***************************************************************************** * 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: St000793 ----------------------------------------------------------------------------- Collection: Set partitions ----------------------------------------------------------------------------- Description: The length of the longest partition in the vacillating tableau corresponding to a set partition. To a set partition $\pi$ of $\{1,\dots,r\}$ with at most $n$ blocks we associate a vacillating tableau, following [1], as follows: create a triangular growth diagram by labelling the columns of a triangular grid with row lengths $r-1, \dots, 0$ from left to right $1$ to $r$, and the rows from the shortest to the longest $1$ to $r$. For each arc $(i,j)$ in the standard representation of $\pi$, place a cross into the cell in column $i$ and row $j$. Next we label the corners of the first column beginning with the corners of the shortest row. The first corner is labelled with the partition $(n)$. If there is a cross in the row separating this corner from the next, label the next corner with the same partition, otherwise with the partition smaller by one. Do the same with the corners of the first row. Finally, apply Fomin's local rules, to obtain the partitions along the diagonal. These will alternate in size between $n$ and $n-1$. This statistic is the length of the longest partition on the diagonal of the diagram. ----------------------------------------------------------------------------- References: [1] Benkart, G., Halverson, T., Harman, N. Dimensions of irreducible modules for partition algebras and tensor power multiplicities for symmetric and alternating groups [[arXiv:1605.06543]] ----------------------------------------------------------------------------- Code: def from_partition(p, n): """ sage: G = from_partition([[1,3,4],[2]], 4); G 0 0 1 1 0 0 sage: G.in_labels() [[3], [2], [2], [2], [2], [3], [3]] sage: G.out_labels() [[3], [3, 1], [3], [3, 1], [3], [4], [3]] sage: G = from_partition([[3,4],[1,2]], 4); G 0 0 1 0 0 1 sage: G.in_labels() [[3], [3], [2], [2], [2], [3], [3]] sage: G.out_labels() [[3], [4], [3], [3, 1], [3], [4], [3]] sage: G = from_partition([[3,4],[2],[1]], 4); G 0 0 1 0 0 0 sage: G.in_labels() [[3], [2], [1], [1], [2], [3], [3]] sage: G.out_labels() [[3], [3, 1], [2, 1], [3, 1], [3], [4], [3]] """ p = SetPartition(p) r = p.size() filling = {(i-1, r-j): 1 for (i,j) in p.arcs()} shape = Partition([r-i-1 for i in range(r-1)]) labels = [[n-1]] la = n-1 O = [i for i,_ in p.arcs()] C = [j for _,j in p.arcs()] for j in range(2,r+1): if j not in C: la -= 1 labels += [[la]] for i in range(1,r): if i not in O: la += 1 labels += [[la]] return GrowthDiagram.rules.RSK()(filling, shape, labels) def statistic(p): return max(len(mu) for mu in from_partition(p, p.size()).out_labels()) ----------------------------------------------------------------------------- Statistic values: {{1}} => 0 {{1,2}} => 1 {{1},{2}} => 2 {{1,2,3}} => 1 {{1,2},{3}} => 2 {{1,3},{2}} => 2 {{1},{2,3}} => 2 {{1},{2},{3}} => 2 {{1,2,3,4}} => 1 {{1,2,3},{4}} => 2 {{1,2,4},{3}} => 2 {{1,2},{3,4}} => 2 {{1,2},{3},{4}} => 2 {{1,3,4},{2}} => 2 {{1,3},{2,4}} => 2 {{1,3},{2},{4}} => 2 {{1,4},{2,3}} => 2 {{1},{2,3,4}} => 2 {{1},{2,3},{4}} => 2 {{1,4},{2},{3}} => 3 {{1},{2,4},{3}} => 2 {{1},{2},{3,4}} => 2 {{1},{2},{3},{4}} => 2 {{1,2,3,4,5}} => 1 {{1,2,3,4},{5}} => 2 {{1,2,3,5},{4}} => 2 {{1,2,3},{4,5}} => 2 {{1,2,3},{4},{5}} => 2 {{1,2,4,5},{3}} => 2 {{1,2,4},{3,5}} => 2 {{1,2,4},{3},{5}} => 2 {{1,2,5},{3,4}} => 2 {{1,2},{3,4,5}} => 2 {{1,2},{3,4},{5}} => 2 {{1,2,5},{3},{4}} => 3 {{1,2},{3,5},{4}} => 2 {{1,2},{3},{4,5}} => 2 {{1,2},{3},{4},{5}} => 2 {{1,3,4,5},{2}} => 2 {{1,3,4},{2,5}} => 2 {{1,3,4},{2},{5}} => 2 {{1,3,5},{2,4}} => 2 {{1,3},{2,4,5}} => 2 {{1,3},{2,4},{5}} => 2 {{1,3,5},{2},{4}} => 2 {{1,3},{2,5},{4}} => 3 {{1,3},{2},{4,5}} => 2 {{1,3},{2},{4},{5}} => 2 {{1,4,5},{2,3}} => 2 {{1,4},{2,3,5}} => 2 {{1,4},{2,3},{5}} => 2 {{1,5},{2,3,4}} => 2 {{1},{2,3,4,5}} => 2 {{1},{2,3,4},{5}} => 2 {{1,5},{2,3},{4}} => 3 {{1},{2,3,5},{4}} => 2 {{1},{2,3},{4,5}} => 2 {{1},{2,3},{4},{5}} => 2 {{1,4,5},{2},{3}} => 3 {{1,4},{2,5},{3}} => 3 {{1,4},{2},{3,5}} => 3 {{1,4},{2},{3},{5}} => 3 {{1,5},{2,4},{3}} => 2 {{1},{2,4,5},{3}} => 2 {{1},{2,4},{3,5}} => 2 {{1},{2,4},{3},{5}} => 2 {{1,5},{2},{3,4}} => 3 {{1},{2,5},{3,4}} => 2 {{1},{2},{3,4,5}} => 2 {{1},{2},{3,4},{5}} => 2 {{1,5},{2},{3},{4}} => 3 {{1},{2,5},{3},{4}} => 3 {{1},{2},{3,5},{4}} => 2 {{1},{2},{3},{4,5}} => 2 {{1},{2},{3},{4},{5}} => 2 {{1,2,3,4,5,6}} => 1 {{1,2,3,4,5},{6}} => 2 {{1,2,3,4,6},{5}} => 2 {{1,2,3,4},{5,6}} => 2 {{1,2,3,4},{5},{6}} => 2 {{1,2,3,5,6},{4}} => 2 {{1,2,3,5},{4,6}} => 2 {{1,2,3,5},{4},{6}} => 2 {{1,2,3,6},{4,5}} => 2 {{1,2,3},{4,5,6}} => 2 {{1,2,3},{4,5},{6}} => 2 {{1,2,3,6},{4},{5}} => 3 {{1,2,3},{4,6},{5}} => 2 {{1,2,3},{4},{5,6}} => 2 {{1,2,3},{4},{5},{6}} => 2 {{1,2,4,5,6},{3}} => 2 {{1,2,4,5},{3,6}} => 2 {{1,2,4,5},{3},{6}} => 2 {{1,2,4,6},{3,5}} => 2 {{1,2,4},{3,5,6}} => 2 {{1,2,4},{3,5},{6}} => 2 {{1,2,4,6},{3},{5}} => 2 {{1,2,4},{3,6},{5}} => 3 {{1,2,4},{3},{5,6}} => 2 {{1,2,4},{3},{5},{6}} => 2 {{1,2,5,6},{3,4}} => 2 {{1,2,5},{3,4,6}} => 2 {{1,2,5},{3,4},{6}} => 2 {{1,2,6},{3,4,5}} => 2 {{1,2},{3,4,5,6}} => 2 {{1,2},{3,4,5},{6}} => 2 {{1,2,6},{3,4},{5}} => 3 {{1,2},{3,4,6},{5}} => 2 {{1,2},{3,4},{5,6}} => 2 {{1,2},{3,4},{5},{6}} => 2 {{1,2,5,6},{3},{4}} => 3 {{1,2,5},{3,6},{4}} => 3 {{1,2,5},{3},{4,6}} => 3 {{1,2,5},{3},{4},{6}} => 3 {{1,2,6},{3,5},{4}} => 2 {{1,2},{3,5,6},{4}} => 2 {{1,2},{3,5},{4,6}} => 2 {{1,2},{3,5},{4},{6}} => 2 {{1,2,6},{3},{4,5}} => 3 {{1,2},{3,6},{4,5}} => 2 {{1,2},{3},{4,5,6}} => 2 {{1,2},{3},{4,5},{6}} => 2 {{1,2,6},{3},{4},{5}} => 3 {{1,2},{3,6},{4},{5}} => 3 {{1,2},{3},{4,6},{5}} => 2 {{1,2},{3},{4},{5,6}} => 2 {{1,2},{3},{4},{5},{6}} => 2 {{1,3,4,5,6},{2}} => 2 {{1,3,4,5},{2,6}} => 2 {{1,3,4,5},{2},{6}} => 2 {{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}} => 3 {{1,3,4},{2},{5,6}} => 2 {{1,3,4},{2},{5},{6}} => 2 {{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}} => 2 {{1,3},{2,4,5},{6}} => 2 {{1,3,6},{2,4},{5}} => 3 {{1,3},{2,4,6},{5}} => 2 {{1,3},{2,4},{5,6}} => 2 {{1,3},{2,4},{5},{6}} => 2 {{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}} => 3 {{1,3},{2,5,6},{4}} => 3 {{1,3},{2,5},{4,6}} => 3 {{1,3},{2,5},{4},{6}} => 3 {{1,3,6},{2},{4,5}} => 2 {{1,3},{2,6},{4,5}} => 3 {{1,3},{2},{4,5,6}} => 2 {{1,3},{2},{4,5},{6}} => 2 {{1,3,6},{2},{4},{5}} => 3 {{1,3},{2,6},{4},{5}} => 3 {{1,3},{2},{4,6},{5}} => 2 {{1,3},{2},{4},{5,6}} => 2 {{1,3},{2},{4},{5},{6}} => 2 {{1,4,5,6},{2,3}} => 2 {{1,4,5},{2,3,6}} => 2 {{1,4,5},{2,3},{6}} => 2 {{1,4,6},{2,3,5}} => 2 {{1,4},{2,3,5,6}} => 2 {{1,4},{2,3,5},{6}} => 2 {{1,4,6},{2,3},{5}} => 2 {{1,4},{2,3,6},{5}} => 3 {{1,4},{2,3},{5,6}} => 2 {{1,4},{2,3},{5},{6}} => 2 {{1,5,6},{2,3,4}} => 2 {{1,5},{2,3,4,6}} => 2 {{1,5},{2,3,4},{6}} => 2 {{1,6},{2,3,4,5}} => 2 {{1},{2,3,4,5,6}} => 2 {{1},{2,3,4,5},{6}} => 2 {{1,6},{2,3,4},{5}} => 3 {{1},{2,3,4,6},{5}} => 2 {{1},{2,3,4},{5,6}} => 2 {{1},{2,3,4},{5},{6}} => 2 {{1,5,6},{2,3},{4}} => 3 {{1,5},{2,3,6},{4}} => 3 {{1,5},{2,3},{4,6}} => 3 {{1,5},{2,3},{4},{6}} => 3 {{1,6},{2,3,5},{4}} => 2 {{1},{2,3,5,6},{4}} => 2 {{1},{2,3,5},{4,6}} => 2 {{1},{2,3,5},{4},{6}} => 2 {{1,6},{2,3},{4,5}} => 3 {{1},{2,3,6},{4,5}} => 2 {{1},{2,3},{4,5,6}} => 2 {{1},{2,3},{4,5},{6}} => 2 {{1,6},{2,3},{4},{5}} => 3 {{1},{2,3,6},{4},{5}} => 3 {{1},{2,3},{4,6},{5}} => 2 {{1},{2,3},{4},{5,6}} => 2 {{1},{2,3},{4},{5},{6}} => 2 {{1,4,5,6},{2},{3}} => 3 {{1,4,5},{2,6},{3}} => 3 {{1,4,5},{2},{3,6}} => 3 {{1,4,5},{2},{3},{6}} => 3 {{1,4,6},{2,5},{3}} => 3 {{1,4},{2,5,6},{3}} => 3 {{1,4},{2,5},{3,6}} => 3 {{1,4},{2,5},{3},{6}} => 3 {{1,4,6},{2},{3,5}} => 3 {{1,4},{2,6},{3,5}} => 3 {{1,4},{2},{3,5,6}} => 3 {{1,4},{2},{3,5},{6}} => 3 {{1,4,6},{2},{3},{5}} => 3 {{1,4},{2,6},{3},{5}} => 3 {{1,4},{2},{3,6},{5}} => 3 {{1,4},{2},{3},{5,6}} => 3 {{1,4},{2},{3},{5},{6}} => 3 {{1,5,6},{2,4},{3}} => 2 {{1,5},{2,4,6},{3}} => 2 {{1,5},{2,4},{3,6}} => 3 {{1,5},{2,4},{3},{6}} => 2 {{1,6},{2,4,5},{3}} => 2 {{1},{2,4,5,6},{3}} => 2 {{1},{2,4,5},{3,6}} => 2 {{1},{2,4,5},{3},{6}} => 2 {{1,6},{2,4},{3,5}} => 2 {{1},{2,4,6},{3,5}} => 2 {{1},{2,4},{3,5,6}} => 2 {{1},{2,4},{3,5},{6}} => 2 {{1,6},{2,4},{3},{5}} => 3 {{1},{2,4,6},{3},{5}} => 2 {{1},{2,4},{3,6},{5}} => 3 {{1},{2,4},{3},{5,6}} => 2 {{1},{2,4},{3},{5},{6}} => 2 {{1,5,6},{2},{3,4}} => 3 {{1,5},{2,6},{3,4}} => 3 {{1,5},{2},{3,4,6}} => 3 {{1,5},{2},{3,4},{6}} => 3 {{1,6},{2,5},{3,4}} => 2 {{1},{2,5,6},{3,4}} => 2 {{1},{2,5},{3,4,6}} => 2 {{1},{2,5},{3,4},{6}} => 2 {{1,6},{2},{3,4,5}} => 3 {{1},{2,6},{3,4,5}} => 2 {{1},{2},{3,4,5,6}} => 2 {{1},{2},{3,4,5},{6}} => 2 {{1,6},{2},{3,4},{5}} => 3 {{1},{2,6},{3,4},{5}} => 3 {{1},{2},{3,4,6},{5}} => 2 {{1},{2},{3,4},{5,6}} => 2 {{1},{2},{3,4},{5},{6}} => 2 {{1,5,6},{2},{3},{4}} => 3 {{1,5},{2,6},{3},{4}} => 4 {{1,5},{2},{3,6},{4}} => 3 {{1,5},{2},{3},{4,6}} => 3 {{1,5},{2},{3},{4},{6}} => 3 {{1,6},{2,5},{3},{4}} => 3 {{1},{2,5,6},{3},{4}} => 3 {{1},{2,5},{3,6},{4}} => 3 {{1},{2,5},{3},{4,6}} => 3 {{1},{2,5},{3},{4},{6}} => 3 {{1,6},{2},{3,5},{4}} => 3 {{1},{2,6},{3,5},{4}} => 2 {{1},{2},{3,5,6},{4}} => 2 {{1},{2},{3,5},{4,6}} => 2 {{1},{2},{3,5},{4},{6}} => 2 {{1,6},{2},{3},{4,5}} => 3 {{1},{2,6},{3},{4,5}} => 3 {{1},{2},{3,6},{4,5}} => 2 {{1},{2},{3},{4,5,6}} => 2 {{1},{2},{3},{4,5},{6}} => 2 {{1,6},{2},{3},{4},{5}} => 3 {{1},{2,6},{3},{4},{5}} => 3 {{1},{2},{3,6},{4},{5}} => 3 {{1},{2},{3},{4,6},{5}} => 2 {{1},{2},{3},{4},{5,6}} => 2 {{1},{2},{3},{4},{5},{6}} => 2 {{1,2,3,4,5,6,7}} => 1 {{1,2,3,4,5,6},{7}} => 2 {{1,2,3,4,5,7},{6}} => 2 {{1,2,3,4,5},{6,7}} => 2 {{1,2,3,4,5},{6},{7}} => 2 {{1,2,3,4,6,7},{5}} => 2 {{1,2,3,4,6},{5,7}} => 2 {{1,2,3,4,6},{5},{7}} => 2 {{1,2,3,4,7},{5,6}} => 2 {{1,2,3,4},{5,6,7}} => 2 {{1,2,3,4},{5,6},{7}} => 2 {{1,2,3,4,7},{5},{6}} => 3 {{1,2,3,4},{5,7},{6}} => 2 {{1,2,3,4},{5},{6,7}} => 2 {{1,2,3,4},{5},{6},{7}} => 2 {{1,2,3,5,6,7},{4}} => 2 {{1,2,3,5,6},{4,7}} => 2 {{1,2,3,5,6},{4},{7}} => 2 {{1,2,3,5,7},{4,6}} => 2 {{1,2,3,5},{4,6,7}} => 2 {{1,2,3,5},{4,6},{7}} => 2 {{1,2,3,5,7},{4},{6}} => 2 {{1,2,3,5},{4,7},{6}} => 3 {{1,2,3,5},{4},{6,7}} => 2 {{1,2,3,5},{4},{6},{7}} => 2 {{1,2,3,6,7},{4,5}} => 2 {{1,2,3,6},{4,5,7}} => 2 {{1,2,3,6},{4,5},{7}} => 2 {{1,2,3,7},{4,5,6}} => 2 {{1,2,3},{4,5,6,7}} => 2 {{1,2,3},{4,5,6},{7}} => 2 {{1,2,3,7},{4,5},{6}} => 3 {{1,2,3},{4,5,7},{6}} => 2 {{1,2,3},{4,5},{6,7}} => 2 {{1,2,3},{4,5},{6},{7}} => 2 {{1,2,3,6,7},{4},{5}} => 3 {{1,2,3,6},{4,7},{5}} => 3 {{1,2,3,6},{4},{5,7}} => 3 {{1,2,3,6},{4},{5},{7}} => 3 {{1,2,3,7},{4,6},{5}} => 2 {{1,2,3},{4,6,7},{5}} => 2 {{1,2,3},{4,6},{5,7}} => 2 {{1,2,3},{4,6},{5},{7}} => 2 {{1,2,3,7},{4},{5,6}} => 3 {{1,2,3},{4,7},{5,6}} => 2 {{1,2,3},{4},{5,6,7}} => 2 {{1,2,3},{4},{5,6},{7}} => 2 {{1,2,3,7},{4},{5},{6}} => 3 {{1,2,3},{4,7},{5},{6}} => 3 {{1,2,3},{4},{5,7},{6}} => 2 {{1,2,3},{4},{5},{6,7}} => 2 {{1,2,3},{4},{5},{6},{7}} => 2 {{1,2,4,5,6,7},{3}} => 2 {{1,2,4,5,6},{3,7}} => 2 {{1,2,4,5,6},{3},{7}} => 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 {{1,2,4,5,7},{3},{6}} => 2 {{1,2,4,5},{3,7},{6}} => 3 {{1,2,4,5},{3},{6,7}} => 2 {{1,2,4,5},{3},{6},{7}} => 2 {{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}} => 2 {{1,2,4},{3,5,6},{7}} => 2 {{1,2,4,7},{3,5},{6}} => 3 {{1,2,4},{3,5,7},{6}} => 2 {{1,2,4},{3,5},{6,7}} => 2 {{1,2,4},{3,5},{6},{7}} => 2 {{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}} => 3 {{1,2,4},{3,6,7},{5}} => 3 {{1,2,4},{3,6},{5,7}} => 3 {{1,2,4},{3,6},{5},{7}} => 3 {{1,2,4,7},{3},{5,6}} => 2 {{1,2,4},{3,7},{5,6}} => 3 {{1,2,4},{3},{5,6,7}} => 2 {{1,2,4},{3},{5,6},{7}} => 2 {{1,2,4,7},{3},{5},{6}} => 3 {{1,2,4},{3,7},{5},{6}} => 3 {{1,2,4},{3},{5,7},{6}} => 2 {{1,2,4},{3},{5},{6,7}} => 2 {{1,2,4},{3},{5},{6},{7}} => 2 {{1,2,5,6,7},{3,4}} => 2 {{1,2,5,6},{3,4,7}} => 2 {{1,2,5,6},{3,4},{7}} => 2 {{1,2,5,7},{3,4,6}} => 2 {{1,2,5},{3,4,6,7}} => 2 {{1,2,5},{3,4,6},{7}} => 2 {{1,2,5,7},{3,4},{6}} => 2 {{1,2,5},{3,4,7},{6}} => 3 {{1,2,5},{3,4},{6,7}} => 2 {{1,2,5},{3,4},{6},{7}} => 2 {{1,2,6,7},{3,4,5}} => 2 {{1,2,6},{3,4,5,7}} => 2 {{1,2,6},{3,4,5},{7}} => 2 {{1,2,7},{3,4,5,6}} => 2 {{1,2},{3,4,5,6,7}} => 2 {{1,2},{3,4,5,6},{7}} => 2 {{1,2,7},{3,4,5},{6}} => 3 {{1,2},{3,4,5,7},{6}} => 2 {{1,2},{3,4,5},{6,7}} => 2 {{1,2},{3,4,5},{6},{7}} => 2 {{1,2,6,7},{3,4},{5}} => 3 {{1,2,6},{3,4,7},{5}} => 3 {{1,2,6},{3,4},{5,7}} => 3 {{1,2,6},{3,4},{5},{7}} => 3 {{1,2,7},{3,4,6},{5}} => 2 {{1,2},{3,4,6,7},{5}} => 2 {{1,2},{3,4,6},{5,7}} => 2 {{1,2},{3,4,6},{5},{7}} => 2 {{1,2,7},{3,4},{5,6}} => 3 {{1,2},{3,4,7},{5,6}} => 2 {{1,2},{3,4},{5,6,7}} => 2 {{1,2},{3,4},{5,6},{7}} => 2 {{1,2,7},{3,4},{5},{6}} => 3 {{1,2},{3,4,7},{5},{6}} => 3 {{1,2},{3,4},{5,7},{6}} => 2 {{1,2},{3,4},{5},{6,7}} => 2 {{1,2},{3,4},{5},{6},{7}} => 2 {{1,2,5,6,7},{3},{4}} => 3 {{1,2,5,6},{3,7},{4}} => 3 {{1,2,5,6},{3},{4,7}} => 3 {{1,2,5,6},{3},{4},{7}} => 3 {{1,2,5,7},{3,6},{4}} => 3 {{1,2,5},{3,6,7},{4}} => 3 {{1,2,5},{3,6},{4,7}} => 3 {{1,2,5},{3,6},{4},{7}} => 3 {{1,2,5,7},{3},{4,6}} => 3 {{1,2,5},{3,7},{4,6}} => 3 {{1,2,5},{3},{4,6,7}} => 3 {{1,2,5},{3},{4,6},{7}} => 3 {{1,2,5,7},{3},{4},{6}} => 3 {{1,2,5},{3,7},{4},{6}} => 3 {{1,2,5},{3},{4,7},{6}} => 3 {{1,2,5},{3},{4},{6,7}} => 3 {{1,2,5},{3},{4},{6},{7}} => 3 {{1,2,6,7},{3,5},{4}} => 2 {{1,2,6},{3,5,7},{4}} => 2 {{1,2,6},{3,5},{4,7}} => 3 {{1,2,6},{3,5},{4},{7}} => 2 {{1,2,7},{3,5,6},{4}} => 2 {{1,2},{3,5,6,7},{4}} => 2 {{1,2},{3,5,6},{4,7}} => 2 {{1,2},{3,5,6},{4},{7}} => 2 {{1,2,7},{3,5},{4,6}} => 2 {{1,2},{3,5,7},{4,6}} => 2 {{1,2},{3,5},{4,6,7}} => 2 {{1,2},{3,5},{4,6},{7}} => 2 {{1,2,7},{3,5},{4},{6}} => 3 {{1,2},{3,5,7},{4},{6}} => 2 {{1,2},{3,5},{4,7},{6}} => 3 {{1,2},{3,5},{4},{6,7}} => 2 {{1,2},{3,5},{4},{6},{7}} => 2 {{1,2,6,7},{3},{4,5}} => 3 {{1,2,6},{3,7},{4,5}} => 3 {{1,2,6},{3},{4,5,7}} => 3 {{1,2,6},{3},{4,5},{7}} => 3 {{1,2,7},{3,6},{4,5}} => 2 {{1,2},{3,6,7},{4,5}} => 2 {{1,2},{3,6},{4,5,7}} => 2 {{1,2},{3,6},{4,5},{7}} => 2 {{1,2,7},{3},{4,5,6}} => 3 {{1,2},{3,7},{4,5,6}} => 2 {{1,2},{3},{4,5,6,7}} => 2 {{1,2},{3},{4,5,6},{7}} => 2 {{1,2,7},{3},{4,5},{6}} => 3 {{1,2},{3,7},{4,5},{6}} => 3 {{1,2},{3},{4,5,7},{6}} => 2 {{1,2},{3},{4,5},{6,7}} => 2 {{1,2},{3},{4,5},{6},{7}} => 2 {{1,2,6,7},{3},{4},{5}} => 3 {{1,2,6},{3,7},{4},{5}} => 4 {{1,2,6},{3},{4,7},{5}} => 3 {{1,2,6},{3},{4},{5,7}} => 3 {{1,2,6},{3},{4},{5},{7}} => 3 {{1,2,7},{3,6},{4},{5}} => 3 {{1,2},{3,6,7},{4},{5}} => 3 {{1,2},{3,6},{4,7},{5}} => 3 {{1,2},{3,6},{4},{5,7}} => 3 {{1,2},{3,6},{4},{5},{7}} => 3 {{1,2,7},{3},{4,6},{5}} => 3 {{1,2},{3,7},{4,6},{5}} => 2 {{1,2},{3},{4,6,7},{5}} => 2 {{1,2},{3},{4,6},{5,7}} => 2 {{1,2},{3},{4,6},{5},{7}} => 2 {{1,2,7},{3},{4},{5,6}} => 3 {{1,2},{3,7},{4},{5,6}} => 3 {{1,2},{3},{4,7},{5,6}} => 2 {{1,2},{3},{4},{5,6,7}} => 2 {{1,2},{3},{4},{5,6},{7}} => 2 {{1,2,7},{3},{4},{5},{6}} => 3 {{1,2},{3,7},{4},{5},{6}} => 3 {{1,2},{3},{4,7},{5},{6}} => 3 {{1,2},{3},{4},{5,7},{6}} => 2 {{1,2},{3},{4},{5},{6,7}} => 2 {{1,2},{3},{4},{5},{6},{7}} => 2 {{1,3,4,5,6,7},{2}} => 2 {{1,3,4,5,6},{2,7}} => 2 {{1,3,4,5,6},{2},{7}} => 2 {{1,3,4,5,7},{2,6}} => 2 {{1,3,4,5},{2,6,7}} => 2 {{1,3,4,5},{2,6},{7}} => 2 {{1,3,4,5,7},{2},{6}} => 2 {{1,3,4,5},{2,7},{6}} => 3 {{1,3,4,5},{2},{6,7}} => 2 {{1,3,4,5},{2},{6},{7}} => 2 {{1,3,4,6,7},{2,5}} => 2 {{1,3,4,6},{2,5,7}} => 2 {{1,3,4,6},{2,5},{7}} => 2 {{1,3,4,7},{2,5,6}} => 2 {{1,3,4},{2,5,6,7}} => 2 {{1,3,4},{2,5,6},{7}} => 2 {{1,3,4,7},{2,5},{6}} => 3 {{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}} => 2 {{1,3,4,6},{2},{5,7}} => 2 {{1,3,4,6},{2},{5},{7}} => 2 {{1,3,4,7},{2,6},{5}} => 3 {{1,3,4},{2,6,7},{5}} => 3 {{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}} => 3 {{1,3,4},{2},{5,6,7}} => 2 {{1,3,4},{2},{5,6},{7}} => 2 {{1,3,4,7},{2},{5},{6}} => 3 {{1,3,4},{2,7},{5},{6}} => 3 {{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}} => 