7}} => 2 {{1,2,5,7},{3},{4,6}} => 1 {{1,2,5},{3,7},{4,6}} => 1 {{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}} => 0 {{1,2,6},{3,5,7},{4}} => 1 {{1,2,6},{3,5},{4,7}} => 2 {{1,2,6},{3,5},{4},{7}} => 2 {{1,2,7},{3,5,6},{4}} => 0 {{1,2},{3,5,6,7},{4}} => 0 {{1,2},{3,5,6},{4,7}} => 2 {{1,2},{3,5,6},{4},{7}} => 2 {{1,2,7},{3,5},{4,6}} => 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 {{1,2,7},{3,5},{4},{6}} => 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 {{1,2,6,7},{3},{4,5}} => 0 {{1,2,6},{3,7},{4,5}} => 1 {{1,2,6},{3},{4,5,7}} => 1 {{1,2,6},{3},{4,5},{7}} => 1 {{1,2,7},{3,6},{4,5}} => 0 {{1,2},{3,6,7},{4,5}} => 0 {{1,2},{3,6},{4,5,7}} => 1 {{1,2},{3,6},{4,5},{7}} => 1 {{1,2,7},{3},{4,5,6}} => 0 {{1,2},{3,7},{4,5,6}} => 0 {{1,2},{3},{4,5,6,7}} => 0 {{1,2},{3},{4,5,6},{7}} => 0 {{1,2,7},{3},{4,5},{6}} => 0 {{1,2},{3,7},{4,5},{6}} => 0 {{1,2},{3},{4,5,7},{6}} => 0 {{1,2},{3},{4,5},{6,7}} => 0 {{1,2},{3},{4,5},{6},{7}} => 0 {{1,2,6,7},{3},{4},{5}} => 0 {{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}} => 0 {{1,2},{3,6,7},{4},{5}} => 0 {{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}} => 0 {{1,2},{3,7},{4,6},{5}} => 0 {{1,2},{3},{4,6,7},{5}} => 0 {{1,2},{3},{4,6},{5,7}} => 1 {{1,2},{3},{4,6},{5},{7}} => 1 {{1,2,7},{3},{4},{5,6}} => 0 {{1,2},{3,7},{4},{5,6}} => 0 {{1,2},{3},{4,7},{5,6}} => 0 {{1,2},{3},{4},{5,6,7}} => 0 {{1,2},{3},{4},{5,6},{7}} => 0 {{1,2,7},{3},{4},{5},{6}} => 0 {{1,2},{3,7},{4},{5},{6}} => 0 {{1,2},{3},{4,7},{5},{6}} => 0 {{1,2},{3},{4},{5,7},{6}} => 0 {{1,2},{3},{4},{5},{6,7}} => 0 {{1,2},{3},{4},{5},{6},{7}} => 0 {{1,3,4,5,6,7},{2}} => 0 {{1,3,4,5,6},{2,7}} => 4 {{1,3,4,5,6},{2},{7}} => 4 {{1,3,4,5,7},{2,6}} => 3 {{1,3,4,5},{2,6,7}} => 3 {{1,3,4,5},{2,6},{7}} => 3 {{1,3,4,5,7},{2},{6}} => 3 {{1,3,4,5},{2,7},{6}} => 3 {{1,3,4,5},{2},{6,7}} => 3 {{1,3,4,5},{2},{6},{7}} => 3 {{1,3,4,6,7},{2,5}} => 2 {{1,3,4,6},{2,5,7}} => 3 {{1,3,4,6},{2,5},{7}} => 3 {{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}} => 2 {{1,3,4,6},{2,7},{5}} => 3 {{1,3,4,6},{2},{5,7}} => 3 {{1,3,4,6},{2},{5},{7}} => 3 {{1,3,4,7},{2,6},{5}} => 2 {{1,3,4},{2,6,7},{5}} => 2 {{1,3,4},{2,6},{5,7}} => 3 {{1,3,4},{2,6},{5},{7}} => 3 {{1,3,4,7},{2},{5,6}} => 2 {{1,3,4},{2,7},{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},{2,7},{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 {{1,3,5,6,7},{2,4}} => 1 {{1,3,5,6},{2,4,7}} => 3 {{1,3,5,6},{2,4},{7}} => 3 {{1,3,5,7},{2,4,6}} => 2 {{1,3,5},{2,4,6,7}} => 2 {{1,3,5},{2,4,6},{7}} => 2 {{1,3,5,7},{2,4},{6}} => 