***************************************************************************** * 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: St000563 ----------------------------------------------------------------------------- Collection: Set partitions ----------------------------------------------------------------------------- Description: The number of overlapping pairs of blocks of a set partition. This is also the number of occurrences of the pattern {{1,3},{2,4}} such that 1,2 are minimal and 3,4 are maximal. ----------------------------------------------------------------------------- References: [1] Kasraoui, A. Average values of some Z-parameters in a random set partition [[arXiv:1304.4813]] ----------------------------------------------------------------------------- Code: def statistic(pi): """ sage: statistic([[1,10],[2,3,7,9],[4],[5,6,12],[8,11]]) 4 """ count = 0 for A, B in Subsets([Set(b) for b in pi], 2): pass if min(A) < min(B) < max(A) < max(B) or min(B) < min(A) < max(B) < max(A): 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}} => 0 {{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}} => 0 {{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}} => 1 {{1,3,4},{2},{5}} => 0 {{1,3,5},{2,4}} => 0 {{1,3},{2,4,5}} => 1 {{1,3},{2,4},{5}} => 1 {{1,3,5},{2},{4}} => 0 {{1,3},{2,5},{4}} => 1 {{1,3},{2},{4,5}} => 0 {{1,3},{2},{4},{5}} => 0 {{1,4,5},{2,3}} => 0 {{1,4},{2,3,5}} => 1 {{1,4},{2,3},{5}} => 0 {{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}} => 0 {{1,5},{2,4},{3}} => 0 {{1},{2,4,5},{3}} => 0 {{1},{2,4},{3,5}} => 1 {{1},{2,4},{3},{5}} => 0 {{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}} => 0 {{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}} => 1 {{1,2,4,5},{3},{6}} => 0 {{1,2,4,6},{3,5}} => 0 {{1,2,4},{3,5,6}} => 1 {{1,2,4},{3,5},{6}} => 1 {{1,2,4,6},{3},{5}} => 0 {{1,2,4},{3,6},{5}} => 1 {{1,2,4},{3},{5,6}} => 0 {{1,2,4},{3},{5},{6}} => 0 {{1,2,5,6},{3,4}} => 0 {{1,2,5},{3,4,6}} => 1 {{1,2,5},{3,4},{6}} => 0 {{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}} => 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}} => 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 {{1,2,6},{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}} => 1 {{1,3,4,5},{2},{6}} => 0 {{1,3,4,6},{2,5}} => 0 {{1,3,4},{2,5,6}} => 1 {{1,3,4},{2,5},{6}} => 1 {{1,3,4,6},{2},{5}} => 0 {{1,3,4},{2,6},{5}} => 1 {{1,3,4},{2},{5,6}} => 0 {{1,3,4},{2},{5},{6}} => 0 {{1,3,5,6},{2,4}} => 0 {{1,3,5},{2,4,6}} => 1 {{1,3,5},{2,4},{6}} => 0 {{1,3,6},{2,4,5}} => 0 {{1,3},{2,4,5,6}} => 1 {{1,3},{2,4,5},{6}} => 1 {{1,3,6},{2,4},{5}} => 0 {{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}} => 0 {{1,3,5},{2,6},{4}} => 1 {{1,3,5},{2},{4,6}} => 1 {{1,3,5},{2},{4},{6}} => 0 {{1,3,6},{2,5},{4}} => 0 {{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}} => 0 {{1,3},{2,6},{4,5}} => 