2 {{1,3,5,6},{2,4,7}} => 2 {{1,3,5,6},{2,4},{7}} => 2 {{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}} => 3 {{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}} => 2 {{1,3},{2,4,5,6},{7}} => 2 {{1,3,7},{2,4,5},{6}} => 3 {{1,3},{2,4,5,7},{6}} => 2 {{1,3},{2,4,5},{6,7}} => 2 {{1,3},{2,4,5},{6},{7}} => 2 {{1,3,6,7},{2,4},{5}} => 3 {{1,3,6},{2,4,7},{5}} => 3 {{1,3,6},{2,4},{5,7}} => 3 {{1,3,6},{2,4},{5},{7}} => 3 {{1,3,7},{2,4,6},{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}} => 3 {{1,3},{2,4,7},{5,6}} => 2 {{1,3},{2,4},{5,6,7}} => 2 {{1,3},{2,4},{5,6},{7}} => 2 {{1,3,7},{2,4},{5},{6}} => 3 {{1,3},{2,4,7},{5},{6}} => 3 {{1,3},{2,4},{5,7},{6}} => 2 {{1,3},{2,4},{5},{6,7}} => 2 {{1,3},{2,4},{5},{6},{7}} => 2 {{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}} => 2 {{1,3,5},{2,6,7},{4}} => 2 {{1,3,5},{2,6},{4,7}} => 3 {{1,3,5},{2,6},{4},{7}} => 2 {{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}} => 3 {{1,3,5},{2},{4,7},{6}} => 3 {{1,3,5},{2},{4},{6,7}} => 2 {{1,3,5},{2},{4},{6},{7}} => 2 {{1,3,6,7},{2,5},{4}} => 3 {{1,3,6},{2,5,7},{4}} => 3 {{1,3,6},{2,5},{4,7}} => 3 {{1,3,6},{2,5},{4},{7}} => 3 {{1,3,7},{2,5,6},{4}} => 3 {{1,3},{2,5,6,7},{4}} => 3 {{1,3},{2,5,6},{4,7}} => 3 {{1,3},{2,5,6},{4},{7}} => 3 {{1,3,7},{2,5},{4,6}} => 3 {{1,3},{2,5,7},{4,6}} => 3 {{1,3},{2,5},{4,6,7}} => 3 {{1,3},{2,5},{4,6},{7}} => 3 {{1,3,7},{2,5},{4},{6}} => 3 {{1,3},{2,5,7},{4},{6}} => 3 {{1,3},{2,5},{4,7},{6}} => 3 {{1,3},{2,5},{4},{6,7}} => 3 {{1,3},{2,5},{4},{6},{7}} => 3 {{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}} => 3 {{1,3},{2,6,7},{4,5}} => 3 {{1,3},{2,6},{4,5,7}} => 3 {{1,3},{2,6},{4,5},{7}} => 3 {{1,3,7},{2},{4,5,6}} => 2 {{1,3},{2,7},{4,5,6}} => 3 {{1,3},{2},{4,5,6,7}} => 2 {{1,3},{2},{4,5,6},{7}} => 2 {{1,3,7},{2},{4,5},{6}} => 3 {{1,3},{2,7},{4,5},{6}} => 3 {{1,3},{2},{4,5,7},{6}} => 2 {{1,3},{2},{4,5},{6,7}} => 2 {{1,3},{2},{4,5},{6},{7}} => 2 {{1,3,6,7},{2},{4},{5}} => 3 {{1,3,6},{2,7},{4},{5}} => 3 {{1,3,6},{2},{4,7},{5}} => 3 {{1,3,6},{2},{4},{5,7}} => 3 {{1,3,6},{2},{4},{5},{7}} => 3 {{1,3,7},{2,6},{4},{5}} => 4 {{1,3},{2,6,7},{4},{5}} => 3 {{1,3},{2,6},{4,7},{5}} => 3 {{1,3},{2,6},{4},{5,7}} => 3 {{1,3},{2,6},{4},{5},{7}} => 3 {{1,3,7},{2},{4,6},{5}} => 2 {{1,3},{2,7},{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}} => 3 {{1,3},{2,7},{4},{5,6}} => 3 {{1,3},{2},{4,7},{5,6}} => 2 {{1,3},{2},{4},{5,6,7}} => 2 {{1,3},{2},{4},{5,6},{7}} => 2 {{1,3,7},{2},{4},{5},{6}} => 3 {{1,3},{2,7},{4},{5},{6}} => 3 {{1,3},{2},{4,7},{5},{6}} => 3 {{1,3},{2},{4},{5,7},{6}} => 2 {{1,3},{2},{4},{5},{6,7}} => 2 {{1,3},{2},{4},{5},{6},{7}} => 2 {{1,4,5,6,7},{2,3}} => 2 {{1,4,5,6},{2,3,7}} => 2 {{1,4,5,6},{2,3},{7}} => 2 {{1,4,5,7},{2,3,6}} => 2 {{1,4,5},{2,3,6,7}} => 2 {{1,4,5},{2,3,6},{7}} => 2 {{1,4,5,7},{2,3},{6}} => 2 {{1,4,5},{2,3,7},{6}} => 3 {{1,4,5},{2,3},{6,7}} => 2 {{1,4,5},{2,3},{6},{7}} => 2 {{1,4,6,7},{2,3,5}} => 2 {{1,4,6},{2,3,5,7}} => 2 {{1,4,6},{2,3,5},{7}} => 2 {{1,4,7},{2,3,5,6}} => 2 {{1,4},{2,3,5,6,7}} => 2 {{1,4},{2,3,5,6},{7}} => 2 {{1,4,7},{2,3,5},{6}} => 3 {{1,4},{2,3,5,7},{6}} => 2 {{1,4},{2,3,5},{6,7}} => 2 {{1,4},{2,3,5},{6},{7}} => 2 {{1,4,6,7},{2,3},{5}} => 2 {{1,4,6},{2,3,7},{5}} => 2 {{1,4,6},{2,3},{5,7}} => 2 {{1,4,6},{2,3},{5},{7}} => 2 {{1,4,7},{2,3,6},{5}} => 3 {{1,4},{2,3,6,7},{5}} => 3 {{1,4},{2,3,6},{5,7}} => 3 {{1,4},{2,3,6},{5},{7}} => 3 {{1,4,7},{2,3},{5,6}} => 2 {{1,4},{2,3,7},{5,6}} => 3 {{1,4},{2,3},{5,6,7}} => 2 {{1,4},{2,3},{5,6},{7}} => 2 {{1,4,7},{2,3},{5},{6}} => 3 {{1,4},{2,3,7},{5},{6}} => 3 {{1,4},{2,3},{5,7},{6}} => 2 {{1,4},{2,3},{5},{6,7}} => 2 {{1,4},{2,3},{5},{6},{7}} => 2 {{1,5,6,7},{2,3,4}} => 2 {{1,5,6},{2,3,4,7}} => 2 {{1,5,6},{2,3,4},{7}} => 2 {{1,5,7},{2,3,4,6}} => 2 {{1,5},{2,3,4,6,7}} => 2 {{1,5},{2,3,4,6},{7}} => 2 {{1,5,7},{2,3,4},{6}} => 2 {{1,5},{2,3,4,7},{6}} => 3 {{1,5},{2,3,4},{6,7}} => 2 {{1,5},{2,3,4},{6},{7}} => 2 {{1,6,7},{2,3,4,5}} => 2 {{1,6},{2,3,4,5,7}} => 2 {{1,6},{2,3,4,5},{7}} => 2 {{1,7},{2,3,4,5,6}} => 2 {{1},{2,3,4,5,6,7}} => 2 {{1},{2,3,4,5,6},{7}} => 2 {{1,7},{2,3,4,5},{6}} => 3 {{1},{2,3,4,5,7},{6}} => 2 {{1},{2,3,4,5},{6,7}} => 2 {{1},{2,3,4,5},{6},{7}} => 2 {{1,6,7},{2,3,4},{5}} => 3 {{1,6},{2,3,4,7},{5}} => 3 {{1,6},{2,3,4},{5,7}} => 3 {{1,6},{2,3,4},{5},{7}} => 3 {{1,7},{2,3,4,6},{5}} => 2 {{1},{2,3,4,6,7},{5}} => 2 {{1},{2,3,4,6},{5,7}} => 2 {{1},{2,3,4,6},{5},{7}} => 2 {{1,7},{2,3,4},{5,6}} => 3 {{1},{2,3,4,7},{5,6}} => 2 {{1},{2,3,4},{5,6,7}} => 2 {{1},{2,3,4},{5,6},{7}} => 2 {{1,7},{2,3,4},{5},{6}} => 3 {{1},{2,3,4,7},{5},{6}} => 3 {{1},{2,3,4},{5,7},{6}} => 2 {{1},{2,3,4},{5},{6,7}} => 2 {{1},{2,3,4},{5},{6},{7}} => 2 {{1,5,6,7},{2,3},{4}} => 3 {{1,5,6},{2,3,7},{4}} => 3 {{1,5,6},{2,3},{4,7}} => 3 {{1,5,6},{2,3},{4},{7}} => 3 {{1,5,7},{2,3,6},{4}} => 3 {{1,5},{2,3,6,7},{4}} => 3 {{1,5},{2,3,6},{4,7}} => 3 {{1,5},{2,3,6},{4},{7}} => 3 {{1,5,7},{2,3},{4,6}} => 3 {{1,5},{2,3,7},{4,6}} => 3 {{1,5},{2,3},{4,6,7}} => 3 {{1,5},{2,3},{4,6},{7}} => 3 {{1,5,7},{2,3},{4},{6}} => 3 {{1,5},{2,3,7},{4},{6}} => 3 {{1,5},{2,3},{4,7},{6}} => 3 {{1,5},{2,3},{4},{6,7}} => 3 {{1,5},{2,3},{4},{6},{7}} => 3 {{1,6,7},{2,3,5},{4}} => 2 {{1,6},{2,3,5,7},{4}} => 2 {{1,6},{2,3,5},{4,7}} => 3 {{1,6},{2,3,5},{4},{7}} => 2 {{1,7},{2,3,5,6},{4}} => 2 {{1},{2,3,5,6,7},{4}} => 2 {{1},{2,3,5,6},{4,7}} => 2 {{1},{2,3,5,6},{4},{7}} => 2 {{1,7},{2,3,5},{4,6}} => 2 {{1},{2,3,5,7},{4,6}} => 2 {{1},{2,3,5},{4,6,7}} => 2 {{1},{2,3,5},{4,6},{7}} => 2 {{1,7},{2,3,5},{4},{6}} => 3 {{1},{2,3,5,7},{4},{6}} => 2 {{1},{2,3,5},{4,7},{6}} => 3 {{1},{2,3,5},{4},{6,7}} => 2 {{1},{2,3,5},{4},{6},{7}} => 2 {{1,6,7},{2,3},{4,5}} => 3 {{1,6},{2,3,7},{4,5}} => 3 {{1,6},{2,3},{4,5,7}} => 3 {{1,6},{2,3},{4,5},{7}} => 3 {{1,7},{2,3,6},{4,5}} => 2 {{1},{2,3,6,7},{4,5}} => 2 {{1},{2,3,6},{4,5,7}} => 2 {{1},{2,3,6},{4,5},{7}} => 2 {{1,7},{2,3},{4,5,6}} => 3 {{1},{2,3,7},{4,5,6}} => 2 {{1},{2,3},{4,5,6,7}} => 2 {{1},{2,3},{4,5,6},{7}} => 2 {{1,7},{2,3},{4,5},{6}} => 3 {{1},{2,3,7},{4,5},{6}} => 3 {{1},{2,3},{4,5,7},{6}} => 2 {{1},{2,3},{4,5},{6,7}} => 2 {{1},{2,3},{4,5},{6},{7}} => 2 {{1,6,7},{2,3},{4},{5}} => 3 {{1,6},{2,3,7},{4},{5}} => 4 {{1,6},{2,3},{4,7},{5}} => 3 {{1,6},{2,3},{4},{5,7}} => 3 {{1,6},{2,3},{4},{5},{7}} => 3 {{1,7},{2,3,6},{4},{5}} => 3 {{1},{2,3,6,7},{4},{5}} => 3 {{1},{2,3,6},{4,7},{5}} => 3 {{1},{2,3,6},{4},{5,7}} => 3 {{1},{2,3,6},{4},{5},{7}} => 3 {{1,7},{2,3},{4,6},{5}} => 3 {{1},{2,3,7},{4,6},{5}} => 2 {{1},{2,3},{4,6,7},{5}} => 2 {{1},{2,3},{4,6},{5,7}} => 2 {{1},{2,3},{4,6},{5},{7}} => 2 {{1,7},{2,3},{4},{5,6}} => 3 {{1},{2,3,7},{4},{5,6}} => 3 {{1},{2,3},{4,7},{5,6}} => 2 {{1},{2,3},{4},{5,6,7}} => 2 {{1},{2,3},{4},{5,6},{7}} => 2 {{1,7},{2,3},{4},{5},{6}} => 3 {{1},{2,3,7},{4},{5},{6}} => 3 {{1},{2,3},{4,7},{5},{6}} => 3 {{1},{2,3},{4},{5,7},{6}} => 2 {{1},{2,3},{4},{5},{6,7}} => 2 {{1},{2,3},{4},{5},{6},{7}} => 2 {{1,4,5,6,7},{2},{3}} => 3 {{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}} => 3 {{1,4,5},{2,6,7},{3}} => 3 {{1,4,5},{2,6},{3,7}} => 3 {{1,4,5},{2,6},{3},{7}} => 3 {{1,4,5,7},{2},{3,6}} => 3 {{1,4,5},{2,7},{3,6}} => 3 {{1,4,5},{2},{3,6,7}} => 3 {{1,4,5},{2},{3,6},{7}} => 3 {{1,4,5,7},{2},{3},{6}} => 3 {{1,4,5},{2,7},{3},{6}} => 3 {{1,4,5},{2},{3,7},{6}} => 3 {{1,4,5},{2},{3},{6,7}} => 3 {{1,4,5},{2},{3},{6},{7}} => 3 {{1,4,6,7},{2,5},{3}} => 3 {{1,4,6},{2,5,7},{3}} => 3 {{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}} => 3 {{1,4},{2,5,6},{3,7}} => 3 {{1,4},{2,5,6},{3},{7}} => 3 {{1,4,7},{2,5},{3,6}} => 3 {{1,4},{2,5,7},{3,6}} => 3 {{1,4},{2,5},{3,6,7}} => 3 {{1,4},{2,5},{3,6},{7}} => 3 {{1,4,7},{2,5},{3},{6}} => 3 {{1,4},{2,5,7},{3},{6}} => 3 {{1,4},{2,5},{3,7},{6}} => 3 {{1,4},{2,5},{3},{6,7}} => 3 {{1,4},{2,5},{3},{6},{7}} => 3 {{1,4,6,7},{2},{3,5}} => 3 {{1,4,6},{2,7},{3,5}} => 3 {{1,4,6},{2},{3,5,7}} => 3 {{1,4,6},{2},{3,5},{7}} => 3 {{1,4,7},{2,6},{3,5}} => 3 {{1,4},{2,6,7},{3,5}} => 3 {{1,4},{2,6},{3,5,7}} => 3 {{1,4},{2,6},{3,5},{7}} => 3 {{1,4,7},{2},{3,5,6}} => 3 {{1,4},{2,7},{3,5,6}} => 3 {{1,4},{2},{3,5,6,7}} => 3 {{1,4},{2},{3,5,6},{7}} => 3 {{1,4,7},{2},{3,5},{6}} => 3 {{1,4},{2,7},{3,5},{6}} => 3 {{1,4},{2},{3,5,7},{6}} => 3 {{1,4},{2},{3,5},{6,7}} => 3 {{1,4},{2},{3,5},{6},{7}} => 3 {{1,4,6,7},{2},{3},{5}} => 3 {{1,4,6},{2,7},{3},{5}} => 3 {{1,4,6},{2},{3,7},{5}} => 3 {{1,4,6},{2},{3},{5,7}} => 3 {{1,4,6},{2},{3},{5},{7}} => 3 {{1,4,7},{2,6},{3},{5}} => 3 {{1,4},{2,6,7},{3},{5}} => 3 {{1,4},{2,6},{3,7},{5}} => 4 {{1,4},{2,6},{3},{5,7}} => 3 {{1,4},{2,6},{3},{5},{7}} => 3 {{1,4,7},{2},{3,6},{5}} => 3 {{1,4},{2,7},{3,6},{5}} => 3 {{1,4},{2},{3,6,7},{5}} => 3 {{1,4},{2},{3,6},{5,7}} => 3 {{1,4},{2},{3,6},{5},{7}} => 3 {{1,4,7},{2},{3},{5,6}} => 3 {{1,4},{2,7},{3},{5,6}} => 3 {{1,4},{2},{3,7},{5,6}} => 3 {{1,4},{2},{3},{5,6,7}} => 3 {{1,4},{2},{3},{5,6},{7}} => 3 {{1,4,7},{2},{3},{5},{6}} => 3 {{1,4},{2,7},{3},{5},{6}} => 3 {{1,4},{2},{3,7},{5},{6}} => 3 {{1,4},{2},{3},{5,7},{6}} => 3 {{1,4},{2},{3},{5},{6,7}} => 3 {{1,4},{2},{3},{5},{6},{7}} => 3 {{1,5,6,7},{2,4},{3}} => 2 {{1,5,6},{2,4,7},{3}} => 2 {{1,5,6},{2,4},{3,7}} => 3 {{1,5,6},{2,4},{3},{7}} => 2 {{1,5,7},{2,4,6},{3}} => 2 {{1,5},{2,4,6,7},{3}} => 2 {{1,5},{2,4,6},{3,7}} => 2 {{1,5},{2,4,6},{3},{7}} => 2 {{1,5,7},{2,4},{3,6}} => 3 {{1,5},{2,4,7},{3,6}} => 3 {{1,5},{2,4},{3,6,7}} => 3 {{1,5},{2,4},{3,6},{7}} => 3 {{1,5,7},{2,4},{3},{6}} => 2 {{1,5},{2,4,7},{3},{6}} => 3 {{1,5},{2,4},{3,7},{6}} => 3 {{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}} => 3 {{1,6},{2,4,5},{3},{7}} => 2 {{1,7},{2,4,5,6},{3}} => 2 {{1},{2,4,5,6,7},{3}} => 2 {{1},{2,4,5,6},{3,7}} => 2 {{1},{2,4,5,6},{3},{7}} => 2 {{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}} => 3 {{1},{2,4,5,7},{3},{6}} => 2 {{1},{2,4,5},{3,7},{6}} => 3 {{1},{2,4,5},{3},{6,7}} => 2 {{1},{2,4,5},{3},{6},{7}} => 2 {{1,6,7},{2,4},{3,5}} => 2 {{1,6},{2,4,7},{3,5}} => 3 {{1,6},{2,4},{3,5,7}} => 2 {{1,6},{2,4},{3,5},{7}} => 2 {{1,7},{2,4,6},{3,5}} => 2 {{1},{2,4,6,7},{3,5}} => 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}} => 2 {{1},{2,4},{3,5,6},{7}} => 2 {{1,7},{2,4},{3,5},{6}} => 3 {{1},{2,4,7},{3,5},{6}} => 3 {{1},{2,4},{3,5,7},{6}} => 2 {{1},{2,4},{3,5},{6,7}} => 2 {{1},{2,4},{3,5},{6},{7}} => 2 {{1,6,7},{2,4},{3},{5}} => 3 {{1,6},{2,4,7},{3},{5}} => 3 {{1,6},{2,4},{3,7},{5}} => 4 {{1,6},{2,4},{3},{5,7}} => 3 {{1,6},{2,4},{3},{5},{7}} => 3 {{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}} => 3 {{1},{2,4,7},{3,6},{5}} => 3 {{1},{2,4},{3,6,7},{5}} => 3 {{1},{2,4},{3,6},{5,7}} => 3 {{1},{2,4},{3,6},{5},{7}} => 3 {{1,7},{2,4},{3},{5,6}} => 3 {{1},{2,4,7},{3},{5,6}} => 2 {{1},{2,4},{3,7},{5,6}} => 3 {{1},{2,4},{3},{5,6,7}} => 2 {{1},{2,4},{3},{5,6},{7}} => 2 {{1,7},{2,4},{3},{5},{6}} => 3 {{1},{2,4,7},{3},{5},{6}} => 3 {{1},{2,4},{3,7},{5},{6}} => 3 {{1},{2,4},{3},{5,7},{6}} => 2 {{1},{2,4},{3},{5},{6,7}} => 2 {{1},{2,4},{3},{5},{6},{7}} => 2 {{1,5,6,7},{2},{3,4}} => 3 {{1,5,6},{2,7},{3,4}} => 3 {{1,5,6},{2},{3,4,7}} => 3 {{1,5,6},{2},{3,4},{7}} => 3 {{1,5,7},{2,6},{3,4}} => 3 {{1,5},{2,6,7},{3,4}} => 3 {{1,5},{2,6},{3,4,7}} => 3 {{1,5},{2,6},{3,4},{7}} => 3 {{1,5,7},{2},{3,4,6}} => 3 {{1,5},{2,7},{3,4,6}} => 3 {{1,5},{2},{3,4,6,7}} => 3 {{1,5},{2},{3,4,6},{7}} => 3 {{1,5,7},{2},{3,4},{6}} => 3 {{1,5},{2,7},{3,4},{6}} => 3 {{1,5},{2},{3,4,7},{6}} => 3 {{1,5},{2},{3,4},{6,7}} => 3 {{1,5},{2},{3,4},{6},{7}} => 3 {{1,6,7},{2,5},{3,4}} => 2 {{1,6},{2,5,7},{3,4}} => 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}} => 2 {{1},{2,5,6},{3,4,7}} => 2 {{1},{2,5,6},{3,4},{7}} => 2 {{1,7},{2,5},{3,4,6}} => 2 {{1},{2,5,7},{3,4,6}} => 2 {{1},{2,5},{3,4,6,7}} => 2 {{1},{2,5},{3,4,6},{7}} => 2 {{1,7},{2,5},{3,4},{6}} => 3 {{1},{2,5,7},{3,4},{6}} => 2 {{1},{2,5},{3,4,7},{6}} => 3 {{1},{2,5},{3,4},{6,7}} => 2 {{1},{2,5},{3,4},{6},{7}} => 2 {{1,6,7},{2},{3,4,5}} => 3 {{1,6},{2,7},{3,4,5}} => 3 {{1,6},{2},{3,4,5,7}} => 3 {{1,6},{2},{3,4,5},{7}} => 3 {{1,7},{2,6},{3,4,5}} => 2 {{1},{2,6,7},{3,4,5}} => 2 {{1},{2,6},{3,4,5,7}} => 2 {{1},{2,6},{3,4,5},{7}} => 2 {{1,7},{2},{3,4,5,6}} => 3 {{1},{2,7},{3,4,5,6}} => 2 {{1},{2},{3,4,5,6,7}} => 2 {{1},{2},{3,4,5,6},{7}} => 2 {{1,7},{2},{3,4,5},{6}} => 3 {{1},{2,7},{3,4,5},{6}} => 3 {{1},{2},{3,4,5,7},{6}} => 2 {{1},{2},{3,4,5},{6,7}} => 2 {{1},{2},{3,4,5},{6},{7}} => 2 {{1,6,7},{2},{3,4},{5}} => 3 {{1,6},{2,7},{3,4},{5}} => 4 {{1,6},{2},{3,4,7},{5}} => 3 {{1,6},{2},{3,4},{5,7}} => 3 {{1,6},{2},{3,4},{5},{7}} => 3 {{1,7},{2,6},{3,4},{5}} => 3 {{1},{2,6,7},{3,4},{5}} => 3 {{1},{2,6},{3,4,7},{5}} => 3 {{1},{2,6},{3,4},{5,7}} => 3 {{1},{2,6},{3,4},{5},{7}} => 3 {{1,7},{2},{3,4,6},{5}} => 3 {{1},{2,7},{3,4,6},{5}} => 2 {{1},{2},{3,4,6,7},{5}} => 2 {{1},{2},{3,4,6},{5,7}} => 2 {{1},{2},{3,4,6},{5},{7}} => 2 {{1,7},{2},{3,4},{5,6}} => 3 {{1},{2,7},{3,4},{5,6}} => 3 {{1},{2},{3,4,7},{5,6}} => 2 {{1},{2},{3,4},{5,6,7}} => 2 {{1},{2},{3,4},{5,6},{7}} => 2 {{1,7},{2},{3,4},{5},{6}} => 3 {{1},{2,7},{3,4},{5},{6}} => 3 {{1},{2},{3,4,7},{5},{6}} => 3 {{1},{2},{3,4},{5,7},{6}} => 2 {{1},{2},{3,4},{5},{6,7}} => 2 {{1},{2},{3,4},{5},{6},{7}} => 2 {{1,5,6,7},{2},{3},{4}} => 3 {{1,5,6},{2,7},{3},{4}} => 4 {{1,5,6},{2},{3,7},{4}} => 3 {{1,5,6},{2},{3},{4,7}} => 3 {{1,5,6},{2},{3},{4},{7}} => 3 {{1,5,7},{2,6},{3},{4}} => 4 {{1,5},{2,6,7},{3},{4}} => 4 {{1,5},{2,6},{3,7},{4}} => 4 {{1,5},{2,6},{3},{4,7}} => 4 {{1,5},{2,6},{3},{4},{7}} => 4 {{1,5,7},{2},{3,6},{4}} => 3 {{1,5},{2,7},{3,6},{4}} => 3 {{1,5},{2},{3,6,7},{4}} => 3 {{1,5},{2},{3,6},{4,7}} => 3 {{1,5},{2},{3,6},{4},{7}} => 3 {{1,5,7},{2},{3},{4,6}} => 3 {{1,5},{2,7},{3},{4,6}} => 4 {{1,5},{2},{3,7},{4,6}} => 3 {{1,5},{2},{3},{4,6,7}} => 3 {{1,5},{2},{3},{4,6},{7}} => 3 {{1,5,7},{2},{3},{4},{6}} => 3 {{1,5},{2,7},{3},{4},{6}} => 4 {{1,5},{2},{3,7},{4},{6}} => 3 {{1,5},{2},{3},{4,7},{6}} => 3 {{1,5},{2},{3},{4},{6,7}} => 3 {{1,5},{2},{3},{4},{6},{7}} => 3 {{1,6,7},{2,5},{3},{4}} => 3 {{1,6},{2,5,7},{3},{4}} => 3 {{1,6},{2,5},{3,7},{4}} => 3 {{1,6},{2,5},{3},{4,7}} => 3 {{1,6},{2,5},{3},{4},{7}} => 3 {{1,7},{2,5,6},{3},{4}} => 3 {{1},{2,5,6,7},{3},{4}} => 3 {{1},{2,5,6},{3,7},{4}} => 3 {{1},{2,5,6},{3},{4,7}} => 3 {{1},{2,5,6},{3},{4},{7}} => 3 {{1,7},{2,5},{3,6},{4}} => 3 {{1},{2,5,7},{3,6},{4}} => 3 {{1},{2,5},{3,6,7},{4}} => 3 {{1},{2,5},{3,6},{4,7}} => 3 {{1},{2,5},{3,6},{4},{7}} => 3 {{1,7},{2,5},{3},{4,6}} => 3 {{1},{2,5,7},{3},{4,6}} => 3 {{1},{2,5},{3,7},{4,6}} => 3 {{1},{2,5},{3},{4,6,7}} => 3 {{1},{2,5},{3},{4,6},{7}} => 3 {{1,7},{2,5},{3},{4},{6}} => 3 {{1},{2,5,7},{3},{4},{6}} => 3 {{1},{2,5},{3,7},{4},{6}} => 3 {{1},{2,5},{3},{4,7},{6}} => 3 {{1},{2,5},{3},{4},{6,7}} => 3 {{1},{2,5},{3},{4},{6},{7}} => 3 {{1,6,7},{2},{3,5},{4}} => 3 {{1,6},{2,7},{3,5},{4}} => 3 {{1,6},{2},{3,5,7},{4}} => 3 {{1,6},{2},{3,5},{4,7}} => 3 {{1,6},{2},{3,5},{4},{7}} => 3 {{1,7},{2,6},{3,5},{4}} => 2 {{1},{2,6,7},{3,5},{4}} => 2 {{1},{2,6},{3,5,7},{4}} => 2 {{1},{2,6},{3,5},{4,7}} => 3 {{1},{2,6},{3,5},{4},{7}} => 2 {{1,7},{2},{3,5,6},{4}} => 3 {{1},{2,7},{3,5,6},{4}} => 2 {{1},{2},{3,5,6,7},{4}} => 2 {{1},{2},{3,5,6},{4,7}} => 2 {{1},{2},{3,5,6},{4},{7}} => 2 {{1,7},{2},{3,5},{4,6}} => 3 {{1},{2,7},{3,5},{4,6}} => 2 {{1},{2},{3,5,7},{4,6}} => 2 {{1},{2},{3,5},{4,6,7}} => 2 {{1},{2},{3,5},{4,6},{7}} => 2 {{1,7},{2},{3,5},{4},{6}} => 3 {{1},{2,7},{3,5},{4},{6}} => 3 {{1},{2},{3,5,7},{4},{6}} => 2 {{1},{2},{3,5},{4,7},{6}} => 3 {{1},{2},{3,5},{4},{6,7}} => 2 {{1},{2},{3,5},{4},{6},{7}} => 2 {{1,6,7},{2},{3},{4,5}} => 3 {{1,6},{2,7},{3},{4,5}} => 4 {{1,6},{2},{3,7},{4,5}} => 3 {{1,6},{2},{3},{4,5,7}} => 3 {{1,6},{2},{3},{4,5},{7}} => 3 {{1,7},{2,6},{3},{4,5}} => 3 {{1},{2,6,7},{3},{4,5}} => 3 {{1},{2,6},{3,7},{4,5}} => 3 {{1},{2,6},{3},{4,5,7}} => 3 {{1},{2,6},{3},{4,5},{7}} => 3 {{1,7},{2},{3,6},{4,5}} => 3 {{1},{2,7},{3,6},{4,5}} => 2 {{1},{2},{3,6,7},{4,5}} => 2 {{1},{2},{3,6},{4,5,7}} => 2 {{1},{2},{3,6},{4,5},{7}} => 2 {{1,7},{2},{3},{4,5,6}} => 3 {{1},{2,7},{3},{4,5,6}} => 3 {{1},{2},{3,7},{4,5,6}} => 2 {{1},{2},{3},{4,5,6,7}} => 2 {{1},{2},{3},{4,5,6},{7}} => 2 {{1,7},{2},{3},{4,5},{6}} => 