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-----------------------------------------------------------------------------
Statistic identifier: St001048
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Collection: Perfect matchings
-----------------------------------------------------------------------------
Description: The number of leaves in the subtree containing 1 in the decreasing labelled binary unordered tree associated with the perfect matching.
The bijection between perfect matchings of $\{1,\dots,2n\}$ and trees with $n+1$ leaves is described in Example 5.2.6 of [1].
This statistic is the difference between [[St001045]] and $n+1$.
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References: [1] Stanley, R. P. Enumerative combinatorics. Vol. 2 [[MathSciNet:1676282]]
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Code:
def statistic(m):
T = matching_to_tree(m)
if 1 in T[0].leaf_labels():
return len(T[0].leaf_labels())
return len(T[1].leaf_labels())
def matching_to_tree(m):
"""
INPUT:
- m, a PerfectMatching on {1,...,2n}.
OUTPUT:
a decreasingly labelled, unordered full binary tree with n+1 leaves.
EXAMPLES::
sage: m = PerfectMatching([(1,4),(2,9),(3,10),(5,7),(6,8),(11,12)])
sage: ascii_art(matching_to_tree(m))
"""
# the children of the smallest label are the largest remaining
# element and its partner
trees = [LabelledRootedTree([LabelledRootedTree([], label=i),
LabelledRootedTree([], label=j)]) for i, j in m]
max_label = m.size()//2+1 # last labelled node
while len(trees) > 1:
max_label += 1
# find tree with smallest child and both children smaller than max_label
A = sorted([T for T in trees if max(T[0].label(), T[1].label()) < max_label],
key = lambda T: min(T[0].label(), T[1].label()))[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 T[0].label() == max_label or T[1].label() == max_label).next()
trees.remove(B)
# replace B with [B[0], A] or [B[1], A]
if B[0].label() == max_label:
C = LabelledRootedTree([A, B[1]])
else:
C = LabelledRootedTree([A, B[0]])
trees.append(C)
return trees[0]
-----------------------------------------------------------------------------
Statistic values:
[(1,2)] => 1
[(1,2),(3,4)] => 2
[(1,3),(2,4)] => 2
[(1,4),(2,3)] => 1
[(1,2),(3,4),(5,6)] => 2
[(1,3),(2,4),(5,6)] => 2
[(1,4),(2,3),(5,6)] => 2
[(1,5),(2,3),(4,6)] => 3
[(1,6),(2,3),(4,5)] => 1
[(1,6),(2,4),(3,5)] => 1
[(1,5),(2,4),(3,6)] => 3
[(1,4),(2,5),(3,6)] => 3
[(1,3),(2,5),(4,6)] => 3
[(1,2),(3,5),(4,6)] => 3
[(1,2),(3,6),(4,5)] => 3
[(1,3),(2,6),(4,5)] => 3
[(1,4),(2,6),(3,5)] => 3
[(1,5),(2,6),(3,4)] => 3
[(1,6),(2,5),(3,4)] => 1
[(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)] => 3
[(1,7),(2,3),(4,5),(6,8)] => 3
[(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)] => 3
[(1,6),(2,4),(3,5),(7,8)] => 3
[(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)] => 3
[(1,7),(2,5),(3,4),(6,8)] => 3
[(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)] => 4
[(1,6),(2,7),(3,4),(5,8)] => 4
[(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)] => 4
[(1,3),(2,8),(4,5),(6,7)] => 4
[(1,4),(2,8),(3,5),(6,7)] => 4
[(1,5),(2,8),(3,4),(6,7)] => 4
[(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)] => 1
[(1,8),(2,7),(3,5),(4,6)] => 1
[(1,7),(2,8),(3,5),(4,6)] => 4
[(1,6),(2,8),(3,5),(4,7)] => 4
[(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)] => 4
[(1,7),(2,6),(3,5),(4,8)] => 4
[(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)] => 4
[(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)] => 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)] => 4
[(1,7),(2,4),(3,6),(5,8)] => 4
[(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)] => 4
[(1,6),(2,3),(4,7),(5,8)] => 4
[(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)] => 4
[(1,3),(2,4),(5,8),(6,7)] => 4
[(1,4),(2,3),(5,8),(6,7)] => 4
[(1,5),(2,3),(4,8),(6,7)] => 4
[(1,6),(2,3),(4,8),(5,7)] => 4
[(1,7),(2,3),(4,8),(5,6)] => 4
[(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)] => 4
[(1,6),(2,4),(3,8),(5,7)] => 4
[(1,5),(2,4),(3,8),(6,7)] => 4
[(1,4),(2,5),(3,8),(6,7)] => 4
[(1,3),(2,5),(4,8),(6,7)] => 4
[(1,2),(3,5),(4,8),(6,7)] => 4
[(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)] => 4
[(1,7),(2,5),(3,8),(4,6)] => 4
[(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)] => 4
[(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)] => 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)] => 4
[(1,7),(2,8),(3,6),(4,5)] => 4
[(1,8),(2,7),(3,6),(4,5)] => 1
[(1,2),(3,4),(5,6),(7,8),(9,10)] => 4
[(1,3),(2,4),(5,6),(7,8),(9,10)] => 4
[(1,4),(2,3),(5,6),(7,8),(9,10)] => 4
[(1,5),(2,3),(4,6),(7,8),(9,10)] => 4
[(1,6),(2,3),(4,5),(7,8),(9,10)] => 4
[(1,7),(2,3),(4,5),(6,8),(9,10)] => 4
[(1,8),(2,3),(4,5),(6,7),(9,10)] => 3
[(1,9),(2,3),(4,5),(6,7),(8,10)] => 4
[(1,10),(2,3),(4,5),(6,7),(8,9)] => 1
[(1,10),(2,4),(3,5),(6,7),(8,9)] => 1
[(1,9),(2,4),(3,5),(6,7),(8,10)] => 4
[(1,8),(2,4),(3,5),(6,7),(9,10)] => 3
[(1,7),(2,4),(3,5),(6,8),(9,10)] => 4
[(1,6),(2,4),(3,5),(7,8),(9,10)] => 4
[(1,5),(2,4),(3,6),(7,8),(9,10)] => 4
[(1,4),(2,5),(3,6),(7,8),(9,10)] => 4
[(1,3),(2,5),(4,6),(7,8),(9,10)] => 4
[(1,2),(3,5),(4,6),(7,8),(9,10)] => 4
[(1,2),(3,6),(4,5),(7,8),(9,10)] => 4
[(1,3),(2,6),(4,5),(7,8),(9,10)] => 4
[(1,4),(2,6),(3,5),(7,8),(9,10)] => 4
[(1,5),(2,6),(3,4),(7,8),(9,10)] => 4
[(1,6),(2,5),(3,4),(7,8),(9,10)] => 4
[(1,7),(2,5),(3,4),(6,8),(9,10)] => 4
[(1,8),(2,5),(3,4),(6,7),(9,10)] => 3
[(1,9),(2,5),(3,4),(6,7),(8,10)] => 4
[(1,10),(2,5),(3,4),(6,7),(8,9)] => 1
[(1,10),(2,6),(3,4),(5,7),(8,9)] => 1
[(1,9),(2,6),(3,4),(5,7),(8,10)] => 4
[(1,8),(2,6),(3,4),(5,7),(9,10)] => 3
[(1,7),(2,6),(3,4),(5,8),(9,10)] => 4
[(1,6),(2,7),(3,4),(5,8),(9,10)] => 4
[(1,5),(2,7),(3,4),(6,8),(9,10)] => 4
[(1,4),(2,7),(3,5),(6,8),(9,10)] => 4
[(1,3),(2,7),(4,5),(6,8),(9,10)] => 4
[(1,2),(3,7),(4,5),(6,8),(9,10)] => 4
[(1,2),(3,8),(4,5),(6,7),(9,10)] => 3
[(1,3),(2,8),(4,5),(6,7),(9,10)] => 3
[(1,4),(2,8),(3,5),(6,7),(9,10)] => 3
[(1,5),(2,8),(3,4),(6,7),(9,10)] => 3
[(1,6),(2,8),(3,4),(5,7),(9,10)] => 3
[(1,7),(2,8),(3,4),(5,6),(9,10)] => 4
[(1,8),(2,7),(3,4),(5,6),(9,10)] => 4
[(1,9),(2,7),(3,4),(5,6),(8,10)] => 3
[(1,10),(2,7),(3,4),(5,6),(8,9)] => 1
[(1,10),(2,8),(3,4),(5,6),(7,9)] => 1
[(1,9),(2,8),(3,4),(5,6),(7,10)] => 4
[(1,8),(2,9),(3,4),(5,6),(7,10)] => 4
[(1,7),(2,9),(3,4),(5,6),(8,10)] => 3
[(1,6),(2,9),(3,4),(5,7),(8,10)] => 4
[(1,5),(2,9),(3,4),(6,7),(8,10)] => 4
[(1,4),(2,9),(3,5),(6,7),(8,10)] => 4
[(1,3),(2,9),(4,5),(6,7),(8,10)] => 4
[(1,2),(3,9),(4,5),(6,7),(8,10)] => 4
[(1,2),(3,10),(4,5),(6,7),(8,9)] => 5
[(1,3),(2,10),(4,5),(6,7),(8,9)] => 5
[(1,4),(2,10),(3,5),(6,7),(8,9)] => 5
[(1,5),(2,10),(3,4),(6,7),(8,9)] => 5
[(1,6),(2,10),(3,4),(5,7),(8,9)] => 5
[(1,7),(2,10),(3,4),(5,6),(8,9)] => 5
[(1,8),(2,10),(3,4),(5,6),(7,9)] => 5
[(1,9),(2,10),(3,4),(5,6),(7,8)] => 5
[(1,10),(2,9),(3,4),(5,6),(7,8)] => 1
[(1,10),(2,9),(3,5),(4,6),(7,8)] => 1
[(1,9),(2,10),(3,5),(4,6),(7,8)] => 5
[(1,8),(2,10),(3,5),(4,6),(7,9)] => 5
[(1,7),(2,10),(3,5),(4,6),(8,9)] => 5
[(1,6),(2,10),(3,5),(4,7),(8,9)] => 5
[(1,5),(2,10),(3,6),(4,7),(8,9)] => 5
[(1,4),(2,10),(3,6),(5,7),(8,9)] => 5
[(1,3),(2,10),(4,6),(5,7),(8,9)] => 5
[(1,2),(3,10),(4,6),(5,7),(8,9)] => 5
