*****************************************************************************
* www.FindStat.org - The Combinatorial Statistic Finder *
* *
* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
* *
* 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: St001051
-----------------------------------------------------------------------------
Collection: Set partitions
-----------------------------------------------------------------------------
Description: The depth of the label 1 in the decreasing labelled unordered tree associated with the set partition.
The bijection between set partitions of $\{1,\dots,n\}$ into $k$ blocks and trees with $n+1-k$ leaves is described in Theorem 1 of [1].
-----------------------------------------------------------------------------
References: [1] Erdős, Péter L., Székely, L. A. Applications of antilexicographic order. I. An enumerative theory of trees [[MathSciNet:1023945]]
-----------------------------------------------------------------------------
Code:
def statistic(p):
return depth_of_1(set_partition_to_tree(p))
def depth_of_1(T):
if T.label() == 1:
return 0
if T.node_number() == 1:
return infinity
else:
return 1 + min(depth_of_1(C) for C in T)
def set_partition_to_tree(p):
# the children of the smallest label are the largest remaining
# element and its partner
trees = [LabelledRootedTree([LabelledRootedTree([], label=e) for e in b]) for b in p]
max_label = p.size()+1-len(p) # last labelled node
while len(trees) > 1:
max_label += 1
# find tree with smallest child and all children smaller than max_label
A = sorted([T for T in trees if max(C.label() for C in T) < max_label],
key = lambda T: min(C.label() for C in T))[0]
trees.remove(A)
# give it's root node the new label
A = LabelledRootedTree(A, label=max_label)
# find tree with child having label max_label
B = (T for T in trees
if any(C.label() == max_label for C in T)).next()
trees.remove(B)
# replace the child of B carrying max_label with A
C = LabelledRootedTree([A] + [T for T in B if T.label() != max_label])
trees.append(C)
return trees[0]
-----------------------------------------------------------------------------
Statistic values:
{{1}} => 1
{{1,2}} => 1
{{1},{2}} => 2
{{1,2,3}} => 1
{{1,2},{3}} => 2
{{1,3},{2}} => 1
{{1},{2,3}} => 2
{{1},{2},{3}} => 3
{{1,2,3,4}} => 1
{{1,2,3},{4}} => 2
{{1,2,4},{3}} => 1
{{1,2},{3,4}} => 2
{{1,2},{3},{4}} => 3
{{1,3,4},{2}} => 1
{{1,3},{2,4}} => 2
{{1,3},{2},{4}} => 2
{{1,4},{2,3}} => 1
{{1},{2,3,4}} => 2
{{1},{2,3},{4}} => 3
{{1,4},{2},{3}} => 1
{{1},{2,4},{3}} => 3
{{1},{2},{3,4}} => 2
{{1},{2},{3},{4}} => 4
{{1,2,3,4,5}} => 1
{{1,2,3,4},{5}} => 2
{{1,2,3,5},{4}} => 1
{{1,2,3},{4,5}} => 2
{{1,2,3},{4},{5}} => 3
{{1,2,4,5},{3}} => 1
{{1,2,4},{3,5}} => 2
{{1,2,4},{3},{5}} => 2
{{1,2,5},{3,4}} => 1
{{1,2},{3,4,5}} => 2
{{1,2},{3,4},{5}} => 3
{{1,2,5},{3},{4}} => 1
{{1,2},{3,5},{4}} => 3
{{1,2},{3},{4,5}} => 2
{{1,2},{3},{4},{5}} => 4
{{1,3,4,5},{2}} => 1
{{1,3,4},{2,5}} => 2
{{1,3,4},{2},{5}} => 2
{{1,3,5},{2,4}} => 1
{{1,3},{2,4,5}} => 2
{{1,3},{2,4},{5}} => 3
{{1,3,5},{2},{4}} => 1
{{1,3},{2,5},{4}} => 3
{{1,3},{2},{4,5}} => 2
{{1,3},{2},{4},{5}} => 3
{{1,4,5},{2,3}} => 1
{{1,4},{2,3,5}} => 2
{{1,4},{2,3},{5}} => 2
{{1,5},{2,3,4}} => 1
{{1},{2,3,4,5}} => 2
{{1},{2,3,4},{5}} => 3
{{1,5},{2,3},{4}} => 1
{{1},{2,3,5},{4}} => 3
{{1},{2,3},{4,5}} => 2
{{1},{2,3},{4},{5}} => 4
{{1,4,5},{2},{3}} => 1
{{1,4},{2,5},{3}} => 2
{{1,4},{2},{3,5}} => 2
{{1,4},{2},{3},{5}} => 2
{{1,5},{2,4},{3}} => 1
{{1},{2,4,5},{3}} => 2
{{1},{2,4},{3,5}} => 3
{{1},{2,4},{3},{5}} => 4
{{1,5},{2},{3,4}} => 1
{{1},{2,5},{3,4}} => 3
{{1},{2},{3,4,5}} => 2
{{1},{2},{3,4},{5}} => 3
{{1,5},{2},{3},{4}} => 1
{{1},{2,5},{3},{4}} => 4
{{1},{2},{3,5},{4}} => 2
{{1},{2},{3},{4,5}} => 3
{{1},{2},{3},{4},{5}} => 5
{{1,2,3,4,5,6}} => 1
{{1,2,3,4,5},{6}} => 2
{{1,2,3,4,6},{5}} => 1
{{1,2,3,4},{5,6}} => 2
{{1,2,3,4},{5},{6}} => 3
{{1,2,3,5,6},{4}} => 1
{{1,2,3,5},{4,6}} => 2
{{1,2,3,5},{4},{6}} => 2
{{1,2,3,6},{4,5}} => 1
{{1,2,3},{4,5,6}} => 2
{{1,2,3},{4,5},{6}} => 3
{{1,2,3,6},{4},{5}} => 1
{{1,2,3},{4,6},{5}} => 3
{{1,2,3},{4},{5,6}} => 2
{{1,2,3},{4},{5},{6}} => 4
{{1,2,4,5,6},{3}} => 1
{{1,2,4,5},{3,6}} => 2
{{1,2,4,5},{3},{6}} => 2
{{1,2,4,6},{3,5}} => 1
{{1,2,4},{3,5,6}} => 2
{{1,2,4},{3,5},{6}} => 3
{{1,2,4,6},{3},{5}} => 1
{{1,2,4},{3,6},{5}} => 3
{{1,2,4},{3},{5,6}} => 2
{{1,2,4},{3},{5},{6}} => 3
{{1,2,5,6},{3,4}} => 1
{{1,2,5},{3,4,6}} => 2
{{1,2,5},{3,4},{6}} => 2
{{1,2,6},{3,4,5}} => 1
{{1,2},{3,4,5,6}} => 2
{{1,2},{3,4,5},{6}} => 3
{{1,2,6},{3,4},{5}} => 1
{{1,2},{3,4,6},{5}} => 3
{{1,2},{3,4},{5,6}} => 2
{{1,2},{3,4},{5},{6}} => 4
{{1,2,5,6},{3},{4}} => 1
{{1,2,5},{3,6},{4}} => 2
{{1,2,5},{3},{4,6}} => 2
{{1,2,5},{3},{4},{6}} => 2
{{1,2,6},{3,5},{4}} => 1
{{1,2},{3,5,6},{4}} => 2
{{1,2},{3,5},{4,6}} => 3
{{1,2},{3,5},{4},{6}} => 4
{{1,2,6},{3},{4,5}} => 1
{{1,2},{3,6},{4,5}} => 3
{{1,2},{3},{4,5,6}} => 2
{{1,2},{3},{4,5},{6}} => 3
{{1,2,6},{3},{4},{5}} => 1
{{1,2},{3,6},{4},{5}} => 4
{{1,2},{3},{4,6},{5}} => 2
{{1,2},{3},{4},{5,6}} => 3
{{1,2},{3},{4},{5},{6}} => 5
{{1,3,4,5,6},{2}} => 1
{{1,3,4,5},{2,6}} => 2
{{1,3,4,5},{2},{6}} => 2
{{1,3,4,6},{2,5}} => 1
{{1,3,4},{2,5,6}} => 2
{{1,3,4},{2,5},{6}} => 3
{{1,3,4,6},{2},{5}} => 1
{{1,3,4},{2,6},{5}} => 3
{{1,3,4},{2},{5,6}} => 2
{{1,3,4},{2},{5},{6}} => 3
{{1,3,5,6},{2,4}} => 1
{{1,3,5},{2,4,6}} => 2
{{1,3,5},{2,4},{6}} => 2
{{1,3,6},{2,4,5}} => 1
{{1,3},{2,4,5,6}} => 2
{{1,3},{2,4,5},{6}} => 3
{{1,3,6},{2,4},{5}} => 1
{{1,3},{2,4,6},{5}} => 3
{{1,3},{2,4},{5,6}} => 2
{{1,3},{2,4},{5},{6}} => 4
{{1,3,5,6},{2},{4}} => 1
{{1,3,5},{2,6},{4}} => 2
{{1,3,5},{2},{4,6}} => 2
{{1,3,5},{2},{4},{6}} => 2