1 {{1,3},{2},{4,5,6}} => 0 {{1,3},{2},{4,5},{6}} => 0 {{1,3,6},{2},{4},{5}} => 0 {{1,3},{2,6},{4},{5}} => 1 {{1,3},{2},{4,6},{5}} => 0 {{1,3},{2},{4},{5,6}} => 0 {{1,3},{2},{4},{5},{6}} => 0 {{1,4,5,6},{2,3}} => 0 {{1,4,5},{2,3,6}} => 1 {{1,4,5},{2,3},{6}} => 0 {{1,4,6},{2,3,5}} => 0 {{1,4},{2,3,5,6}} => 1 {{1,4},{2,3,5},{6}} => 1 {{1,4,6},{2,3},{5}} => 0 {{1,4},{2,3,6},{5}} => 1 {{1,4},{2,3},{5,6}} => 0 {{1,4},{2,3},{5},{6}} => 0 {{1,5,6},{2,3,4}} => 0 {{1,5},{2,3,4,6}} => 1 {{1,5},{2,3,4},{6}} => 0 {{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}} => 0 {{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}} => 0 {{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}} => 1 {{1,4,5},{2},{3,6}} => 1 {{1,4,5},{2},{3},{6}} => 0 {{1,4,6},{2,5},{3}} => 0 {{1,4},{2,5,6},{3}} => 1 {{1,4},{2,5},{3,6}} => 3 {{1,4},{2,5},{3},{6}} => 1 {{1,4,6},{2},{3,5}} => 0 {{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}} => 0 {{1,4},{2,6},{3},{5}} => 1 {{1,4},{2},{3,6},{5}} => 1 {{1,4},{2},{3},{5,6}} => 0 {{1,4},{2},{3},{5},{6}} => 0 {{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}} => 0 {{1,6},{2,4,5},{3}} => 0 {{1},{2,4,5,6},{3}} => 0 {{1},{2,4,5},{3,6}} => 1 {{1},{2,4,5},{3},{6}} => 0 {{1,6},{2,4},{3,5}} => 1 {{1},{2,4,6},{3,5}} => 0 {{1},{2,4},{3,5,6}} => 1 {{1},{2,4},{3,5},{6}} => 1 {{1,6},{2,4},{3},{5}} => 0 {{1},{2,4,6},{3},{5}} => 0 {{1},{2,4},{3,6},{5}} => 1 {{1},{2,4},{3},{5,6}} => 0 {{1},{2,4},{3},{5},{6}} => 0 {{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}} => 0 {{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}} => 0 {{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}} => 0 {{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}} => 0 {{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}} => 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},{4,5,6}} => 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}} => 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 {{1,2,3,4,7},{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}} => 1 {{1,2,3,5,6},{4},{7}} => 0 {{1,2,3,5,7},{4,6}} => 0 {{1,2,3,5},{4,6,7}} => 1 {{1,2,3,5},{4,6},{7}} => 1 {{1,2,3,5,7},{4},{6}} => 0 {{1,2,3,5},{4,7},{6}} => 1 {{1,2,3,5},{4},{6,7}} => 0 {{1,2,3,5},{4},{6},{7}} => 0 {{1,2,3,6,7},{4,5}} => 0 {{1,2,3,6},{4,5,7}} => 1 {{1,2,3,6},{4,5},{7}} => 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 {{1,2,3,7},{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}} => 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}} => 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 {{1,2,3,7},{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}} => 1 {{1,2,4,5,6},{3},{7}} => 0 {{1,2,4,5,7},{3,6}} => 0 {{1,2,4,5},{3,6,7}} => 1 {{1,2,4,5},{3,6},{7}} => 1 {{1,2,4,5,7},{3},{6}} => 0 {{1,2,4,5},{3,7},{6}} => 1 {{1,2,4,5},{3},{6,7}} => 0 {{1,2,4,5},{3},{6},{7}} => 0 {{1,2,4,6,7},{3,5}} => 0 {{1,2,4,6},{3,5,7}} => 1 {{1,2,4,6},{3,5},{7}} => 0 {{1,2,4,7},{3,5,6}} => 0 {{1,2,4},{3,5,6,7}} => 1 {{1,2,4},{3,5,6},{7}} => 1 {{1,2,4,7},{3,5},{6}} => 0 {{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}} => 0 {{1,2,4,6},{3,7},{5}} => 1 {{1,2,4,6},{3},{5,7}} => 1 {{1,2,4,6},{3},{5},{7}} => 0 {{1,2,4,7},{3,6},{5}} => 0 {{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}} => 0 {{1,2,4},{3,7},{5,6}} => 1 {{1,2,4},{3},{5,6,7}} => 0 {{1,2,4},{3},{5,6},{7}} => 0 {{1,2,4,7},{3},{5},{6}} => 0 {{1,2,4},{3,7},{5},{6}} => 1 {{1,2,4},{3},{5,7},{6}} => 0 {{1,2,4},{3},{5},{6,7}} => 0 {{1,2,4},{3},{5},{6},{7}} => 0 {{1,2,5,6,7},{3,4}} => 0 {{1,2,5,6},{3,4,7}} => 1 {{1,2,5,6},{3,4},{7}} => 0 {{1,2,5,7},{3,4,6}} => 0 {{1,2,5},{3,4,6,7}} => 1 {{1,2,5},{3,4,6},{7}} => 1 {{1,2,5,7},{3,4},{6}} => 0 {{1,2,5},{3,4,7},{6}} => 1 {{1,2,5},{3,4},{6,7}} => 0 {{1,2,5},{3,4},{6},{7}} => 0 {{1,2,6,7},{3,4,5}} => 0 {{1,2,6},{3,4,5,7}} => 1 {{1,2,6},{3,4,5},{7}} => 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 {{1,2,7},{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}} => 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}} => 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 {{1,2,7},{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}} => 1 {{1,2,5,6},{3},{4,7}} => 1 {{1,2,5,6},{3},{4},{7}} => 0 {{1,2,5,7},{3,6},{4}} => 0 {{1,2,5},{3,6,7},{4}} => 1 {{1,2,5},{3,6},{4,7}} => 3 {{1,2,5},{3,6},{4},{7}} => 1 {{1,2,5,7},{3},{4,6}} => 0 {{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}} => 0 {{1,2,5},{3,7},{4},{6}} => 1 {{1,2,5},{3},{4,7},{6}} => 1 {{1,2,5},{3},{4},{6,7}} => 0 {{1,2,5},{3},{4},{6},{7}} => 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}} => 0 {{1,2,7},{3,5,6},{4}} => 0 {{1,2},{3,5,6,7},{4}} => 0 {{1,2},{3,5,6},{4,7}} => 1 {{1,2},{3,5,6},{4},{7}} => 0 {{1,2,7},{3,5},{4,6}} => 1 {{1,2},{3,5,7},{4,6}} => 0 {{1,2},{3,5},{4,6,7}} => 1 {{1,2},{3,5},{4,6},{7}} => 1 {{1,2,7},{3,5},{4},{6}} => 0 {{1,2},{3,5,7},{4},{6}} => 0 {{1,2},{3,5},{4,7},{6}} => 1 {{1,2},{3,5},{4},{6,7}} => 0 {{1,2},{3,5},{4},{6},{7}} => 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}} => 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}} => 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 {{1,2,7},{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}} => 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}} => 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}} => 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 {{1,2,7},{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}} => 1 {{1,3,4,5,6},{2},{7}} => 0 {{1,3,4,5,7},{2,6}} => 0 {{1,3,4,5},{2,6,7}} => 1 {{1,3,4,5},{2,6},{7}} => 1 {{1,3,4,5,7},{2},{6}} => 0 {{1,3,4,5},{2,7},{6}} => 1 {{1,3,4,5},{2},{6,7}} => 0 {{1,3,4,5},{2},{6},{7}} => 0 {{1,3,4,6,7},{2,5}} => 0 {{1,3,4,6},{2,5,7}} => 1 {{1,3,4,6},{2,5},{7}} => 