3 {{1},{2,7},{3},{4,5},{6}} => 3 {{1},{2},{3,7},{4,5},{6}} => 3 {{1},{2},{3},{4,5,7},{6}} => 2 {{1},{2},{3},{4,5},{6,7}} => 2 {{1},{2},{3},{4,5},{6},{7}} => 2 {{1,6,7},{2},{3},{4},{5}} => 3 {{1,6},{2,7},{3},{4},{5}} => 4 {{1,6},{2},{3,7},{4},{5}} => 4 {{1,6},{2},{3},{4,7},{5}} => 3 {{1,6},{2},{3},{4},{5,7}} => 3 {{1,6},{2},{3},{4},{5},{7}} => 3 {{1,7},{2,6},{3},{4},{5}} => 3 {{1},{2,6,7},{3},{4},{5}} => 3 {{1},{2,6},{3,7},{4},{5}} => 4 {{1},{2,6},{3},{4,7},{5}} => 3 {{1},{2,6},{3},{4},{5,7}} => 3 {{1},{2,6},{3},{4},{5},{7}} => 3 {{1,7},{2},{3,6},{4},{5}} => 3 {{1},{2,7},{3,6},{4},{5}} => 3 {{1},{2},{3,6,7},{4},{5}} => 3 {{1},{2},{3,6},{4,7},{5}} => 3 {{1},{2},{3,6},{4},{5,7}} => 3 {{1},{2},{3,6},{4},{5},{7}} => 3 {{1,7},{2},{3},{4,6},{5}} => 3 {{1},{2,7},{3},{4,6},{5}} => 3 {{1},{2},{3,7},{4,6},{5}} => 2 {{1},{2},{3},{4,6,7},{5}} => 2 {{1},{2},{3},{4,6},{5,7}} => 2 {{1},{2},{3},{4,6},{5},{7}} => 2 {{1,7},{2},{3},{4},{5,6}} => 3 {{1},{2,7},{3},{4},{5,6}} => 3 {{1},{2},{3,7},{4},{5,6}} => 3 {{1},{2},{3},{4,7},{5,6}} => 2 {{1},{2},{3},{4},{5,6,7}} => 2 {{1},{2},{3},{4},{5,6},{7}} => 2 {{1,7},{2},{3},{4},{5},{6}} => 3 {{1},{2,7},{3},{4},{5},{6}} => 3 {{1},{2},{3,7},{4},{5},{6}} => 3 {{1},{2},{3},{4,7},{5},{6}} => 3 {{1},{2},{3},{4},{5,7},{6}} => 2 {{1},{2},{3},{4},{5},{6,7}} => 2 {{1},{2},{3},{4},{5},{6},{7}} => 2 {{1,2},{3,4},{5,6},{7,8}} => 2 {{1,3},{2,4},{5,6},{7,8}} => 2 {{1,4},{2,3},{5,6},{7,8}} => 2 {{1,5},{2,3},{4,6},{7,8}} => 3 {{1,6},{2,3},{4,5},{7,8}} => 3 {{1,7},{2,3},{4,5},{6,8}} => 3 {{1,8},{2,3},{4,5},{6,7}} => 3 {{1,8},{2,4},{3,5},{6,7}} => 3 {{1,7},{2,4},{3,5},{6,8}} => 3 {{1,6},{2,4},{3,5},{7,8}} => 2 {{1,5},{2,4},{3,6},{7,8}} => 3 {{1,4},{2,5},{3,6},{7,8}} => 3 {{1,3},{2,5},{4,6},{7,8}} => 3 {{1,2},{3,5},{4,6},{7,8}} => 2 {{1,2},{3,6},{4,5},{7,8}} => 2 {{1,3},{2,6},{4,5},{7,8}} => 3 {{1,4},{2,6},{3,5},{7,8}} => 3 {{1,5},{2,6},{3,4},{7,8}} => 3 {{1,6},{2,5},{3,4},{7,8}} => 2 {{1,7},{2,5},{3,4},{6,8}} => 3 {{1,8},{2,5},{3,4},{6,7}} => 3 {{1,8},{2,6},{3,4},{5,7}} => 3 {{1,7},{2,6},{3,4},{5,8}} => 3 {{1,6},{2,7},{3,4},{5,8}} => 4 {{1,5},{2,7},{3,4},{6,8}} => 3 {{1,4},{2,7},{3,5},{6,8}} => 3 {{1,3},{2,7},{4,5},{6,8}} => 3 {{1,2},{3,7},{4,5},{6,8}} => 3 {{1,2},{3,8},{4,5},{6,7}} => 3 {{1,3},{2,8},{4,5},{6,7}} => 3 {{1,4},{2,8},{3,5},{6,7}} => 3 {{1,5},{2,8},{3,4},{6,7}} => 3 {{1,6},{2,8},{3,4},{5,7}} => 4 {{1,7},{2,8},{3,4},{5,6}} => 4 {{1,8},{2,7},{3,4},{5,6}} => 3 {{1,8},{2,7},{3,5},{4,6}} => 2 {{1,7},{2,8},{3,5},{4,6}} => 3 {{1,6},{2,8},{3,5},{4,7}} => 3 {{1,5},{2,8},{3,6},{4,7}} => 3 {{1,4},{2,8},{3,6},{5,7}} => 3 {{1,3},{2,8},{4,6},{5,7}} => 3 {{1,2},{3,8},{4,6},{5,7}} => 2 {{1,2},{3,7},{4,6},{5,8}} => 3 {{1,3},{2,7},{4,6},{5,8}} => 3 {{1,4},{2,7},{3,6},{5,8}} => 3 {{1,5},{2,7},{3,6},{4,8}} => 3 {{1,6},{2,7},{3,5},{4,8}} => 4 {{1,7},{2,6},{3,5},{4,8}} => 3 {{1,8},{2,6},{3,5},{4,7}} => 3 {{1,8},{2,5},{3,6},{4,7}} => 3 {{1,7},{2,5},{3,6},{4,8}} => 3 {{1,6},{2,5},{3,7},{4,8}} => 4 {{1,5},{2,6},{3,7},{4,8}} => 4 {{1,4},{2,6},{3,7},{5,8}} => 4 {{1,3},{2,6},{4,7},{5,8}} => 3 {{1,2},{3,6},{4,7},{5,8}} => 3 {{1,2},{3,5},{4,7},{6,8}} => 3 {{1,3},{2,5},{4,7},{6,8}} => 3 {{1,4},{2,5},{3,7},{6,8}} => 3 {{1,5},{2,4},{3,7},{6,8}} => 3 {{1,6},{2,4},{3,7},{5,8}} => 4 {{1,7},{2,4},{3,6},{5,8}} => 3 {{1,8},{2,4},{3,6},{5,7}} => 3 {{1,8},{2,3},{4,6},{5,7}} => 3 {{1,7},{2,3},{4,6},{5,8}} => 3 {{1,6},{2,3},{4,7},{5,8}} => 3 {{1,5},{2,3},{4,7},{6,8}} => 3 {{1,4},{2,3},{5,7},{6,8}} => 2 {{1,3},{2,4},{5,7},{6,8}} => 2 {{1,2},{3,4},{5,7},{6,8}} => 2 {{1,2},{3,4},{5,8},{6,7}} => 2 {{1,3},{2,4},{5,8},{6,7}} => 2 {{1,4},{2,3},{5,8},{6,7}} => 2 {{1,5},{2,3},{4,8},{6,7}} => 3 {{1,6},{2,3},{4,8},{5,7}} => 3 {{1,7},{2,3},{4,8},{5,6}} => 3 {{1,8},{2,3},{4,7},{5,6}} => 3 {{1,8},{2,4},{3,7},{5,6}} => 3 {{1,7},{2,4},{3,8},{5,6}} => 4 {{1,6},{2,4},{3,8},{5,7}} => 4 {{1,5},{2,4},{3,8},{6,7}} => 3 {{1,4},{2,5},{3,8},{6,7}} => 3 {{1,3},{2,5},{4,8},{6,7}} => 3 {{1,2},{3,5},{4,8},{6,7}} => 3 {{1,2},{3,6},{4,8},{5,7}} => 3 {{1,3},{2,6},{4,8},{5,7}} => 3 {{1,4},{2,6},{3,8},{5,7}} => 4 {{1,5},{2,6},{3,8},{4,7}} => 4 {{1,6},{2,5},{3,8},{4,7}} => 3 {{1,7},{2,5},{3,8},{4,6}} => 3 {{1,8},{2,5},{3,7},{4,6}} => 3 {{1,8},{2,6},{3,7},{4,5}} => 3 {{1,7},{2,6},{3,8},{4,5}} => 3 {{1,6},{2,7},{3,8},{4,5}} => 4 {{1,5},{2,7},{3,8},{4,6}} => 4 {{1,4},{2,7},{3,8},{5,6}} => 4 {{1,3},{2,7},{4,8},{5,6}} => 3 {{1,2},{3,7},{4,8},{5,6}} => 3 {{1,2},{3,8},{4,7},{5,6}} => 2 {{1,3},{2,8},{4,7},{5,6}} => 3 {{1,4},{2,8},{3,7},{5,6}} => 3 {{1,5},{2,8},{3,7},{4,6}} => 3 {{1,6},{2,8},{3,7},{4,5}} => 3 {{1,7},{2,8},{3,6},{4,5}} => 3 {{1,8},{2,7},{3,6},{4,5}} => 2 {{1},{2},{3},{4},{5},{6},{7},{8}} => 2 {{1},{2},{3},{4},{5},{6},{7,8}} => 2 {{1},{2},{3},{4},{5},{6,8},{7}} => 2 {{1},{2},{3},{4},{5},{6,7,8}} => 2 {{1},{2},{3},{4},{5,8},{6},{7}} => 3 {{1},{2},{3},{4},{5,8},{6,7}} => 2 {{1},{2},{3},{4},{5,6,8},{7}} => 2 {{1},{2},{3},{4},{5,6,7,8}} => 2 {{1},{2},{3},{4,8},{5},{6},{7}} => 3 {{1},{2},{3},{4,8},{5,6},{7}} => 3 {{1},{2},{3},{4,8},{5,7},{6}} => 2 {{1},{2},{3},{4,8},{5,6,7}} => 2 {{1},{2},{3},{4,5,6,7,8}} => 2 {{1},{2},{3,8},{4},{5},{6},{7}} => 3 {{1},{2},{3,8},{4,5},{6},{7}} => 3 {{1},{2},{3,8},{4,6},{5},{7}} => 3 {{1},{2},{3,8},{4,5,6},{7}} => 3 {{1},{2},{3,4,8},{5,6,7}} => 2 {{1},{2},{3,4,5,6,7,8}} => 2 {{1},{2,3},{4,7,8},{5,6}} => 2 {{1},{2,3},{4,5,6,8},{7}} => 2 {{1},{2,8},{3},{4},{5},{6},{7}} => 3 {{1},{2,4,6,8},{3},{5},{7}} => 2 {{1},{2,4,8},{3},{5,7},{6}} => 2 {{1},{2,4,5,8},{3},{6,7}} => 2 {{1},{2,4,5,6,7,8},{3}} => 2 {{1},{2,8},{3,4},{5},{6},{7}} => 3 {{1},{2,8},{3,4},{5,6,7}} => 3 {{1},{2,5,8},{3,4},{6,7}} => 2 {{1},{2,3,5},{4},{6,7,8}} => 2 {{1},{2,8},{3,5},{4},{6},{7}} => 3 {{1},{2,6,8},{3,5},{4},{7}} => 2 {{1},{2,8},{3,5,7},{4},{6}} => 3 {{1},{2,3,5,6,7,8},{4}} => 2 {{1},{2,8},{3,4,5},{6},{7}} => 3 {{1},{2,8},{3,4,5},{6,7}} => 3 {{1},{2,8},{3,7},{4,6},{5}} => 2 {{1},{2,3,4,7,8},{5},{6}} => 3 {{1},{2,3,4,6,7,8},{5}} => 2 {{1},{2,3,8},{4,5,7},{6}} => 2 {{1},{2,3,4,5,8},{6},{7}} => 3 {{1},{2,3,4,5,7,8},{6}} => 2 {{1},{2,3,4,5,6,7},{8}} => 2 {{1},{2,3,4,8},{5,6,7}} => 2 {{1},{2,3,4,5,8},{6,7}} => 2 {{1},{2,3,4,5,6,8},{7}} => 2 {{1},{2,3,4,5,6,7,8}} => 2 {{1,2},{3},{4,6,7,8},{5}} => 2 {{1,2},{3,4},{5,7,8},{6}} => 2 {{1,2},{3,4},{5,6,8},{7}} => 2 {{1,2},{3,6,7,8},{4},{5}} => 3 {{1,2},{3,5,6},{4},{7,8}} => 2 {{1,2},{3,7,8},{4},{5,6}} => 3 {{1,2},{3,5,8},{4},{6,7}} => 2 {{1,2},{3,5,6,8},{4},{7}} => 2 {{1,2},{3,6,8},{4,5},{7}} => 2 {{1,2},{3,4,6},{5},{7,8}} => 2 {{1,2},{3,7,8},{4,6},{5}} => 2 {{1,2},{3,8},{4,6,7},{5}} => 2 {{1,2},{3,4,8},{5},{6,7}} => 3 {{1,2},{3,4,6,8},{5},{7}} => 2 {{1,2},{3,8},{4,5,7},{6}} => 2 {{1,2},{3,4,8},{5,7},{6}} => 2 {{1,2},{3,4,5,6,7,8}} => 2 {{1,3},{2},{4,6,8},{5},{7}} => 2 {{1,3},{2},{4,7,8},{5,6}} => 2 {{1,3},{2},{4,8},{5,7},{6}} => 2 {{1,3},{2},{4,5,6,8},{7}} => 2 {{1,8},{2},{3},{4},{5},{6},{7}} => 3 {{1,5,6,7,8},{2},{3},{4}} => 3 {{1,6,7,8},{2},{3},{4,5}} => 3 {{1,4,5,6},{2},{3},{7,8}} => 3 {{1,4,7,8},{2},{3},{5,6}} => 3 {{1,4,5,8},{2},{3},{6,7}} => 3 {{1,4,5,6,7,8},{2},{3}} => 3 {{1,3,4},{2},{5,6},{7,8}} => 2 {{1,3,4},{2},{5,7,8},{6}} => 2 {{1,3,4},{2},{5,8},{6,7}} => 2 {{1,5,6},{2},{3,4},{7,8}} => 3 {{1,7,8},{2},{3,4},{5,6}} => 3 {{1,5,8},{2},{3,4},{6,7}} => 3 {{1,3,5},{2},{4},{6,8},{7}} => 2 {{1,3,5},{2},{4},{6,7,8}} => 2 {{1,6,7,8},{2},{3,5},{4}} => 3 {{1,7,8},{2},{3,5,6},{4}} => 3 {{1,3,5,7},{2},{4},{6},{8}} => 2 {{1,3,5,6,7,8},{2},{4}} => 2 {{1,3,6},{2},{4,5},{7,8}} => 2 {{1,7,8},{2},{3,6},{4,5}} => 3 {{1,3,8},{2},{4,5},{6,7}} => 3 {{1,3,7},{2},{4,6},{5},{8}} => 2 {{1,3,8},{2},{4,6,7},{5}} => 2 {{1,8},{2},{3,4,5,6},{7}} => 3 {{1,3,8},{2},{4,7},{5,6}} => 2 {{1,3,4,5,6,7,8},{2}} => 2 {{1,4},{2,3},{5,7,8},{6}} => 2 {{1,4},{2,3},{5,6,8},{7}} => 2 {{1,8},{2,3},{4},{5},{6},{7}} => 3 {{1,8},{2,3},{4},{5,6,7}} => 3 {{1,6,8},{2,3},{4,5},{7}} => 3 {{1,4,6},{2,3},{5},{7,8}} => 2 {{1,8},{2,3},{4,6,7},{5}} => 3 {{1,4,8},{2,3},{5},{6,7}} => 3 {{1,4,6,8},{2,3},{5},{7}} => 2 {{1,8},{2,3},{4,5,7},{6}} => 3 {{1,4,8},{2,3},{5,7},{6}} => 