{{1,3,6},{2,5},{4}} => 1
{{1,3},{2,5,6},{4}} => 2
{{1,3},{2,5},{4,6}} => 3
{{1,3},{2,5},{4},{6}} => 4
{{1,3,6},{2},{4,5}} => 1
{{1,3},{2,6},{4,5}} => 3
{{1,3},{2},{4,5,6}} => 2
{{1,3},{2},{4,5},{6}} => 3
{{1,3,6},{2},{4},{5}} => 1
{{1,3},{2,6},{4},{5}} => 4
{{1,3},{2},{4,6},{5}} => 2
{{1,3},{2},{4},{5,6}} => 3
{{1,3},{2},{4},{5},{6}} => 4
{{1,4,5,6},{2,3}} => 1
{{1,4,5},{2,3,6}} => 2
{{1,4,5},{2,3},{6}} => 2
{{1,4,6},{2,3,5}} => 1
{{1,4},{2,3,5,6}} => 2
{{1,4},{2,3,5},{6}} => 3
{{1,4,6},{2,3},{5}} => 1
{{1,4},{2,3,6},{5}} => 3
{{1,4},{2,3},{5,6}} => 2
{{1,4},{2,3},{5},{6}} => 3
{{1,5,6},{2,3,4}} => 1
{{1,5},{2,3,4,6}} => 2
{{1,5},{2,3,4},{6}} => 2
{{1,6},{2,3,4,5}} => 1
{{1},{2,3,4,5,6}} => 2
{{1},{2,3,4,5},{6}} => 3
{{1,6},{2,3,4},{5}} => 1
{{1},{2,3,4,6},{5}} => 3
{{1},{2,3,4},{5,6}} => 2
{{1},{2,3,4},{5},{6}} => 4
{{1,5,6},{2,3},{4}} => 1
{{1,5},{2,3,6},{4}} => 2
{{1,5},{2,3},{4,6}} => 2
{{1,5},{2,3},{4},{6}} => 2
{{1,6},{2,3,5},{4}} => 1
{{1},{2,3,5,6},{4}} => 2
{{1},{2,3,5},{4,6}} => 3
{{1},{2,3,5},{4},{6}} => 4
{{1,6},{2,3},{4,5}} => 1
{{1},{2,3,6},{4,5}} => 3
{{1},{2,3},{4,5,6}} => 2
{{1},{2,3},{4,5},{6}} => 3
{{1,6},{2,3},{4},{5}} => 1
{{1},{2,3,6},{4},{5}} => 4
{{1},{2,3},{4,6},{5}} => 2
{{1},{2,3},{4},{5,6}} => 3
{{1},{2,3},{4},{5},{6}} => 5
{{1,4,5,6},{2},{3}} => 1
{{1,4,5},{2,6},{3}} => 2
{{1,4,5},{2},{3,6}} => 2
{{1,4,5},{2},{3},{6}} => 2
{{1,4,6},{2,5},{3}} => 1
{{1,4},{2,5,6},{3}} => 2
{{1,4},{2,5},{3,6}} => 3
{{1,4},{2,5},{3},{6}} => 3
{{1,4,6},{2},{3,5}} => 1
{{1,4},{2,6},{3,5}} => 3
{{1,4},{2},{3,5,6}} => 2
{{1,4},{2},{3,5},{6}} => 3
{{1,4,6},{2},{3},{5}} => 1
{{1,4},{2,6},{3},{5}} => 3
{{1,4},{2},{3,6},{5}} => 3
{{1,4},{2},{3},{5,6}} => 2
{{1,4},{2},{3},{5},{6}} => 3
{{1,5,6},{2,4},{3}} => 1
{{1,5},{2,4,6},{3}} => 2
{{1,5},{2,4},{3,6}} => 2
{{1,5},{2,4},{3},{6}} => 2
{{1,6},{2,4,5},{3}} => 1
{{1},{2,4,5,6},{3}} => 2
{{1},{2,4,5},{3,6}} => 3
{{1},{2,4,5},{3},{6}} => 3
{{1,6},{2,4},{3,5}} => 1
{{1},{2,4,6},{3,5}} => 3
{{1},{2,4},{3,5,6}} => 2
{{1},{2,4},{3,5},{6}} => 4
{{1,6},{2,4},{3},{5}} => 1
{{1},{2,4,6},{3},{5}} => 2
{{1},{2,4},{3,6},{5}} => 4
{{1},{2,4},{3},{5,6}} => 3
{{1},{2,4},{3},{5},{6}} => 5
{{1,5,6},{2},{3,4}} => 1
{{1,5},{2,6},{3,4}} => 2
{{1,5},{2},{3,4,6}} => 2
{{1,5},{2},{3,4},{6}} => 2
{{1,6},{2,5},{3,4}} => 1
{{1},{2,5,6},{3,4}} => 2
{{1},{2,5},{3,4,6}} => 3
{{1},{2,5},{3,4},{6}} => 4
{{1,6},{2},{3,4,5}} => 1
{{1},{2,6},{3,4,5}} => 3
{{1},{2},{3,4,5,6}} => 2
{{1},{2},{3,4,5},{6}} => 3
{{1,6},{2},{3,4},{5}} => 1
{{1},{2,6},{3,4},{5}} => 4
{{1},{2},{3,4,6},{5}} => 2
{{1},{2},{3,4},{5,6}} => 3
{{1},{2},{3,4},{5},{6}} => 4
{{1,5,6},{2},{3},{4}} => 1
{{1,5},{2,6},{3},{4}} => 2
{{1,5},{2},{3,6},{4}} => 2
{{1,5},{2},{3},{4,6}} => 2
{{1,5},{2},{3},{4},{6}} => 2
{{1,6},{2,5},{3},{4}} => 1
{{1},{2,5,6},{3},{4}} => 3
{{1},{2,5},{3,6},{4}} => 4
{{1},{2,5},{3},{4,6}} => 2
{{1},{2,5},{3},{4},{6}} => 5
{{1,6},{2},{3,5},{4}} => 1
{{1},{2,6},{3,5},{4}} => 4
{{1},{2},{3,5,6},{4}} => 3
{{1},{2},{3,5},{4,6}} => 2
{{1},{2},{3,5},{4},{6}} => 3
{{1,6},{2},{3},{4,5}} => 1
{{1},{2,6},{3},{4,5}} => 3
{{1},{2},{3,6},{4,5}} => 3
{{1},{2},{3},{4,5,6}} => 2
{{1},{2},{3},{4,5},{6}} => 4
{{1,6},{2},{3},{4},{5}} => 1
{{1},{2,6},{3},{4},{5}} => 5
{{1},{2},{3,6},{4},{5}} => 2
{{1},{2},{3},{4,6},{5}} => 4
{{1},{2},{3},{4},{5,6}} => 3
{{1},{2},{3},{4},{5},{6}} => 6
{{1,2,3,4,5,6,7}} => 1
{{1,2,3,4,5,6},{7}} => 2
{{1,2,3,4,5,7},{6}} => 1
{{1,2,3,4,5},{6,7}} => 2
{{1,2,3,4,5},{6},{7}} => 3
{{1,2,3,4,6,7},{5}} => 1
{{1,2,3,4,6},{5,7}} => 2
{{1,2,3,4,6},{5},{7}} => 2
{{1,2,3,4,7},{5,6}} => 1
{{1,2,3,4},{5,6,7}} => 2
{{1,2,3,4},{5,6},{7}} => 3
{{1,2,3,4,7},{5},{6}} => 1
{{1,2,3,4},{5,7},{6}} => 3
{{1,2,3,4},{5},{6,7}} => 2
{{1,2,3,4},{5},{6},{7}} => 4
{{1,2,3,5,6,7},{4}} => 1
{{1,2,3,5,6},{4,7}} => 2
{{1,2,3,5,6},{4},{7}} => 2
{{1,2,3,5,7},{4,6}} => 1
{{1,2,3,5},{4,6,7}} => 2
{{1,2,3,5},{4,6},{7}} => 3
{{1,2,3,5,7},{4},{6}} => 1
{{1,2,3,5},{4,7},{6}} => 3
{{1,2,3,5},{4},{6,7}} => 2
{{1,2,3,5},{4},{6},{7}} => 3
{{1,2,3,6,7},{4,5}} => 1
{{1,2,3,6},{4,5,7}} => 2
{{1,2,3,6},{4,5},{7}} => 2
{{1,2,3,7},{4,5,6}} => 1
{{1,2,3},{4,5,6,7}} => 2
{{1,2,3},{4,5,6},{7}} => 3
{{1,2,3,7},{4,5},{6}} => 1
{{1,2,3},{4,5,7},{6}} => 3
{{1,2,3},{4,5},{6,7}} => 2
{{1,2,3},{4,5},{6},{7}} => 4
{{1,2,3,6,7},{4},{5}} => 1
{{1,2,3,6},{4,7},{5}} => 2
{{1,2,3,6},{4},{5,7}} => 2
{{1,2,3,6},{4},{5},{7}} => 2
{{1,2,3,7},{4,6},{5}} => 1
{{1,2,3},{4,6,7},{5}} => 2
{{1,2,3},{4,6},{5,7}} => 3
{{1,2,3},{4,6},{5},{7}} => 4
{{1,2,3,7},{4},{5,6}} => 1
{{1,2,3},{4,7},{5,6}} => 3
{{1,2,3},{4},{5,6,7}} => 2
{{1,2,3},{4},{5,6},{7}} => 3
{{1,2,3,7},{4},{5},{6}} => 1
{{1,2,3},{4,7},{5},{6}} => 4
{{1,2,3},{4},{5,7},{6}} => 2
{{1,2,3},{4},{5},{6,7}} => 3
{{1,2,3},{4},{5},{6},{7}} => 5
{{1,2,4,5,6,7},{3}} => 1
{{1,2,4,5,6},{3,7}} => 2
{{1,2,4,5,6},{3},{7}} => 2
{{1,2,4,5,7},{3,6}} => 1
{{1,2,4,5},{3,6,7}} => 2
{{1,2,4,5},{3,6},{7}} => 3
{{1,2,4,5,7},{3},{6}} => 1
{{1,2,4,5},{3,7},{6}} => 3
{{1,2,4,5},{3},{6,7}} => 2
{{1,2,4,5},{3},{6},{7}} => 3
{{1,2,4,6,7},{3,5}} => 1
{{1,2,4,6},{3,5,7}} => 2
{{1,2,4,6},{3,5},{7}} => 2
{{1,2,4,7},{3,5,6}} => 1
{{1,2,4},{3,5,6,7}} => 2
{{1,2,4},{3,5,6},{7}} => 3
{{1,2,4,7},{3,5},{6}} => 1
{{1,2,4},{3,5,7},{6}} => 3
{{1,2,4},{3,5},{6,7}} => 2
{{1,2,4},{3,5},{6},{7}} => 4
{{1,2,4,6,7},{3},{5}} => 1
{{1,2,4,6},{3,7},{5}} => 2
{{1,2,4,6},{3},{5,7}} => 2
{{1,2,4,6},{3},{5},{7}} => 2
{{1,2,4,7},{3,6},{5}} => 1
{{1,2,4},{3,6,7},{5}} => 2
{{1,2,4},{3,6},{5,7}} => 3
{{1,2,4},{3,6},{5},{7}} => 4
{{1,2,4,7},{3},{5,6}} => 1
{{1,2,4},{3,7},{5,6}} => 3
{{1,2,4},{3},{5,6,7}} => 2
{{1,2,4},{3},{5,6},{7}} => 3
{{1,2,4,7},{3},{5},{6}} => 1
{{1,2,4},{3,7},{5},{6}} => 4
{{1,2,4},{3},{5,7},{6}} => 2