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},{2,4,5}} => 1 {{1,3,6},{2,4,5,7}} => 2 {{1,3,6},{2,4,5},{7}} => 2 {{1,3,7},{2,4,5,6}} => 1 {{1,3},{2,4,5,6,7}} => 1 {{1,3},{2,4,5,6},{7}} => 1 {{1,3,7},{2,4,5},{6}} => 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 {{1,3,6,7},{2,4},{5}} => 1 {{1,3,6},{2,4,7},{5}} => 2 {{1,3,6},{2,4},{5,7}} => 2 {{1,3,6},{2,4},{5},{7}} => 2 {{1,3,7},{2,4,6},{5}} => 1 {{1,3},{2,4,6,7},{5}} => 1 {{1,3},{2,4,6},{5,7}} => 2 {{1,3},{2,4,6},{5},{7}} => 2 {{1,3,7},{2,4},{5,6}} => 1 {{1,3},{2,4,7},{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}} => 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}} => 3 {{1,3,5,6},{2},{4,7}} => 3 {{1,3,5,6},{2},{4},{7}} => 3 {{1,3,5,7},{2,6},{4}} => 2 {{1,3,5},{2,6,7},{4}} => 2 {{1,3,5},{2,6},{4,7}} => 3 {{1,3,5},{2,6},{4},{7}} => 3 {{1,3,5,7},{2},{4,6}} => 2 {{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}} => 2 {{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}} => 1 {{1,3,6},{2,5,7},{4}} => 2 {{1,3,6},{2,5},{4,7}} => 3 {{1,3,6},{2,5},{4},{7}} => 3 {{1,3,7},{2,5,6},{4}} => 1 {{1,3},{2,5,6,7},{4}} => 1 {{1,3},{2,5,6},{4,7}} => 3 {{1,3},{2,5,6},{4},{7}} => 3 {{1,3,7},{2,5},{4,6}} => 2 {{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}} => 2 {{1,3},{2,5},{4},{6},{7}} => 2 {{1,3,6,7},{2},{4,5}} => 1 {{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}} => 1 {{1,3},{2,6,7},{4,5}} => 1 {{1,3},{2,6},{4,5,7}} => 2 {{1,3},{2,6},{4,5},{7}} => 2 {{1,3,7},{2},{4,5,6}} => 1 {{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}} => 1 {{1,3},{2,7},{4,5},{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 {{1,3,6,7},{2},{4},{5}} => 1 {{1,3,6},{2,7},{4},{5}} => 2 {{1,3,6},{2},{4,7},{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}} => 1 {{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}} => 2 {{1,3,7},{2},{4,6},{5}} => 1 {{1,3},{2,7},{4,6},{5}} => 1 {{1,3},{2},{4,6,7},{5}} => 1 {{1,3},{2},{4,6},{5,7}} => 2 {{1,3},{2},{4,6},{5},{7}} => 2 {{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},{5,6,7}} => 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}} => 0 {{1,4,5,6},{2,3,7}} => 3 {{1,4,5,6},{2,3},{7}} => 3 {{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}} => 1 {{1,4,6},{2,3,5,7}} => 2 {{1,4,6},{2,3,5},{7}} => 2 {{1,4,7},{2,3,5,6}} => 1 {{1,4},{2,3,5,6,7}} => 1 {{1,4},{2,3,5,6},{7}} => 1 {{1,4,7},{2,3,5},{6}} => 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 {{1,4,6,7},{2,3},{5}} => 1 {{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}} => 1 {{1,4},{2,3,6,7},{5}} => 1 {{1,4},{2,3,6},{5,7}} => 2 {{1,4},{2,3,6},{5},{7}} => 2 {{1,4,7},{2,3},{5,6}} => 1 {{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}} => 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},{2,3,4}} => 0 {{1,5,6},{2,3,4,7}} => 2 {{1,5,6},{2,3,4},{7}} => 2 {{1,5,7},{2,3,4,6}} => 1 {{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},{2,3,4,7},{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}} => 0 {{1,6},{2,3,4,5,7}} => 1 {{1,6},{2,3,4,5},{7}} => 1 {{1,7},{2,3,4,5,6}} => 0 {{1},{2,3,4,5,6,7}} => 0 {{1},{2,3,4,5,6},{7}} => 0 {{1,7},{2,3,4,5},{6}} => 0 {{1},{2,3,4,5,7},{6}} => 0 {{1},{2,3,4,5},{6,7}} => 0 {{1},{2,3,4,5},{6},{7}} => 0 {{1,6,7},{2,3,4},{5}} => 0 {{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},{2,3,4,6},{5}} => 0 {{1},{2,3,4,6,7},{5}} => 0 {{1},{2,3,4,6},{5,7}} => 1 {{1},{2,3,4,6},{5},{7}} => 1 {{1,7},{2,3,4},{5,6}} => 0 {{1},{2,3,4,7},{5,6}} => 0 {{1},{2,3,4},{5,6,7}} => 0 {{1},{2,3,4},{5,6},{7}} => 0 {{1,7},{2,3,4},{5},{6}} => 0 {{1},{2,3,4,7},{5},{6}} => 0 {{1},{2,3,4},{5,7},{6}} => 0 {{1},{2,3,4},{5},{6,7}} => 0 {{1},{2,3,4},{5},{6},{7}} => 0 {{1,5,6,7},{2,3},{4}} => 0 {{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}} => 1 {{1,5},{2,3,6,7},{4}} => 1 {{1,5},{2,3,6},{4,7}} => 2 {{1,5},{2,3,6},{4},{7}} => 2 {{1,5,7},{2,3},{4,6}} => 1 {{1,5},{2,3,7},{4,6}} => 1 {{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},{2,3,7},{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},{2,3,5},{4}} => 0 {{1,6},{2,3,5,7},{4}} => 1 {{1,6},{2,3,5},{4,7}} => 2 {{1,6},{2,3,5},{4},{7}} => 2 {{1,7},{2,3,5,6},{4}} => 0 {{1},{2,3,5,6,7},{4}} => 0 {{1},{2,3,5,6},{4,7}} => 2 {{1},{2,3,5,6},{4},{7}} => 2 {{1,7},{2,3,5},{4,6}} => 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 {{1,7},{2,3,5},{4},{6}} => 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 {{1,6,7},{2,3},{4,5}} => 0 {{1,6},{2,3,7},{4,5}} => 1 {{1,6},{2,3},{4,5,7}} => 1 {{1,6},{2,3},{4,5},{7}} => 1 {{1,7},{2,3,6},{4,5}} => 0 {{1},{2,3,6,7},{4,5}} => 0 {{1},{2,3,6},{4,5,7}} => 1 {{1},{2,3,6},{4,5},{7}} => 1 {{1,7},{2,3},{4,5,6}} => 0 {{1},{2,3,7},{4,5,6}} => 0 {{1},{2,3},{4,5,6,7}} => 0 {{1},{2,3},{4,5,6},{7}} => 0 {{1,7},{2,3},{4,5},{6}} => 0 {{1},{2,3,7},{4,5},{6}} => 0 {{1},{2,3},{4,5,7},{6}} => 0 {{1},{2,3},{4,5},{6,7}} => 0 {{1},{2,3},{4,5},{6},{7}} => 0 {{1,6,7},{2,3},{4},{5}} => 0 {{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},{2,3,6},{4},{5}} => 0 {{1},{2,3,6,7},{4},{5}} => 0 {{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}} => 0 {{1},{2,3,7},{4,6},{5}} => 0 {{1},{2,3},{4,6,7},{5}} => 0 {{1},{2,3},{4,6},{5,7}} => 