2 {{1,4,5,6,7,8},{2,3}} => 2 {{1,2,4},{3},{5,6},{7,8}} => 2 {{1,2,4},{3},{5,8},{6,7}} => 2 {{1,2,4},{3},{5,6,8},{7}} => 2 {{1,5},{2,4},{3},{6,8},{7}} => 2 {{1,8},{2,4},{3},{5},{6},{7}} => 3 {{1,5,6},{2,4},{3},{7,8}} => 2 {{1,7,8},{2,4},{3},{5,6}} => 3 {{1,5,7},{2,4},{3},{6},{8}} => 2 {{1,5,8},{2,4},{3},{6,7}} => 2 {{1,6,7,8},{2,5},{3},{4}} => 3 {{1,7,8},{2,5,6},{3},{4}} => 3 {{1,8},{2,5,6,7},{3},{4}} => 3 {{1,6},{2,4,5},{3},{7,8}} => 2 {{1,8},{2,4,5},{3},{6,7}} => 3 {{1,2,6},{3},{4,5},{7,8}} => 3 {{1,7,8},{2,6},{3},{4,5}} => 3 {{1,8},{2,6,7},{3},{4,5}} => 3 {{1,2,8},{3},{4,5},{6,7}} => 3 {{1,2,6,8},{3},{4,5},{7}} => 3 {{1,2,4,6},{3},{5},{7,8}} => 2 {{1,7},{2,4,6},{3},{5},{8}} => 3 {{1,2,4,8},{3},{5},{6,7}} => 3 {{1,2,4,6,8},{3},{5},{7}} => 2 {{1,8},{2,4,7},{3},{5,6}} => 3 {{1,2,8},{3},{4,7},{5,6}} => 3 {{1,2,8},{3},{4,5,7},{6}} => 3 {{1,2,4,8},{3},{5,7},{6}} => 2 {{1,2,4,5,6,7,8},{3}} => 2 {{1,8},{2,3,4},{5},{6},{7}} => 3 {{1,6,8},{2,3,4},{5},{7}} => 3 {{1,6,8},{2,5},{3,4},{7}} => 2 {{1,8},{2,5,7},{3,4},{6}} => 3 {{1,2,5,6,7,8},{3,4}} => 2 {{1,6},{2,3,5},{4},{7,8}} => 2 {{1,8},{2,3,5},{4},{6,7}} => 3 {{1,6,8},{2,3,5},{4},{7}} => 2 {{1,2,6},{3,5},{4},{7,8}} => 2 {{1,7},{2,6},{3,5},{4},{8}} => 2 {{1,7,8},{2,6},{3,5},{4}} => 2 {{1,8},{2,6,7},{3,5},{4}} => 2 {{1,2,8},{3,5},{4},{6,7}} => 3 {{1,2,6,8},{3,5},{4},{7}} => 2 {{1,8},{2,7},{3,5,6},{4}} => 2 {{1,2,8},{3,5,6},{4},{7}} => 3 {{1,8},{2,3,7},{4},{5,6}} => 3 {{1,2,8},{3,7},{4},{5,6}} => 3 {{1,8},{2,3,5,7},{4},{6}} => 3 {{1,2,8},{3,5,7},{4},{6}} => 3 {{1,2,3,5,6,7},{4},{8}} => 2 {{1,2,3,5,6,7,8},{4}} => 2 {{1,8},{2,3,6},{4,5},{7}} => 3 {{1,8},{2,3,7},{4,5},{6}} => 3 {{1,2,3,6,7,8},{4,5}} => 2 {{1,8},{2,7},{3,4,6},{5}} => 2 {{1,8},{2,3,7},{4,6},{5}} => 2 {{1,2,8},{3,7},{4,6},{5}} => 2 {{1,2,3,4,7},{5},{6},{8}} => 3 {{1,2,3,4,6,7},{5},{8}} => 2 {{1,2,3,4,6,7,8},{5}} => 2 {{1,2,3,4,5,6},{7,8}} => 2 {{1,2,3,7},{4,5,6},{8}} => 2 {{1,2,3,4,7},{5,6},{8}} => 2 {{1,2,3,4,7,8},{5,6}} => 2 {{1,2,3,4,5,7},{6},{8}} => 2 {{1,2,3,4,5,7,8},{6}} => 2 {{1,2,3,4,5,6,7},{8}} => 2 {{1,8},{2,3,4,5,6,7}} => 2 {{1,2,3,4,5,8},{6,7}} => 2 {{1,2,3,4,5,6,8},{7}} => 2 {{1,2,3,4,5,6,7,8}} => 1 {{1,3,5,6,7,8},{2,4}} => 2 {{1,3,4,6,7,8},{2,5}} => 2 {{1,2,4,6,7,8},{3,5}} => 2 {{1,3,4,5,7,8},{2,6}} => 2 {{1,2,4,5,7,8},{3,6}} => 2 {{1,2,3,5,7,8},{4,6}} => 2 {{1,3,4,5,6,8},{2,7}} => 2 {{1,2,4,5,6,8},{3,7}} => 2 {{1,2,3,5,6,8},{4,7}} => 2 {{1,2,3,4,6,8},{5,7}} => 2 {{1,3,4,5,6,7},{2,8}} => 2 {{1,2,4,5,6,7},{3,8}} => 2 {{1,2,3,5,6,7},{4,8}} => 2 {{1,2,3,4,6,7},{5,8}} => 2 {{1,2,3,4,5,7},{6,8}} => 2 {{1,5,7,8},{2,6},{3},{4}} => 4 {{1,3,7,8},{2,5},{4},{6}} => 3 {{1,5,6,8},{2,7},{3},{4}} => 4 {{1,2,4,8},{3,7},{5},{6}} => 4 {{1,3,6,8},{2,4},{5},{7}} => 3 {{1,2,5,8},{3,6},{4},{7}} => 3 {{1,3,4,8},{2,6},{5},{7}} => 3 {{1,2,4,8},{3,6},{5},{7}} => 3 {{1,4,6,7},{2,8},{3},{5}} => 3 {{1,3,6,7},{2,8},{4},{5}} => 3 {{1,4,5,7},{2,8},{3},{6}} => 3 {{1,3,5,7},{2,8},{4},{6}} => 3 {{1,2,5,7},{3,8},{4},{6}} => 3 {{1,3,4,7},{2,8},{5},{6}} => 3 {{1,2,4,7},{3,8},{5},{6}} => 3 {{1,2,5,6},{3,8},{4},{7}} => 3 {{1,3,5,7},{2,6},{4},{8}} => 2 {{1,3,5,7},{2,4},{6},{8}} => 2 {{1,4,7},{2,6,8},{3},{5}} => 3 {{1,2,7},{3,6,8},{4},{5}} => 3 {{1,2,7},{3,5,8},{4},{6}} => 3 {{1,3,7},{2,4,8},{5},{6}} => 4 {{1,4,6},{2,7,8},{3},{5}} => 3 {{1,3,6},{2,7,8},{4},{5}} => 3 {{1,2,4},{3,7,8},{5},{6}} => 3 {{1,2,6},{3,5,8},{4},{7}} => 3 {{1,3,6},{2,4,8},{5},{7}} => 3 {{1,3,5},{2,6,8},{4},{7}} => 2 {{1,3,4},{2,6,8},{5},{7}} => 3 {{1,2,4},{3,6,8},{5},{7}} => 3 {{1,4,8},{2,6},{3,7},{5}} => 4 {{1,3,8},{2,6},{4,7},{5}} => 3 {{1,2,8},{3,6},{4,7},{5}} => 3 {{1,4,8},{2,5},{3,7},{6}} => 4 {{1,3,8},{2,5},{4,7},{6}} => 3 {{1,2,8},{3,5},{4,7},{6}} => 3 {{1,4,8},{2,5},{3,6},{7}} => 3 {{1,4,7},{2,6},{3,8},{5}} => 3 {{1,3,7},{2,6},{4,8},{5}} => 4 {{1,2,7},{3,6},{4,8},{5}} => 3 {{1,4,7},{2,5},{3,8},{6}} => 3 {{1,3,7},{2,5},{4,8},{6}} => 4 {{1,2,7},{3,5},{4,8},{6}} => 4 {{1,4,6},{2,7},{3,8},{5}} => 3 {{1,3,6},{2,7},{4,8},{5}} => 3 {{1,2,6},{3,7},{4,8},{5}} => 4 {{1,3,5},{2,7},{4,8},{6}} => 4 {{1,2,5},{3,7},{4,8},{6}} => 4 {{1,3,4},{2,7},{5,8},{6}} => 3 {{1,2,4},{3,7},{5,8},{6}} => 3 {{1,3,6},{2,5},{4,8},{7}} => 3 {{1,2,6},{3,5},{4,8},{7}} => 3 {{1,3,5},{2,6},{4,8},{7}} => 3 {{1,2,5},{3,6},{4,8},{7}} => 3 {{1,3,4},{2,6},{5,8},{7}} => 3 {{1,2,4},{3,6},{5,8},{7}} => 3 {{1,3,5},{2,4},{6,8},{7}} => 2 {{1,4,7},{2,5},{3,6},{8}} => 3 {{1,3,7},{2,5},{4,6},{8}} => 3 {{1,3,5,8},{2},{4,6},{7}} => 3 {{1,3,5,7},{2},{4},{6,8}} => 2 {{1,5,7},{2,4},{3},{6,8}} => 2 {{1,5},{2,4,8},{3},{6,7}} => 3 {{1,5,8},{2,4},{3,6},{7}} => 3 {{1,6,8},{2,4},{3,5},{7}} => 2 {{1},{2,3,5,8},{4,6},{7}} => 3 {{1,5,8},{2,6},{3,4},{7}} => 3 {{1,4,8},{2,6},{3,5},{7}} => 3 {{1,4},{2,5,8},{3},{6,7}} => 3 {{1,4,7},{2,5},{3},{6,8}} => 3 {{1,4},{2},{3,6,7},{5,8}} => 3 {{1,4},{2},{3,6},{5,7,8}} => 3 {{1,4},{2},{3,7},{5,6,8}} => 3 {{1,4},{2},{3,5,8},{6,7}} => 3 {{1,5},{2},{3,4,8},{6,7}} => 3 {{1,2,5},{3},{4,7,8},{6}} => 3 {{1,2,5,7},{3},{4,8},{6}} => 3 {{1},{2,3,5,7},{4},{6,8}} => 2 {{1,5,7},{2},{3,4},{6,8}} => 3 {{1,4,7},{2},{3,5},{6,8}} => 3 {{1,4},{2},{3,8},{5,6,7}} => 3 {{1,4,6},{2},{3,8},{5,7}} => 3 {{1,4,6},{2},{3,7},{5,8}} => 3 {{1},{2,6},{3,4,7},{5,8}} => 3 {{1,6},{2,3,7},{4},{5,8}} => 4 {{1,2},{3,6,7},{4,8},{5}} => 3 {{1,2},{3,6},{4,7,8},{5}} => 3 {{1,6},{2,3},{4},{5,7,8}} => 3 {{1},{2,6},{3,4},{5,7,8}} => 3 {{1},{2,7},{3,4},{5,6,8}} => 3 {{1,7},{2,3},{4},{5,6,8}} => 3 {{1,2},{3,7},{4,6,8},{5}} => 2 {{1,2},{3,5,8},{4,7},{6}} => 3 {{1,7},{2,3,8},{4,5},{6}} => 4 {{1},{2,5},{3,4,8},{6,7}} => 3 {{1},{2,4},{3,5,8},{6,7}} => 2 {{1},{2,4},{3,7},{5,6,8}} => 3 {{1},{2,4},{3,6},{5,7,8}} => 3 {{1},{2,4},{3,6,7},{5,8}} => 3 {{1,3},{2,6,7},{4},{5,8}} => 3 {{1,3},{2,6},{4},{5,7,8}} => 3 {{1,3},{2,7},{4},{5,6,8}} => 3 {{1,3},{2,7,8},{4,5},{6}} => 3 {{1,3,8},{2,4,7},{5},{6}} => 3 {{1,4,8},{2,3,7},{5},{6}} => 4 {{1,4,7},{2,3,8},{5},{6}} => 3 {{1,3,7},{2,8},{4,5},{6}} => 3 {{1,3},{2,8},{4},{5,6,7}} => 3 {{1,3,6},{2,8},{4},{5,7}} => 3 {{1,3,6},{2,7},{4},{5,8}} => 3 {{1},{2,4,6},{3,7},{5,8}} => 3 {{1},{2,4,6},{3,8},{5,7}} => 2 {{1},{2,4},{3,8},{5,6,7}} => 3 {{1},{2,4,7},{3,5},{6,8}} => 3 {{1},{2,5,7},{3,4},{6,8}} => 2 {{1},{2,8},{3,4,6},{5,7}} => 2 {{1,8},{2,3,6},{4},{5,7}} => 3 {{1,2,6},{3,8},{4,7},{5}} => 3 {{1,7},{2,3,6},{4},{5,8}} => 3 {{1},{2,7},{3,4,6},{5,8}} => 3 {{1,2},{3,6,8},{4,7},{5}} => 3 {{1,2},{3,5,7},{4,8},{6}} => 2 {{1,2},{3,7},{4,5,8},{6}} => 3 {{1,4,8},{2,7},{3},{5,6}} => 3 {{1,3,7},{2,8},{4},{5,6}} => 3 {{1,3,7},{2,8},{4,6},{5}} => 2 {{1,3,7},{2},{4,5,8},{6}} => 3 {{1,7},{2,3},{4,5,8},{6}} => 3 {{1,7},{2,3,8},{4,6},{5}} => 3 {{1,7},{2,3,8},{4},{5,6}} => 4 {{1,7,8},{2,5},{3,6},{4}} => 3 {{1,7},{2,4,6,8},{3},{5}} => 3 {{1,7},{2,4,5},{3,8},{6}} => 4 {{1,4,6},{2,5},{3},{7,8}} => 3 {{1,5,7,8},{2},{3,6},{4}} => 3 {{1,5,8},{2,7},{3,6},{4}} => 3 {{1,8},{2,5,7},{3,6},{4}} => 3 {{1,5,8},{2,6,7},{3},{4}} => 4 {{1,4,5,7},{2},{3,8},{6}} => 3 {{1,3,5},{2,6},{4},{7,8}} => 2 {{1,3,6},{2,8},{4,7},{5}} => 3 {{1,4,6,8},{2},{3,7},{5}} => 3 {{1,8},{2,4,6},{3,7},{5}} => 2 {{1,4,8},{2,5},{3},{6,7}} => 3 {{1,3,5},{2,8},{4},{6,7}} => 3 {{1,5},{2,3,8},{4},{6,7}} => 3 {{1,8},{2,6},{3,4,7},{5}} => 3 {{1,6,8},{2},{3,4,7},{5}} => 3 {{1,6,8},{2,4},{3,7},{5}} => 4 {{1,6},{2,3,8},{4,7},{5}} => 3 {{1,6},{2,3,7,8},{4},{5}} => 4 {{1,5},{2,3,7},{4,8},{6}} => 4 {{1,5},{2,3,6},{4},{7,8}} => 3 {{1,5,7},{2,4},{3,8},{6}} => 3 {{1,6,7},{2,4,8},{3},{5}} => 3 {{1,6,8},{2,5,7},{3},{4}} => 3 {{1,6,8},{2,7},{3,5},{4}} => 3 {{1,6,8},{2,7},{3},{4,5}} => 4 {{1,6,7},{2,8},{3,4},{5}} => 4 {{1,5,7},{2},{3,4,8},{6}} => 3 {{1,7},{2,5},{3,4,8},{6}} => 4 {{1,7},{2,6,8},{3,4},{5}} => 3 {{1,4,8},{2,3,6},{5},{7}} => 3 {{1,5},{2,4,8},{3,7},{6}} => 4 {{1,5},{2,4,7},{3,8},{6}} => 3 {{1,5},{2,4,8},{3,6},{7}} => 3 {{1,6},{2,4,8},{3,5},{7}} => 3 {{1,6},{2,5},{3,4,8},{7}} => 3 {{1,6},{2,3,5},{4,8},{7}} => 3 {{1,5},{2,3,6},{4,8},{7}} => 3 {{1,5},{2,6},{3,4,8},{7}} => 3 {{1,4,8},{2,7},{3,6},{5}} => 3 {{1,4,7},{2,8},{3,6},{5}} => 3 {{1,4,6},{2,8},{3,7},{5}} => 