[(1,2),(3,9),(4,6),(5,7),(8,10)] => 4
[(1,3),(2,9),(4,6),(5,7),(8,10)] => 4
[(1,4),(2,9),(3,6),(5,7),(8,10)] => 4
[(1,5),(2,9),(3,6),(4,7),(8,10)] => 4
[(1,6),(2,9),(3,5),(4,7),(8,10)] => 4
[(1,7),(2,9),(3,5),(4,6),(8,10)] => 3
[(1,8),(2,9),(3,5),(4,6),(7,10)] => 4
[(1,9),(2,8),(3,5),(4,6),(7,10)] => 4
[(1,10),(2,8),(3,5),(4,6),(7,9)] => 1
[(1,10),(2,7),(3,5),(4,6),(8,9)] => 1
[(1,9),(2,7),(3,5),(4,6),(8,10)] => 3
[(1,8),(2,7),(3,5),(4,6),(9,10)] => 4
[(1,7),(2,8),(3,5),(4,6),(9,10)] => 4
[(1,6),(2,8),(3,5),(4,7),(9,10)] => 3
[(1,5),(2,8),(3,6),(4,7),(9,10)] => 3
[(1,4),(2,8),(3,6),(5,7),(9,10)] => 3
[(1,3),(2,8),(4,6),(5,7),(9,10)] => 3
[(1,2),(3,8),(4,6),(5,7),(9,10)] => 3
[(1,2),(3,7),(4,6),(5,8),(9,10)] => 4
[(1,3),(2,7),(4,6),(5,8),(9,10)] => 4
[(1,4),(2,7),(3,6),(5,8),(9,10)] => 4
[(1,5),(2,7),(3,6),(4,8),(9,10)] => 4
[(1,6),(2,7),(3,5),(4,8),(9,10)] => 4
[(1,7),(2,6),(3,5),(4,8),(9,10)] => 4
[(1,8),(2,6),(3,5),(4,7),(9,10)] => 3
[(1,9),(2,6),(3,5),(4,7),(8,10)] => 4
[(1,10),(2,6),(3,5),(4,7),(8,9)] => 1
[(1,10),(2,5),(3,6),(4,7),(8,9)] => 1
[(1,9),(2,5),(3,6),(4,7),(8,10)] => 4
[(1,8),(2,5),(3,6),(4,7),(9,10)] => 3
[(1,7),(2,5),(3,6),(4,8),(9,10)] => 4
[(1,6),(2,5),(3,7),(4,8),(9,10)] => 3
[(1,5),(2,6),(3,7),(4,8),(9,10)] => 3
[(1,4),(2,6),(3,7),(5,8),(9,10)] => 3
[(1,3),(2,6),(4,7),(5,8),(9,10)] => 3
[(1,2),(3,6),(4,7),(5,8),(9,10)] => 3
[(1,2),(3,5),(4,7),(6,8),(9,10)] => 3
[(1,3),(2,5),(4,7),(6,8),(9,10)] => 3
[(1,4),(2,5),(3,7),(6,8),(9,10)] => 3
[(1,5),(2,4),(3,7),(6,8),(9,10)] => 3
[(1,6),(2,4),(3,7),(5,8),(9,10)] => 3
[(1,7),(2,4),(3,6),(5,8),(9,10)] => 4
[(1,8),(2,4),(3,6),(5,7),(9,10)] => 3
[(1,9),(2,4),(3,6),(5,7),(8,10)] => 4
[(1,10),(2,4),(3,6),(5,7),(8,9)] => 1
[(1,10),(2,3),(4,6),(5,7),(8,9)] => 1
[(1,9),(2,3),(4,6),(5,7),(8,10)] => 4
[(1,8),(2,3),(4,6),(5,7),(9,10)] => 3
[(1,7),(2,3),(4,6),(5,8),(9,10)] => 4
[(1,6),(2,3),(4,7),(5,8),(9,10)] => 3
[(1,5),(2,3),(4,7),(6,8),(9,10)] => 3
[(1,4),(2,3),(5,7),(6,8),(9,10)] => 3
[(1,3),(2,4),(5,7),(6,8),(9,10)] => 3
[(1,2),(3,4),(5,7),(6,8),(9,10)] => 3
[(1,2),(3,4),(5,8),(6,7),(9,10)] => 3
[(1,3),(2,4),(5,8),(6,7),(9,10)] => 3
[(1,4),(2,3),(5,8),(6,7),(9,10)] => 3
[(1,5),(2,3),(4,8),(6,7),(9,10)] => 3
[(1,6),(2,3),(4,8),(5,7),(9,10)] => 3
[(1,7),(2,3),(4,8),(5,6),(9,10)] => 4
[(1,8),(2,3),(4,7),(5,6),(9,10)] => 4
[(1,9),(2,3),(4,7),(5,6),(8,10)] => 3
[(1,10),(2,3),(4,7),(5,6),(8,9)] => 1
[(1,10),(2,4),(3,7),(5,6),(8,9)] => 1
[(1,9),(2,4),(3,7),(5,6),(8,10)] => 3
[(1,8),(2,4),(3,7),(5,6),(9,10)] => 4
[(1,7),(2,4),(3,8),(5,6),(9,10)] => 4
[(1,6),(2,4),(3,8),(5,7),(9,10)] => 3
[(1,5),(2,4),(3,8),(6,7),(9,10)] => 3
[(1,4),(2,5),(3,8),(6,7),(9,10)] => 3
[(1,3),(2,5),(4,8),(6,7),(9,10)] => 3
[(1,2),(3,5),(4,8),(6,7),(9,10)] => 3
[(1,2),(3,6),(4,8),(5,7),(9,10)] => 3
[(1,3),(2,6),(4,8),(5,7),(9,10)] => 3
[(1,4),(2,6),(3,8),(5,7),(9,10)] => 3
[(1,5),(2,6),(3,8),(4,7),(9,10)] => 3
[(1,6),(2,5),(3,8),(4,7),(9,10)] => 3
[(1,7),(2,5),(3,8),(4,6),(9,10)] => 4
[(1,8),(2,5),(3,7),(4,6),(9,10)] => 4
[(1,9),(2,5),(3,7),(4,6),(8,10)] => 3
[(1,10),(2,5),(3,7),(4,6),(8,9)] => 1
[(1,10),(2,6),(3,7),(4,5),(8,9)] => 1
[(1,9),(2,6),(3,7),(4,5),(8,10)] => 3
[(1,8),(2,6),(3,7),(4,5),(9,10)] => 4
[(1,7),(2,6),(3,8),(4,5),(9,10)] => 4
[(1,6),(2,7),(3,8),(4,5),(9,10)] => 4
[(1,5),(2,7),(3,8),(4,6),(9,10)] => 4
[(1,4),(2,7),(3,8),(5,6),(9,10)] => 4
[(1,3),(2,7),(4,8),(5,6),(9,10)] => 4
[(1,2),(3,7),(4,8),(5,6),(9,10)] => 4
[(1,2),(3,8),(4,7),(5,6),(9,10)] => 4
[(1,3),(2,8),(4,7),(5,6),(9,10)] => 4
[(1,4),(2,8),(3,7),(5,6),(9,10)] => 4
[(1,5),(2,8),(3,7),(4,6),(9,10)] => 4
[(1,6),(2,8),(3,7),(4,5),(9,10)] => 4
[(1,7),(2,8),(3,6),(4,5),(9,10)] => 4
[(1,8),(2,7),(3,6),(4,5),(9,10)] => 4
[(1,9),(2,7),(3,6),(4,5),(8,10)] => 3
[(1,10),(2,7),(3,6),(4,5),(8,9)] => 1
[(1,10),(2,8),(3,6),(4,5),(7,9)] => 1
[(1,9),(2,8),(3,6),(4,5),(7,10)] => 4
[(1,8),(2,9),(3,6),(4,5),(7,10)] => 4
[(1,7),(2,9),(3,6),(4,5),(8,10)] => 3
[(1,6),(2,9),(3,7),(4,5),(8,10)] => 3
[(1,5),(2,9),(3,7),(4,6),(8,10)] => 3
[(1,4),(2,9),(3,7),(5,6),(8,10)] => 3
[(1,3),(2,9),(4,7),(5,6),(8,10)] => 3
[(1,2),(3,9),(4,7),(5,6),(8,10)] => 3
[(1,2),(3,10),(4,7),(5,6),(8,9)] => 5
[(1,3),(2,10),(4,7),(5,6),(8,9)] => 5
[(1,4),(2,10),(3,7),(5,6),(8,9)] => 5
[(1,5),(2,10),(3,7),(4,6),(8,9)] => 5
[(1,6),(2,10),(3,7),(4,5),(8,9)] => 5
[(1,7),(2,10),(3,6),(4,5),(8,9)] => 5
[(1,8),(2,10),(3,6),(4,5),(7,9)] => 5
[(1,9),(2,10),(3,6),(4,5),(7,8)] => 5
[(1,10),(2,9),(3,6),(4,5),(7,8)] => 1
[(1,10),(2,9),(3,7),(4,5),(6,8)] => 1
[(1,9),(2,10),(3,7),(4,5),(6,8)] => 5
[(1,8),(2,10),(3,7),(4,5),(6,9)] => 5
[(1,7),(2,10),(3,8),(4,5),(6,9)] => 5
[(1,6),(2,10),(3,8),(4,5),(7,9)] => 5
[(1,5),(2,10),(3,8),(4,6),(7,9)] => 5
[(1,4),(2,10),(3,8),(5,6),(7,9)] => 5
[(1,3),(2,10),(4,8),(5,6),(7,9)] => 5
[(1,2),(3,10),(4,8),(5,6),(7,9)] => 5
[(1,2),(3,9),(4,8),(5,6),(7,10)] => 2
[(1,3),(2,9),(4,8),(5,6),(7,10)] => 2
[(1,4),(2,9),(3,8),(5,6),(7,10)] => 2
[(1,5),(2,9),(3,8),(4,6),(7,10)] => 2
[(1,6),(2,9),(3,8),(4,5),(7,10)] => 2
[(1,7),(2,9),(3,8),(4,5),(6,10)] => 5
[(1,8),(2,9),(3,7),(4,5),(6,10)] => 5
[(1,9),(2,8),(3,7),(4,5),(6,10)] => 5
[(1,10),(2,8),(3,7),(4,5),(6,9)] => 1
[(1,10),(2,7),(3,8),(4,5),(6,9)] => 1
[(1,9),(2,7),(3,8),(4,5),(6,10)] => 5
[(1,8),(2,7),(3,9),(4,5),(6,10)] => 5
[(1,7),(2,8),(3,9),(4,5),(6,10)] => 5
[(1,6),(2,8),(3,9),(4,5),(7,10)] => 2
[(1,5),(2,8),(3,9),(4,6),(7,10)] => 2
[(1,4),(2,8),(3,9),(5,6),(7,10)] => 2
[(1,3),(2,8),(4,9),(5,6),(7,10)] => 2
[(1,2),(3,8),(4,9),(5,6),(7,10)] => 2
[(1,2),(3,7),(4,9),(5,6),(8,10)] => 3
[(1,3),(2,7),(4,9),(5,6),(8,10)] => 3
[(1,4),(2,7),(3,9),(5,6),(8,10)] => 3
[(1,5),(2,7),(3,9),(4,6),(8,10)] => 3
[(1,6),(2,7),(3,9),(4,5),(8,10)] => 3
[(1,7),(2,6),(3,9),(4,5),(8,10)] => 3
[(1,8),(2,6),(3,9),(4,5),(7,10)] => 4
[(1,9),(2,6),(3,8),(4,5),(7,10)] => 4
[(1,10),(2,6),(3,8),(4,5),(7,9)] => 1
[(1,10),(2,5),(3,8),(4,6),(7,9)] => 1
[(1,9),(2,5),(3,8),(4,6),(7,10)] => 4
[(1,8),(2,5),(3,9),(4,6),(7,10)] => 4
[(1,7),(2,5),(3,9),(4,6),(8,10)] => 3
[(1,6),(2,5),(3,9),(4,7),(8,10)] => 4
[(1,5),(2,6),(3,9),(4,7),(8,10)] => 4
[(1,4),(2,6),(3,9),(5,7),(8,10)] => 4
[(1,3),(2,6),(4,9),(5,7),(8,10)] => 4
[(1,2),(3,6),(4,9),(5,7),(8,10)] => 4
[(1,2),(3,5),(4,9),(6,7),(8,10)] => 4
[(1,3),(2,5),(4,9),(6,7),(8,10)] => 4
[(1,4),(2,5),(3,9),(6,7),(8,10)] => 4
[(1,5),(2,4),(3,9),(6,7),(8,10)] => 4
[(1,6),(2,4),(3,9),(5,7),(8,10)] => 4
[(1,7),(2,4),(3,9),(5,6),(8,10)] => 3
[(1,8),(2,4),(3,9),(5,6),(7,10)] => 4
[(1,9),(2,4),(3,8),(5,6),(7,10)] => 4
[(1,10),(2,4),(3,8),(5,6),(7,9)] => 1
[(1,10),(2,3),(4,8),(5,6),(7,9)] => 1
[(1,9),(2,3),(4,8),(5,6),(7,10)] => 4
[(1,8),(2,3),(4,9),(5,6),(7,10)] => 4
[(1,7),(2,3),(4,9),(5,6),(8,10)] => 3
[(1,6),(2,3),(4,9),(5,7),(8,10)] => 4
[(1,5),(2,3),(4,9),(6,7),(8,10)] => 4
[(1,4),(2,3),(5,9),(6,7),(8,10)] => 4
[(1,3),(2,4),(5,9),(6,7),(8,10)] => 4
[(1,2),(3,4),(5,9),(6,7),(8,10)] => 4
[(1,2),(3,4),(5,10),(6,7),(8,9)] => 5
[(1,3),(2,4),(5,10),(6,7),(8,9)] => 5
[(1,4),(2,3),(5,10),(6,7),(8,9)] => 5
[(1,5),(2,3),(4,10),(6,7),(8,9)] => 5
[(1,6),(2,3),(4,10),(5,7),(8,9)] => 5
[(1,7),(2,3),(4,10),(5,6),(8,9)] => 5
[(1,8),(2,3),(4,10),(5,6),(7,9)] => 5
[(1,9),(2,3),(4,10),(5,6),(7,8)] => 5
[(1,10),(2,3),(4,9),(5,6),(7,8)] => 1
[(1,10),(2,4),(3,9),(5,6),(7,8)] => 1