1 {{1},{2,3},{4,6},{5},{7}} => 1 {{1,7},{2,3},{4},{5,6}} => 0 {{1},{2,3,7},{4},{5,6}} => 0 {{1},{2,3},{4,7},{5,6}} => 0 {{1},{2,3},{4},{5,6,7}} => 0 {{1},{2,3},{4},{5,6},{7}} => 0 {{1,7},{2,3},{4},{5},{6}} => 0 {{1},{2,3,7},{4},{5},{6}} => 0 {{1},{2,3},{4,7},{5},{6}} => 0 {{1},{2,3},{4},{5,7},{6}} => 0 {{1},{2,3},{4},{5},{6,7}} => 0 {{1},{2,3},{4},{5},{6},{7}} => 0 {{1,4,5,6,7},{2},{3}} => 0 {{1,4,5,6},{2,7},{3}} => 3 {{1,4,5,6},{2},{3,7}} => 3 {{1,4,5,6},{2},{3},{7}} => 3 {{1,4,5,7},{2,6},{3}} => 2 {{1,4,5},{2,6,7},{3}} => 2 {{1,4,5},{2,6},{3,7}} => 3 {{1,4,5},{2,6},{3},{7}} => 3 {{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}} => 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},{2,5},{3}} => 1 {{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}} => 1 {{1,4},{2,5,6,7},{3}} => 1 {{1,4},{2,5,6},{3,7}} => 3 {{1,4},{2,5,6},{3},{7}} => 3 {{1,4,7},{2,5},{3,6}} => 2 {{1,4},{2,5,7},{3,6}} => 2 {{1,4},{2,5},{3,6,7}} => 2 {{1,4},{2,5},{3,6},{7}} => 2 {{1,4,7},{2,5},{3},{6}} => 2 {{1,4},{2,5,7},{3},{6}} => 2 {{1,4},{2,5},{3,7},{6}} => 2 {{1,4},{2,5},{3},{6,7}} => 2 {{1,4},{2,5},{3},{6},{7}} => 2 {{1,4,6,7},{2},{3,5}} => 1 {{1,4,6},{2,7},{3,5}} => 2 {{1,4,6},{2},{3,5,7}} => 2 {{1,4,6},{2},{3,5},{7}} => 2 {{1,4,7},{2,6},{3,5}} => 1 {{1,4},{2,6,7},{3,5}} => 1 {{1,4},{2,6},{3,5,7}} => 2 {{1,4},{2,6},{3,5},{7}} => 2 {{1,4,7},{2},{3,5,6}} => 1 {{1,4},{2,7},{3,5,6}} => 1 {{1,4},{2},{3,5,6,7}} => 1 {{1,4},{2},{3,5,6},{7}} => 1 {{1,4,7},{2},{3,5},{6}} => 1 {{1,4},{2,7},{3,5},{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 {{1,4,6,7},{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}} => 2 {{1,4,6},{2},{3},{5},{7}} => 2 {{1,4,7},{2,6},{3},{5}} => 1 {{1,4},{2,6,7},{3},{5}} => 1 {{1,4},{2,6},{3,7},{5}} => 2 {{1,4},{2,6},{3},{5,7}} => 2 {{1,4},{2,6},{3},{5},{7}} => 2 {{1,4,7},{2},{3,6},{5}} => 1 {{1,4},{2,7},{3,6},{5}} => 1 {{1,4},{2},{3,6,7},{5}} => 1 {{1,4},{2},{3,6},{5,7}} => 2 {{1,4},{2},{3,6},{5},{7}} => 2 {{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},{5,6,7}} => 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}} => 0 {{1,5,6},{2,4,7},{3}} => 2 {{1,5,6},{2,4},{3,7}} => 3 {{1,5,6},{2,4},{3},{7}} => 3 {{1,5,7},{2,4,6},{3}} => 1 {{1,5},{2,4,6,7},{3}} => 1 {{1,5},{2,4,6},{3,7}} => 3 {{1,5},{2,4,6},{3},{7}} => 3 {{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}} => 0 {{1,6},{2,4,5,7},{3}} => 1 {{1,6},{2,4,5},{3,7}} => 3 {{1,6},{2,4,5},{3},{7}} => 3 {{1,7},{2,4,5,6},{3}} => 0 {{1},{2,4,5,6,7},{3}} => 0 {{1},{2,4,5,6},{3,7}} => 3 {{1},{2,4,5,6},{3},{7}} => 3 {{1,7},{2,4,5},{3,6}} => 