{{1,2,4},{3},{5},{6,7}} => 3
{{1,2,4},{3},{5},{6},{7}} => 4
{{1,2,5,6,7},{3,4}} => 1
{{1,2,5,6},{3,4,7}} => 2
{{1,2,5,6},{3,4},{7}} => 2
{{1,2,5,7},{3,4,6}} => 1
{{1,2,5},{3,4,6,7}} => 2
{{1,2,5},{3,4,6},{7}} => 3
{{1,2,5,7},{3,4},{6}} => 1
{{1,2,5},{3,4,7},{6}} => 3
{{1,2,5},{3,4},{6,7}} => 2
{{1,2,5},{3,4},{6},{7}} => 3
{{1,2,6,7},{3,4,5}} => 1
{{1,2,6},{3,4,5,7}} => 2
{{1,2,6},{3,4,5},{7}} => 2
{{1,2,7},{3,4,5,6}} => 1
{{1,2},{3,4,5,6,7}} => 2
{{1,2},{3,4,5,6},{7}} => 3
{{1,2,7},{3,4,5},{6}} => 1
{{1,2},{3,4,5,7},{6}} => 3
{{1,2},{3,4,5},{6,7}} => 2
{{1,2},{3,4,5},{6},{7}} => 4
{{1,2,6,7},{3,4},{5}} => 1
{{1,2,6},{3,4,7},{5}} => 2
{{1,2,6},{3,4},{5,7}} => 2
{{1,2,6},{3,4},{5},{7}} => 2
{{1,2,7},{3,4,6},{5}} => 1
{{1,2},{3,4,6,7},{5}} => 2
{{1,2},{3,4,6},{5,7}} => 3
{{1,2},{3,4,6},{5},{7}} => 4
{{1,2,7},{3,4},{5,6}} => 1
{{1,2},{3,4,7},{5,6}} => 3
{{1,2},{3,4},{5,6,7}} => 2
{{1,2},{3,4},{5,6},{7}} => 3
{{1,2,7},{3,4},{5},{6}} => 1
{{1,2},{3,4,7},{5},{6}} => 4
{{1,2},{3,4},{5,7},{6}} => 2
{{1,2},{3,4},{5},{6,7}} => 3
{{1,2},{3,4},{5},{6},{7}} => 5
{{1,2,5,6,7},{3},{4}} => 1
{{1,2,5,6},{3,7},{4}} => 2
{{1,2,5,6},{3},{4,7}} => 2
{{1,2,5,6},{3},{4},{7}} => 2
{{1,2,5,7},{3,6},{4}} => 1
{{1,2,5},{3,6,7},{4}} => 2
{{1,2,5},{3,6},{4,7}} => 3
{{1,2,5},{3,6},{4},{7}} => 3
{{1,2,5,7},{3},{4,6}} => 1
{{1,2,5},{3,7},{4,6}} => 3
{{1,2,5},{3},{4,6,7}} => 2
{{1,2,5},{3},{4,6},{7}} => 3
{{1,2,5,7},{3},{4},{6}} => 1
{{1,2,5},{3,7},{4},{6}} => 3
{{1,2,5},{3},{4,7},{6}} => 3
{{1,2,5},{3},{4},{6,7}} => 2
{{1,2,5},{3},{4},{6},{7}} => 3
{{1,2,6,7},{3,5},{4}} => 1
{{1,2,6},{3,5,7},{4}} => 2
{{1,2,6},{3,5},{4,7}} => 2
{{1,2,6},{3,5},{4},{7}} => 2
{{1,2,7},{3,5,6},{4}} => 1
{{1,2},{3,5,6,7},{4}} => 2
{{1,2},{3,5,6},{4,7}} => 3
{{1,2},{3,5,6},{4},{7}} => 3
{{1,2,7},{3,5},{4,6}} => 1
{{1,2},{3,5,7},{4,6}} => 3
{{1,2},{3,5},{4,6,7}} => 2
{{1,2},{3,5},{4,6},{7}} => 4
{{1,2,7},{3,5},{4},{6}} => 1
{{1,2},{3,5,7},{4},{6}} => 2
{{1,2},{3,5},{4,7},{6}} => 4
{{1,2},{3,5},{4},{6,7}} => 3
{{1,2},{3,5},{4},{6},{7}} => 5
{{1,2,6,7},{3},{4,5}} => 1
{{1,2,6},{3,7},{4,5}} => 2
{{1,2,6},{3},{4,5,7}} => 2
{{1,2,6},{3},{4,5},{7}} => 2
{{1,2,7},{3,6},{4,5}} => 1
{{1,2},{3,6,7},{4,5}} => 2
{{1,2},{3,6},{4,5,7}} => 3
{{1,2},{3,6},{4,5},{7}} => 4
{{1,2,7},{3},{4,5,6}} => 1
{{1,2},{3,7},{4,5,6}} => 3
{{1,2},{3},{4,5,6,7}} => 2
{{1,2},{3},{4,5,6},{7}} => 3
{{1,2,7},{3},{4,5},{6}} => 1
{{1,2},{3,7},{4,5},{6}} => 4
{{1,2},{3},{4,5,7},{6}} => 2
{{1,2},{3},{4,5},{6,7}} => 3
{{1,2},{3},{4,5},{6},{7}} => 4
{{1,2,6,7},{3},{4},{5}} => 1
{{1,2,6},{3,7},{4},{5}} => 2
{{1,2,6},{3},{4,7},{5}} => 2
{{1,2,6},{3},{4},{5,7}} => 2
{{1,2,6},{3},{4},{5},{7}} => 2
{{1,2,7},{3,6},{4},{5}} => 1
{{1,2},{3,6,7},{4},{5}} => 3
{{1,2},{3,6},{4,7},{5}} => 4
{{1,2},{3,6},{4},{5,7}} => 2
{{1,2},{3,6},{4},{5},{7}} => 5
{{1,2,7},{3},{4,6},{5}} => 1
{{1,2},{3,7},{4,6},{5}} => 4
{{1,2},{3},{4,6,7},{5}} => 3
{{1,2},{3},{4,6},{5,7}} => 2
{{1,2},{3},{4,6},{5},{7}} => 3
{{1,2,7},{3},{4},{5,6}} => 1
{{1,2},{3,7},{4},{5,6}} => 3
{{1,2},{3},{4,7},{5,6}} => 3
{{1,2},{3},{4},{5,6,7}} => 2
{{1,2},{3},{4},{5,6},{7}} => 4
{{1,2,7},{3},{4},{5},{6}} => 1
{{1,2},{3,7},{4},{5},{6}} => 5
{{1,2},{3},{4,7},{5},{6}} => 2
{{1,2},{3},{4},{5,7},{6}} => 4
{{1,2},{3},{4},{5},{6,7}} => 3
{{1,2},{3},{4},{5},{6},{7}} => 6
{{1,3,4,5,6,7},{2}} => 1
{{1,3,4,5,6},{2,7}} => 2
{{1,3,4,5,6},{2},{7}} => 2
{{1,3,4,5,7},{2,6}} => 1
{{1,3,4,5},{2,6,7}} => 2
{{1,3,4,5},{2,6},{7}} => 3
{{1,3,4,5,7},{2},{6}} => 1
{{1,3,4,5},{2,7},{6}} => 3
{{1,3,4,5},{2},{6,7}} => 2
{{1,3,4,5},{2},{6},{7}} => 3
{{1,3,4,6,7},{2,5}} => 1
{{1,3,4,6},{2,5,7}} => 2
{{1,3,4,6},{2,5},{7}} => 2
{{1,3,4,7},{2,5,6}} => 1
{{1,3,4},{2,5,6,7}} => 2
{{1,3,4},{2,5,6},{7}} => 3
{{1,3,4,7},{2,5},{6}} => 1
{{1,3,4},{2,5,7},{6}} => 3
{{1,3,4},{2,5},{6,7}} => 2
{{1,3,4},{2,5},{6},{7}} => 4
{{1,3,4,6,7},{2},{5}} => 1
{{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}} => 1
{{1,3,4},{2,6,7},{5}} => 2
{{1,3,4},{2,6},{5,7}} => 3
{{1,3,4},{2,6},{5},{7}} => 4
{{1,3,4,7},{2},{5,6}} => 1
{{1,3,4},{2,7},{5,6}} => 3
{{1,3,4},{2},{5,6,7}} => 2
{{1,3,4},{2},{5,6},{7}} => 3
{{1,3,4,7},{2},{5},{6}} => 1
{{1,3,4},{2,7},{5},{6}} => 4
{{1,3,4},{2},{5,7},{6}} => 2
{{1,3,4},{2},{5},{6,7}} => 3
{{1,3,4},{2},{5},{6},{7}} => 4
{{1,3,5,6,7},{2,4}} => 1
{{1,3,5,6},{2,4,7}} => 2
{{1,3,5,6},{2,4},{7}} => 2
{{1,3,5,7},{2,4,6}} => 1
{{1,3,5},{2,4,6,7}} => 2
{{1,3,5},{2,4,6},{7}} => 3
{{1,3,5,7},{2,4},{6}} => 1
{{1,3,5},{2,4,7},{6}} => 3
{{1,3,5},{2,4},{6,7}} => 2
{{1,3,5},{2,4},{6},{7}} => 3
{{1,3,6,7},{2,4,5}} => 1
{{1,3,6},{2,4,5,7}} => 2
{{1,3,6},{2,4,5},{7}} => 2
{{1,3,7},{2,4,5,6}} => 1
{{1,3},{2,4,5,6,7}} => 2
{{1,3},{2,4,5,6},{7}} => 3
{{1,3,7},{2,4,5},{6}} => 1
{{1,3},{2,4,5,7},{6}} => 3
{{1,3},{2,4,5},{6,7}} => 2
{{1,3},{2,4,5},{6},{7}} => 4
{{1,3,6,7},{2,4},{5}} => 1
{{1,3,6},{2,4,7},{5}} => 2
{{1,3,6},{2,4},{5,7}} => 2
{{1,3,6},{2,4},{5},{7}} => 2
{{1,3,7},{2,4,6},{5}} => 1
{{1,3},{2,4,6,7},{5}} => 2
{{1,3},{2,4,6},{5,7}} => 3
{{1,3},{2,4,6},{5},{7}} => 4
{{1,3,7},{2,4},{5,6}} => 1
{{1,3},{2,4,7},{5,6}} => 3
{{1,3},{2,4},{5,6,7}} => 2
{{1,3},{2,4},{5,6},{7}} => 3
{{1,3,7},{2,4},{5},{6}} => 1
{{1,3},{2,4,7},{5},{6}} => 4
{{1,3},{2,4},{5,7},{6}} => 2
{{1,3},{2,4},{5},{6,7}} => 3
{{1,3},{2,4},{5},{6},{7}} => 5
{{1,3,5,6,7},{2},{4}} => 1
{{1,3,5,6},{2,7},{4}} => 2
{{1,3,5,6},{2},{4,7}} => 2
{{1,3,5,6},{2},{4},{7}} => 2
{{1,3,5,7},{2,6},{4}} => 1
{{1,3,5},{2,6,7},{4}} => 2
{{1,3,5},{2,6},{4,7}} => 3
{{1,3,5},{2,6},{4},{7}} => 3
{{1,3,5,7},{2},{4,6}} => 1
{{1,3,5},{2,7},{4,6}} => 3
{{1,3,5},{2},{4,6,7}} => 2
{{1,3,5},{2},{4,6},{7}} => 3
{{1,3,5,7},{2},{4},{6}} => 1
{{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}} => 3