[(1,9),(2,4),(3,10),(5,6),(7,8)] => 5
[(1,8),(2,4),(3,10),(5,6),(7,9)] => 5
[(1,7),(2,4),(3,10),(5,6),(8,9)] => 5
[(1,6),(2,4),(3,10),(5,7),(8,9)] => 5
[(1,5),(2,4),(3,10),(6,7),(8,9)] => 5
[(1,4),(2,5),(3,10),(6,7),(8,9)] => 5
[(1,3),(2,5),(4,10),(6,7),(8,9)] => 5
[(1,2),(3,5),(4,10),(6,7),(8,9)] => 5
[(1,2),(3,6),(4,10),(5,7),(8,9)] => 5
[(1,3),(2,6),(4,10),(5,7),(8,9)] => 5
[(1,4),(2,6),(3,10),(5,7),(8,9)] => 5
[(1,5),(2,6),(3,10),(4,7),(8,9)] => 5
[(1,6),(2,5),(3,10),(4,7),(8,9)] => 5
[(1,7),(2,5),(3,10),(4,6),(8,9)] => 5
[(1,8),(2,5),(3,10),(4,6),(7,9)] => 5
[(1,9),(2,5),(3,10),(4,6),(7,8)] => 5
[(1,10),(2,5),(3,9),(4,6),(7,8)] => 1
[(1,10),(2,6),(3,9),(4,5),(7,8)] => 1
[(1,9),(2,6),(3,10),(4,5),(7,8)] => 5
[(1,8),(2,6),(3,10),(4,5),(7,9)] => 5
[(1,7),(2,6),(3,10),(4,5),(8,9)] => 5
[(1,6),(2,7),(3,10),(4,5),(8,9)] => 5
[(1,5),(2,7),(3,10),(4,6),(8,9)] => 5
[(1,4),(2,7),(3,10),(5,6),(8,9)] => 5
[(1,3),(2,7),(4,10),(5,6),(8,9)] => 5
[(1,2),(3,7),(4,10),(5,6),(8,9)] => 5
[(1,2),(3,8),(4,10),(5,6),(7,9)] => 5
[(1,3),(2,8),(4,10),(5,6),(7,9)] => 5
[(1,4),(2,8),(3,10),(5,6),(7,9)] => 5
[(1,5),(2,8),(3,10),(4,6),(7,9)] => 5
[(1,6),(2,8),(3,10),(4,5),(7,9)] => 5
[(1,7),(2,8),(3,10),(4,5),(6,9)] => 5
[(1,8),(2,7),(3,10),(4,5),(6,9)] => 5
[(1,9),(2,7),(3,10),(4,5),(6,8)] => 5
[(1,10),(2,7),(3,9),(4,5),(6,8)] => 1
[(1,10),(2,8),(3,9),(4,5),(6,7)] => 1
[(1,9),(2,8),(3,10),(4,5),(6,7)] => 5
[(1,8),(2,9),(3,10),(4,5),(6,7)] => 5
[(1,7),(2,9),(3,10),(4,5),(6,8)] => 5
[(1,6),(2,9),(3,10),(4,5),(7,8)] => 5
[(1,5),(2,9),(3,10),(4,6),(7,8)] => 5
[(1,4),(2,9),(3,10),(5,6),(7,8)] => 5
[(1,3),(2,9),(4,10),(5,6),(7,8)] => 5
[(1,2),(3,9),(4,10),(5,6),(7,8)] => 5
[(1,2),(3,10),(4,9),(5,6),(7,8)] => 5
[(1,3),(2,10),(4,9),(5,6),(7,8)] => 5
[(1,4),(2,10),(3,9),(5,6),(7,8)] => 5
[(1,5),(2,10),(3,9),(4,6),(7,8)] => 5
[(1,6),(2,10),(3,9),(4,5),(7,8)] => 5
[(1,7),(2,10),(3,9),(4,5),(6,8)] => 5
[(1,8),(2,10),(3,9),(4,5),(6,7)] => 5
[(1,9),(2,10),(3,8),(4,5),(6,7)] => 5
[(1,10),(2,9),(3,8),(4,5),(6,7)] => 1
[(1,10),(2,9),(3,8),(4,6),(5,7)] => 1
[(1,9),(2,10),(3,8),(4,6),(5,7)] => 5
[(1,8),(2,10),(3,9),(4,6),(5,7)] => 5
[(1,7),(2,10),(3,9),(4,6),(5,8)] => 5
[(1,6),(2,10),(3,9),(4,7),(5,8)] => 5
[(1,5),(2,10),(3,9),(4,7),(6,8)] => 5
[(1,4),(2,10),(3,9),(5,7),(6,8)] => 5
[(1,3),(2,10),(4,9),(5,7),(6,8)] => 5
[(1,2),(3,10),(4,9),(5,7),(6,8)] => 5
[(1,2),(3,9),(4,10),(5,7),(6,8)] => 5
[(1,3),(2,9),(4,10),(5,7),(6,8)] => 5
[(1,4),(2,9),(3,10),(5,7),(6,8)] => 5
[(1,5),(2,9),(3,10),(4,7),(6,8)] => 5
[(1,6),(2,9),(3,10),(4,7),(5,8)] => 5
[(1,7),(2,9),(3,10),(4,6),(5,8)] => 5
[(1,8),(2,9),(3,10),(4,6),(5,7)] => 5
[(1,9),(2,8),(3,10),(4,6),(5,7)] => 5
[(1,10),(2,8),(3,9),(4,6),(5,7)] => 1
[(1,10),(2,7),(3,9),(4,6),(5,8)] => 1
[(1,9),(2,7),(3,10),(4,6),(5,8)] => 5
[(1,8),(2,7),(3,10),(4,6),(5,9)] => 5
[(1,7),(2,8),(3,10),(4,6),(5,9)] => 5
[(1,6),(2,8),(3,10),(4,7),(5,9)] => 5
[(1,5),(2,8),(3,10),(4,7),(6,9)] => 5
[(1,4),(2,8),(3,10),(5,7),(6,9)] => 5
[(1,3),(2,8),(4,10),(5,7),(6,9)] => 5
[(1,2),(3,8),(4,10),(5,7),(6,9)] => 5
[(1,2),(3,7),(4,10),(5,8),(6,9)] => 5
[(1,3),(2,7),(4,10),(5,8),(6,9)] => 5
[(1,4),(2,7),(3,10),(5,8),(6,9)] => 5
[(1,5),(2,7),(3,10),(4,8),(6,9)] => 5
[(1,6),(2,7),(3,10),(4,8),(5,9)] => 5
[(1,7),(2,6),(3,10),(4,8),(5,9)] => 5
[(1,8),(2,6),(3,10),(4,7),(5,9)] => 5
[(1,9),(2,6),(3,10),(4,7),(5,8)] => 5
[(1,10),(2,6),(3,9),(4,7),(5,8)] => 1
[(1,10),(2,5),(3,9),(4,7),(6,8)] => 1
[(1,9),(2,5),(3,10),(4,7),(6,8)] => 5
[(1,8),(2,5),(3,10),(4,7),(6,9)] => 5
[(1,7),(2,5),(3,10),(4,8),(6,9)] => 5
[(1,6),(2,5),(3,10),(4,8),(7,9)] => 5
[(1,5),(2,6),(3,10),(4,8),(7,9)] => 5
[(1,4),(2,6),(3,10),(5,8),(7,9)] => 5
[(1,3),(2,6),(4,10),(5,8),(7,9)] => 5
[(1,2),(3,6),(4,10),(5,8),(7,9)] => 5
[(1,2),(3,5),(4,10),(6,8),(7,9)] => 5
[(1,3),(2,5),(4,10),(6,8),(7,9)] => 5
[(1,4),(2,5),(3,10),(6,8),(7,9)] => 5
[(1,5),(2,4),(3,10),(6,8),(7,9)] => 5
[(1,6),(2,4),(3,10),(5,8),(7,9)] => 5
[(1,7),(2,4),(3,10),(5,8),(6,9)] => 5
[(1,8),(2,4),(3,10),(5,7),(6,9)] => 5
[(1,9),(2,4),(3,10),(5,7),(6,8)] => 5
[(1,10),(2,4),(3,9),(5,7),(6,8)] => 1
[(1,10),(2,3),(4,9),(5,7),(6,8)] => 1
[(1,9),(2,3),(4,10),(5,7),(6,8)] => 5
[(1,8),(2,3),(4,10),(5,7),(6,9)] => 5
[(1,7),(2,3),(4,10),(5,8),(6,9)] => 5
[(1,6),(2,3),(4,10),(5,8),(7,9)] => 5
[(1,5),(2,3),(4,10),(6,8),(7,9)] => 5
[(1,4),(2,3),(5,10),(6,8),(7,9)] => 5
[(1,3),(2,4),(5,10),(6,8),(7,9)] => 5
[(1,2),(3,4),(5,10),(6,8),(7,9)] => 5
[(1,2),(3,4),(5,9),(6,8),(7,10)] => 2
[(1,3),(2,4),(5,9),(6,8),(7,10)] => 2
[(1,4),(2,3),(5,9),(6,8),(7,10)] => 2
[(1,5),(2,3),(4,9),(6,8),(7,10)] => 2
[(1,6),(2,3),(4,9),(5,8),(7,10)] => 2
[(1,7),(2,3),(4,9),(5,8),(6,10)] => 5
[(1,8),(2,3),(4,9),(5,7),(6,10)] => 5
[(1,9),(2,3),(4,8),(5,7),(6,10)] => 5
[(1,10),(2,3),(4,8),(5,7),(6,9)] => 1
[(1,10),(2,4),(3,8),(5,7),(6,9)] => 1
[(1,9),(2,4),(3,8),(5,7),(6,10)] => 5
[(1,8),(2,4),(3,9),(5,7),(6,10)] => 5
[(1,7),(2,4),(3,9),(5,8),(6,10)] => 5
[(1,6),(2,4),(3,9),(5,8),(7,10)] => 2
[(1,5),(2,4),(3,9),(6,8),(7,10)] => 2
[(1,4),(2,5),(3,9),(6,8),(7,10)] => 2
[(1,3),(2,5),(4,9),(6,8),(7,10)] => 2
[(1,2),(3,5),(4,9),(6,8),(7,10)] => 2
[(1,2),(3,6),(4,9),(5,8),(7,10)] => 2
[(1,3),(2,6),(4,9),(5,8),(7,10)] => 2
[(1,4),(2,6),(3,9),(5,8),(7,10)] => 2
[(1,5),(2,6),(3,9),(4,8),(7,10)] => 2
[(1,6),(2,5),(3,9),(4,8),(7,10)] => 2
[(1,7),(2,5),(3,9),(4,8),(6,10)] => 5
[(1,8),(2,5),(3,9),(4,7),(6,10)] => 5
[(1,9),(2,5),(3,8),(4,7),(6,10)] => 5
[(1,10),(2,5),(3,8),(4,7),(6,9)] => 1
[(1,10),(2,6),(3,8),(4,7),(5,9)] => 1
[(1,9),(2,6),(3,8),(4,7),(5,10)] => 5
[(1,8),(2,6),(3,9),(4,7),(5,10)] => 5
[(1,7),(2,6),(3,9),(4,8),(5,10)] => 5
[(1,6),(2,7),(3,9),(4,8),(5,10)] => 5
[(1,5),(2,7),(3,9),(4,8),(6,10)] => 5
[(1,4),(2,7),(3,9),(5,8),(6,10)] => 5
[(1,3),(2,7),(4,9),(5,8),(6,10)] => 5
[(1,2),(3,7),(4,9),(5,8),(6,10)] => 5
[(1,2),(3,8),(4,9),(5,7),(6,10)] => 5
[(1,3),(2,8),(4,9),(5,7),(6,10)] => 5
[(1,4),(2,8),(3,9),(5,7),(6,10)] => 5
[(1,5),(2,8),(3,9),(4,7),(6,10)] => 5
[(1,6),(2,8),(3,9),(4,7),(5,10)] => 5
[(1,7),(2,8),(3,9),(4,6),(5,10)] => 5
[(1,8),(2,7),(3,9),(4,6),(5,10)] => 5
[(1,9),(2,7),(3,8),(4,6),(5,10)] => 5
[(1,10),(2,7),(3,8),(4,6),(5,9)] => 1
[(1,10),(2,8),(3,7),(4,6),(5,9)] => 1
[(1,9),(2,8),(3,7),(4,6),(5,10)] => 5
[(1,8),(2,9),(3,7),(4,6),(5,10)] => 5
[(1,7),(2,9),(3,8),(4,6),(5,10)] => 5
[(1,6),(2,9),(3,8),(4,7),(5,10)] => 5
[(1,5),(2,9),(3,8),(4,7),(6,10)] => 5
[(1,4),(2,9),(3,8),(5,7),(6,10)] => 5
[(1,3),(2,9),(4,8),(5,7),(6,10)] => 5
[(1,2),(3,9),(4,8),(5,7),(6,10)] => 5
[(1,2),(3,10),(4,8),(5,7),(6,9)] => 5
[(1,3),(2,10),(4,8),(5,7),(6,9)] => 5
[(1,4),(2,10),(3,8),(5,7),(6,9)] => 5
[(1,5),(2,10),(3,8),(4,7),(6,9)] => 5
[(1,6),(2,10),(3,8),(4,7),(5,9)] => 5
[(1,7),(2,10),(3,8),(4,6),(5,9)] => 5
[(1,8),(2,10),(3,7),(4,6),(5,9)] => 5
[(1,9),(2,10),(3,7),(4,6),(5,8)] => 5
[(1,10),(2,9),(3,7),(4,6),(5,8)] => 1
[(1,10),(2,9),(3,6),(4,7),(5,8)] => 1
[(1,9),(2,10),(3,6),(4,7),(5,8)] => 5
[(1,8),(2,10),(3,6),(4,7),(5,9)] => 5
[(1,7),(2,10),(3,6),(4,8),(5,9)] => 5
[(1,6),(2,10),(3,7),(4,8),(5,9)] => 5
[(1,5),(2,10),(3,7),(4,8),(6,9)] => 5
[(1,4),(2,10),(3,7),(5,8),(6,9)] => 5
[(1,3),(2,10),(4,7),(5,8),(6,9)] => 5
[(1,2),(3,10),(4,7),(5,8),(6,9)] => 5
[(1,2),(3,9),(4,7),(5,8),(6,10)] => 5
[(1,3),(2,9),(4,7),(5,8),(6,10)] => 5