2 {{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}} => 2 {{1},{2,4,5},{3,7},{6}} => 2 {{1},{2,4,5},{3},{6,7}} => 2 {{1},{2,4,5},{3},{6},{7}} => 2 {{1,6,7},{2,4},{3,5}} => 1 {{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}} => 1 {{1},{2,4,6,7},{3,5}} => 1 {{1},{2,4,6},{3,5,7}} => 2 {{1},{2,4,6},{3,5},{7}} => 2 {{1,7},{2,4},{3,5,6}} => 1 {{1},{2,4,7},{3,5,6}} => 1 {{1},{2,4},{3,5,6,7}} => 1 {{1},{2,4},{3,5,6},{7}} => 1 {{1,7},{2,4},{3,5},{6}} => 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 {{1,6,7},{2,4},{3},{5}} => 1 {{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}} => 1 {{1},{2,4,6,7},{3},{5}} => 1 {{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}} => 1 {{1},{2,4,7},{3,6},{5}} => 1 {{1},{2,4},{3,6,7},{5}} => 1 {{1},{2,4},{3,6},{5,7}} => 2 {{1},{2,4},{3,6},{5},{7}} => 2 {{1,7},{2,4},{3},{5,6}} => 1 {{1},{2,4,7},{3},{5,6}} => 1 {{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}} => 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 {{1,5,6,7},{2},{3,4}} => 0 {{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}} => 1 {{1,5},{2,6,7},{3,4}} => 1 {{1,5},{2,6},{3,4,7}} => 2 {{1,5},{2,6},{3,4},{7}} => 2 {{1,5,7},{2},{3,4,6}} => 1 {{1,5},{2,7},{3,4,6}} => 1 {{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},{3,4,7},{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}} => 0 {{1,6},{2,5,7},{3,4}} => 1 {{1,6},{2,5},{3,4,7}} => 2 {{1,6},{2,5},{3,4},{7}} => 2 {{1,7},{2,5,6},{3,4}} => 0 {{1},{2,5,6,7},{3,4}} => 0 {{1},{2,5,6},{3,4,7}} => 2 {{1},{2,5,6},{3,4},{7}} => 2 {{1,7},{2,5},{3,4,6}} => 1 {{1},{2,5,7},{3,4,6}} => 1 {{1},{2,5},{3,4,6,7}} => 1 {{1},{2,5},{3,4,6},{7}} => 1 {{1,7},{2,5},{3,4},{6}} => 1 {{1},{2,5,7},{3,4},{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},{3,4,5}} => 0 {{1,6},{2,7},{3,4,5}} => 1 {{1,6},{2},{3,4,5,7}} => 1 {{1,6},{2},{3,4,5},{7}} => 1 {{1,7},{2,6},{3,4,5}} => 0 {{1},{2,6,7},{3,4,5}} => 0 {{1},{2,6},{3,4,5,7}} => 1 {{1},{2,6},{3,4,5},{7}} => 1 {{1,7},{2},{3,4,5,6}} => 0 {{1},{2,7},{3,4,5,6}} => 0 {{1},{2},{3,4,5,6,7}} => 0 {{1},{2},{3,4,5,6},{7}} => 0 {{1,7},{2},{3,4,5},{6}} => 0 {{1},{2,7},{3,4,5},{6}} => 0 {{1},{2},{3,4,5,7},{6}} => 0 {{1},{2},{3,4,5},{6,7}} => 0 {{1},{2},{3,4,5},{6},{7}} => 0 {{1,6,7},{2},{3,4},{5}} => 0 {{1,6},{2,7},{3,4},{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}} => 0 {{1},{2,6,7},{3,4},{5}} => 0 {{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},{3,4,6},{5}} => 0 {{1},{2,7},{3,4,6},{5}} => 0 {{1},{2},{3,4,6,7},{5}} => 0 {{1},{2},{3,4,6},{5,7}} => 1 {{1},{2},{3,4,6},{5},{7}} => 