{{1,3,6,7},{2,5},{4}} => 1
{{1,3,6},{2,5,7},{4}} => 2
{{1,3,6},{2,5},{4,7}} => 2
{{1,3,6},{2,5},{4},{7}} => 2
{{1,3,7},{2,5,6},{4}} => 1
{{1,3},{2,5,6,7},{4}} => 2
{{1,3},{2,5,6},{4,7}} => 3
{{1,3},{2,5,6},{4},{7}} => 3
{{1,3,7},{2,5},{4,6}} => 1
{{1,3},{2,5,7},{4,6}} => 3
{{1,3},{2,5},{4,6,7}} => 2
{{1,3},{2,5},{4,6},{7}} => 4
{{1,3,7},{2,5},{4},{6}} => 1
{{1,3},{2,5,7},{4},{6}} => 2
{{1,3},{2,5},{4,7},{6}} => 4
{{1,3},{2,5},{4},{6,7}} => 3
{{1,3},{2,5},{4},{6},{7}} => 5
{{1,3,6,7},{2},{4,5}} => 1
{{1,3,6},{2,7},{4,5}} => 2
{{1,3,6},{2},{4,5,7}} => 2
{{1,3,6},{2},{4,5},{7}} => 2
{{1,3,7},{2,6},{4,5}} => 1
{{1,3},{2,6,7},{4,5}} => 2
{{1,3},{2,6},{4,5,7}} => 3
{{1,3},{2,6},{4,5},{7}} => 4
{{1,3,7},{2},{4,5,6}} => 1
{{1,3},{2,7},{4,5,6}} => 3
{{1,3},{2},{4,5,6,7}} => 2
{{1,3},{2},{4,5,6},{7}} => 3
{{1,3,7},{2},{4,5},{6}} => 1
{{1,3},{2,7},{4,5},{6}} => 4
{{1,3},{2},{4,5,7},{6}} => 2
{{1,3},{2},{4,5},{6,7}} => 3
{{1,3},{2},{4,5},{6},{7}} => 4
{{1,3,6,7},{2},{4},{5}} => 1
{{1,3,6},{2,7},{4},{5}} => 2
{{1,3,6},{2},{4,7},{5}} => 2
{{1,3,6},{2},{4},{5,7}} => 2
{{1,3,6},{2},{4},{5},{7}} => 2
{{1,3,7},{2,6},{4},{5}} => 1
{{1,3},{2,6,7},{4},{5}} => 3
{{1,3},{2,6},{4,7},{5}} => 4
{{1,3},{2,6},{4},{5,7}} => 2
{{1,3},{2,6},{4},{5},{7}} => 5
{{1,3,7},{2},{4,6},{5}} => 1
{{1,3},{2,7},{4,6},{5}} => 4
{{1,3},{2},{4,6,7},{5}} => 3
{{1,3},{2},{4,6},{5,7}} => 2
{{1,3},{2},{4,6},{5},{7}} => 3
{{1,3,7},{2},{4},{5,6}} => 1
{{1,3},{2,7},{4},{5,6}} => 3
{{1,3},{2},{4,7},{5,6}} => 3
{{1,3},{2},{4},{5,6,7}} => 2
{{1,3},{2},{4},{5,6},{7}} => 4
{{1,3,7},{2},{4},{5},{6}} => 1
{{1,3},{2,7},{4},{5},{6}} => 5
{{1,3},{2},{4,7},{5},{6}} => 2
{{1,3},{2},{4},{5,7},{6}} => 4
{{1,3},{2},{4},{5},{6,7}} => 3
{{1,3},{2},{4},{5},{6},{7}} => 5
{{1,4,5,6,7},{2,3}} => 1
{{1,4,5,6},{2,3,7}} => 2
{{1,4,5,6},{2,3},{7}} => 2
{{1,4,5,7},{2,3,6}} => 1
{{1,4,5},{2,3,6,7}} => 2
{{1,4,5},{2,3,6},{7}} => 3
{{1,4,5,7},{2,3},{6}} => 1
{{1,4,5},{2,3,7},{6}} => 3
{{1,4,5},{2,3},{6,7}} => 2
{{1,4,5},{2,3},{6},{7}} => 3
{{1,4,6,7},{2,3,5}} => 1
{{1,4,6},{2,3,5,7}} => 2
{{1,4,6},{2,3,5},{7}} => 2
{{1,4,7},{2,3,5,6}} => 1
{{1,4},{2,3,5,6,7}} => 2
{{1,4},{2,3,5,6},{7}} => 3
{{1,4,7},{2,3,5},{6}} => 1
{{1,4},{2,3,5,7},{6}} => 3
{{1,4},{2,3,5},{6,7}} => 2
{{1,4},{2,3,5},{6},{7}} => 4
{{1,4,6,7},{2,3},{5}} => 1
{{1,4,6},{2,3,7},{5}} => 2
{{1,4,6},{2,3},{5,7}} => 2
{{1,4,6},{2,3},{5},{7}} => 2
{{1,4,7},{2,3,6},{5}} => 1
{{1,4},{2,3,6,7},{5}} => 2
{{1,4},{2,3,6},{5,7}} => 3
{{1,4},{2,3,6},{5},{7}} => 4
{{1,4,7},{2,3},{5,6}} => 1
{{1,4},{2,3,7},{5,6}} => 3
{{1,4},{2,3},{5,6,7}} => 2
{{1,4},{2,3},{5,6},{7}} => 3
{{1,4,7},{2,3},{5},{6}} => 1
{{1,4},{2,3,7},{5},{6}} => 4
{{1,4},{2,3},{5,7},{6}} => 2
{{1,4},{2,3},{5},{6,7}} => 3
{{1,4},{2,3},{5},{6},{7}} => 4
{{1,5,6,7},{2,3,4}} => 1
{{1,5,6},{2,3,4,7}} => 2
{{1,5,6},{2,3,4},{7}} => 2
{{1,5,7},{2,3,4,6}} => 1
{{1,5},{2,3,4,6,7}} => 2
{{1,5},{2,3,4,6},{7}} => 3
{{1,5,7},{2,3,4},{6}} => 1
{{1,5},{2,3,4,7},{6}} => 3
{{1,5},{2,3,4},{6,7}} => 2
{{1,5},{2,3,4},{6},{7}} => 3
{{1,6,7},{2,3,4,5}} => 1
{{1,6},{2,3,4,5,7}} => 2
{{1,6},{2,3,4,5},{7}} => 2
{{1,7},{2,3,4,5,6}} => 1
{{1},{2,3,4,5,6,7}} => 2
{{1},{2,3,4,5,6},{7}} => 3
{{1,7},{2,3,4,5},{6}} => 1
{{1},{2,3,4,5,7},{6}} => 3
{{1},{2,3,4,5},{6,7}} => 2
{{1},{2,3,4,5},{6},{7}} => 4
{{1,6,7},{2,3,4},{5}} => 1
{{1,6},{2,3,4,7},{5}} => 2
{{1,6},{2,3,4},{5,7}} => 2
{{1,6},{2,3,4},{5},{7}} => 2
{{1,7},{2,3,4,6},{5}} => 1
{{1},{2,3,4,6,7},{5}} => 2
{{1},{2,3,4,6},{5,7}} => 3
{{1},{2,3,4,6},{5},{7}} => 4
{{1,7},{2,3,4},{5,6}} => 1
{{1},{2,3,4,7},{5,6}} => 3
{{1},{2,3,4},{5,6,7}} => 2
{{1},{2,3,4},{5,6},{7}} => 3
{{1,7},{2,3,4},{5},{6}} => 1
{{1},{2,3,4,7},{5},{6}} => 4
{{1},{2,3,4},{5,7},{6}} => 2
{{1},{2,3,4},{5},{6,7}} => 3
{{1},{2,3,4},{5},{6},{7}} => 5
{{1,5,6,7},{2,3},{4}} => 1
{{1,5,6},{2,3,7},{4}} => 2
{{1,5,6},{2,3},{4,7}} => 2
{{1,5,6},{2,3},{4},{7}} => 2
{{1,5,7},{2,3,6},{4}} => 1
{{1,5},{2,3,6,7},{4}} => 2
{{1,5},{2,3,6},{4,7}} => 3
{{1,5},{2,3,6},{4},{7}} => 3
{{1,5,7},{2,3},{4,6}} => 1
{{1,5},{2,3,7},{4,6}} => 3
{{1,5},{2,3},{4,6,7}} => 2
{{1,5},{2,3},{4,6},{7}} => 3
{{1,5,7},{2,3},{4},{6}} => 1
{{1,5},{2,3,7},{4},{6}} => 3
{{1,5},{2,3},{4,7},{6}} => 3
{{1,5},{2,3},{4},{6,7}} => 2
{{1,5},{2,3},{4},{6},{7}} => 3
{{1,6,7},{2,3,5},{4}} => 1
{{1,6},{2,3,5,7},{4}} => 2
{{1,6},{2,3,5},{4,7}} => 2
{{1,6},{2,3,5},{4},{7}} => 2
{{1,7},{2,3,5,6},{4}} => 1
{{1},{2,3,5,6,7},{4}} => 2
{{1},{2,3,5,6},{4,7}} => 3
{{1},{2,3,5,6},{4},{7}} => 3
{{1,7},{2,3,5},{4,6}} => 1
{{1},{2,3,5,7},{4,6}} => 3
{{1},{2,3,5},{4,6,7}} => 2
{{1},{2,3,5},{4,6},{7}} => 4
{{1,7},{2,3,5},{4},{6}} => 1
{{1},{2,3,5,7},{4},{6}} => 2
{{1},{2,3,5},{4,7},{6}} => 4
{{1},{2,3,5},{4},{6,7}} => 3
{{1},{2,3,5},{4},{6},{7}} => 5
{{1,6,7},{2,3},{4,5}} => 1
{{1,6},{2,3,7},{4,5}} => 2
{{1,6},{2,3},{4,5,7}} => 2
{{1,6},{2,3},{4,5},{7}} => 2
{{1,7},{2,3,6},{4,5}} => 1
{{1},{2,3,6,7},{4,5}} => 2
{{1},{2,3,6},{4,5,7}} => 3
{{1},{2,3,6},{4,5},{7}} => 4
{{1,7},{2,3},{4,5,6}} => 1
{{1},{2,3,7},{4,5,6}} => 3
{{1},{2,3},{4,5,6,7}} => 2
{{1},{2,3},{4,5,6},{7}} => 3
{{1,7},{2,3},{4,5},{6}} => 1
{{1},{2,3,7},{4,5},{6}} => 4
{{1},{2,3},{4,5,7},{6}} => 2
{{1},{2,3},{4,5},{6,7}} => 3
{{1},{2,3},{4,5},{6},{7}} => 4
{{1,6,7},{2,3},{4},{5}} => 1
{{1,6},{2,3,7},{4},{5}} => 2
{{1,6},{2,3},{4,7},{5}} => 2
{{1,6},{2,3},{4},{5,7}} => 2
{{1,6},{2,3},{4},{5},{7}} => 2
{{1,7},{2,3,6},{4},{5}} => 1
{{1},{2,3,6,7},{4},{5}} => 3
{{1},{2,3,6},{4,7},{5}} => 4
{{1},{2,3,6},{4},{5,7}} => 2
{{1},{2,3,6},{4},{5},{7}} => 5
{{1,7},{2,3},{4,6},{5}} => 1
{{1},{2,3,7},{4,6},{5}} => 4
{{1},{2,3},{4,6,7},{5}} => 3
{{1},{2,3},{4,6},{5,7}} => 2
{{1},{2,3},{4,6},{5},{7}} => 3
{{1,7},{2,3},{4},{5,6}} => 1