[(1,4),(2,9),(3,7),(5,8),(6,10)] => 5
[(1,5),(2,9),(3,7),(4,8),(6,10)] => 5
[(1,6),(2,9),(3,7),(4,8),(5,10)] => 5
[(1,7),(2,9),(3,6),(4,8),(5,10)] => 5
[(1,8),(2,9),(3,6),(4,7),(5,10)] => 5
[(1,9),(2,8),(3,6),(4,7),(5,10)] => 5
[(1,10),(2,8),(3,6),(4,7),(5,9)] => 1
[(1,10),(2,7),(3,6),(4,8),(5,9)] => 1
[(1,9),(2,7),(3,6),(4,8),(5,10)] => 5
[(1,8),(2,7),(3,6),(4,9),(5,10)] => 5
[(1,7),(2,8),(3,6),(4,9),(5,10)] => 5
[(1,6),(2,8),(3,7),(4,9),(5,10)] => 5
[(1,5),(2,8),(3,7),(4,9),(6,10)] => 5
[(1,4),(2,8),(3,7),(5,9),(6,10)] => 5
[(1,3),(2,8),(4,7),(5,9),(6,10)] => 5
[(1,2),(3,8),(4,7),(5,9),(6,10)] => 5
[(1,2),(3,7),(4,8),(5,9),(6,10)] => 5
[(1,3),(2,7),(4,8),(5,9),(6,10)] => 5
[(1,4),(2,7),(3,8),(5,9),(6,10)] => 5
[(1,5),(2,7),(3,8),(4,9),(6,10)] => 5
[(1,6),(2,7),(3,8),(4,9),(5,10)] => 5
[(1,7),(2,6),(3,8),(4,9),(5,10)] => 5
[(1,8),(2,6),(3,7),(4,9),(5,10)] => 5
[(1,9),(2,6),(3,7),(4,8),(5,10)] => 5
[(1,10),(2,6),(3,7),(4,8),(5,9)] => 1
[(1,10),(2,5),(3,7),(4,8),(6,9)] => 1
[(1,9),(2,5),(3,7),(4,8),(6,10)] => 5
[(1,8),(2,5),(3,7),(4,9),(6,10)] => 5
[(1,7),(2,5),(3,8),(4,9),(6,10)] => 5
[(1,6),(2,5),(3,8),(4,9),(7,10)] => 2
[(1,5),(2,6),(3,8),(4,9),(7,10)] => 2
[(1,4),(2,6),(3,8),(5,9),(7,10)] => 2
[(1,3),(2,6),(4,8),(5,9),(7,10)] => 2
[(1,2),(3,6),(4,8),(5,9),(7,10)] => 2
[(1,2),(3,5),(4,8),(6,9),(7,10)] => 2
[(1,3),(2,5),(4,8),(6,9),(7,10)] => 2
[(1,4),(2,5),(3,8),(6,9),(7,10)] => 2
[(1,5),(2,4),(3,8),(6,9),(7,10)] => 2
[(1,6),(2,4),(3,8),(5,9),(7,10)] => 2
[(1,7),(2,4),(3,8),(5,9),(6,10)] => 5
[(1,8),(2,4),(3,7),(5,9),(6,10)] => 5
[(1,9),(2,4),(3,7),(5,8),(6,10)] => 5
[(1,10),(2,4),(3,7),(5,8),(6,9)] => 1
[(1,10),(2,3),(4,7),(5,8),(6,9)] => 1
[(1,9),(2,3),(4,7),(5,8),(6,10)] => 5
[(1,8),(2,3),(4,7),(5,9),(6,10)] => 5
[(1,7),(2,3),(4,8),(5,9),(6,10)] => 5
[(1,6),(2,3),(4,8),(5,9),(7,10)] => 2
[(1,5),(2,3),(4,8),(6,9),(7,10)] => 2
[(1,4),(2,3),(5,8),(6,9),(7,10)] => 2
[(1,3),(2,4),(5,8),(6,9),(7,10)] => 2
[(1,2),(3,4),(5,8),(6,9),(7,10)] => 2
[(1,2),(3,4),(5,7),(6,9),(8,10)] => 4
[(1,3),(2,4),(5,7),(6,9),(8,10)] => 4
[(1,4),(2,3),(5,7),(6,9),(8,10)] => 4
[(1,5),(2,3),(4,7),(6,9),(8,10)] => 4
[(1,6),(2,3),(4,7),(5,9),(8,10)] => 4
[(1,7),(2,3),(4,6),(5,9),(8,10)] => 3
[(1,8),(2,3),(4,6),(5,9),(7,10)] => 4
[(1,9),(2,3),(4,6),(5,8),(7,10)] => 4
[(1,10),(2,3),(4,6),(5,8),(7,9)] => 1
[(1,10),(2,4),(3,6),(5,8),(7,9)] => 1
[(1,9),(2,4),(3,6),(5,8),(7,10)] => 4
[(1,8),(2,4),(3,6),(5,9),(7,10)] => 4
[(1,7),(2,4),(3,6),(5,9),(8,10)] => 3
[(1,6),(2,4),(3,7),(5,9),(8,10)] => 4
[(1,5),(2,4),(3,7),(6,9),(8,10)] => 4
[(1,4),(2,5),(3,7),(6,9),(8,10)] => 4
[(1,3),(2,5),(4,7),(6,9),(8,10)] => 4
[(1,2),(3,5),(4,7),(6,9),(8,10)] => 4
[(1,2),(3,6),(4,7),(5,9),(8,10)] => 4
[(1,3),(2,6),(4,7),(5,9),(8,10)] => 4
[(1,4),(2,6),(3,7),(5,9),(8,10)] => 4
[(1,5),(2,6),(3,7),(4,9),(8,10)] => 4
[(1,6),(2,5),(3,7),(4,9),(8,10)] => 4
[(1,7),(2,5),(3,6),(4,9),(8,10)] => 3
[(1,8),(2,5),(3,6),(4,9),(7,10)] => 4
[(1,9),(2,5),(3,6),(4,8),(7,10)] => 4
[(1,10),(2,5),(3,6),(4,8),(7,9)] => 1
[(1,10),(2,6),(3,5),(4,8),(7,9)] => 1
[(1,9),(2,6),(3,5),(4,8),(7,10)] => 4
[(1,8),(2,6),(3,5),(4,9),(7,10)] => 4
[(1,7),(2,6),(3,5),(4,9),(8,10)] => 3
[(1,6),(2,7),(3,5),(4,9),(8,10)] => 3
[(1,5),(2,7),(3,6),(4,9),(8,10)] => 3
[(1,4),(2,7),(3,6),(5,9),(8,10)] => 3
[(1,3),(2,7),(4,6),(5,9),(8,10)] => 3
[(1,2),(3,7),(4,6),(5,9),(8,10)] => 3
[(1,2),(3,8),(4,6),(5,9),(7,10)] => 2
[(1,3),(2,8),(4,6),(5,9),(7,10)] => 2
[(1,4),(2,8),(3,6),(5,9),(7,10)] => 2
[(1,5),(2,8),(3,6),(4,9),(7,10)] => 2
[(1,6),(2,8),(3,5),(4,9),(7,10)] => 2
[(1,7),(2,8),(3,5),(4,9),(6,10)] => 5
[(1,8),(2,7),(3,5),(4,9),(6,10)] => 5
[(1,9),(2,7),(3,5),(4,8),(6,10)] => 5
[(1,10),(2,7),(3,5),(4,8),(6,9)] => 1
[(1,10),(2,8),(3,5),(4,7),(6,9)] => 1
[(1,9),(2,8),(3,5),(4,7),(6,10)] => 5
[(1,8),(2,9),(3,5),(4,7),(6,10)] => 5
[(1,7),(2,9),(3,5),(4,8),(6,10)] => 5
[(1,6),(2,9),(3,5),(4,8),(7,10)] => 2
[(1,5),(2,9),(3,6),(4,8),(7,10)] => 2
[(1,4),(2,9),(3,6),(5,8),(7,10)] => 2
[(1,3),(2,9),(4,6),(5,8),(7,10)] => 2
[(1,2),(3,9),(4,6),(5,8),(7,10)] => 2
[(1,2),(3,10),(4,6),(5,8),(7,9)] => 5
[(1,3),(2,10),(4,6),(5,8),(7,9)] => 5
[(1,4),(2,10),(3,6),(5,8),(7,9)] => 5
[(1,5),(2,10),(3,6),(4,8),(7,9)] => 5
[(1,6),(2,10),(3,5),(4,8),(7,9)] => 5
[(1,7),(2,10),(3,5),(4,8),(6,9)] => 5
[(1,8),(2,10),(3,5),(4,7),(6,9)] => 5
[(1,9),(2,10),(3,5),(4,7),(6,8)] => 5
[(1,10),(2,9),(3,5),(4,7),(6,8)] => 1
[(1,10),(2,9),(3,4),(5,7),(6,8)] => 1
[(1,9),(2,10),(3,4),(5,7),(6,8)] => 5
[(1,8),(2,10),(3,4),(5,7),(6,9)] => 5
[(1,7),(2,10),(3,4),(5,8),(6,9)] => 5
[(1,6),(2,10),(3,4),(5,8),(7,9)] => 5
[(1,5),(2,10),(3,4),(6,8),(7,9)] => 5
[(1,4),(2,10),(3,5),(6,8),(7,9)] => 5
[(1,3),(2,10),(4,5),(6,8),(7,9)] => 5
[(1,2),(3,10),(4,5),(6,8),(7,9)] => 5
[(1,2),(3,9),(4,5),(6,8),(7,10)] => 2
[(1,3),(2,9),(4,5),(6,8),(7,10)] => 2
[(1,4),(2,9),(3,5),(6,8),(7,10)] => 2
[(1,5),(2,9),(3,4),(6,8),(7,10)] => 2
[(1,6),(2,9),(3,4),(5,8),(7,10)] => 2
[(1,7),(2,9),(3,4),(5,8),(6,10)] => 5
[(1,8),(2,9),(3,4),(5,7),(6,10)] => 5
[(1,9),(2,8),(3,4),(5,7),(6,10)] => 5
[(1,10),(2,8),(3,4),(5,7),(6,9)] => 1
[(1,10),(2,7),(3,4),(5,8),(6,9)] => 1
[(1,9),(2,7),(3,4),(5,8),(6,10)] => 5
[(1,8),(2,7),(3,4),(5,9),(6,10)] => 5
[(1,7),(2,8),(3,4),(5,9),(6,10)] => 5
[(1,6),(2,8),(3,4),(5,9),(7,10)] => 2
[(1,5),(2,8),(3,4),(6,9),(7,10)] => 2
[(1,4),(2,8),(3,5),(6,9),(7,10)] => 2
[(1,3),(2,8),(4,5),(6,9),(7,10)] => 2
[(1,2),(3,8),(4,5),(6,9),(7,10)] => 2
[(1,2),(3,7),(4,5),(6,9),(8,10)] => 3
[(1,3),(2,7),(4,5),(6,9),(8,10)] => 3
[(1,4),(2,7),(3,5),(6,9),(8,10)] => 3
[(1,5),(2,7),(3,4),(6,9),(8,10)] => 3
[(1,6),(2,7),(3,4),(5,9),(8,10)] => 3
[(1,7),(2,6),(3,4),(5,9),(8,10)] => 3
[(1,8),(2,6),(3,4),(5,9),(7,10)] => 4
[(1,9),(2,6),(3,4),(5,8),(7,10)] => 4
[(1,10),(2,6),(3,4),(5,8),(7,9)] => 1
[(1,10),(2,5),(3,4),(6,8),(7,9)] => 1
[(1,9),(2,5),(3,4),(6,8),(7,10)] => 4
[(1,8),(2,5),(3,4),(6,9),(7,10)] => 4
[(1,7),(2,5),(3,4),(6,9),(8,10)] => 3
[(1,6),(2,5),(3,4),(7,9),(8,10)] => 4
[(1,5),(2,6),(3,4),(7,9),(8,10)] => 4
[(1,4),(2,6),(3,5),(7,9),(8,10)] => 4
[(1,3),(2,6),(4,5),(7,9),(8,10)] => 4
[(1,2),(3,6),(4,5),(7,9),(8,10)] => 4
[(1,2),(3,5),(4,6),(7,9),(8,10)] => 4
[(1,3),(2,5),(4,6),(7,9),(8,10)] => 4
[(1,4),(2,5),(3,6),(7,9),(8,10)] => 4
[(1,5),(2,4),(3,6),(7,9),(8,10)] => 4
[(1,6),(2,4),(3,5),(7,9),(8,10)] => 4
[(1,7),(2,4),(3,5),(6,9),(8,10)] => 3
[(1,8),(2,4),(3,5),(6,9),(7,10)] => 4
[(1,9),(2,4),(3,5),(6,8),(7,10)] => 4
[(1,10),(2,4),(3,5),(6,8),(7,9)] => 1
[(1,10),(2,3),(4,5),(6,8),(7,9)] => 1
[(1,9),(2,3),(4,5),(6,8),(7,10)] => 4
[(1,8),(2,3),(4,5),(6,9),(7,10)] => 4
[(1,7),(2,3),(4,5),(6,9),(8,10)] => 3
[(1,6),(2,3),(4,5),(7,9),(8,10)] => 4
[(1,5),(2,3),(4,6),(7,9),(8,10)] => 4
[(1,4),(2,3),(5,6),(7,9),(8,10)] => 4
[(1,3),(2,4),(5,6),(7,9),(8,10)] => 4
[(1,2),(3,4),(5,6),(7,9),(8,10)] => 4
[(1,2),(3,4),(5,6),(7,10),(8,9)] => 2
[(1,3),(2,4),(5,6),(7,10),(8,9)] => 2
[(1,4),(2,3),(5,6),(7,10),(8,9)] => 2
[(1,5),(2,3),(4,6),(7,10),(8,9)] => 2
[(1,6),(2,3),(4,5),(7,10),(8,9)] => 2
[(1,7),(2,3),(4,5),(6,10),(8,9)] => 5
[(1,8),(2,3),(4,5),(6,10),(7,9)] => 5
[(1,9),(2,3),(4,5),(6,10),(7,8)] => 5
[(1,10),(2,3),(4,5),(6,9),(7,8)] => 1
[(1,10),(2,4),(3,5),(6,9),(7,8)] => 1
[(1,9),(2,4),(3,5),(6,10),(7,8)] => 5