3 {{1,4,7},{2,8},{3,5},{6}} => 3 {{1,5},{2,8},{3,4,7},{6}} => 3 {{1,5},{2,3,8},{4,7},{6}} => 3 {{1,2,5},{3,8},{4,7},{6}} => 3 {{1,5},{2,7},{3,4,8},{6}} => 4 {{1,4,8},{2,7},{3,5},{6}} => 4 {{1,7},{2,6},{3,4,8},{5}} => 3 {{1,7},{2,3,6},{4,8},{5}} => 3 {{1,8},{2,3,6},{4,7},{5}} => 3 {{1,8},{2,3,5},{4,7},{6}} => 3 {{1,8},{2,5},{3,4,7},{6}} => 3 {{1,8},{2,4,7},{3,5},{6}} => 3 {{1,8},{2,4,7},{3,6},{5}} => 3 {{1,7},{2,4,8},{3,6},{5}} => 3 {{1,3,5},{2,8},{4,7},{6}} => 3 {{1,3,8},{2,7},{4,6},{5}} => 3 {{1,6},{2,4,8},{3,7},{5}} => 4 {{1,6},{2,4,7},{3,8},{5}} => 3 {{1,7},{2,4,6},{3,8},{5}} => 3 {{1,7},{2,4,8},{3,5},{6}} => 4 {{1,7},{2,3,5},{4,8},{6}} => 4 {{1,2,7},{3,8},{4,6},{5}} => 3 {{1,7},{2,8},{3,4,6},{5}} => 3 {{1,6},{2,8},{3,4,7},{5}} => 3 {{1,6},{2,3,7},{4,8},{5}} => 4 {{1,6},{2,7},{3,4,8},{5}} => 4 {{1,3,5},{2},{4,6,8},{7}} => 2 {{1,3},{2,4,6,8},{5},{7}} => 2 {{1},{2,4,6,8},{3},{5,7}} => 2 {{1,3},{2},{4,6,8},{5,7}} => 2 {{1,3,6},{2},{4,8},{5,7}} => 3 {{1,3,6},{2},{4,7},{5,8}} => 3 {{1,3,5},{2},{4,7},{6,8}} => 3 {{1,3,5,7},{2},{4,6},{8}} => 2 {{1,3,7},{2},{4,6,8},{5}} => 2 {{1,3,7},{2},{4,6},{5,8}} => 3 {{1,3,5,7},{2},{4,8},{6}} => 2 {{1,3},{2,4,8},{5,7},{6}} => 2 {{1},{2,4,8},{3,5,7},{6}} => 2 {{1,4},{2,8},{3,5,7},{6}} => 3 {{1,4},{2,5,7},{3,8},{6}} => 3 {{1,3},{2,5,7},{4,8},{6}} => 3 {{1,3},{2,7},{4,6,8},{5}} => 3 {{1,3,7},{2,4,6},{5},{8}} => 2 {{1,7},{2,4,6},{3},{5,8}} => 3 {{1,5,7},{2,4,8},{3},{6}} => 2 {{1},{2,8},{3,5,7},{4,6}} => 2 {{1,7},{2,4,6},{3,5},{8}} => 2 {{1,4,7},{2,6},{3,5},{8}} => 3 {{1},{2,5,8},{3,7},{4,6}} => 3 {{1},{2,5,8},{3,6},{4,7}} => 3 {{1},{2,4,8},{3,6},{5,7}} => 3 {{1},{2,4,6,8},{3,5},{7}} => 2 {{1,4},{2,6,8},{3,5},{7}} => 3 {{1,4},{2,5},{3,6,8},{7}} => 3 {{1,3},{2,5},{4,6,8},{7}} => 3 {{1,5},{2,4,6,8},{3},{7}} => 2 {{1,5},{2,4},{3,6,8},{7}} => 3 {{1},{2,6,8},{3,5,7},{4}} => 2 {{1,6},{2,8},{3,5,7},{4}} => 3 {{1,6},{2,4,8},{3},{5,7}} => 3 {{1,6},{2,4,7},{3},{5,8}} => 3 {{1,5},{2,4,7},{3},{6,8}} => 3 {{1,5,7},{2,4,6},{3},{8}} => 2 {{1,5,7},{2,4},{3,6},{8}} => 3 {{1},{2,6,8},{3,5},{4,7}} => 3 {{1},{2,4,6,8},{3,7},{5}} => 2 {{1,6},{2,7},{3,5,8},{4}} => 3 {{1,3,5},{2,7},{4},{6,8}} => 3 {{1,7},{2,6,8},{3,5},{4}} => 2 {{1,7},{2,6},{3,5,8},{4}} => 3 {{1,2},{3,4,6},{5,8},{7}} => 3 {{1,2},{3,6},{4,5,8},{7}} => 3 {{1,2},{3,5,6},{4,8},{7}} => 3 {{1,2,5,6},{3},{4,8},{7}} => 3 {{1,2,6},{3},{4,5,8},{7}} => 3 {{1,6},{2,3},{4,5,8},{7}} => 3 {{1,5,6},{2,3},{4,8},{7}} => 3 {{1,5,6},{2,3,8},{4},{7}} => 3 {{1,5,6},{2,8},{3,4},{7}} => 3 {{1,5},{2,8},{3,4,6},{7}} => 3 {{1,5},{2,3,8},{4,6},{7}} => 3 {{1,6},{2,3,5,8},{4},{7}} => 3 {{1,2,5},{3,8},{4,6},{7}} => 3 {{1,2,4},{3,6},{5},{7,8}} => 3 {{1,2,4,6},{3},{5,8},{7}} => 3 {{1,2,4},{3,8},{5,7},{6}} => 3 {{1,2,4},{3,8},{5},{6,7}} => 3 {{1,4},{2,3,8},{5},{6,7}} => 3 {{1,3,4},{2,8},{5},{6,7}} => 3 {{1,3,4},{2,8},{5,7},{6}} => 3 {{1,4},{2,3,8},{5,7},{6}} => 3 {{1,4,6},{2,3},{5,8},{7}} => 3 {{1,4},{2,3,6},{5},{7,8}} => 3 {{1,4},{2,3,6,8},{5},{7}} => 3 {{1,4},{2,3,6},{5,8},{7}} => 3 {{1,8},{2,4,5},{3,7},{6}} => 3 {{1,3,8},{2,6},{4,5},{7}} => 3 {{1,3,4},{2,6},{5},{7,8}} => 3 {{1,6},{2,5,8},{3,4},{7}} => 3 {{1,6},{2,4,5},{3,8},{7}} => 3 {{1,4,5},{2,8},{3,6},{7}} => 3 {{1,3,8},{2,5,6},{4},{7}} => 3 {{1,3,8},{2,5},{4},{6,7}} => 3 {{1,5},{2,4},{3,7,8},{6}} => 3 {{1,5,6},{2,4},{3,8},{7}} => 3 {{1,4},{2,8},{3,5,6},{7}} => 3 {{1,4},{2,7,8},{3,5},{6}} => 3 {{1,4,7},{2,8},{3},{5,6}} => 3 {{1,5,7},{2,8},{3,4},{6}} => 3 {{1,5,7},{2,3,8},{4},{6}} => 3 {{1,2,5},{3,7},{4},{6,8}} => 3 {{1,5},{2,3,7},{4},{6,8}} => 3 {{1,4,5},{2,7},{3},{6,8}} => 3 {{1,4},{2,7},{3},{5,6,8}} => 3 {{1,4},{2,6,7},{3},{5,8}} => 3 {{1,4},{2,6},{3},{5,7,8}} => 3 {{1,6},{2,5,7,8},{3},{4}} => 3 {{1,6,7},{2,5,8},{3},{4}} => 3 {{1,7},{2,5,6,8},{3},{4}} => 3 {{1,7},{2,6,8},{3},{4,5}} => 3 {{1,7},{2,3,6,8},{4},{5}} => 3 {{1,2,8},{3,6},{4},{5,7}} => 3 {{1,8},{2,6},{3},{4,5,7}} => 3 {{1,8},{2,5,6},{3},{4,7}} => 3 {{1,8},{2,5},{3},{4,6,7}} => 3 {{1,7,8},{2,5},{3},{4,6}} => 3 {{1,8},{2,4},{3,6,7},{5}} => 3 {{1,7,8},{2,4},{3,6},{5}} => 3 {{1,4},{2,3,7},{5,8},{6}} => 3 {{1,3},{2,7},{4,5,8},{6}} => 3 {{1,3},{2,6,7},{4,8},{5}} => 3 {{1,3},{2,6},{4,7,8},{5}} => 3 {{1,6},{2,4,7,8},{3},{5}} => 3 {{1,7},{2,4,8},{3},{5,6}} => 3 {{1,7},{2,4,5,8},{3},{6}} => 3 {{1,7},{2,5,8},{3,4},{6}} => 3 {{1,7},{2,3,5,8},{4},{6}} => 3 {{1,2,7},{3},{4,6},{5,8}} => 3 {{1,7},{2},{3,4,6},{5,8}} => 3 {{1,7},{2},{3,6},{4,5,8}} => 3 {{1,7},{2},{3,5,6},{4,8}} => 3 {{1,6,7},{2},{3,5},{4,8}} => 3 {{1,6},{2},{3,5},{4,7,8}} => 3 {{1,5},{2},{3,7,8},{4,6}} => 3 {{1,5},{2},{3,8},{4,6,7}} => 3 {{1,5,6},{2},{3,8},{4,7}} => 3 {{1,6},{2},{3,8},{4,5,7}} => 3 {{1,6},{2},{3,4,8},{5,7}} => 3 {{1,2,6},{3},{4,8},{5,7}} => 3 {{1,2,6,8},{3},{4,7},{5}} => 3 {{1,6,8},{2,3},{4,7},{5}} => 3 {{1,6,8},{2},{3,7},{4,5}} => 3 {{1,5,6,8},{2},{3,7},{4}} => 3 {{1,5,8},{2},{3,6,7},{4}} => 3 {{1,3},{2,4,5,6,7,8}} => 2 {{1,4},{2,3,5,6,7,8}} => 2 {{1,5},{2,3,4,6,7,8}} => 2 {{1,6},{2,4},{3},{5,7,8}} => 3 {{1,7},{2,4,5},{3},{6,8}} => 3 {{1,8},{2,4,5},{3,6},{7}} => 3 {{1,8},{2,4},{3,5,6},{7}} => 3 {{1,5,8},{2,3},{4,6},{7}} => 3 {{1,8},{2,5},{3,4,6},{7}} => 3 {{1,4,8},{2},{3,5,6},{7}} => 3 {{1,4},{2},{3,6,8},{5,7}} => 3 {{1,5,7},{2,3},{4},{6,8}} => 3 {{1,4,6},{2},{3},{5,7,8}} => 3 {{1},{2,5,6},{3,7},{4,8}} => 3 {{1},{2,5,6},{3},{4,7,8}} => 3 {{1},{2,5},{3,7},{4,6,8}} => 3 {{1},{2},{3,6,7},{4,5,8}} => 2 {{1},{2,3,6,7},{4},{5,8}} => 3 {{1},{2,3,6},{4,8},{5,7}} => 3 {{1},{2},{3,4,6,8},{5,7}} => 2 {{1},{2},{3,6},{4,5,7,8}} => 2 {{1},{2,5},{3},{4,6,7,8}} => 3 {{1},{2,5},{3,6},{4,7,8}} => 3 {{1},{2,5},{3,6,7},{4,8}} => 3 {{1},{2},{3,5,6,7},{4,8}} => 2 {{1},{2},{3,5,6},{4,7,8}} => 2 {{1},{2},{3,5},{4,6,7,8}} => 2 {{1},{2,4,8},{3,5},{6,7}} => 3 {{1},{2,4},{3,6,8},{5,7}} => 3 {{1},{2,4,7},{3,6},{5,8}} => 3 {{1,3},{2,8},{4,5,7},{6}} => 3 {{1,3},{2,4,7,8},{5},{6}} => 3 {{1,7},{2,3,4,8},{5},{6}} => 4 {{1},{2,4,7},{3},{5,6,8}} => 2 {{1,7},{2},{3,4,5},{6,8}} => 3 {{1},{2,3,7},{4,8},{5,6}} => 3 {{1},{2},{3,7},{4,5,6,8}} => 2 {{1},{2},{3,5,7},{4,6,8}} => 2 {{1},{2,6},{3,5},{4,7,8}} => 3 {{1},{2,6},{3,5,7},{4,8}} => 2 {{1,5},{2},{3,6,7},{4,8}} => 3 {{1,5},{2},{3,6},{4,7,8}} => 3 {{1,5},{2},{3},{4,6,7,8}} => 3 {{1},{2,6},{3},{4,5,7,8}} => 3 {{1,6},{2},{3,4},{5,7,8}} => 3 {{1,2,6},{3},{4,7,8},{5}} => 3 {{1,6},{2},{3,4,7},{5,8}} => 3 {{1},{2,6},{3,7},{4,5,8}} => 3 {{1,5},{2},{3,7},{4,6,8}} => 3 {{1,5},{2,6},{3},{4,7,8}} => 4 {{1,6},{2,3,4,5,7,8}} => 2 {{1,7},{2,3,4,5,6,8}} => 2 {{1},{2},{3},{4},{5},{6},{7},{8},{9}} => 2 {{1},{2},{3},{4},{5},{6},{7},{8,9}} => 2 {{1},{2},{3},{4},{5},{6},{7,9},{8}} => 2 {{1},{2},{3},{4},{5},{6,9},{7},{8}} => 3 {{1},{2},{3},{4},{5,9},{6},{7},{8}} => 3 {{1},{2},{3},{4,9},{5},{6},{7},{8}} => 3 {{1},{2},{3,9},{4},{5},{6},{7},{8}} => 3 {{1},{2,9},{3},{4},{5},{6},{7},{8}} => 3 {{1,9},{2},{3},{4},{5},{6},{7},{8}} => 3 {{1},{2},{3},{4},{5},{6},{7,8,9}} => 2 {{1},{2},{3},{4},{5},{6,9},{7,8}} => 2 {{1},{2},{3},{4},{5,9},{6,7},{8}} => 3 {{1},{2},{3},{4,9},{5,6},{7},{8}} => 3 {{1},{2},{3,9},{4,5},{6},{7},{8}} => 3 {{1},{2,9},{3,4},{5},{6},{7},{8}} => 3 {{1,9},{2,3},{4},{5},{6},{7},{8}} => 3 {{1,2,3,4,5,6,7,8},{9}} => 2 {{1},{2,3,4,5,6,7,8,9}} => 2 {{1,2,3,4,5,6,8},{7},{9}} => 2 {{1},{2,3,4,5,6,7,9},{8}} => 2 {{1,2,3,4,5,8},{6,7},{9}} => 2 {{1,2,3,4,5,7,8},{6},{9}} => 2 {{1},{2,3,4,5,6,9},{7,8}} => 2 {{1},{2,3,4,5,6,8,9},{7}} => 2 {{1,2},{3,4},{5,6},{7,8},{9,10}} => 2 {{1,4},{2,3},{5,6},{7,8},{9,10}} => 2 {{1,6},{2,3},{4,5},{7,8},{9,10}} => 3 {{1,8},{2,3},{4,5},{6,7},{9,10}} => 3 {{1,10},{2,3},{4,5},{6,7},{8,9}} => 3 {{1,2},{3,6},{4,5},{7,8},{9,10}} => 2 {{1,6},{2,5},{3,4},{7,8},{9,10}} => 2 {{1,8},{2,5},{3,4},{6,7},{9,10}} => 3 {{1,10},{2,5},{3,4},{6,7},{8,9}} => 3 {{1,2},{3,8},{4,5},{6,7},{9,10}} => 3 {{1,8},{2,7},{3,4},{5,6},{9,10}} => 3 {{1,10},{2,7},{3,4},{5,6},{8,9}} => 3 {{1,2},{3,10},{4,5},{6,7},{8,9}} => 3 {{1,10},{2,9},{3,4},{5,6},{7,8}} => 3 {{1,2},{3,4},{5,8},{6,7},{9,10}} => 2 {{1,4},{2,3},{5,8},{6,7},{9,10}} => 2 {{1,8},{2,3},{4,7},{5,6},{9,10}} => 3 {{1,10},{2,3},{4,7},{5,6},{8,9}} => 