{{1},{2,3,7},{4},{5,6}} => 3
{{1},{2,3},{4,7},{5,6}} => 3
{{1},{2,3},{4},{5,6,7}} => 2
{{1},{2,3},{4},{5,6},{7}} => 4
{{1,7},{2,3},{4},{5},{6}} => 1
{{1},{2,3,7},{4},{5},{6}} => 5
{{1},{2,3},{4,7},{5},{6}} => 2
{{1},{2,3},{4},{5,7},{6}} => 4
{{1},{2,3},{4},{5},{6,7}} => 3
{{1},{2,3},{4},{5},{6},{7}} => 6
{{1,4,5,6,7},{2},{3}} => 1
{{1,4,5,6},{2,7},{3}} => 2
{{1,4,5,6},{2},{3,7}} => 2
{{1,4,5,6},{2},{3},{7}} => 2
{{1,4,5,7},{2,6},{3}} => 1
{{1,4,5},{2,6,7},{3}} => 2
{{1,4,5},{2,6},{3,7}} => 3
{{1,4,5},{2,6},{3},{7}} => 3
{{1,4,5,7},{2},{3,6}} => 1
{{1,4,5},{2,7},{3,6}} => 3
{{1,4,5},{2},{3,6,7}} => 2
{{1,4,5},{2},{3,6},{7}} => 3
{{1,4,5,7},{2},{3},{6}} => 1
{{1,4,5},{2,7},{3},{6}} => 3
{{1,4,5},{2},{3,7},{6}} => 3
{{1,4,5},{2},{3},{6,7}} => 2
{{1,4,5},{2},{3},{6},{7}} => 3
{{1,4,6,7},{2,5},{3}} => 1
{{1,4,6},{2,5,7},{3}} => 2
{{1,4,6},{2,5},{3,7}} => 2
{{1,4,6},{2,5},{3},{7}} => 2
{{1,4,7},{2,5,6},{3}} => 1
{{1,4},{2,5,6,7},{3}} => 2
{{1,4},{2,5,6},{3,7}} => 3
{{1,4},{2,5,6},{3},{7}} => 3
{{1,4,7},{2,5},{3,6}} => 1
{{1,4},{2,5,7},{3,6}} => 3
{{1,4},{2,5},{3,6,7}} => 2
{{1,4},{2,5},{3,6},{7}} => 4
{{1,4,7},{2,5},{3},{6}} => 1
{{1,4},{2,5,7},{3},{6}} => 2
{{1,4},{2,5},{3,7},{6}} => 4
{{1,4},{2,5},{3},{6,7}} => 3
{{1,4},{2,5},{3},{6},{7}} => 4
{{1,4,6,7},{2},{3,5}} => 1
{{1,4,6},{2,7},{3,5}} => 2
{{1,4,6},{2},{3,5,7}} => 2
{{1,4,6},{2},{3,5},{7}} => 2
{{1,4,7},{2,6},{3,5}} => 1
{{1,4},{2,6,7},{3,5}} => 2
{{1,4},{2,6},{3,5,7}} => 3
{{1,4},{2,6},{3,5},{7}} => 4
{{1,4,7},{2},{3,5,6}} => 1
{{1,4},{2,7},{3,5,6}} => 3
{{1,4},{2},{3,5,6,7}} => 2
{{1,4},{2},{3,5,6},{7}} => 3
{{1,4,7},{2},{3,5},{6}} => 1
{{1,4},{2,7},{3,5},{6}} => 4
{{1,4},{2},{3,5,7},{6}} => 2
{{1,4},{2},{3,5},{6,7}} => 3
{{1,4},{2},{3,5},{6},{7}} => 4
{{1,4,6,7},{2},{3},{5}} => 1
{{1,4,6},{2,7},{3},{5}} => 2
{{1,4,6},{2},{3,7},{5}} => 2
{{1,4,6},{2},{3},{5,7}} => 2
{{1,4,6},{2},{3},{5},{7}} => 2
{{1,4,7},{2,6},{3},{5}} => 1
{{1,4},{2,6,7},{3},{5}} => 3
{{1,4},{2,6},{3,7},{5}} => 4
{{1,4},{2,6},{3},{5,7}} => 2
{{1,4},{2,6},{3},{5},{7}} => 4
{{1,4,7},{2},{3,6},{5}} => 1
{{1,4},{2,7},{3,6},{5}} => 4
{{1,4},{2},{3,6,7},{5}} => 3
{{1,4},{2},{3,6},{5,7}} => 2
{{1,4},{2},{3,6},{5},{7}} => 4
{{1,4,7},{2},{3},{5,6}} => 1
{{1,4},{2,7},{3},{5,6}} => 3
{{1,4},{2},{3,7},{5,6}} => 3
{{1,4},{2},{3},{5,6,7}} => 2
{{1,4},{2},{3},{5,6},{7}} => 3
{{1,4,7},{2},{3},{5},{6}} => 1
{{1,4},{2,7},{3},{5},{6}} => 4
{{1,4},{2},{3,7},{5},{6}} => 4
{{1,4},{2},{3},{5,7},{6}} => 2
{{1,4},{2},{3},{5},{6,7}} => 3
{{1,4},{2},{3},{5},{6},{7}} => 4
{{1,5,6,7},{2,4},{3}} => 1
{{1,5,6},{2,4,7},{3}} => 2
{{1,5,6},{2,4},{3,7}} => 2
{{1,5,6},{2,4},{3},{7}} => 2
{{1,5,7},{2,4,6},{3}} => 1
{{1,5},{2,4,6,7},{3}} => 2
{{1,5},{2,4,6},{3,7}} => 3
{{1,5},{2,4,6},{3},{7}} => 3
{{1,5,7},{2,4},{3,6}} => 1
{{1,5},{2,4,7},{3,6}} => 3
{{1,5},{2,4},{3,6,7}} => 2
{{1,5},{2,4},{3,6},{7}} => 3
{{1,5,7},{2,4},{3},{6}} => 1
{{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}} => 3
{{1,6,7},{2,4,5},{3}} => 1
{{1,6},{2,4,5,7},{3}} => 2
{{1,6},{2,4,5},{3,7}} => 2
{{1,6},{2,4,5},{3},{7}} => 2
{{1,7},{2,4,5,6},{3}} => 1
{{1},{2,4,5,6,7},{3}} => 2
{{1},{2,4,5,6},{3,7}} => 3
{{1},{2,4,5,6},{3},{7}} => 3
{{1,7},{2,4,5},{3,6}} => 1
{{1},{2,4,5,7},{3,6}} => 3
{{1},{2,4,5},{3,6,7}} => 2
{{1},{2,4,5},{3,6},{7}} => 4
{{1,7},{2,4,5},{3},{6}} => 1
{{1},{2,4,5,7},{3},{6}} => 2
{{1},{2,4,5},{3,7},{6}} => 4
{{1},{2,4,5},{3},{6,7}} => 3
{{1},{2,4,5},{3},{6},{7}} => 4
{{1,6,7},{2,4},{3,5}} => 1
{{1,6},{2,4,7},{3,5}} => 2
{{1,6},{2,4},{3,5,7}} => 2
{{1,6},{2,4},{3,5},{7}} => 2
{{1,7},{2,4,6},{3,5}} => 1
{{1},{2,4,6,7},{3,5}} => 2
{{1},{2,4,6},{3,5,7}} => 3
{{1},{2,4,6},{3,5},{7}} => 4
{{1,7},{2,4},{3,5,6}} => 1
{{1},{2,4,7},{3,5,6}} => 3
{{1},{2,4},{3,5,6,7}} => 2
{{1},{2,4},{3,5,6},{7}} => 3
{{1,7},{2,4},{3,5},{6}} => 1
{{1},{2,4,7},{3,5},{6}} => 4
{{1},{2,4},{3,5,7},{6}} => 2
{{1},{2,4},{3,5},{6,7}} => 3
{{1},{2,4},{3,5},{6},{7}} => 5
{{1,6,7},{2,4},{3},{5}} => 1
{{1,6},{2,4,7},{3},{5}} => 2
{{1,6},{2,4},{3,7},{5}} => 2
{{1,6},{2,4},{3},{5,7}} => 2
{{1,6},{2,4},{3},{5},{7}} => 2
{{1,7},{2,4,6},{3},{5}} => 1
{{1},{2,4,6,7},{3},{5}} => 3
{{1},{2,4,6},{3,7},{5}} => 4
{{1},{2,4,6},{3},{5,7}} => 2
{{1},{2,4,6},{3},{5},{7}} => 3
{{1,7},{2,4},{3,6},{5}} => 1
{{1},{2,4,7},{3,6},{5}} => 4
{{1},{2,4},{3,6,7},{5}} => 3
{{1},{2,4},{3,6},{5,7}} => 2
{{1},{2,4},{3,6},{5},{7}} => 5
{{1,7},{2,4},{3},{5,6}} => 1
{{1},{2,4,7},{3},{5,6}} => 3
{{1},{2,4},{3,7},{5,6}} => 3
{{1},{2,4},{3},{5,6,7}} => 2
{{1},{2,4},{3},{5,6},{7}} => 4
{{1,7},{2,4},{3},{5},{6}} => 1
{{1},{2,4,7},{3},{5},{6}} => 2
{{1},{2,4},{3,7},{5},{6}} => 5
{{1},{2,4},{3},{5,7},{6}} => 3
{{1},{2,4},{3},{5},{6,7}} => 4
{{1},{2,4},{3},{5},{6},{7}} => 6
{{1,5,6,7},{2},{3,4}} => 1
{{1,5,6},{2,7},{3,4}} => 2
{{1,5,6},{2},{3,4,7}} => 2
{{1,5,6},{2},{3,4},{7}} => 2
{{1,5,7},{2,6},{3,4}} => 1
{{1,5},{2,6,7},{3,4}} => 2
{{1,5},{2,6},{3,4,7}} => 3
{{1,5},{2,6},{3,4},{7}} => 3
{{1,5,7},{2},{3,4,6}} => 1
{{1,5},{2,7},{3,4,6}} => 3
{{1,5},{2},{3,4,6,7}} => 2
{{1,5},{2},{3,4,6},{7}} => 3
{{1,5,7},{2},{3,4},{6}} => 1
{{1,5},{2,7},{3,4},{6}} => 3
{{1,5},{2},{3,4,7},{6}} => 3
{{1,5},{2},{3,4},{6,7}} => 2
{{1,5},{2},{3,4},{6},{7}} => 3
{{1,6,7},{2,5},{3,4}} => 1
{{1,6},{2,5,7},{3,4}} => 2
{{1,6},{2,5},{3,4,7}} => 2
{{1,6},{2,5},{3,4},{7}} => 2
{{1,7},{2,5,6},{3,4}} => 1
{{1},{2,5,6,7},{3,4}} => 2
{{1},{2,5,6},{3,4,7}} => 3
{{1},{2,5,6},{3,4},{7}} => 3
{{1,7},{2,5},{3,4,6}} => 1
{{1},{2,5,7},{3,4,6}} => 3
{{1},{2,5},{3,4,6,7}} => 2
{{1},{2,5},{3,4,6},{7}} => 4
{{1,7},{2,5},{3,4},{6}} => 1
{{1},{2,5,7},{3,4},{6}} => 2
{{1},{2,5},{3,4,7},{6}} => 4
{{1},{2,5},{3,4},{6,7}} => 3
{{1},{2,5},{3,4},{6},{7}} => 5
{{1,6,7},{2},{3,4,5}} => 1
{{1,6},{2,7},{3,4,5}} => 2