1 {{1,7},{2},{3,4},{5,6}} => 0 {{1},{2,7},{3,4},{5,6}} => 0 {{1},{2},{3,4,7},{5,6}} => 0 {{1},{2},{3,4},{5,6,7}} => 0 {{1},{2},{3,4},{5,6},{7}} => 0 {{1,7},{2},{3,4},{5},{6}} => 0 {{1},{2,7},{3,4},{5},{6}} => 0 {{1},{2},{3,4,7},{5},{6}} => 0 {{1},{2},{3,4},{5,7},{6}} => 0 {{1},{2},{3,4},{5},{6,7}} => 0 {{1},{2},{3,4},{5},{6},{7}} => 0 {{1,5,6,7},{2},{3},{4}} => 0 {{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}} => 2 {{1,5,7},{2,6},{3},{4}} => 1 {{1,5},{2,6,7},{3},{4}} => 1 {{1,5},{2,6},{3,7},{4}} => 2 {{1,5},{2,6},{3},{4,7}} => 2 {{1,5},{2,6},{3},{4},{7}} => 2 {{1,5,7},{2},{3,6},{4}} => 1 {{1,5},{2,7},{3,6},{4}} => 1 {{1,5},{2},{3,6,7},{4}} => 1 {{1,5},{2},{3,6},{4,7}} => 2 {{1,5},{2},{3,6},{4},{7}} => 2 {{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},{4,6,7}} => 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}} => 0 {{1,6},{2,5,7},{3},{4}} => 1 {{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}} => 0 {{1},{2,5,6,7},{3},{4}} => 0 {{1},{2,5,6},{3,7},{4}} => 2 {{1},{2,5,6},{3},{4,7}} => 2 {{1},{2,5,6},{3},{4},{7}} => 2 {{1,7},{2,5},{3,6},{4}} => 1 {{1},{2,5,7},{3,6},{4}} => 1 {{1},{2,5},{3,6,7},{4}} => 1 {{1},{2,5},{3,6},{4,7}} => 2 {{1},{2,5},{3,6},{4},{7}} => 2 {{1,7},{2,5},{3},{4,6}} => 1 {{1},{2,5,7},{3},{4,6}} => 1 {{1},{2,5},{3,7},{4,6}} => 1 {{1},{2,5},{3},{4,6,7}} => 1 {{1},{2,5},{3},{4,6},{7}} => 1 {{1,7},{2,5},{3},{4},{6}} => 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 {{1,6,7},{2},{3,5},{4}} => 0 {{1,6},{2,7},{3,5},{4}} => 1 {{1,6},{2},{3,5,7},{4}} => 1 {{1,6},{2},{3,5},{4,7}} => 2 {{1,6},{2},{3,5},{4},{7}} => 2 {{1,7},{2,6},{3,5},{4}} => 0 {{1},{2,6,7},{3,5},{4}} => 0 {{1},{2,6},{3,5,7},{4}} => 1 {{1},{2,6},{3,5},{4,7}} => 2 {{1},{2,6},{3,5},{4},{7}} => 2 {{1,7},{2},{3,5,6},{4}} => 0 {{1},{2,7},{3,5,6},{4}} => 0 {{1},{2},{3,5,6,7},{4}} => 0 {{1},{2},{3,5,6},{4,7}} => 2 {{1},{2},{3,5,6},{4},{7}} => 2 {{1,7},{2},{3,5},{4,6}} => 1 {{1},{2,7},{3,5},{4,6}} => 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 {{1,7},{2},{3,5},{4},{6}} => 1 {{1},{2,7},{3,5},{4},{6}} => 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 {{1,6,7},{2},{3},{4,5}} => 0 {{1,6},{2,7},{3},{4,5}} => 1 {{1,6},{2},{3,7},{4,5}} => 1 {{1,6},{2},{3},{4,5,7}} => 1 {{1,6},{2},{3},{4,5},{7}} => 1 {{1,7},{2,6},{3},{4,5}} => 0 {{1},{2,6,7},{3},{4,5}} => 0 {{1},{2,6},{3,7},{4,5}} => 1 {{1},{2,6},{3},{4,5,7}} => 1 {{1},{2,6},{3},{4,5},{7}} => 1 {{1,7},{2},{3,6},{4,5}} => 0 {{1},{2,7},{3,6},{4,5}} => 0 {{1},{2},{3,6,7},{4,5}} => 0 {{1},{2},{3,6},{4,5,7}} => 1 {{1},{2},{3,6},{4,5},{7}} => 1 {{1,7},{2},{3},{4,5,6}} => 0 {{1},{2,7},{3},{4,5,6}} => 0 {{1},{2},{3,7},{4,5,6}} => 0 {{1},{2},{3},{4,5,6,7}} => 0 {{1},{2},{3},{4,5,6},{7}} => 0 {{1,7},{2},{3},{4,5},{6}} => 0 {{1},{2,7},{3},{4,5},{6}} => 0 {{1},{2},{3,7},{4,5},{6}} => 0 {{1},{2},{3},{4,5,7},{6}} => 0 {{1},{2},{3},{4,5},{6,7}} => 0 {{1},{2},{3},{4,5},{6},{7}} => 0 {{1,6,7},{2},{3},{4},{5}} => 0 {{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}} => 0 {{1},{2,6,7},{3},{4},{5}} => 0 {{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}} => 0 {{1},{2,7},{3,6},{4},{5}} => 0 {{1},{2},{3,6,7},{4},{5}} => 0 {{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}} => 0 {{1},{2,7},{3},{4,6},{5}} => 0 {{1},{2},{3,7},{4,6},{5}} => 0 {{1},{2},{3},{4,6,7},{5}} => 0 {{1},{2},{3},{4,6},{5,7}} => 1 {{1},{2},{3},{4,6},{5},{7}} => 1 {{1,7},{2},{3},{4},{5,6}} => 0 {{1},{2,7},{3},{4},{5,6}} => 0 {{1},{2},{3,7},{4},{5,6}} => 0 {{1},{2},{3},{4,7},{5,6}} => 0 {{1},{2},{3},{4},{5,6,7}} => 0 {{1},{2},{3},{4},{5,6},{7}} => 0 {{1,7},{2},{3},{4},{5},{6}} => 0 {{1},{2,7},{3},{4},{5},{6}} => 0 {{1},{2},{3,7},{4},{5},{6}} => 0 {{1},{2},{3},{4,7},{5},{6}} => 0 {{1},{2},{3},{4},{5,7},{6}} => 0 {{1},{2},{3},{4},{5},{6,7}} => 0 {{1},{2},{3},{4},{5},{6},{7}} => 0 {{1},{2},{3,4,5,6,7,8}} => 0 {{1},{2,4,5,6,7,8},{3}} => 0 {{1},{2,3,5,6,7,8},{4}} => 0 {{1},{2,3,4,6,7,8},{5}} => 0 {{1},{2,3,4,5,7,8},{6}} => 0 {{1},{2,3,4,5,6,7},{8}} => 0 {{1},{2,3,4,5,6,8},{7}} => 0 {{1},{2,3,4,5,6,7,8}} => 0 {{1,2},{3,4,5,6,7,8}} => 0 {{1,4,5,6,7,8},{2},{3}} => 0 {{1,3,5,6,7,8},{2},{4}} => 1 {{1,3,4,5,6,7,8},{2}} => 0 {{1,4,5,6,7,8},{2,3}} => 0 {{1,2,4,5,6,7,8},{3}} => 0 {{1,2,5,6,7,8},{3,4}} => 0 {{1,2,3,5,6,7,8},{4}} => 0 {{1,2,3,6,7,8},{4,5}} => 0 {{1,2,3,4,6,7,8},{5}} => 0 {{1,2,3,4,5,6},{7,8}} => 0 {{1,2,3,4,7,8},{5,6}} => 0 {{1,2,3,4,5,7,8},{6}} => 0 {{1,2,3,4,5,6,7},{8}} => 0 {{1,8},{2,3,4,5,6,7}} => 0 {{1,2,3,4,5,8},{6,7}} => 0 {{1,2,3,4,5,6,8},{7}} => 0 {{1,2,3,4,5,6,7,8}} => 0 {{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}} => 3 {{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}} => 4 {{1,2,4,5,6,8},{3,7}} => 3 {{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}} => 5 {{1,2,4,5,6,7},{3,8}} => 4 {{1,2,3,5,6,7},{4,8}} => 3 {{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}} => 1 {{1,5},{2,3,4,6,7,8}} => 1 {{1,6},{2,3,4,5,7,8}} => 1 {{1,7},{2,3,4,5,6,8}} => 1 ----------------------------------------------------------------------------- Created: Aug 06, 2016 at 09:27 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Aug 06, 2016 at 09:27 by Martin Rubey