0 {{1,3,4,7},{2,5,6}} => 0 {{1,3,4},{2,5,6,7}} => 1 {{1,3,4},{2,5,6},{7}} => 1 {{1,3,4,7},{2,5},{6}} => 0 {{1,3,4},{2,5,7},{6}} => 1 {{1,3,4},{2,5},{6,7}} => 1 {{1,3,4},{2,5},{6},{7}} => 1 {{1,3,4,6,7},{2},{5}} => 0 {{1,3,4,6},{2,7},{5}} => 1 {{1,3,4,6},{2},{5,7}} => 1 {{1,3,4,6},{2},{5},{7}} => 0 {{1,3,4,7},{2,6},{5}} => 0 {{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}} => 0 {{1,3,4},{2,7},{5,6}} => 1 {{1,3,4},{2},{5,6,7}} => 0 {{1,3,4},{2},{5,6},{7}} => 0 {{1,3,4,7},{2},{5},{6}} => 0 {{1,3,4},{2,7},{5},{6}} => 1 {{1,3,4},{2},{5,7},{6}} => 0 {{1,3,4},{2},{5},{6,7}} => 0 {{1,3,4},{2},{5},{6},{7}} => 0 {{1,3,5,6,7},{2,4}} => 0 {{1,3,5,6},{2,4,7}} => 1 {{1,3,5,6},{2,4},{7}} => 0 {{1,3,5,7},{2,4,6}} => 0 {{1,3,5},{2,4,6,7}} => 1 {{1,3,5},{2,4,6},{7}} => 1 {{1,3,5,7},{2,4},{6}} => 0 {{1,3,5},{2,4,7},{6}} => 1 {{1,3,5},{2,4},{6,7}} => 0 {{1,3,5},{2,4},{6},{7}} => 0 {{1,3,6,7},{2,4,5}} => 0 {{1,3,6},{2,4,5,7}} => 1 {{1,3,6},{2,4,5},{7}} => 0 {{1,3,7},{2,4,5,6}} => 0 {{1,3},{2,4,5,6,7}} => 1 {{1,3},{2,4,5,6},{7}} => 1 {{1,3,7},{2,4,5},{6}} => 0 {{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}} => 0 {{1,3,6},{2,4,7},{5}} => 1 {{1,3,6},{2,4},{5,7}} => 1 {{1,3,6},{2,4},{5},{7}} => 0 {{1,3,7},{2,4,6},{5}} => 0 {{1,3},{2,4,6,7},{5}} => 1 {{1,3},{2,4,6},{5,7}} => 2 {{1,3},{2,4,6},{5},{7}} => 1 {{1,3,7},{2,4},{5,6}} => 0 {{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}} => 0 {{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}} => 0 {{1,3,5,6},{2,7},{4}} => 1 {{1,3,5,6},{2},{4,7}} => 1 {{1,3,5,6},{2},{4},{7}} => 0 {{1,3,5,7},{2,6},{4}} => 0 {{1,3,5},{2,6,7},{4}} => 1 {{1,3,5},{2,6},{4,7}} => 3 {{1,3,5},{2,6},{4},{7}} => 1 {{1,3,5,7},{2},{4,6}} => 0 {{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}} => 0 {{1,3,5},{2,7},{4},{6}} => 1 {{1,3,5},{2},{4,7},{6}} => 1 {{1,3,5},{2},{4},{6,7}} => 0 {{1,3,5},{2},{4},{6},{7}} => 0 {{1,3,6,7},{2,5},{4}} => 0 {{1,3,6},{2,5,7},{4}} => 1 {{1,3,6},{2,5},{4,7}} => 2 {{1,3,6},{2,5},{4},{7}} => 0 {{1,3,7},{2,5,6},{4}} => 0 {{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}} => 1 {{1,3},{2,5,7},{4,6}} => 1 {{1,3},{2,5},{4,6,7}} => 2 {{1,3},{2,5},{4,6},{7}} => 2 {{1,3,7},{2,5},{4},{6}} => 0 {{1,3},{2,5,7},{4},{6}} => 1 {{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}} => 0 {{1,3,6},{2,7},{4,5}} => 1 {{1,3,6},{2},{4,5,7}} => 1 {{1,3,6},{2},{4,5},{7}} => 0 {{1,3,7},{2,6},{4,5}} => 0 {{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}} => 0 {{1,3},{2,7},{4,5,6}} => 1 {{1,3},{2},{4,5,6,7}} => 0 {{1,3},{2},{4,5,6},{7}} => 0 {{1,3,7},{2},{4,5},{6}} => 0 {{1,3},{2,7},{4,5},{6}} => 1 {{1,3},{2},{4,5,7},{6}} => 0 {{1,3},{2},{4,5},{6,7}} => 0 {{1,3},{2},{4,5},{6},{7}} => 0 {{1,3,6,7},{2},{4},{5}} => 0 {{1,3,6},{2,7},{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}} => 0 {{1,3,7},{2,6},{4},{5}} => 0 {{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}} => 0 {{1,3},{2,7},{4,6},{5}} => 1 {{1,3},{2},{4,6,7},{5}} => 0 {{1,3},{2},{4,6},{5,7}} => 1 {{1,3},{2},{4,6},{5},{7}} => 0 {{1,3,7},{2},{4},{5,6}} => 0 {{1,3},{2,7},{4},{5,6}} => 1 {{1,3},{2},{4,7},{5,6}} => 0 {{1,3},{2},{4},{5,6,7}} => 0 {{1,3},{2},{4},{5,6},{7}} => 0 {{1,3,7},{2},{4},{5},{6}} => 0 {{1,3},{2,7},{4},{5},{6}} => 1 {{1,3},{2},{4,7},{5},{6}} => 0 {{1,3},{2},{4},{5,7},{6}} => 0 {{1,3},{2},{4},{5},{6,7}} => 0 {{1,3},{2},{4},{5},{6},{7}} => 0 {{1,4,5,6,7},{2,3}} => 0 {{1,4,5,6},{2,3,7}} => 1 {{1,4,5,6},{2,3},{7}} => 0 {{1,4,5,7},{2,3,6}} => 0 {{1,4,5},{2,3,6,7}} => 1 {{1,4,5},{2,3,6},{7}} => 1 {{1,4,5,7},{2,3},{6}} => 0 {{1,4,5},{2,3,7},{6}} => 1 {{1,4,5},{2,3},{6,7}} => 0 {{1,4,5},{2,3},{6},{7}} => 0 {{1,4,6,7},{2,3,5}} => 0 {{1,4,6},{2,3,5,7}} => 1 {{1,4,6},{2,3,5},{7}} => 0 {{1,4,7},{2,3,5,6}} => 0 {{1,4},{2,3,5,6,7}} => 1 {{1,4},{2,3,5,6},{7}} => 1 {{1,4,7},{2,3,5},{6}} => 0 {{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}} => 0 {{1,4,6},{2,3,7},{5}} => 1 {{1,4,6},{2,3},{5,7}} => 1 {{1,4,6},{2,3},{5},{7}} => 0 {{1,4,7},{2,3,6},{5}} => 0 {{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}} => 0 {{1,4},{2,3,7},{5,6}} => 1 {{1,4},{2,3},{5,6,7}} => 0 {{1,4},{2,3},{5,6},{7}} => 0 {{1,4,7},{2,3},{5},{6}} => 0 {{1,4},{2,3,7},{5},{6}} => 1 {{1,4},{2,3},{5,7},{6}} => 0 {{1,4},{2,3},{5},{6,7}} => 0 {{1,4},{2,3},{5},{6},{7}} => 0 {{1,5,6,7},{2,3,4}} => 0 {{1,5,6},{2,3,4,7}} => 1 {{1,5,6},{2,3,4},{7}} => 0 {{1,5,7},{2,3,4,6}} => 0 {{1,5},{2,3,4,6,7}} => 1 {{1,5},{2,3,4,6},{7}} => 1 {{1,5,7},{2,3,4},{6}} => 0 {{1,5},{2,3,4,7},{6}} => 1 {{1,5},{2,3,4},{6,7}} => 0 {{1,5},{2,3,4},{6},{7}} => 0 {{1,6,7},{2,3,4,5}} => 0 {{1,6},{2,3,4,5,7}} => 1 {{1,6},{2,3,4,5},{7}} => 0 {{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}} => 0 {{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}} => 0 {{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}} => 1 {{1,5,6},{2,3},{4,7}} => 1 {{1,5,6},{2,3},{4},{7}} => 0 {{1,5,7},{2,3,6},{4}} => 0 {{1,5},{2,3,6,7},{4}} => 1 {{1,5},{2,3,6},{4,7}} => 3 {{1,5},{2,3,6},{4},{7}} => 1 {{1,5,7},{2,3},{4,6}} => 0 {{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}} => 0 {{1,5},{2,3,7},{4},{6}} => 1 {{1,5},{2,3},{4,7},{6}} => 1 {{1,5},{2,3},{4},{6,7}} => 0 {{1,5},{2,3},{4},{6},{7}} => 0 {{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}} => 0 {{1,7},{2,3,5,6},{4}} => 0 {{1},{2,3,5,6,7},{4}} => 0 {{1},{2,3,5,6},{4,7}} => 1 {{1},{2,3,5,6},{4},{7}} => 0 {{1,7},{2,3,5},{4,6}} => 1 {{1},{2,3,5,7},{4,6}} => 0 {{1},{2,3,5},{4,6,7}} => 1 {{1},{2,3,5},{4,6},{7}} => 1 {{1,7},{2,3,5},{4},{6}} => 0 {{1},{2,3,5,7},{4},{6}} => 0 {{1},{2,3,5},{4,7},{6}} => 1 {{1},{2,3,5},{4},{6,7}} => 0 {{1},{2,3,5},{4},{6},{7}} => 0 {{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}} => 0 {{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}} => 