{{1,6},{2},{3,4,5,7}} => 2
{{1,6},{2},{3,4,5},{7}} => 2
{{1,7},{2,6},{3,4,5}} => 1
{{1},{2,6,7},{3,4,5}} => 2
{{1},{2,6},{3,4,5,7}} => 3
{{1},{2,6},{3,4,5},{7}} => 4
{{1,7},{2},{3,4,5,6}} => 1
{{1},{2,7},{3,4,5,6}} => 3
{{1},{2},{3,4,5,6,7}} => 2
{{1},{2},{3,4,5,6},{7}} => 3
{{1,7},{2},{3,4,5},{6}} => 1
{{1},{2,7},{3,4,5},{6}} => 4
{{1},{2},{3,4,5,7},{6}} => 2
{{1},{2},{3,4,5},{6,7}} => 3
{{1},{2},{3,4,5},{6},{7}} => 4
{{1,6,7},{2},{3,4},{5}} => 1
{{1,6},{2,7},{3,4},{5}} => 2
{{1,6},{2},{3,4,7},{5}} => 2
{{1,6},{2},{3,4},{5,7}} => 2
{{1,6},{2},{3,4},{5},{7}} => 2
{{1,7},{2,6},{3,4},{5}} => 1
{{1},{2,6,7},{3,4},{5}} => 3
{{1},{2,6},{3,4,7},{5}} => 4
{{1},{2,6},{3,4},{5,7}} => 2
{{1},{2,6},{3,4},{5},{7}} => 5
{{1,7},{2},{3,4,6},{5}} => 1
{{1},{2,7},{3,4,6},{5}} => 4
{{1},{2},{3,4,6,7},{5}} => 3
{{1},{2},{3,4,6},{5,7}} => 2
{{1},{2},{3,4,6},{5},{7}} => 3
{{1,7},{2},{3,4},{5,6}} => 1
{{1},{2,7},{3,4},{5,6}} => 3
{{1},{2},{3,4,7},{5,6}} => 3
{{1},{2},{3,4},{5,6,7}} => 2
{{1},{2},{3,4},{5,6},{7}} => 4
{{1,7},{2},{3,4},{5},{6}} => 1
{{1},{2,7},{3,4},{5},{6}} => 5
{{1},{2},{3,4,7},{5},{6}} => 2
{{1},{2},{3,4},{5,7},{6}} => 4
{{1},{2},{3,4},{5},{6,7}} => 3
{{1},{2},{3,4},{5},{6},{7}} => 5
{{1,5,6,7},{2},{3},{4}} => 1
{{1,5,6},{2,7},{3},{4}} => 2
{{1,5,6},{2},{3,7},{4}} => 2
{{1,5,6},{2},{3},{4,7}} => 2
{{1,5,6},{2},{3},{4},{7}} => 2
{{1,5,7},{2,6},{3},{4}} => 1
{{1,5},{2,6,7},{3},{4}} => 2
{{1,5},{2,6},{3,7},{4}} => 3
{{1,5},{2,6},{3},{4,7}} => 3
{{1,5},{2,6},{3},{4},{7}} => 3
{{1,5,7},{2},{3,6},{4}} => 1
{{1,5},{2,7},{3,6},{4}} => 3
{{1,5},{2},{3,6,7},{4}} => 2
{{1,5},{2},{3,6},{4,7}} => 3
{{1,5},{2},{3,6},{4},{7}} => 3
{{1,5,7},{2},{3},{4,6}} => 1
{{1,5},{2,7},{3},{4,6}} => 3
{{1,5},{2},{3,7},{4,6}} => 3
{{1,5},{2},{3},{4,6,7}} => 2
{{1,5},{2},{3},{4,6},{7}} => 3
{{1,5,7},{2},{3},{4},{6}} => 1
{{1,5},{2,7},{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}} => 2
{{1,5},{2},{3},{4},{6},{7}} => 3
{{1,6,7},{2,5},{3},{4}} => 1
{{1,6},{2,5,7},{3},{4}} => 2
{{1,6},{2,5},{3,7},{4}} => 2
{{1,6},{2,5},{3},{4,7}} => 2
{{1,6},{2,5},{3},{4},{7}} => 2
{{1,7},{2,5,6},{3},{4}} => 1
{{1},{2,5,6,7},{3},{4}} => 2
{{1},{2,5,6},{3,7},{4}} => 3
{{1},{2,5,6},{3},{4,7}} => 3
{{1},{2,5,6},{3},{4},{7}} => 4
{{1,7},{2,5},{3,6},{4}} => 1
{{1},{2,5,7},{3,6},{4}} => 2
{{1},{2,5},{3,6,7},{4}} => 3
{{1},{2,5},{3,6},{4,7}} => 4
{{1},{2,5},{3,6},{4},{7}} => 5
{{1,7},{2,5},{3},{4,6}} => 1
{{1},{2,5,7},{3},{4,6}} => 2
{{1},{2,5},{3,7},{4,6}} => 4
{{1},{2,5},{3},{4,6,7}} => 3
{{1},{2,5},{3},{4,6},{7}} => 3
{{1,7},{2,5},{3},{4},{6}} => 1
{{1},{2,5,7},{3},{4},{6}} => 4
{{1},{2,5},{3,7},{4},{6}} => 5
{{1},{2,5},{3},{4,7},{6}} => 2
{{1},{2,5},{3},{4},{6,7}} => 3
{{1},{2,5},{3},{4},{6},{7}} => 6
{{1,6,7},{2},{3,5},{4}} => 1
{{1,6},{2,7},{3,5},{4}} => 2
{{1,6},{2},{3,5,7},{4}} => 2
{{1,6},{2},{3,5},{4,7}} => 2
{{1,6},{2},{3,5},{4},{7}} => 2
{{1,7},{2,6},{3,5},{4}} => 1
{{1},{2,6,7},{3,5},{4}} => 3
{{1},{2,6},{3,5,7},{4}} => 2
{{1},{2,6},{3,5},{4,7}} => 4
{{1},{2,6},{3,5},{4},{7}} => 5
{{1,7},{2},{3,5,6},{4}} => 1
{{1},{2,7},{3,5,6},{4}} => 3
{{1},{2},{3,5,6,7},{4}} => 2
{{1},{2},{3,5,6},{4,7}} => 3
{{1},{2},{3,5,6},{4},{7}} => 4
{{1,7},{2},{3,5},{4,6}} => 1
{{1},{2,7},{3,5},{4,6}} => 4
{{1},{2},{3,5,7},{4,6}} => 2
{{1},{2},{3,5},{4,6,7}} => 3
{{1},{2},{3,5},{4,6},{7}} => 3
{{1,7},{2},{3,5},{4},{6}} => 1
{{1},{2,7},{3,5},{4},{6}} => 5
{{1},{2},{3,5,7},{4},{6}} => 4
{{1},{2},{3,5},{4,7},{6}} => 2
{{1},{2},{3,5},{4},{6,7}} => 3
{{1},{2},{3,5},{4},{6},{7}} => 4
{{1,6,7},{2},{3},{4,5}} => 1
{{1,6},{2,7},{3},{4,5}} => 2
{{1,6},{2},{3,7},{4,5}} => 2
{{1,6},{2},{3},{4,5,7}} => 2
{{1,6},{2},{3},{4,5},{7}} => 2
{{1,7},{2,6},{3},{4,5}} => 1
{{1},{2,6,7},{3},{4,5}} => 3
{{1},{2,6},{3,7},{4,5}} => 4
{{1},{2,6},{3},{4,5,7}} => 2
{{1},{2,6},{3},{4,5},{7}} => 4
{{1,7},{2},{3,6},{4,5}} => 1
{{1},{2,7},{3,6},{4,5}} => 4
{{1},{2},{3,6,7},{4,5}} => 3
{{1},{2},{3,6},{4,5,7}} => 2
{{1},{2},{3,6},{4,5},{7}} => 4
{{1,7},{2},{3},{4,5,6}} => 1
{{1},{2,7},{3},{4,5,6}} => 3
{{1},{2},{3,7},{4,5,6}} => 3
{{1},{2},{3},{4,5,6,7}} => 2
{{1},{2},{3},{4,5,6},{7}} => 3
{{1,7},{2},{3},{4,5},{6}} => 1
{{1},{2,7},{3},{4,5},{6}} => 4
{{1},{2},{3,7},{4,5},{6}} => 4
{{1},{2},{3},{4,5,7},{6}} => 2
{{1},{2},{3},{4,5},{6,7}} => 3
{{1},{2},{3},{4,5},{6},{7}} => 5
{{1,6,7},{2},{3},{4},{5}} => 1
{{1,6},{2,7},{3},{4},{5}} => 2
{{1,6},{2},{3,7},{4},{5}} => 2
{{1,6},{2},{3},{4,7},{5}} => 2
{{1,6},{2},{3},{4},{5,7}} => 2
{{1,6},{2},{3},{4},{5},{7}} => 2
{{1,7},{2,6},{3},{4},{5}} => 1
{{1},{2,6,7},{3},{4},{5}} => 3
{{1},{2,6},{3,7},{4},{5}} => 5
{{1},{2,6},{3},{4,7},{5}} => 2
{{1},{2,6},{3},{4},{5,7}} => 4
{{1},{2,6},{3},{4},{5},{7}} => 6
{{1,7},{2},{3,6},{4},{5}} => 1
{{1},{2,7},{3,6},{4},{5}} => 5
{{1},{2},{3,6,7},{4},{5}} => 3
{{1},{2},{3,6},{4,7},{5}} => 2
{{1},{2},{3,6},{4},{5,7}} => 4
{{1},{2},{3,6},{4},{5},{7}} => 3
{{1,7},{2},{3},{4,6},{5}} => 1
{{1},{2,7},{3},{4,6},{5}} => 3
{{1},{2},{3,7},{4,6},{5}} => 3
{{1},{2},{3},{4,6,7},{5}} => 2
{{1},{2},{3},{4,6},{5,7}} => 3
{{1},{2},{3},{4,6},{5},{7}} => 5
{{1,7},{2},{3},{4},{5,6}} => 1
{{1},{2,7},{3},{4},{5,6}} => 4
{{1},{2},{3,7},{4},{5,6}} => 4
{{1},{2},{3},{4,7},{5,6}} => 2
{{1},{2},{3},{4},{5,6,7}} => 3
{{1},{2},{3},{4},{5,6},{7}} => 4
{{1,7},{2},{3},{4},{5},{6}} => 1
{{1},{2,7},{3},{4},{5},{6}} => 6
{{1},{2},{3,7},{4},{5},{6}} => 2
{{1},{2},{3},{4,7},{5},{6}} => 5
{{1},{2},{3},{4},{5,7},{6}} => 3
{{1},{2},{3},{4},{5},{6,7}} => 4
{{1},{2},{3},{4},{5},{6},{7}} => 7
{{1,2},{3,4},{5,6},{7,8}} => 3
{{1,3},{2,4},{5,6},{7,8}} => 3
{{1,4},{2,3},{5,6},{7,8}} => 3
{{1,5},{2,3},{4,6},{7,8}} => 3
{{1,6},{2,3},{4,5},{7,8}} => 2
{{1,7},{2,3},{4,5},{6,8}} => 2
{{1,8},{2,3},{4,5},{6,7}} => 1