[(1,8),(2,4),(3,5),(6,10),(7,9)] => 5
[(1,7),(2,4),(3,5),(6,10),(8,9)] => 5
[(1,6),(2,4),(3,5),(7,10),(8,9)] => 2
[(1,5),(2,4),(3,6),(7,10),(8,9)] => 2
[(1,4),(2,5),(3,6),(7,10),(8,9)] => 2
[(1,3),(2,5),(4,6),(7,10),(8,9)] => 2
[(1,2),(3,5),(4,6),(7,10),(8,9)] => 2
[(1,2),(3,6),(4,5),(7,10),(8,9)] => 2
[(1,3),(2,6),(4,5),(7,10),(8,9)] => 2
[(1,4),(2,6),(3,5),(7,10),(8,9)] => 2
[(1,5),(2,6),(3,4),(7,10),(8,9)] => 2
[(1,6),(2,5),(3,4),(7,10),(8,9)] => 2
[(1,7),(2,5),(3,4),(6,10),(8,9)] => 5
[(1,8),(2,5),(3,4),(6,10),(7,9)] => 5
[(1,9),(2,5),(3,4),(6,10),(7,8)] => 5
[(1,10),(2,5),(3,4),(6,9),(7,8)] => 1
[(1,10),(2,6),(3,4),(5,9),(7,8)] => 1
[(1,9),(2,6),(3,4),(5,10),(7,8)] => 5
[(1,8),(2,6),(3,4),(5,10),(7,9)] => 5
[(1,7),(2,6),(3,4),(5,10),(8,9)] => 5
[(1,6),(2,7),(3,4),(5,10),(8,9)] => 5
[(1,5),(2,7),(3,4),(6,10),(8,9)] => 5
[(1,4),(2,7),(3,5),(6,10),(8,9)] => 5
[(1,3),(2,7),(4,5),(6,10),(8,9)] => 5
[(1,2),(3,7),(4,5),(6,10),(8,9)] => 5
[(1,2),(3,8),(4,5),(6,10),(7,9)] => 5
[(1,3),(2,8),(4,5),(6,10),(7,9)] => 5
[(1,4),(2,8),(3,5),(6,10),(7,9)] => 5
[(1,5),(2,8),(3,4),(6,10),(7,9)] => 5
[(1,6),(2,8),(3,4),(5,10),(7,9)] => 5
[(1,7),(2,8),(3,4),(5,10),(6,9)] => 5
[(1,8),(2,7),(3,4),(5,10),(6,9)] => 5
[(1,9),(2,7),(3,4),(5,10),(6,8)] => 5
[(1,10),(2,7),(3,4),(5,9),(6,8)] => 1
[(1,10),(2,8),(3,4),(5,9),(6,7)] => 1
[(1,9),(2,8),(3,4),(5,10),(6,7)] => 5
[(1,8),(2,9),(3,4),(5,10),(6,7)] => 5
[(1,7),(2,9),(3,4),(5,10),(6,8)] => 5
[(1,6),(2,9),(3,4),(5,10),(7,8)] => 5
[(1,5),(2,9),(3,4),(6,10),(7,8)] => 5
[(1,4),(2,9),(3,5),(6,10),(7,8)] => 5
[(1,3),(2,9),(4,5),(6,10),(7,8)] => 5
[(1,2),(3,9),(4,5),(6,10),(7,8)] => 5
[(1,2),(3,10),(4,5),(6,9),(7,8)] => 5
[(1,3),(2,10),(4,5),(6,9),(7,8)] => 5
[(1,4),(2,10),(3,5),(6,9),(7,8)] => 5
[(1,5),(2,10),(3,4),(6,9),(7,8)] => 5
[(1,6),(2,10),(3,4),(5,9),(7,8)] => 5
[(1,7),(2,10),(3,4),(5,9),(6,8)] => 5
[(1,8),(2,10),(3,4),(5,9),(6,7)] => 5
[(1,9),(2,10),(3,4),(5,8),(6,7)] => 5
[(1,10),(2,9),(3,4),(5,8),(6,7)] => 1
[(1,10),(2,9),(3,5),(4,8),(6,7)] => 1
[(1,9),(2,10),(3,5),(4,8),(6,7)] => 5
[(1,8),(2,10),(3,5),(4,9),(6,7)] => 5
[(1,7),(2,10),(3,5),(4,9),(6,8)] => 5
[(1,6),(2,10),(3,5),(4,9),(7,8)] => 5
[(1,5),(2,10),(3,6),(4,9),(7,8)] => 5
[(1,4),(2,10),(3,6),(5,9),(7,8)] => 5
[(1,3),(2,10),(4,6),(5,9),(7,8)] => 5
[(1,2),(3,10),(4,6),(5,9),(7,8)] => 5
[(1,2),(3,9),(4,6),(5,10),(7,8)] => 5
[(1,3),(2,9),(4,6),(5,10),(7,8)] => 5
[(1,4),(2,9),(3,6),(5,10),(7,8)] => 5
[(1,5),(2,9),(3,6),(4,10),(7,8)] => 5
[(1,6),(2,9),(3,5),(4,10),(7,8)] => 5
[(1,7),(2,9),(3,5),(4,10),(6,8)] => 5
[(1,8),(2,9),(3,5),(4,10),(6,7)] => 5
[(1,9),(2,8),(3,5),(4,10),(6,7)] => 5
[(1,10),(2,8),(3,5),(4,9),(6,7)] => 1
[(1,10),(2,7),(3,5),(4,9),(6,8)] => 1
[(1,9),(2,7),(3,5),(4,10),(6,8)] => 5
[(1,8),(2,7),(3,5),(4,10),(6,9)] => 5
[(1,7),(2,8),(3,5),(4,10),(6,9)] => 5
[(1,6),(2,8),(3,5),(4,10),(7,9)] => 5
[(1,5),(2,8),(3,6),(4,10),(7,9)] => 5
[(1,4),(2,8),(3,6),(5,10),(7,9)] => 5
[(1,3),(2,8),(4,6),(5,10),(7,9)] => 5
[(1,2),(3,8),(4,6),(5,10),(7,9)] => 5
[(1,2),(3,7),(4,6),(5,10),(8,9)] => 5
[(1,3),(2,7),(4,6),(5,10),(8,9)] => 5
[(1,4),(2,7),(3,6),(5,10),(8,9)] => 5
[(1,5),(2,7),(3,6),(4,10),(8,9)] => 5
[(1,6),(2,7),(3,5),(4,10),(8,9)] => 5
[(1,7),(2,6),(3,5),(4,10),(8,9)] => 5
[(1,8),(2,6),(3,5),(4,10),(7,9)] => 5
[(1,9),(2,6),(3,5),(4,10),(7,8)] => 5
[(1,10),(2,6),(3,5),(4,9),(7,8)] => 1
[(1,10),(2,5),(3,6),(4,9),(7,8)] => 1
[(1,9),(2,5),(3,6),(4,10),(7,8)] => 5
[(1,8),(2,5),(3,6),(4,10),(7,9)] => 5
[(1,7),(2,5),(3,6),(4,10),(8,9)] => 5
[(1,6),(2,5),(3,7),(4,10),(8,9)] => 5
[(1,5),(2,6),(3,7),(4,10),(8,9)] => 5
[(1,4),(2,6),(3,7),(5,10),(8,9)] => 5
[(1,3),(2,6),(4,7),(5,10),(8,9)] => 5
[(1,2),(3,6),(4,7),(5,10),(8,9)] => 5
[(1,2),(3,5),(4,7),(6,10),(8,9)] => 5
[(1,3),(2,5),(4,7),(6,10),(8,9)] => 5
[(1,4),(2,5),(3,7),(6,10),(8,9)] => 5
[(1,5),(2,4),(3,7),(6,10),(8,9)] => 5
[(1,6),(2,4),(3,7),(5,10),(8,9)] => 5
[(1,7),(2,4),(3,6),(5,10),(8,9)] => 5
[(1,8),(2,4),(3,6),(5,10),(7,9)] => 5
[(1,9),(2,4),(3,6),(5,10),(7,8)] => 5
[(1,10),(2,4),(3,6),(5,9),(7,8)] => 1
[(1,10),(2,3),(4,6),(5,9),(7,8)] => 1
[(1,9),(2,3),(4,6),(5,10),(7,8)] => 5
[(1,8),(2,3),(4,6),(5,10),(7,9)] => 5
[(1,7),(2,3),(4,6),(5,10),(8,9)] => 5
[(1,6),(2,3),(4,7),(5,10),(8,9)] => 5
[(1,5),(2,3),(4,7),(6,10),(8,9)] => 5
[(1,4),(2,3),(5,7),(6,10),(8,9)] => 5
[(1,3),(2,4),(5,7),(6,10),(8,9)] => 5
[(1,2),(3,4),(5,7),(6,10),(8,9)] => 5
[(1,2),(3,4),(5,8),(6,10),(7,9)] => 5
[(1,3),(2,4),(5,8),(6,10),(7,9)] => 5
[(1,4),(2,3),(5,8),(6,10),(7,9)] => 5
[(1,5),(2,3),(4,8),(6,10),(7,9)] => 5
[(1,6),(2,3),(4,8),(5,10),(7,9)] => 5
[(1,7),(2,3),(4,8),(5,10),(6,9)] => 5
[(1,8),(2,3),(4,7),(5,10),(6,9)] => 5
[(1,9),(2,3),(4,7),(5,10),(6,8)] => 5
[(1,10),(2,3),(4,7),(5,9),(6,8)] => 1
[(1,10),(2,4),(3,7),(5,9),(6,8)] => 1
[(1,9),(2,4),(3,7),(5,10),(6,8)] => 5
[(1,8),(2,4),(3,7),(5,10),(6,9)] => 5
[(1,7),(2,4),(3,8),(5,10),(6,9)] => 5
[(1,6),(2,4),(3,8),(5,10),(7,9)] => 5
[(1,5),(2,4),(3,8),(6,10),(7,9)] => 5
[(1,4),(2,5),(3,8),(6,10),(7,9)] => 5
[(1,3),(2,5),(4,8),(6,10),(7,9)] => 5
[(1,2),(3,5),(4,8),(6,10),(7,9)] => 5
[(1,2),(3,6),(4,8),(5,10),(7,9)] => 5
[(1,3),(2,6),(4,8),(5,10),(7,9)] => 5
[(1,4),(2,6),(3,8),(5,10),(7,9)] => 5
[(1,5),(2,6),(3,8),(4,10),(7,9)] => 5
[(1,6),(2,5),(3,8),(4,10),(7,9)] => 5
[(1,7),(2,5),(3,8),(4,10),(6,9)] => 5
[(1,8),(2,5),(3,7),(4,10),(6,9)] => 5
[(1,9),(2,5),(3,7),(4,10),(6,8)] => 5
[(1,10),(2,5),(3,7),(4,9),(6,8)] => 1
[(1,10),(2,6),(3,7),(4,9),(5,8)] => 1
[(1,9),(2,6),(3,7),(4,10),(5,8)] => 5
[(1,8),(2,6),(3,7),(4,10),(5,9)] => 5
[(1,7),(2,6),(3,8),(4,10),(5,9)] => 5
[(1,6),(2,7),(3,8),(4,10),(5,9)] => 5
[(1,5),(2,7),(3,8),(4,10),(6,9)] => 5
[(1,4),(2,7),(3,8),(5,10),(6,9)] => 5
[(1,3),(2,7),(4,8),(5,10),(6,9)] => 5
[(1,2),(3,7),(4,8),(5,10),(6,9)] => 5
[(1,2),(3,8),(4,7),(5,10),(6,9)] => 5
[(1,3),(2,8),(4,7),(5,10),(6,9)] => 5
[(1,4),(2,8),(3,7),(5,10),(6,9)] => 5
[(1,5),(2,8),(3,7),(4,10),(6,9)] => 5
[(1,6),(2,8),(3,7),(4,10),(5,9)] => 5
[(1,7),(2,8),(3,6),(4,10),(5,9)] => 5
[(1,8),(2,7),(3,6),(4,10),(5,9)] => 5
[(1,9),(2,7),(3,6),(4,10),(5,8)] => 5
[(1,10),(2,7),(3,6),(4,9),(5,8)] => 1
[(1,10),(2,8),(3,6),(4,9),(5,7)] => 1
[(1,9),(2,8),(3,6),(4,10),(5,7)] => 5
[(1,8),(2,9),(3,6),(4,10),(5,7)] => 5
[(1,7),(2,9),(3,6),(4,10),(5,8)] => 5
[(1,6),(2,9),(3,7),(4,10),(5,8)] => 5
[(1,5),(2,9),(3,7),(4,10),(6,8)] => 5
[(1,4),(2,9),(3,7),(5,10),(6,8)] => 5
[(1,3),(2,9),(4,7),(5,10),(6,8)] => 5
[(1,2),(3,9),(4,7),(5,10),(6,8)] => 5
[(1,2),(3,10),(4,7),(5,9),(6,8)] => 5
[(1,3),(2,10),(4,7),(5,9),(6,8)] => 5
[(1,4),(2,10),(3,7),(5,9),(6,8)] => 5
[(1,5),(2,10),(3,7),(4,9),(6,8)] => 5
[(1,6),(2,10),(3,7),(4,9),(5,8)] => 5
[(1,7),(2,10),(3,6),(4,9),(5,8)] => 5
[(1,8),(2,10),(3,6),(4,9),(5,7)] => 5
[(1,9),(2,10),(3,6),(4,8),(5,7)] => 5
[(1,10),(2,9),(3,6),(4,8),(5,7)] => 1
[(1,10),(2,9),(3,7),(4,8),(5,6)] => 1
[(1,9),(2,10),(3,7),(4,8),(5,6)] => 5
[(1,8),(2,10),(3,7),(4,9),(5,6)] => 5
[(1,7),(2,10),(3,8),(4,9),(5,6)] => 5
[(1,6),(2,10),(3,8),(4,9),(5,7)] => 5
[(1,5),(2,10),(3,8),(4,9),(6,7)] => 5
[(1,4),(2,10),(3,8),(5,9),(6,7)] => 5
[(1,3),(2,10),(4,8),(5,9),(6,7)] => 5
[(1,2),(3,10),(4,8),(5,9),(6,7)] => 5
[(1,2),(3,9),(4,8),(5,10),(6,7)] => 5
[(1,3),(2,9),(4,8),(5,10),(6,7)] => 5
[(1,4),(2,9),(3,8),(5,10),(6,7)] => 5