3 {{1,2},{3,8},{4,7},{5,6},{9,10}} => 2 {{1,8},{2,7},{3,6},{4,5},{9,10}} => 2 {{1,10},{2,7},{3,6},{4,5},{8,9}} => 3 {{1,2},{3,10},{4,7},{5,6},{8,9}} => 3 {{1,10},{2,9},{3,6},{4,5},{7,8}} => 3 {{1,2},{3,4},{5,10},{6,7},{8,9}} => 3 {{1,4},{2,3},{5,10},{6,7},{8,9}} => 3 {{1,10},{2,3},{4,9},{5,6},{7,8}} => 3 {{1,2},{3,10},{4,9},{5,6},{7,8}} => 3 {{1,10},{2,9},{3,8},{4,5},{6,7}} => 3 {{1,2},{3,4},{5,6},{7,10},{8,9}} => 2 {{1,4},{2,3},{5,6},{7,10},{8,9}} => 2 {{1,6},{2,3},{4,5},{7,10},{8,9}} => 3 {{1,10},{2,3},{4,5},{6,9},{7,8}} => 3 {{1,2},{3,6},{4,5},{7,10},{8,9}} => 2 {{1,6},{2,5},{3,4},{7,10},{8,9}} => 2 {{1,10},{2,5},{3,4},{6,9},{7,8}} => 3 {{1,2},{3,10},{4,5},{6,9},{7,8}} => 3 {{1,10},{2,9},{3,4},{5,8},{6,7}} => 3 {{1,2},{3,4},{5,10},{6,9},{7,8}} => 2 {{1,4},{2,3},{5,10},{6,9},{7,8}} => 2 {{1,10},{2,3},{4,9},{5,8},{6,7}} => 3 {{1,2},{3,10},{4,9},{5,8},{6,7}} => 2 {{1,10},{2,9},{3,8},{4,7},{5,6}} => 2 {{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}} => 2 {{1},{2},{3},{4},{5},{6},{7},{8},{9,10}} => 2 {{1},{2},{3},{4},{5},{6},{7},{8,10},{9}} => 2 {{1},{2},{3},{4},{5},{6},{7,10},{8},{9}} => 3 {{1},{2},{3},{4},{5},{6,10},{7},{8},{9}} => 3 {{1},{2},{3},{4},{5,10},{6},{7},{8},{9}} => 3 {{1},{2},{3},{4,10},{5},{6},{7},{8},{9}} => 3 {{1},{2},{3,10},{4},{5},{6},{7},{8},{9}} => 3 {{1},{2,10},{3},{4},{5},{6},{7},{8},{9}} => 3 {{1,10},{2},{3},{4},{5},{6},{7},{8},{9}} => 3 {{1,2,3,4,5,6,7,8,9},{10}} => 2 {{1},{2,3,4,5,6,7,8,9,10}} => 2 {{1,2,3,4,5,6,7,9},{8},{10}} => 2 {{1},{2,3,4,5,6,7,8,10},{9}} => 2 {{1,2,3,4,5,6,7,8,9,10},{11}} => 2 {{1},{2,3,4,5,6,7,8,9,10,11}} => 2 {{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}} => 2 {{1,2},{3,4},{5,6},{7,8},{9,12},{10,11}} => 2 {{1,2},{3,4},{5,6},{7,10},{8,9},{11,12}} => 2 {{1,2},{3,4},{5,6},{7,12},{8,9},{10,11}} => 3 {{1,2},{3,4},{5,6},{7,12},{8,11},{9,10}} => 2 {{1,2},{3,4},{5,8},{6,7},{9,10},{11,12}} => 2 {{1,2},{3,4},{5,8},{6,7},{9,12},{10,11}} => 2 {{1,2},{3,4},{5,10},{6,7},{8,9},{11,12}} => 3 {{1,2},{3,4},{5,12},{6,7},{8,9},{10,11}} => 3 {{1,2},{3,4},{5,12},{6,7},{8,11},{9,10}} => 3 {{1,2},{3,4},{5,10},{6,9},{7,8},{11,12}} => 2 {{1,2},{3,4},{5,12},{6,9},{7,8},{10,11}} => 3 {{1,2},{3,4},{5,12},{6,11},{7,8},{9,10}} => 3 {{1,2},{3,4},{5,12},{6,11},{7,10},{8,9}} => 2 {{1,2},{3,6},{4,5},{7,8},{9,10},{11,12}} => 2 {{1,2},{3,6},{4,5},{7,8},{9,12},{10,11}} => 2 {{1,2},{3,6},{4,5},{7,10},{8,9},{11,12}} => 2 {{1,2},{3,6},{4,5},{7,12},{8,9},{10,11}} => 3 {{1,2},{3,6},{4,5},{7,12},{8,11},{9,10}} => 2 {{1,2},{3,8},{4,5},{6,7},{9,10},{11,12}} => 3 {{1,2},{3,8},{4,5},{6,7},{9,12},{10,11}} => 3 {{1,2},{3,10},{4,5},{6,7},{8,9},{11,12}} => 3 {{1,2},{3,12},{4,5},{6,7},{8,9},{10,11}} => 3 {{1,2},{3,12},{4,5},{6,7},{8,11},{9,10}} => 3 {{1,2},{3,10},{4,5},{6,9},{7,8},{11,12}} => 3 {{1,2},{3,12},{4,5},{6,9},{7,8},{10,11}} => 3 {{1,2},{3,12},{4,5},{6,11},{7,8},{9,10}} => 3 {{1,2},{3,12},{4,5},{6,11},{7,10},{8,9}} => 3 {{1,2},{3,8},{4,7},{5,6},{9,10},{11,12}} => 2 {{1,2},{3,8},{4,7},{5,6},{9,12},{10,11}} => 2 {{1,2},{3,10},{4,7},{5,6},{8,9},{11,12}} => 3 {{1,2},{3,12},{4,7},{5,6},{8,9},{10,11}} => 3 {{1,2},{3,12},{4,7},{5,6},{8,11},{9,10}} => 3 {{1,2},{3,10},{4,9},{5,6},{7,8},{11,12}} => 3 {{1,2},{3,12},{4,9},{5,6},{7,8},{10,11}} => 3 {{1,2},{3,12},{4,11},{5,6},{7,8},{9,10}} => 3 {{1,2},{3,12},{4,11},{5,6},{7,10},{8,9}} => 3 {{1,2},{3,10},{4,9},{5,8},{6,7},{11,12}} => 2 {{1,2},{3,12},{4,9},{5,8},{6,7},{10,11}} => 3 {{1,2},{3,12},{4,11},{5,8},{6,7},{9,10}} => 3 {{1,2},{3,12},{4,11},{5,10},{6,7},{8,9}} => 3 {{1,2},{3,12},{4,11},{5,10},{6,9},{7,8}} => 2 {{1,4},{2,3},{5,6},{7,8},{9,10},{11,12}} => 2 {{1,4},{2,3},{5,6},{7,8},{9,12},{10,11}} => 2 {{1,4},{2,3},{5,6},{7,10},{8,9},{11,12}} => 2 {{1,4},{2,3},{5,6},{7,12},{8,9},{10,11}} => 3 {{1,4},{2,3},{5,6},{7,12},{8,11},{9,10}} => 2 {{1,4},{2,3},{5,8},{6,7},{9,10},{11,12}} => 2 {{1,4},{2,3},{5,8},{6,7},{9,12},{10,11}} => 2 {{1,4},{2,3},{5,10},{6,7},{8,9},{11,12}} => 3 {{1,4},{2,3},{5,12},{6,7},{8,9},{10,11}} => 3 {{1,4},{2,3},{5,12},{6,7},{8,11},{9,10}} => 3 {{1,4},{2,3},{5,10},{6,9},{7,8},{11,12}} => 2 {{1,4},{2,3},{5,12},{6,9},{7,8},{10,11}} => 3 {{1,4},{2,3},{5,12},{6,11},{7,8},{9,10}} => 3 {{1,4},{2,3},{5,12},{6,11},{7,10},{8,9}} => 2 {{1,6},{2,3},{4,5},{7,8},{9,10},{11,12}} => 3 {{1,6},{2,3},{4,5},{7,8},{9,12},{10,11}} => 3 {{1,6},{2,3},{4,5},{7,10},{8,9},{11,12}} => 3 {{1,6},{2,3},{4,5},{7,12},{8,9},{10,11}} => 3 {{1,6},{2,3},{4,5},{7,12},{8,11},{9,10}} => 3 {{1,8},{2,3},{4,5},{6,7},{9,10},{11,12}} => 3 {{1,8},{2,3},{4,5},{6,7},{9,12},{10,11}} => 3 {{1,10},{2,3},{4,5},{6,7},{8,9},{11,12}} => 3 {{1,12},{2,3},{4,5},{6,7},{8,9},{10,11}} => 3 {{1,12},{2,3},{4,5},{6,7},{8,11},{9,10}} => 3 {{1,10},{2,3},{4,5},{6,9},{7,8},{11,12}} => 3 {{1,12},{2,3},{4,5},{6,9},{7,8},{10,11}} => 3 {{1,12},{2,3},{4,5},{6,11},{7,8},{9,10}} => 3 {{1,12},{2,3},{4,5},{6,11},{7,10},{8,9}} => 3 {{1,8},{2,3},{4,7},{5,6},{9,10},{11,12}} => 3 {{1,8},{2,3},{4,7},{5,6},{9,12},{10,11}} => 3 {{1,10},{2,3},{4,7},{5,6},{8,9},{11,12}} => 3 {{1,12},{2,3},{4,7},{5,6},{8,9},{10,11}} => 3 {{1,12},{2,3},{4,7},{5,6},{8,11},{9,10}} => 3 {{1,10},{2,3},{4,9},{5,6},{7,8},{11,12}} => 3 {{1,12},{2,3},{4,9},{5,6},{7,8},{10,11}} => 3 {{1,12},{2,3},{4,11},{5,6},{7,8},{9,10}} => 3 {{1,12},{2,3},{4,11},{5,6},{7,10},{8,9}} => 3 {{1,10},{2,3},{4,9},{5,8},{6,7},{11,12}} => 3 {{1,12},{2,3},{4,9},{5,8},{6,7},{10,11}} => 3 {{1,12},{2,3},{4,11},{5,8},{6,7},{9,10}} => 3 {{1,12},{2,3},{4,11},{5,10},{6,7},{8,9}} => 3 {{1,12},{2,3},{4,11},{5,10},{6,9},{7,8}} => 3 {{1,6},{2,5},{3,4},{7,8},{9,10},{11,12}} => 2 {{1,6},{2,5},{3,4},{7,8},{9,12},{10,11}} => 2 {{1,6},{2,5},{3,4},{7,10},{8,9},{11,12}} => 2 {{1,6},{2,5},{3,4},{7,12},{8,9},{10,11}} => 3 {{1,6},{2,5},{3,4},{7,12},{8,11},{9,10}} => 2 {{1,8},{2,5},{3,4},{6,7},{9,10},{11,12}} => 3 {{1,8},{2,5},{3,4},{6,7},{9,12},{10,11}} => 3 {{1,10},{2,5},{3,4},{6,7},{8,9},{11,12}} => 3 {{1,12},{2,5},{3,4},{6,7},{8,9},{10,11}} => 3 {{1,12},{2,5},{3,4},{6,7},{8,11},{9,10}} => 3 {{1,10},{2,5},{3,4},{6,9},{7,8},{11,12}} => 3 {{1,12},{2,5},{3,4},{6,9},{7,8},{10,11}} => 3 {{1,12},{2,5},{3,4},{6,11},{7,8},{9,10}} => 3 {{1,12},{2,5},{3,4},{6,11},{7,10},{8,9}} => 3 {{1,8},{2,7},{3,4},{5,6},{9,10},{11,12}} => 3 {{1,8},{2,7},{3,4},{5,6},{9,12},{10,11}} => 3 {{1,10},{2,7},{3,4},{5,6},{8,9},{11,12}} => 3 {{1,12},{2,7},{3,4},{5,6},{8,9},{10,11}} => 3 {{1,12},{2,7},{3,4},{5,6},{8,11},{9,10}} => 3 {{1,10},{2,9},{3,4},{5,6},{7,8},{11,12}} => 3 {{1,12},{2,9},{3,4},{5,6},{7,8},{10,11}} => 3 {{1,12},{2,11},{3,4},{5,6},{7,8},{9,10}} => 3 {{1,12},{2,11},{3,4},{5,6},{7,10},{8,9}} => 3 {{1,10},{2,9},{3,4},{5,8},{6,7},{11,12}} => 3 {{1,12},{2,9},{3,4},{5,8},{6,7},{10,11}} => 3 {{1,12},{2,11},{3,4},{5,8},{6,7},{9,10}} => 3 {{1,12},{2,11},{3,4},{5,10},{6,7},{8,9}} => 3 {{1,12},{2,11},{3,4},{5,10},{6,9},{7,8}} => 3 {{1,8},{2,7},{3,6},{4,5},{9,10},{11,12}} => 2 {{1,8},{2,7},{3,6},{4,5},{9,12},{10,11}} => 2 {{1,10},{2,7},{3,6},{4,5},{8,9},{11,12}} => 3 {{1,12},{2,7},{3,6},{4,5},{8,9},{10,11}} => 3 {{1,12},{2,7},{3,6},{4,5},{8,11},{9,10}} => 3 {{1,10},{2,9},{3,6},{4,5},{7,8},{11,12}} => 3 {{1,12},{2,9},{3,6},{4,5},{7,8},{10,11}} => 3 {{1,12},{2,11},{3,6},{4,5},{7,8},{9,10}} => 3 {{1,12},{2,11},{3,6},{4,5},{7,10},{8,9}} => 3 {{1,10},{2,9},{3,8},{4,5},{6,7},{11,12}} => 3 {{1,12},{2,9},{3,8},{4,5},{6,7},{10,11}} => 3 {{1,12},{2,11},{3,8},{4,5},{6,7},{9,10}} => 3 {{1,12},{2,11},{3,10},{4,5},{6,7},{8,9}} => 3 {{1,12},{2,11},{3,10},{4,5},{6,9},{7,8}} => 3 {{1,10},{2,9},{3,8},{4,7},{5,6},{11,12}} => 2 {{1,12},{2,9},{3,8},{4,7},{5,6},{10,11}} => 3 {{1,12},{2,11},{3,8},{4,7},{5,6},{9,10}} => 3 {{1,12},{2,11},{3,10},{4,7},{5,6},{8,9}} => 3 {{1,12},{2,11},{3,10},{4,9},{5,6},{7,8}} => 3 {{1,12},{2,11},{3,10},{4,9},{5,8},{6,7}} => 2 ----------------------------------------------------------------------------- Created: May 10, 2017 at 22:55 by Martin Rubey ----------------------------------------------------------------------------- Last Updated: Nov 11, 2021 at 12:50 by Martin Rubey