{{1,8},{2,4},{3,5},{6,7}} => 1
{{1,7},{2,4},{3,5},{6,8}} => 2
{{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}} => 3
{{1,2},{3,6},{4,5},{7,8}} => 3
{{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}} => 2
{{1,8},{2,5},{3,4},{6,7}} => 1
{{1,8},{2,6},{3,4},{5,7}} => 1
{{1,7},{2,6},{3,4},{5,8}} => 2
{{1,6},{2,7},{3,4},{5,8}} => 3
{{1,5},{2,7},{3,4},{6,8}} => 2
{{1,4},{2,7},{3,5},{6,8}} => 2
{{1,3},{2,7},{4,5},{6,8}} => 2
{{1,2},{3,7},{4,5},{6,8}} => 2
{{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}} => 3
{{1,7},{2,8},{3,4},{5,6}} => 2
{{1,8},{2,7},{3,4},{5,6}} => 1
{{1,8},{2,7},{3,5},{4,6}} => 1
{{1,7},{2,8},{3,5},{4,6}} => 2
{{1,6},{2,8},{3,5},{4,7}} => 3
{{1,5},{2,8},{3,6},{4,7}} => 4
{{1,4},{2,8},{3,6},{5,7}} => 4
{{1,3},{2,8},{4,6},{5,7}} => 4
{{1,2},{3,8},{4,6},{5,7}} => 4
{{1,2},{3,7},{4,6},{5,8}} => 4
{{1,3},{2,7},{4,6},{5,8}} => 4
{{1,4},{2,7},{3,6},{5,8}} => 4
{{1,5},{2,7},{3,6},{4,8}} => 4
{{1,6},{2,7},{3,5},{4,8}} => 3
{{1,7},{2,6},{3,5},{4,8}} => 2
{{1,8},{2,6},{3,5},{4,7}} => 1
{{1,8},{2,5},{3,6},{4,7}} => 1
{{1,7},{2,5},{3,6},{4,8}} => 2
{{1,6},{2,5},{3,7},{4,8}} => 3
{{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}} => 4
{{1,2},{3,6},{4,7},{5,8}} => 4
{{1,2},{3,5},{4,7},{6,8}} => 2
{{1,3},{2,5},{4,7},{6,8}} => 2
{{1,4},{2,5},{3,7},{6,8}} => 2
{{1,5},{2,4},{3,7},{6,8}} => 2
{{1,6},{2,4},{3,7},{5,8}} => 3
{{1,7},{2,4},{3,6},{5,8}} => 2
{{1,8},{2,4},{3,6},{5,7}} => 1
{{1,8},{2,3},{4,6},{5,7}} => 1
{{1,7},{2,3},{4,6},{5,8}} => 2
{{1,6},{2,3},{4,7},{5,8}} => 3
{{1,5},{2,3},{4,7},{6,8}} => 2
{{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}} => 3
{{1,3},{2,4},{5,8},{6,7}} => 3
{{1,4},{2,3},{5,8},{6,7}} => 3
{{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}} => 2
{{1,8},{2,3},{4,7},{5,6}} => 1
{{1,8},{2,4},{3,7},{5,6}} => 1
{{1,7},{2,4},{3,8},{5,6}} => 2
{{1,6},{2,4},{3,8},{5,7}} => 3
{{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}} => 4
{{1,3},{2,6},{4,8},{5,7}} => 4
{{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}} => 2
{{1,8},{2,5},{3,7},{4,6}} => 1
{{1,8},{2,6},{3,7},{4,5}} => 1
{{1,7},{2,6},{3,8},{4,5}} => 2
{{1,6},{2,7},{3,8},{4,5}} => 3
{{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}} => 4
{{1,2},{3,7},{4,8},{5,6}} => 4
{{1,2},{3,8},{4,7},{5,6}} => 4
{{1,3},{2,8},{4,7},{5,6}} => 4
{{1,4},{2,8},{3,7},{5,6}} => 4
{{1,5},{2,8},{3,7},{4,6}} => 4
{{1,6},{2,8},{3,7},{4,5}} => 3
{{1,7},{2,8},{3,6},{4,5}} => 2
{{1,8},{2,7},{3,6},{4,5}} => 1
{{1},{2},{3,4,5,6,7,8}} => 2
{{1},{2,4,5,6,7,8},{3}} => 2
{{1},{2,3,5,6,7,8},{4}} => 2
{{1},{2,3,4,6,7,8},{5}} => 2
{{1},{2,3,4,5,8},{6},{7}} => 4
{{1},{2,3,4,5,7,8},{6}} => 2
{{1},{2,3,4,5,6,7},{8}} => 3
{{1},{2,3,4,8},{5,6,7}} => 3
{{1},{2,3,4,5,8},{6,7}} => 3
{{1},{2,3,4,5,6,8},{7}} => 3
{{1},{2,3,4,5,6,7,8}} => 2
{{1,2},{3,4,5,6,7,8}} => 2
{{1,4,5,6,7,8},{2},{3}} => 1
{{1,3,5,6,7,8},{2},{4}} => 1
{{1,3,4,5,6,7,8},{2}} => 1
{{1,4,5,6,7,8},{2,3}} => 1
{{1,2,4,5,6,7,8},{3}} => 1
{{1,2,5,6,7,8},{3,4}} => 1
{{1,2,3,5,6,7},{4},{8}} => 2
{{1,2,3,5,6,7,8},{4}} => 1
{{1,2,3,6,7,8},{4,5}} => 1
{{1,2,3,4,7},{5},{6},{8}} => 2
{{1,2,3,4,6,7},{5},{8}} => 2
{{1,2,3,4,6,7,8},{5}} => 1
{{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}} => 1
{{1,2,3,4,5,7},{6},{8}} => 2
{{1,2,3,4,5,7,8},{6}} => 1
{{1,2,3,4,5,6,7},{8}} => 2
{{1,8},{2,3,4,5,6,7}} => 1
{{1,2,3,4,5,8},{6,7}} => 1
{{1,2,3,4,5,6,8},{7}} => 1
{{1,2,3,4,5,6,7,8}} => 1
{{1,3,5,6,7,8},{2,4}} => 1
{{1,3,4,6,7,8},{2,5}} => 1
{{1,2,4,6,7,8},{3,5}} => 1
{{1,3,4,5,7,8},{2,6}} => 1
{{1,2,4,5,7,8},{3,6}} => 1
{{1,2,3,5,7,8},{4,6}} => 1
{{1,3,4,5,6,8},{2,7}} => 1
{{1,2,4,5,6,8},{3,7}} => 1
{{1,2,3,5,6,8},{4,7}} => 1
{{1,2,3,4,6,8},{5,7}} => 1
{{1,3,4,5,6,7},{2,8}} => 2
{{1,2,4,5,6,7},{3,8}} => 2
{{1,2,3,5,6,7},{4,8}} => 2
{{1,2,3,4,6,7},{5,8}} => 2
{{1,2,3,4,5,7},{6,8}} => 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}} => 2
{{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
{{1,2,3,4,5,6,8},{7},{9}} => 2
{{1},{2,3,4,5,6,7,9},{8}} => 3
{{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}} => 3
{{1},{2,3,4,5,6,8,9},{7}} => 2
{{1,2},{3,4},{5,6},{7,8},{9,10}} => 3
{{1,4},{2,3},{5,6},{7,8},{9,10}} => 3
{{1,6},{2,3},{4,5},{7,8},{9,10}} => 3
{{1,8},{2,3},{4,5},{6,7},{9,10}} => 2
{{1,10},{2,3},{4,5},{6,7},{8,9}} => 1
{{1,2},{3,6},{4,5},{7,8},{9,10}} => 3
{{1,6},{2,5},{3,4},{7,8},{9,10}} => 3
{{1,8},{2,5},{3,4},{6,7},{9,10}} => 2
{{1,10},{2,5},{3,4},{6,7},{8,9}} => 1
{{1,2},{3,8},{4,5},{6,7},{9,10}} => 3
{{1,8},{2,7},{3,4},{5,6},{9,10}} => 2
{{1,10},{2,7},{3,4},{5,6},{8,9}} => 1
{{1,2},{3,10},{4,5},{6,7},{8,9}} => 4
{{1,10},{2,9},{3,4},{5,6},{7,8}} => 1
{{1,2},{3,4},{5,8},{6,7},{9,10}} => 3
{{1,4},{2,3},{5,8},{6,7},{9,10}} => 3
{{1,8},{2,3},{4,7},{5,6},{9,10}} => 2
{{1,10},{2,3},{4,7},{5,6},{8,9}} => 1
{{1,2},{3,8},{4,7},{5,6},{9,10}} => 4
{{1,8},{2,7},{3,6},{4,5},{9,10}} => 2
{{1,10},{2,7},{3,6},{4,5},{8,9}} => 1
{{1,2},{3,10},{4,7},{5,6},{8,9}} => 4
{{1,10},{2,9},{3,6},{4,5},{7,8}} => 1
{{1,2},{3,4},{5,10},{6,7},{8,9}} => 4
{{1,4},{2,3},{5,10},{6,7},{8,9}} => 4
{{1,10},{2,3},{4,9},{5,6},{7,8}} => 1
{{1,2},{3,10},{4,9},{5,6},{7,8}} => 4
{{1,10},{2,9},{3,8},{4,5},{6,7}} => 1
{{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}} => 2
{{1,10},{2,3},{4,5},{6,9},{7,8}} => 1
{{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}} => 1
{{1,2},{3,10},{4,5},{6,9},{7,8}} => 4
{{1,10},{2,9},{3,4},{5,8},{6,7}} => 1
{{1,2},{3,4},{5,10},{6,9},{7,8}} => 4
{{1,4},{2,3},{5,10},{6,9},{7,8}} => 4
{{1,10},{2,3},{4,9},{5,8},{6,7}} => 1
{{1,2},{3,10},{4,9},{5,8},{6,7}} => 5
{{1,10},{2,9},{3,8},{4,7},{5,6}} => 1
{{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}} => 3
{{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}} => 3