[(1,5),(2,9),(3,8),(4,10),(6,7)] => 5
[(1,6),(2,9),(3,8),(4,10),(5,7)] => 5
[(1,7),(2,9),(3,8),(4,10),(5,6)] => 5
[(1,8),(2,9),(3,7),(4,10),(5,6)] => 5
[(1,9),(2,8),(3,7),(4,10),(5,6)] => 5
[(1,10),(2,8),(3,7),(4,9),(5,6)] => 1
[(1,10),(2,7),(3,8),(4,9),(5,6)] => 1
[(1,9),(2,7),(3,8),(4,10),(5,6)] => 5
[(1,8),(2,7),(3,9),(4,10),(5,6)] => 5
[(1,7),(2,8),(3,9),(4,10),(5,6)] => 5
[(1,6),(2,8),(3,9),(4,10),(5,7)] => 5
[(1,5),(2,8),(3,9),(4,10),(6,7)] => 5
[(1,4),(2,8),(3,9),(5,10),(6,7)] => 5
[(1,3),(2,8),(4,9),(5,10),(6,7)] => 5
[(1,2),(3,8),(4,9),(5,10),(6,7)] => 5
[(1,2),(3,7),(4,9),(5,10),(6,8)] => 5
[(1,3),(2,7),(4,9),(5,10),(6,8)] => 5
[(1,4),(2,7),(3,9),(5,10),(6,8)] => 5
[(1,5),(2,7),(3,9),(4,10),(6,8)] => 5
[(1,6),(2,7),(3,9),(4,10),(5,8)] => 5
[(1,7),(2,6),(3,9),(4,10),(5,8)] => 5
[(1,8),(2,6),(3,9),(4,10),(5,7)] => 5
[(1,9),(2,6),(3,8),(4,10),(5,7)] => 5
[(1,10),(2,6),(3,8),(4,9),(5,7)] => 1
[(1,10),(2,5),(3,8),(4,9),(6,7)] => 1
[(1,9),(2,5),(3,8),(4,10),(6,7)] => 5
[(1,8),(2,5),(3,9),(4,10),(6,7)] => 5
[(1,7),(2,5),(3,9),(4,10),(6,8)] => 5
[(1,6),(2,5),(3,9),(4,10),(7,8)] => 5
[(1,5),(2,6),(3,9),(4,10),(7,8)] => 5
[(1,4),(2,6),(3,9),(5,10),(7,8)] => 5
[(1,3),(2,6),(4,9),(5,10),(7,8)] => 5
[(1,2),(3,6),(4,9),(5,10),(7,8)] => 5
[(1,2),(3,5),(4,9),(6,10),(7,8)] => 5
[(1,3),(2,5),(4,9),(6,10),(7,8)] => 5
[(1,4),(2,5),(3,9),(6,10),(7,8)] => 5
[(1,5),(2,4),(3,9),(6,10),(7,8)] => 5
[(1,6),(2,4),(3,9),(5,10),(7,8)] => 5
[(1,7),(2,4),(3,9),(5,10),(6,8)] => 5
[(1,8),(2,4),(3,9),(5,10),(6,7)] => 5
[(1,9),(2,4),(3,8),(5,10),(6,7)] => 5
[(1,10),(2,4),(3,8),(5,9),(6,7)] => 1
[(1,10),(2,3),(4,8),(5,9),(6,7)] => 1
[(1,9),(2,3),(4,8),(5,10),(6,7)] => 5
[(1,8),(2,3),(4,9),(5,10),(6,7)] => 5
[(1,7),(2,3),(4,9),(5,10),(6,8)] => 5
[(1,6),(2,3),(4,9),(5,10),(7,8)] => 5
[(1,5),(2,3),(4,9),(6,10),(7,8)] => 5
[(1,4),(2,3),(5,9),(6,10),(7,8)] => 5
[(1,3),(2,4),(5,9),(6,10),(7,8)] => 5
[(1,2),(3,4),(5,9),(6,10),(7,8)] => 5
[(1,2),(3,4),(5,10),(6,9),(7,8)] => 5
[(1,3),(2,4),(5,10),(6,9),(7,8)] => 5
[(1,4),(2,3),(5,10),(6,9),(7,8)] => 5
[(1,5),(2,3),(4,10),(6,9),(7,8)] => 5
[(1,6),(2,3),(4,10),(5,9),(7,8)] => 5
[(1,7),(2,3),(4,10),(5,9),(6,8)] => 5
[(1,8),(2,3),(4,10),(5,9),(6,7)] => 5
[(1,9),(2,3),(4,10),(5,8),(6,7)] => 5
[(1,10),(2,3),(4,9),(5,8),(6,7)] => 1
[(1,10),(2,4),(3,9),(5,8),(6,7)] => 1
[(1,9),(2,4),(3,10),(5,8),(6,7)] => 5
[(1,8),(2,4),(3,10),(5,9),(6,7)] => 5
[(1,7),(2,4),(3,10),(5,9),(6,8)] => 5
[(1,6),(2,4),(3,10),(5,9),(7,8)] => 5
[(1,5),(2,4),(3,10),(6,9),(7,8)] => 5
[(1,4),(2,5),(3,10),(6,9),(7,8)] => 5
[(1,3),(2,5),(4,10),(6,9),(7,8)] => 5
[(1,2),(3,5),(4,10),(6,9),(7,8)] => 5
[(1,2),(3,6),(4,10),(5,9),(7,8)] => 5
[(1,3),(2,6),(4,10),(5,9),(7,8)] => 5
[(1,4),(2,6),(3,10),(5,9),(7,8)] => 5
[(1,5),(2,6),(3,10),(4,9),(7,8)] => 5
[(1,6),(2,5),(3,10),(4,9),(7,8)] => 5
[(1,7),(2,5),(3,10),(4,9),(6,8)] => 5
[(1,8),(2,5),(3,10),(4,9),(6,7)] => 5
[(1,9),(2,5),(3,10),(4,8),(6,7)] => 5
[(1,10),(2,5),(3,9),(4,8),(6,7)] => 1
[(1,10),(2,6),(3,9),(4,8),(5,7)] => 1
[(1,9),(2,6),(3,10),(4,8),(5,7)] => 5
[(1,8),(2,6),(3,10),(4,9),(5,7)] => 5
[(1,7),(2,6),(3,10),(4,9),(5,8)] => 5
[(1,6),(2,7),(3,10),(4,9),(5,8)] => 5
[(1,5),(2,7),(3,10),(4,9),(6,8)] => 5
[(1,4),(2,7),(3,10),(5,9),(6,8)] => 5
[(1,3),(2,7),(4,10),(5,9),(6,8)] => 5
[(1,2),(3,7),(4,10),(5,9),(6,8)] => 5
[(1,2),(3,8),(4,10),(5,9),(6,7)] => 5
[(1,3),(2,8),(4,10),(5,9),(6,7)] => 5
[(1,4),(2,8),(3,10),(5,9),(6,7)] => 5
[(1,5),(2,8),(3,10),(4,9),(6,7)] => 5
[(1,6),(2,8),(3,10),(4,9),(5,7)] => 5
[(1,7),(2,8),(3,10),(4,9),(5,6)] => 5
[(1,8),(2,7),(3,10),(4,9),(5,6)] => 5
[(1,9),(2,7),(3,10),(4,8),(5,6)] => 5
[(1,10),(2,7),(3,9),(4,8),(5,6)] => 1
[(1,10),(2,8),(3,9),(4,7),(5,6)] => 1
[(1,9),(2,8),(3,10),(4,7),(5,6)] => 5
[(1,8),(2,9),(3,10),(4,7),(5,6)] => 5
[(1,7),(2,9),(3,10),(4,8),(5,6)] => 5
[(1,6),(2,9),(3,10),(4,8),(5,7)] => 5
[(1,5),(2,9),(3,10),(4,8),(6,7)] => 5
[(1,4),(2,9),(3,10),(5,8),(6,7)] => 5
[(1,3),(2,9),(4,10),(5,8),(6,7)] => 5
[(1,2),(3,9),(4,10),(5,8),(6,7)] => 5
[(1,2),(3,10),(4,9),(5,8),(6,7)] => 5
[(1,3),(2,10),(4,9),(5,8),(6,7)] => 5
[(1,4),(2,10),(3,9),(5,8),(6,7)] => 5
[(1,5),(2,10),(3,9),(4,8),(6,7)] => 5
[(1,6),(2,10),(3,9),(4,8),(5,7)] => 5
[(1,7),(2,10),(3,9),(4,8),(5,6)] => 5
[(1,8),(2,10),(3,9),(4,7),(5,6)] => 5
[(1,9),(2,10),(3,8),(4,7),(5,6)] => 5
[(1,10),(2,9),(3,8),(4,7),(5,6)] => 1
[(1,12),(2,11),(3,10),(4,9),(5,8),(6,7)] => 1
[(1,2),(3,10),(4,9),(5,8),(6,7),(11,12)] => 5
[(1,12),(2,3),(4,9),(5,8),(6,7),(10,11)] => 1
[(1,2),(3,12),(4,9),(5,8),(6,7),(10,11)] => 6
[(1,10),(2,3),(4,9),(5,8),(6,7),(11,12)] => 5
[(1,12),(2,11),(3,4),(5,8),(6,7),(9,10)] => 1
[(1,2),(3,4),(5,8),(6,7),(9,10),(11,12)] => 5
[(1,12),(2,3),(4,11),(5,8),(6,7),(9,10)] => 1
[(1,2),(3,12),(4,11),(5,8),(6,7),(9,10)] => 6
[(1,4),(2,3),(5,8),(6,7),(9,10),(11,12)] => 5
[(1,12),(2,9),(3,4),(5,8),(6,7),(10,11)] => 1
[(1,2),(3,4),(5,8),(6,7),(9,12),(10,11)] => 5
[(1,10),(2,9),(3,4),(5,8),(6,7),(11,12)] => 5
[(1,4),(2,3),(5,8),(6,7),(9,12),(10,11)] => 5
[(1,12),(2,11),(3,10),(4,5),(6,7),(8,9)] => 1
[(1,2),(3,10),(4,5),(6,7),(8,9),(11,12)] => 4
[(1,12),(2,3),(4,5),(6,7),(8,9),(10,11)] => 1
[(1,2),(3,12),(4,5),(6,7),(8,9),(10,11)] => 6
[(1,10),(2,3),(4,5),(6,7),(8,9),(11,12)] => 3
[(1,12),(2,11),(3,4),(5,10),(6,7),(8,9)] => 1
[(1,2),(3,4),(5,10),(6,7),(8,9),(11,12)] => 4
[(1,12),(2,3),(4,11),(5,10),(6,7),(8,9)] => 1
[(1,2),(3,12),(4,11),(5,10),(6,7),(8,9)] => 6
[(1,4),(2,3),(5,10),(6,7),(8,9),(11,12)] => 4
[(1,12),(2,5),(3,4),(6,7),(8,9),(10,11)] => 1
[(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)] => 6
[(1,10),(2,5),(3,4),(6,7),(8,9),(11,12)] => 3
[(1,4),(2,3),(5,12),(6,7),(8,9),(10,11)] => 6
[(1,12),(2,11),(3,8),(4,5),(6,7),(9,10)] => 1
[(1,2),(3,8),(4,5),(6,7),(9,10),(11,12)] => 5
[(1,12),(2,3),(4,5),(6,7),(8,11),(9,10)] => 1
[(1,2),(3,12),(4,5),(6,7),(8,11),(9,10)] => 6
[(1,8),(2,3),(4,5),(6,7),(9,10),(11,12)] => 5
[(1,12),(2,9),(3,8),(4,5),(6,7),(10,11)] => 1
[(1,2),(3,8),(4,5),(6,7),(9,12),(10,11)] => 3
[(1,10),(2,9),(3,8),(4,5),(6,7),(11,12)] => 5
[(1,8),(2,3),(4,5),(6,7),(9,12),(10,11)] => 3
[(1,12),(2,5),(3,4),(6,7),(8,11),(9,10)] => 1
[(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)] => 6
[(1,8),(2,5),(3,4),(6,7),(9,10),(11,12)] => 5
[(1,4),(2,3),(5,12),(6,7),(8,11),(9,10)] => 6
[(1,8),(2,5),(3,4),(6,7),(9,12),(10,11)] => 3
[(1,12),(2,11),(3,10),(4,9),(5,6),(7,8)] => 1
[(1,2),(3,10),(4,9),(5,6),(7,8),(11,12)] => 3
[(1,12),(2,3),(4,9),(5,6),(7,8),(10,11)] => 1
[(1,2),(3,12),(4,9),(5,6),(7,8),(10,11)] => 6
[(1,10),(2,3),(4,9),(5,6),(7,8),(11,12)] => 4
[(1,12),(2,11),(3,4),(5,6),(7,8),(9,10)] => 1
[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)] => 3
[(1,12),(2,3),(4,11),(5,6),(7,8),(9,10)] => 1
[(1,2),(3,12),(4,11),(5,6),(7,8),(9,10)] => 6
[(1,4),(2,3),(5,6),(7,8),(9,10),(11,12)] => 3
[(1,12),(2,9),(3,4),(5,6),(7,8),(10,11)] => 1
[(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)] => 5
[(1,10),(2,9),(3,4),(5,6),(7,8),(11,12)] => 4
[(1,4),(2,3),(5,6),(7,8),(9,12),(10,11)] => 5
[(1,12),(2,11),(3,10),(4,5),(6,9),(7,8)] => 1
[(1,2),(3,10),(4,5),(6,9),(7,8),(11,12)] => 3
[(1,12),(2,3),(4,5),(6,9),(7,8),(10,11)] => 1
[(1,2),(3,12),(4,5),(6,9),(7,8),(10,11)] => 6
[(1,10),(2,3),(4,5),(6,9),(7,8),(11,12)] => 4