0 {{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}} => 0 {{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}} => 0 {{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}} => 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},{5,6,7}} => 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}} => 1 {{1,4,5,6},{2},{3,7}} => 1 {{1,4,5,6},{2},{3},{7}} => 0 {{1,4,5,7},{2,6},{3}} => 0 {{1,4,5},{2,6,7},{3}} => 1 {{1,4,5},{2,6},{3,7}} => 3 {{1,4,5},{2,6},{3},{7}} => 1 {{1,4,5,7},{2},{3,6}} => 0 {{1,4,5},{2,7},{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}} => 0 {{1,4,5},{2,7},{3},{6}} => 1 {{1,4,5},{2},{3,7},{6}} => 1 {{1,4,5},{2},{3},{6,7}} => 0 {{1,4,5},{2},{3},{6},{7}} => 0 {{1,4,6,7},{2,5},{3}} => 0 {{1,4,6},{2,5,7},{3}} => 1 {{1,4,6},{2,5},{3,7}} => 2 {{1,4,6},{2,5},{3},{7}} => 0 {{1,4,7},{2,5,6},{3}} => 0 {{1,4},{2,5,6,7},{3}} => 1 {{1,4},{2,5,6},{3,7}} => 3 {{1,4},{2,5,6},{3},{7}} => 1 {{1,4,7},{2,5},{3,6}} => 1 {{1,4},{2,5,7},{3,6}} => 2 {{1,4},{2,5},{3,6,7}} => 3 {{1,4},{2,5},{3,6},{7}} => 3 {{1,4,7},{2,5},{3},{6}} => 0 {{1,4},{2,5,7},{3},{6}} => 1 {{1,4},{2,5},{3,7},{6}} => 3 {{1,4},{2,5},{3},{6,7}} => 1 {{1,4},{2,5},{3},{6},{7}} => 1 {{1,4,6,7},{2},{3,5}} => 0 {{1,4,6},{2,7},{3,5}} => 1 {{1,4,6},{2},{3,5,7}} => 1 {{1,4,6},{2},{3,5},{7}} => 0 {{1,4,7},{2,6},{3,5}} => 0 {{1,4},{2,6,7},{3,5}} => 2 {{1,4},{2,6},{3,5,7}} => 3 {{1,4},{2,6},{3,5},{7}} => 2 {{1,4,7},{2},{3,5,6}} => 0 {{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}} => 0 {{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}} => 0 {{1,4,6},{2,7},{3},{5}} => 1 {{1,4,6},{2},{3,7},{5}} => 1 {{1,4,6},{2},{3},{5,7}} => 1 {{1,4,6},{2},{3},{5},{7}} => 0 {{1,4,7},{2,6},{3},{5}} => 0 {{1,4},{2,6,7},{3},{5}} => 1 {{1,4},{2,6},{3,7},{5}} => 3 {{1,4},{2,6},{3},{5,7}} => 2 {{1,4},{2,6},{3},{5},{7}} => 1 {{1,4,7},{2},{3,6},{5}} => 0 {{1,4},{2,7},{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}} => 0 {{1,4},{2,7},{3},{5,6}} => 1 {{1,4},{2},{3,7},{5,6}} => 1 {{1,4},{2},{3},{5,6,7}} => 0 {{1,4},{2},{3},{5,6},{7}} => 0 {{1,4,7},{2},{3},{5},{6}} => 0 {{1,4},{2,7},{3},{5},{6}} => 1 {{1,4},{2},{3,7},{5},{6}} => 1 {{1,4},{2},{3},{5,7},{6}} => 0 {{1,4},{2},{3},{5},{6,7}} => 0 {{1,4},{2},{3},{5},{6},{7}} => 0 {{1,5,6,7},{2,4},{3}} => 0 {{1,5,6},{2,4,7},{3}} => 1 {{1,5,6},{2,4},{3,7}} => 2 {{1,5,6},{2,4},{3},{7}} => 0 {{1,5,7},{2,4,6},{3}} => 0 {{1,5},{2,4,6,7},{3}} => 1 {{1,5},{2,4,6},{3,7}} => 3 {{1,5},{2,4,6},{3},{7}} => 1 {{1,5,7},{2,4},{3,6}} => 1 {{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}} => 0 {{1,5},{2,4,7},{3},{6}} => 1 {{1,5},{2,4},{3,7},{6}} => 2 {{1,5},{2,4},{3},{6,7}} => 0 {{1,5},{2,4},{3},{6},{7}} => 0 {{1,6,7},{2,4,5},{3}} => 0 {{1,6},{2,4,5,7},{3}} => 1 {{1,6},{2,4,5},{3,7}} => 2 {{1,6},{2,4,5},{3},{7}} => 0 {{1,7},{2,4,5,6},{3}} => 0 {{1},{2,4,5,6,7},{3}} => 0 {{1},{2,4,5,6},{3,7}} => 