{{1,2},{3,4},{5,6},{7,8},{9,12},{10,11}} => 4
{{1,2},{3,4},{5,6},{7,10},{8,9},{11,12}} => 3
{{1,2},{3,4},{5,6},{7,12},{8,9},{10,11}} => 4
{{1,2},{3,4},{5,6},{7,12},{8,11},{9,10}} => 3
{{1,2},{3,4},{5,8},{6,7},{9,10},{11,12}} => 4
{{1,2},{3,4},{5,8},{6,7},{9,12},{10,11}} => 4
{{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}} => 4
{{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}} => 3
{{1,2},{3,4},{5,12},{6,9},{7,8},{10,11}} => 4
{{1,2},{3,4},{5,12},{6,11},{7,8},{9,10}} => 5
{{1,2},{3,4},{5,12},{6,11},{7,10},{8,9}} => 5
{{1,2},{3,6},{4,5},{7,8},{9,10},{11,12}} => 3
{{1,2},{3,6},{4,5},{7,8},{9,12},{10,11}} => 4
{{1,2},{3,6},{4,5},{7,10},{8,9},{11,12}} => 3
{{1,2},{3,6},{4,5},{7,12},{8,9},{10,11}} => 4
{{1,2},{3,6},{4,5},{7,12},{8,11},{9,10}} => 3
{{1,2},{3,8},{4,5},{6,7},{9,10},{11,12}} => 4
{{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}} => 4
{{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}} => 4
{{1,2},{3,12},{4,5},{6,11},{7,8},{9,10}} => 5
{{1,2},{3,12},{4,5},{6,11},{7,10},{8,9}} => 5
{{1,2},{3,8},{4,7},{5,6},{9,10},{11,12}} => 4
{{1,2},{3,8},{4,7},{5,6},{9,12},{10,11}} => 3
{{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}} => 4
{{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}} => 4
{{1,2},{3,12},{4,11},{5,6},{7,8},{9,10}} => 5
{{1,2},{3,12},{4,11},{5,6},{7,10},{8,9}} => 5
{{1,2},{3,10},{4,9},{5,8},{6,7},{11,12}} => 5
{{1,2},{3,12},{4,9},{5,8},{6,7},{10,11}} => 5
{{1,2},{3,12},{4,11},{5,8},{6,7},{9,10}} => 5
{{1,2},{3,12},{4,11},{5,10},{6,7},{8,9}} => 5
{{1,2},{3,12},{4,11},{5,10},{6,9},{7,8}} => 6
{{1,4},{2,3},{5,6},{7,8},{9,10},{11,12}} => 3
{{1,4},{2,3},{5,6},{7,8},{9,12},{10,11}} => 4
{{1,4},{2,3},{5,6},{7,10},{8,9},{11,12}} => 3
{{1,4},{2,3},{5,6},{7,12},{8,9},{10,11}} => 4
{{1,4},{2,3},{5,6},{7,12},{8,11},{9,10}} => 3
{{1,4},{2,3},{5,8},{6,7},{9,10},{11,12}} => 4
{{1,4},{2,3},{5,8},{6,7},{9,12},{10,11}} => 4
{{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}} => 4
{{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}} => 3
{{1,4},{2,3},{5,12},{6,9},{7,8},{10,11}} => 4
{{1,4},{2,3},{5,12},{6,11},{7,8},{9,10}} => 5
{{1,4},{2,3},{5,12},{6,11},{7,10},{8,9}} => 5
{{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}} => 4
{{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}} => 4
{{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}} => 2
{{1,10},{2,3},{4,5},{6,7},{8,9},{11,12}} => 2
{{1,12},{2,3},{4,5},{6,7},{8,9},{10,11}} => 1
{{1,12},{2,3},{4,5},{6,7},{8,11},{9,10}} => 1
{{1,10},{2,3},{4,5},{6,9},{7,8},{11,12}} => 2
{{1,12},{2,3},{4,5},{6,9},{7,8},{10,11}} => 1
{{1,12},{2,3},{4,5},{6,11},{7,8},{9,10}} => 1
{{1,12},{2,3},{4,5},{6,11},{7,10},{8,9}} => 1
{{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}} => 2
{{1,10},{2,3},{4,7},{5,6},{8,9},{11,12}} => 2
{{1,12},{2,3},{4,7},{5,6},{8,9},{10,11}} => 1
{{1,12},{2,3},{4,7},{5,6},{8,11},{9,10}} => 1
{{1,10},{2,3},{4,9},{5,6},{7,8},{11,12}} => 2
{{1,12},{2,3},{4,9},{5,6},{7,8},{10,11}} => 1
{{1,12},{2,3},{4,11},{5,6},{7,8},{9,10}} => 1
{{1,12},{2,3},{4,11},{5,6},{7,10},{8,9}} => 1
{{1,10},{2,3},{4,9},{5,8},{6,7},{11,12}} => 2
{{1,12},{2,3},{4,9},{5,8},{6,7},{10,11}} => 1
{{1,12},{2,3},{4,11},{5,8},{6,7},{9,10}} => 1
{{1,12},{2,3},{4,11},{5,10},{6,7},{8,9}} => 1
{{1,12},{2,3},{4,11},{5,10},{6,9},{7,8}} => 1
{{1,6},{2,5},{3,4},{7,8},{9,10},{11,12}} => 3
{{1,6},{2,5},{3,4},{7,8},{9,12},{10,11}} => 4
{{1,6},{2,5},{3,4},{7,10},{8,9},{11,12}} => 3
{{1,6},{2,5},{3,4},{7,12},{8,9},{10,11}} => 4
{{1,6},{2,5},{3,4},{7,12},{8,11},{9,10}} => 3
{{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}} => 2
{{1,10},{2,5},{3,4},{6,7},{8,9},{11,12}} => 2
{{1,12},{2,5},{3,4},{6,7},{8,9},{10,11}} => 1
{{1,12},{2,5},{3,4},{6,7},{8,11},{9,10}} => 1
{{1,10},{2,5},{3,4},{6,9},{7,8},{11,12}} => 2
{{1,12},{2,5},{3,4},{6,9},{7,8},{10,11}} => 1
{{1,12},{2,5},{3,4},{6,11},{7,8},{9,10}} => 1
{{1,12},{2,5},{3,4},{6,11},{7,10},{8,9}} => 1
{{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}} => 2
{{1,10},{2,7},{3,4},{5,6},{8,9},{11,12}} => 2
{{1,12},{2,7},{3,4},{5,6},{8,9},{10,11}} => 1
{{1,12},{2,7},{3,4},{5,6},{8,11},{9,10}} => 1
{{1,10},{2,9},{3,4},{5,6},{7,8},{11,12}} => 2
{{1,12},{2,9},{3,4},{5,6},{7,8},{10,11}} => 1
{{1,12},{2,11},{3,4},{5,6},{7,8},{9,10}} => 1
{{1,12},{2,11},{3,4},{5,6},{7,10},{8,9}} => 1
{{1,10},{2,9},{3,4},{5,8},{6,7},{11,12}} => 2
{{1,12},{2,9},{3,4},{5,8},{6,7},{10,11}} => 1
{{1,12},{2,11},{3,4},{5,8},{6,7},{9,10}} => 1
{{1,12},{2,11},{3,4},{5,10},{6,7},{8,9}} => 1
{{1,12},{2,11},{3,4},{5,10},{6,9},{7,8}} => 1
{{1,8},{2,7},{3,6},{4,5},{9,10},{11,12}} => 3
{{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}} => 2
{{1,12},{2,7},{3,6},{4,5},{8,9},{10,11}} => 1
{{1,12},{2,7},{3,6},{4,5},{8,11},{9,10}} => 1
{{1,10},{2,9},{3,6},{4,5},{7,8},{11,12}} => 2
{{1,12},{2,9},{3,6},{4,5},{7,8},{10,11}} => 1
{{1,12},{2,11},{3,6},{4,5},{7,8},{9,10}} => 1
{{1,12},{2,11},{3,6},{4,5},{7,10},{8,9}} => 1
{{1,10},{2,9},{3,8},{4,5},{6,7},{11,12}} => 2
{{1,12},{2,9},{3,8},{4,5},{6,7},{10,11}} => 1
{{1,12},{2,11},{3,8},{4,5},{6,7},{9,10}} => 1
{{1,12},{2,11},{3,10},{4,5},{6,7},{8,9}} => 1
{{1,12},{2,11},{3,10},{4,5},{6,9},{7,8}} => 1
{{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}} => 1
{{1,12},{2,11},{3,8},{4,7},{5,6},{9,10}} => 1
{{1,12},{2,11},{3,10},{4,7},{5,6},{8,9}} => 1
{{1,12},{2,11},{3,10},{4,9},{5,6},{7,8}} => 1
{{1,12},{2,11},{3,10},{4,9},{5,8},{6,7}} => 1
-----------------------------------------------------------------------------
Created: Nov 18, 2017 at 18:23 by Martin Rubey
-----------------------------------------------------------------------------
Last Updated: Apr 03, 2018 at 21:07 by Martin Rubey