[(1,12),(2,11),(3,4),(5,10),(6,9),(7,8)] => 1
[(1,2),(3,4),(5,10),(6,9),(7,8),(11,12)] => 3
[(1,12),(2,3),(4,11),(5,10),(6,9),(7,8)] => 1
[(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)] => 6
[(1,4),(2,3),(5,10),(6,9),(7,8),(11,12)] => 3
[(1,12),(2,5),(3,4),(6,9),(7,8),(10,11)] => 1
[(1,2),(3,4),(5,12),(6,9),(7,8),(10,11)] => 6
[(1,10),(2,5),(3,4),(6,9),(7,8),(11,12)] => 4
[(1,4),(2,3),(5,12),(6,9),(7,8),(10,11)] => 6
[(1,12),(2,11),(3,6),(4,5),(7,8),(9,10)] => 1
[(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)] => 3
[(1,12),(2,3),(4,5),(6,11),(7,8),(9,10)] => 1
[(1,2),(3,12),(4,5),(6,11),(7,8),(9,10)] => 6
[(1,6),(2,3),(4,5),(7,8),(9,10),(11,12)] => 3
[(1,12),(2,9),(3,6),(4,5),(7,8),(10,11)] => 1
[(1,2),(3,6),(4,5),(7,8),(9,12),(10,11)] => 5
[(1,10),(2,9),(3,6),(4,5),(7,8),(11,12)] => 4
[(1,6),(2,3),(4,5),(7,8),(9,12),(10,11)] => 5
[(1,12),(2,5),(3,4),(6,11),(7,8),(9,10)] => 1
[(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)] => 6
[(1,6),(2,5),(3,4),(7,8),(9,10),(11,12)] => 3
[(1,4),(2,3),(5,12),(6,11),(7,8),(9,10)] => 6
[(1,6),(2,5),(3,4),(7,8),(9,12),(10,11)] => 5
[(1,12),(2,11),(3,10),(4,7),(5,6),(8,9)] => 1
[(1,2),(3,10),(4,7),(5,6),(8,9),(11,12)] => 4
[(1,12),(2,3),(4,7),(5,6),(8,9),(10,11)] => 1
[(1,2),(3,12),(4,7),(5,6),(8,9),(10,11)] => 6
[(1,10),(2,3),(4,7),(5,6),(8,9),(11,12)] => 3
[(1,12),(2,11),(3,4),(5,6),(7,10),(8,9)] => 1
[(1,2),(3,4),(5,6),(7,10),(8,9),(11,12)] => 4
[(1,12),(2,3),(4,11),(5,6),(7,10),(8,9)] => 1
[(1,2),(3,12),(4,11),(5,6),(7,10),(8,9)] => 6
[(1,4),(2,3),(5,6),(7,10),(8,9),(11,12)] => 4
[(1,12),(2,7),(3,4),(5,6),(8,9),(10,11)] => 1
[(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)] => 6
[(1,10),(2,7),(3,4),(5,6),(8,9),(11,12)] => 3
[(1,4),(2,3),(5,6),(7,12),(8,9),(10,11)] => 6
[(1,12),(2,11),(3,8),(4,7),(5,6),(9,10)] => 1
[(1,2),(3,8),(4,7),(5,6),(9,10),(11,12)] => 5
[(1,12),(2,3),(4,7),(5,6),(8,11),(9,10)] => 1
[(1,2),(3,12),(4,7),(5,6),(8,11),(9,10)] => 6
[(1,8),(2,3),(4,7),(5,6),(9,10),(11,12)] => 5
[(1,12),(2,9),(3,8),(4,7),(5,6),(10,11)] => 1
[(1,2),(3,8),(4,7),(5,6),(9,12),(10,11)] => 3
[(1,10),(2,9),(3,8),(4,7),(5,6),(11,12)] => 5
[(1,8),(2,3),(4,7),(5,6),(9,12),(10,11)] => 3
[(1,12),(2,7),(3,4),(5,6),(8,11),(9,10)] => 1
[(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)] => 6
[(1,8),(2,7),(3,4),(5,6),(9,10),(11,12)] => 5
[(1,4),(2,3),(5,6),(7,12),(8,11),(9,10)] => 6
[(1,8),(2,7),(3,4),(5,6),(9,12),(10,11)] => 3
[(1,12),(2,11),(3,6),(4,5),(7,10),(8,9)] => 1
[(1,2),(3,6),(4,5),(7,10),(8,9),(11,12)] => 4
[(1,12),(2,3),(4,5),(6,11),(7,10),(8,9)] => 1
[(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)] => 6
[(1,6),(2,3),(4,5),(7,10),(8,9),(11,12)] => 4
[(1,12),(2,7),(3,6),(4,5),(8,9),(10,11)] => 1
[(1,2),(3,6),(4,5),(7,12),(8,9),(10,11)] => 6
[(1,10),(2,7),(3,6),(4,5),(8,9),(11,12)] => 3
[(1,6),(2,3),(4,5),(7,12),(8,9),(10,11)] => 6
[(1,12),(2,5),(3,4),(6,11),(7,10),(8,9)] => 1
[(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)] => 6
[(1,6),(2,5),(3,4),(7,10),(8,9),(11,12)] => 4
[(1,4),(2,3),(5,12),(6,11),(7,10),(8,9)] => 6
[(1,6),(2,5),(3,4),(7,12),(8,9),(10,11)] => 6
[(1,12),(2,7),(3,6),(4,5),(8,11),(9,10)] => 1
[(1,2),(3,6),(4,5),(7,12),(8,11),(9,10)] => 6
[(1,8),(2,7),(3,6),(4,5),(9,10),(11,12)] => 5
[(1,6),(2,3),(4,5),(7,12),(8,11),(9,10)] => 6
[(1,8),(2,7),(3,6),(4,5),(9,12),(10,11)] => 3
[(1,6),(2,5),(3,4),(7,12),(8,11),(9,10)] => 6
[(1,2),(3,4),(5,6),(7,8),(9,11),(10,12)] => 5
[(1,2),(3,4),(5,6),(7,9),(8,10),(11,12)] => 4
[(1,2),(3,4),(5,6),(7,9),(8,11),(10,12)] => 5
[(1,2),(3,4),(5,6),(7,10),(8,11),(9,12)] => 5
[(1,2),(3,4),(5,7),(6,8),(9,10),(11,12)] => 3
[(1,2),(3,4),(5,7),(6,8),(9,11),(10,12)] => 5
[(1,2),(3,4),(5,7),(6,9),(8,10),(11,12)] => 4
[(1,2),(3,4),(5,7),(6,9),(8,11),(10,12)] => 5
[(1,2),(3,4),(5,7),(6,10),(8,11),(9,12)] => 5
[(1,2),(3,4),(5,8),(6,9),(7,10),(11,12)] => 4
[(1,2),(3,4),(5,8),(6,9),(7,11),(10,12)] => 3
[(1,2),(3,4),(5,8),(6,10),(7,11),(9,12)] => 5
[(1,2),(3,4),(5,9),(6,10),(7,11),(8,12)] => 2
[(1,2),(3,5),(4,6),(7,8),(9,10),(11,12)] => 3
[(1,2),(3,5),(4,6),(7,8),(9,11),(10,12)] => 5
[(1,2),(3,5),(4,6),(7,9),(8,10),(11,12)] => 4
[(1,2),(3,5),(4,6),(7,9),(8,11),(10,12)] => 5
[(1,2),(3,5),(4,6),(7,10),(8,11),(9,12)] => 5
[(1,2),(3,5),(4,7),(6,8),(9,10),(11,12)] => 3
[(1,2),(3,5),(4,7),(6,8),(9,11),(10,12)] => 5
[(1,2),(3,5),(4,7),(6,9),(8,10),(11,12)] => 4
[(1,2),(3,5),(4,7),(6,9),(8,11),(10,12)] => 5
[(1,2),(3,5),(4,7),(6,10),(8,11),(9,12)] => 5
[(1,2),(3,5),(4,8),(6,9),(7,10),(11,12)] => 4
[(1,2),(3,5),(4,8),(6,9),(7,11),(10,12)] => 3
[(1,2),(3,5),(4,8),(6,10),(7,11),(9,12)] => 5
[(1,2),(3,5),(4,9),(6,10),(7,11),(8,12)] => 2
[(1,2),(3,6),(4,7),(5,8),(9,10),(11,12)] => 3
[(1,2),(3,6),(4,7),(5,8),(9,11),(10,12)] => 5
[(1,2),(3,6),(4,7),(5,9),(8,10),(11,12)] => 4
[(1,2),(3,6),(4,7),(5,9),(8,11),(10,12)] => 5
[(1,2),(3,6),(4,7),(5,10),(8,11),(9,12)] => 5
[(1,2),(3,6),(4,8),(5,9),(7,10),(11,12)] => 4
[(1,2),(3,6),(4,8),(5,9),(7,11),(10,12)] => 3
[(1,2),(3,6),(4,8),(5,10),(7,11),(9,12)] => 5
[(1,2),(3,6),(4,9),(5,10),(7,11),(8,12)] => 2
[(1,2),(3,7),(4,8),(5,9),(6,10),(11,12)] => 4
[(1,2),(3,7),(4,8),(5,9),(6,11),(10,12)] => 3
[(1,2),(3,7),(4,8),(5,10),(6,11),(9,12)] => 5
[(1,2),(3,7),(4,9),(5,10),(6,11),(8,12)] => 2
[(1,2),(3,8),(4,9),(5,10),(6,11),(7,12)] => 6
[(1,3),(2,4),(5,6),(7,8),(9,10),(11,12)] => 3
[(1,3),(2,4),(5,6),(7,8),(9,11),(10,12)] => 5
[(1,3),(2,4),(5,6),(7,9),(8,10),(11,12)] => 4
[(1,3),(2,4),(5,6),(7,9),(8,11),(10,12)] => 5
[(1,3),(2,4),(5,6),(7,10),(8,11),(9,12)] => 5
[(1,3),(2,4),(5,7),(6,8),(9,10),(11,12)] => 3
[(1,3),(2,4),(5,7),(6,8),(9,11),(10,12)] => 5
[(1,3),(2,4),(5,7),(6,9),(8,10),(11,12)] => 4
[(1,3),(2,4),(5,7),(6,9),(8,11),(10,12)] => 5
[(1,3),(2,4),(5,7),(6,10),(8,11),(9,12)] => 5
[(1,3),(2,4),(5,8),(6,9),(7,10),(11,12)] => 4
[(1,3),(2,4),(5,8),(6,9),(7,11),(10,12)] => 3
[(1,3),(2,4),(5,8),(6,10),(7,11),(9,12)] => 5
[(1,3),(2,4),(5,9),(6,10),(7,11),(8,12)] => 2
[(1,3),(2,5),(4,6),(7,8),(9,10),(11,12)] => 3
[(1,3),(2,5),(4,6),(7,8),(9,11),(10,12)] => 5
[(1,3),(2,5),(4,6),(7,9),(8,10),(11,12)] => 4
[(1,3),(2,5),(4,6),(7,9),(8,11),(10,12)] => 5
[(1,3),(2,5),(4,6),(7,10),(8,11),(9,12)] => 5
[(1,3),(2,5),(4,7),(6,8),(9,10),(11,12)] => 3
[(1,3),(2,5),(4,7),(6,8),(9,11),(10,12)] => 5
[(1,3),(2,5),(4,7),(6,9),(8,10),(11,12)] => 4
[(1,3),(2,5),(4,7),(6,9),(8,11),(10,12)] => 5
[(1,3),(2,5),(4,7),(6,10),(8,11),(9,12)] => 5
[(1,3),(2,5),(4,8),(6,9),(7,10),(11,12)] => 4
[(1,3),(2,5),(4,8),(6,9),(7,11),(10,12)] => 3
[(1,3),(2,5),(4,8),(6,10),(7,11),(9,12)] => 5
[(1,3),(2,5),(4,9),(6,10),(7,11),(8,12)] => 2
[(1,3),(2,6),(4,7),(5,8),(9,10),(11,12)] => 3
[(1,3),(2,6),(4,7),(5,8),(9,11),(10,12)] => 5
[(1,3),(2,6),(4,7),(5,9),(8,10),(11,12)] => 4
[(1,3),(2,6),(4,7),(5,9),(8,11),(10,12)] => 5
[(1,3),(2,6),(4,7),(5,10),(8,11),(9,12)] => 5
[(1,3),(2,6),(4,8),(5,9),(7,10),(11,12)] => 4
[(1,3),(2,6),(4,8),(5,9),(7,11),(10,12)] => 3
[(1,3),(2,6),(4,8),(5,10),(7,11),(9,12)] => 5
[(1,3),(2,6),(4,9),(5,10),(7,11),(8,12)] => 2
[(1,3),(2,7),(4,8),(5,9),(6,10),(11,12)] => 4
[(1,3),(2,7),(4,8),(5,9),(6,11),(10,12)] => 3
[(1,3),(2,7),(4,8),(5,10),(6,11),(9,12)] => 5
[(1,3),(2,7),(4,9),(5,10),(6,11),(8,12)] => 2
[(1,3),(2,8),(4,9),(5,10),(6,11),(7,12)] => 6