1 {{1},{2,4,5,6},{3},{7}} => 0 {{1,7},{2,4,5},{3,6}} => 1 {{1},{2,4,5,7},{3,6}} => 0 {{1},{2,4,5},{3,6,7}} => 1 {{1},{2,4,5},{3,6},{7}} => 1 {{1,7},{2,4,5},{3},{6}} => 0 {{1},{2,4,5,7},{3},{6}} => 0 {{1},{2,4,5},{3,7},{6}} => 1 {{1},{2,4,5},{3},{6,7}} => 0 {{1},{2,4,5},{3},{6},{7}} => 0 {{1,6,7},{2,4},{3,5}} => 1 {{1,6},{2,4,7},{3,5}} => 1 {{1,6},{2,4},{3,5,7}} => 2 {{1,6},{2,4},{3,5},{7}} => 1 {{1,7},{2,4,6},{3,5}} => 0 {{1},{2,4,6,7},{3,5}} => 0 {{1},{2,4,6},{3,5,7}} => 1 {{1},{2,4,6},{3,5},{7}} => 0 {{1,7},{2,4},{3,5,6}} => 1 {{1},{2,4,7},{3,5,6}} => 0 {{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}} => 0 {{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}} => 0 {{1,6},{2,4,7},{3},{5}} => 1 {{1,6},{2,4},{3,7},{5}} => 2 {{1,6},{2,4},{3},{5,7}} => 1 {{1,6},{2,4},{3},{5},{7}} => 0 {{1,7},{2,4,6},{3},{5}} => 0 {{1},{2,4,6,7},{3},{5}} => 0 {{1},{2,4,6},{3,7},{5}} => 1 {{1},{2,4,6},{3},{5,7}} => 1 {{1},{2,4,6},{3},{5},{7}} => 0 {{1,7},{2,4},{3,6},{5}} => 1 {{1},{2,4,7},{3,6},{5}} => 0 {{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}} => 0 {{1},{2,4,7},{3},{5,6}} => 0 {{1},{2,4},{3,7},{5,6}} => 1 {{1},{2,4},{3},{5,6,7}} => 0 {{1},{2,4},{3},{5,6},{7}} => 0 {{1,7},{2,4},{3},{5},{6}} => 0 {{1},{2,4,7},{3},{5},{6}} => 0 {{1},{2,4},{3,7},{5},{6}} => 1 {{1},{2,4},{3},{5,7},{6}} => 0 {{1},{2,4},{3},{5},{6,7}} => 0 {{1},{2,4},{3},{5},{6},{7}} => 0 {{1,5,6,7},{2},{3,4}} => 0 {{1,5,6},{2,7},{3,4}} => 1 {{1,5,6},{2},{3,4,7}} => 1 {{1,5,6},{2},{3,4},{7}} => 0 {{1,5,7},{2,6},{3,4}} => 0 {{1,5},{2,6,7},{3,4}} => 1 {{1,5},{2,6},{3,4,7}} => 3 {{1,5},{2,6},{3,4},{7}} => 1 {{1,5,7},{2},{3,4,6}} => 0 {{1,5},{2,7},{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}} => 0 {{1,5},{2,7},{3,4},{6}} => 1 {{1,5},{2},{3,4,7},{6}} => 1 {{1,5},{2},{3,4},{6,7}} => 0 {{1,5},{2},{3,4},{6},{7}} => 0 {{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}} => 0 {{1,7},{2,5,6},{3,4}} => 0 {{1},{2,5,6,7},{3,4}} => 0 {{1},{2,5,6},{3,4,7}} => 1 {{1},{2,5,6},{3,4},{7}} => 0 {{1,7},{2,5},{3,4,6}} => 1 {{1},{2,5,7},{3,4,6}} => 0 {{1},{2,5},{3,4,6,7}} => 1 {{1},{2,5},{3,4,6},{7}} => 1 {{1,7},{2,5},{3,4},{6}} => 0 {{1},{2,5,7},{3,4},{6}} => 0 {{1},{2,5},{3,4,7},{6}} => 1 {{1},{2,5},{3,4},{6,7}} => 0 {{1},{2,5},{3,4},{6},{7}} => 0 {{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}} => 0 {{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}} => 0 {{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}} => 0 {{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}} => 0 {{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}} => 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},{5,6,7}} => 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}} => 1 {{1,5,6},{2},{3,7},{4}} => 1 {{1,5,6},{2},{3},{4,7}} => 1 {{1,5,6},{2},{3},{4},{7}} => 0 {{1,5,7},{2,6},{3},{4}} => 0 {{1,5},{2,6,7},{3},{4}} => 1 {{1,5},{2,6},{3,7},{4}} => 3 {{1,5},{2,6},{3},{4,7}} => 3 {{1,5},{2,6},{3},{4},{7}} => 1 {{1,5,7},{2},{3,6},{4}} => 0 {{1,5},{2,7},{3,6},{4}} => 2 {{1,5},{2},{3,6,7},{4}} => 1 {{1,5},{2},{3,6},{4,7}} => 3 {{1,5},{2},{3,6},{4},{7}} => 1 {{1,5,7},{2},{3},{4,6}} => 0 {{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}} => 0 {{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}} => 0 {{1,5},{2},{3},{4},{6},{7}} => 0 {{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}} => 0 {{1,7},{2,5,6},{3},{4}} => 0 {{1},{2,5,6,7},{3},{4}} => 0 {{1},{2,5,6},{3,7},{4}} => 1 {{1},{2,5,6},{3},{4,7}} => 1 {{1},{2,5,6},{3},{4},{7}} => 0 {{1,7},{2,5},{3,6},{4}} => 1 {{1},{2,5,7},{3,6},{4}} => 0 {{1},{2,5},{3,6,7},{4}} => 1 {{1},{2,5},{3,6},{4,7}} => 3 {{1},{2,5},{3,6},{4},{7}} => 1 {{1,7},{2,5},{3},{4,6}} => 1 {{1},{2,5,7},{3},{4,6}} => 0 {{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}} => 0 {{1},{2,5,7},{3},{4},{6}} => 0 {{1},{2,5},{3,7},{4},{6}} => 1 {{1},{2,5},{3},{4,7},{6}} => 1 {{1},{2,5},{3},{4},{6,7}} => 0 {{1},{2,5},{3},{4},{6},{7}} => 0 {{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}} => 0 {{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}} => 0 {{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}} => 1 {{1},{2},{3,5,6},{4},{7}} => 0 {{1,7},{2},{3,5},{4,6}} => 1 {{1},{2,7},{3,5},{4,6}} => 1 {{1},{2},{3,5,7},{4,6}} => 0 {{1},{2},{3,5},{4,6,7}} => 1 {{1},{2},{3,5},{4,6},{7}} => 1 {{1,7},{2},{3,5},{4},{6}} => 0 {{1},{2,7},{3,5},{4},{6}} => 0 {{1},{2},{3,5,7},{4},{6}} => 0 {{1},{2},{3,5},{4,7},{6}} => 1 {{1},{2},{3,5},{4},{6,7}} => 0 {{1},{2},{3,5},{4},{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},{4,5,7}} => 1 {{1,6},{2},{3},{4,5},{7}} => 0 {{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}} => 0 {{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}} => 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},{4,5,6,7}} => 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}} => 0 {{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}} => 0 {{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}} => 0 {{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}} => 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},{5,6,7}} => 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}} => 0 {{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}} => 0 {{1,3,4,6,7,8},{2,5}} => 0 {{1,2,4,6,7,8},{3,5}} => 0 {{1,3,4,5,7,8},{2,6}} => 0 {{1,2,4,5,7,8},{3,6}} => 0 {{1,2,3,5,7,8},{4,6}} => 0 {{1,3,4,5,6,8},{2,7}} => 0 {{1,2,4,5,6,8},{3,7}} => 0 {{1,2,3,5,6,8},{4,7}} => 0 {{1,2,3,4,6,8},{5,7}} => 0 {{1,3,4,5,6,7},{2,8}} => 1 {{1,2,4,5,6,7},{3,8}} => 1 {{1,2,3,5,6,7},{4,8}} => 1 {{1,2,3,4,6,7},{5,8}} => 1 {{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 05, 2016 at 21:00 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Aug 11, 2016 at 15:18 by Martin Rubey