[(1,4),(2,5),(3,6),(7,8),(9,10),(11,12)] => 3
[(1,4),(2,5),(3,6),(7,8),(9,11),(10,12)] => 5
[(1,4),(2,5),(3,6),(7,9),(8,10),(11,12)] => 4
[(1,4),(2,5),(3,6),(7,9),(8,11),(10,12)] => 5
[(1,4),(2,5),(3,6),(7,10),(8,11),(9,12)] => 5
[(1,4),(2,5),(3,7),(6,8),(9,10),(11,12)] => 3
[(1,4),(2,5),(3,7),(6,8),(9,11),(10,12)] => 5
[(1,4),(2,5),(3,7),(6,9),(8,10),(11,12)] => 4
[(1,4),(2,5),(3,7),(6,9),(8,11),(10,12)] => 5
[(1,4),(2,5),(3,7),(6,10),(8,11),(9,12)] => 5
[(1,4),(2,5),(3,8),(6,9),(7,10),(11,12)] => 4
[(1,4),(2,5),(3,8),(6,9),(7,11),(10,12)] => 3
[(1,4),(2,5),(3,8),(6,10),(7,11),(9,12)] => 5
[(1,4),(2,5),(3,9),(6,10),(7,11),(8,12)] => 2
[(1,4),(2,6),(3,7),(5,8),(9,10),(11,12)] => 3
[(1,4),(2,6),(3,7),(5,8),(9,11),(10,12)] => 5
[(1,4),(2,6),(3,7),(5,9),(8,10),(11,12)] => 4
[(1,4),(2,6),(3,7),(5,9),(8,11),(10,12)] => 5
[(1,4),(2,6),(3,7),(5,10),(8,11),(9,12)] => 5
[(1,4),(2,6),(3,8),(5,9),(7,10),(11,12)] => 4
[(1,4),(2,6),(3,8),(5,9),(7,11),(10,12)] => 3
[(1,4),(2,6),(3,8),(5,10),(7,11),(9,12)] => 5
[(1,4),(2,6),(3,9),(5,10),(7,11),(8,12)] => 2
[(1,4),(2,7),(3,8),(5,9),(6,10),(11,12)] => 4
[(1,4),(2,7),(3,8),(5,9),(6,11),(10,12)] => 3
[(1,4),(2,7),(3,8),(5,10),(6,11),(9,12)] => 5
[(1,4),(2,7),(3,9),(5,10),(6,11),(8,12)] => 2
[(1,4),(2,8),(3,9),(5,10),(6,11),(7,12)] => 6
[(1,5),(2,6),(3,7),(4,8),(9,10),(11,12)] => 3
[(1,5),(2,6),(3,7),(4,8),(9,11),(10,12)] => 5
[(1,5),(2,6),(3,7),(4,9),(8,10),(11,12)] => 4
[(1,5),(2,6),(3,7),(4,9),(8,11),(10,12)] => 5
[(1,5),(2,6),(3,7),(4,10),(8,11),(9,12)] => 5
[(1,5),(2,6),(3,8),(4,9),(7,10),(11,12)] => 4
[(1,5),(2,6),(3,8),(4,9),(7,11),(10,12)] => 3
[(1,5),(2,6),(3,8),(4,10),(7,11),(9,12)] => 5
[(1,5),(2,6),(3,9),(4,10),(7,11),(8,12)] => 2
[(1,5),(2,7),(3,8),(4,9),(6,10),(11,12)] => 4
[(1,5),(2,7),(3,8),(4,9),(6,11),(10,12)] => 3
[(1,5),(2,7),(3,8),(4,10),(6,11),(9,12)] => 5
[(1,5),(2,7),(3,9),(4,10),(6,11),(8,12)] => 2
[(1,5),(2,8),(3,9),(4,10),(6,11),(7,12)] => 6
[(1,6),(2,7),(3,8),(4,9),(5,10),(11,12)] => 4
[(1,6),(2,7),(3,8),(4,9),(5,11),(10,12)] => 3
[(1,6),(2,7),(3,8),(4,10),(5,11),(9,12)] => 5
[(1,6),(2,7),(3,9),(4,10),(5,11),(8,12)] => 2
[(1,6),(2,8),(3,9),(4,10),(5,11),(7,12)] => 6
[(1,7),(2,8),(3,9),(4,10),(5,11),(6,12)] => 6
[(1,2),(3,14),(4,5),(6,13),(7,12),(8,11),(9,10)] => 7
[(1,2),(3,14),(4,13),(5,6),(7,12),(8,9),(10,11)] => 7
[(1,2),(3,14),(4,13),(5,6),(7,12),(8,11),(9,10)] => 7
[(1,2),(3,14),(4,13),(5,8),(6,7),(9,12),(10,11)] => 7
[(1,2),(3,14),(4,13),(5,10),(6,7),(8,9),(11,12)] => 7
[(1,2),(3,14),(4,13),(5,12),(6,7),(8,9),(10,11)] => 7
[(1,2),(3,14),(4,13),(5,12),(6,7),(8,11),(9,10)] => 7
[(1,2),(3,14),(4,11),(5,10),(6,9),(7,8),(12,13)] => 7
[(1,2),(3,14),(4,13),(5,10),(6,9),(7,8),(11,12)] => 7
[(1,2),(3,14),(4,13),(5,12),(6,9),(7,8),(10,11)] => 7
[(1,2),(3,14),(4,13),(5,12),(6,11),(7,8),(9,10)] => 7
[(1,2),(3,14),(4,13),(5,12),(6,11),(7,10),(8,9)] => 7
[(1,4),(2,3),(5,14),(6,13),(7,12),(8,11),(9,10)] => 7
[(1,12),(2,3),(4,11),(5,10),(6,9),(7,8),(13,14)] => 6
[(1,12),(2,11),(3,4),(5,10),(6,7),(8,9),(13,14)] => 5
[(1,12),(2,11),(3,4),(5,10),(6,9),(7,8),(13,14)] => 6
[(1,12),(2,11),(3,6),(4,5),(7,10),(8,9),(13,14)] => 5
[(1,12),(2,11),(3,8),(4,5),(6,7),(9,10),(13,14)] => 4
[(1,12),(2,11),(3,10),(4,5),(6,7),(8,9),(13,14)] => 5
[(1,12),(2,11),(3,10),(4,5),(6,9),(7,8),(13,14)] => 6
[(1,10),(2,9),(3,8),(4,7),(5,6),(11,14),(12,13)] => 4
[(1,12),(2,9),(3,8),(4,7),(5,6),(10,11),(13,14)] => 3
[(1,12),(2,11),(3,8),(4,7),(5,6),(9,10),(13,14)] => 4
[(1,12),(2,11),(3,10),(4,7),(5,6),(8,9),(13,14)] => 5
[(1,12),(2,11),(3,10),(4,9),(5,6),(7,8),(13,14)] => 6
[(1,12),(2,11),(3,10),(4,9),(5,8),(6,7),(13,14)] => 6
[(1,2),(3,16),(4,15),(5,14),(6,7),(8,13),(9,12),(10,11)] => 8
[(1,2),(3,16),(4,15),(5,14),(6,13),(7,8),(9,10),(11,12)] => 8
[(1,2),(3,16),(4,15),(5,14),(6,13),(7,8),(9,12),(10,11)] => 8
[(1,2),(3,16),(4,15),(5,14),(6,11),(7,10),(8,9),(12,13)] => 8
[(1,2),(3,16),(4,15),(5,14),(6,13),(7,10),(8,9),(11,12)] => 8
[(1,2),(3,16),(4,15),(5,14),(6,13),(7,12),(8,9),(10,11)] => 8
[(1,2),(3,16),(4,15),(5,14),(6,13),(7,12),(8,11),(9,10)] => 8
[(1,14),(2,13),(3,12),(4,5),(6,11),(7,10),(8,9),(15,16)] => 7
[(1,14),(2,13),(3,12),(4,11),(5,6),(7,8),(9,10),(15,16)] => 6
[(1,14),(2,13),(3,12),(4,11),(5,6),(7,10),(8,9),(15,16)] => 7
[(1,14),(2,13),(3,12),(4,9),(5,8),(6,7),(10,11),(15,16)] => 5
[(1,14),(2,13),(3,12),(4,11),(5,8),(6,7),(9,10),(15,16)] => 6
[(1,14),(2,13),(3,12),(4,11),(5,10),(6,7),(8,9),(15,16)] => 7
[(1,14),(2,13),(3,12),(4,11),(5,10),(6,9),(7,8),(15,16)] => 7
[(1,16),(2,15),(3,14),(4,13),(5,12),(6,11),(7,10),(8,9),(17,18)] => 8
[(1,2),(3,18),(4,17),(5,16),(6,15),(7,14),(8,13),(9,12),(10,11)] => 9
[(1,16),(2,15),(3,14),(4,13),(5,12),(6,11),(7,8),(9,10),(17,18)] => 8
[(1,2),(3,18),(4,17),(5,16),(6,15),(7,14),(8,13),(9,10),(11,12)] => 9
[(1,16),(2,15),(3,14),(4,13),(5,12),(6,9),(7,8),(10,11),(17,18)] => 7
[(1,16),(2,15),(3,14),(4,13),(5,12),(6,7),(8,11),(9,10),(17,18)] => 8
[(1,2),(3,18),(4,17),(5,16),(6,15),(7,14),(8,11),(9,10),(12,13)] => 9
[(1,2),(3,18),(4,17),(5,16),(6,15),(7,14),(8,9),(10,13),(11,12)] => 9
[(1,18),(2,17),(3,16),(4,15),(5,14),(6,13),(7,12),(8,11),(9,10),(19,20)] => 9
[(1,2),(3,20),(4,19),(5,18),(6,17),(7,16),(8,15),(9,14),(10,13),(11,12)] => 10
[(1,18),(2,17),(3,16),(4,15),(5,14),(6,13),(7,12),(8,9),(10,11),(19,20)] => 9
[(1,2),(3,20),(4,19),(5,18),(6,17),(7,16),(8,15),(9,14),(10,11),(12,13)] => 10
[(1,20),(2,19),(3,18),(4,17),(5,16),(6,15),(7,14),(8,13),(9,12),(10,11),(21,22)] => 10
[(1,2),(3,22),(4,21),(5,20),(6,19),(7,18),(8,17),(9,16),(10,15),(11,14),(12,13)] => 11
[(1,2),(3,4),(5,6),(7,9),(8,12),(10,11)] => 2
[(1,2),(3,4),(5,6),(7,10),(8,12),(9,11)] => 2
[(1,2),(3,4),(5,6),(7,11),(8,9),(10,12)] => 5
[(1,2),(3,4),(5,6),(7,11),(8,10),(9,12)] => 5
[(1,2),(3,4),(5,6),(7,11),(8,12),(9,10)] => 2
[(1,2),(3,4),(5,6),(7,12),(8,10),(9,11)] => 6
[(1,2),(3,4),(5,7),(6,8),(9,12),(10,11)] => 5
[(1,2),(3,4),(5,7),(6,9),(8,12),(10,11)] => 2
[(1,2),(3,4),(5,7),(6,10),(8,9),(11,12)] => 4
[(1,2),(3,4),(5,7),(6,10),(8,12),(9,11)] => 2
[(1,2),(3,4),(5,7),(6,11),(8,9),(10,12)] => 5
[(1,2),(3,4),(5,7),(6,11),(8,10),(9,12)] => 5
[(1,2),(3,4),(5,7),(6,11),(8,12),(9,10)] => 2
[(1,2),(3,4),(5,7),(6,12),(8,9),(10,11)] => 6
[(1,2),(3,4),(5,7),(6,12),(8,10),(9,11)] => 6
[(1,2),(3,4),(5,7),(6,12),(8,11),(9,10)] => 6
[(1,2),(3,4),(5,8),(6,7),(9,11),(10,12)] => 3
[(1,2),(3,4),(5,8),(6,9),(7,12),(10,11)] => 6
[(1,2),(3,4),(5,8),(6,10),(7,12),(9,11)] => 6
[(1,2),(3,4),(5,8),(6,10),(7,9),(11,12)] => 4
[(1,2),(3,4),(5,8),(6,11),(7,12),(9,10)] => 6
[(1,2),(3,4),(5,8),(6,11),(7,10),(9,12)] => 5
[(1,2),(3,4),(5,8),(6,11),(7,9),(10,12)] => 3
[(1,2),(3,4),(5,8),(6,12),(7,11),(9,10)] => 6
[(1,2),(3,4),(5,8),(6,12),(7,10),(9,11)] => 6
[(1,2),(3,4),(5,8),(6,12),(7,9),(10,11)] => 6
[(1,2),(3,4),(5,9),(6,7),(8,10),(11,12)] => 5
[(1,2),(3,4),(5,9),(6,7),(8,11),(10,12)] => 4
[(1,2),(3,4),(5,9),(6,7),(8,12),(10,11)] => 2
[(1,2),(3,4),(5,9),(6,8),(7,12),(10,11)] => 6
[(1,2),(3,4),(5,9),(6,8),(7,11),(10,12)] => 4
[(1,2),(3,4),(5,9),(6,8),(7,10),(11,12)] => 3
[(1,2),(3,4),(5,9),(6,10),(7,12),(8,11)] => 6
[(1,2),(3,4),(5,9),(6,10),(7,8),(11,12)] => 3
[(1,2),(3,4),(5,9),(6,11),(7,12),(8,10)] => 6
[(1,2),(3,4),(5,9),(6,11),(7,10),(8,12)] => 2
[(1,2),(3,4),(5,9),(6,11),(7,8),(10,12)] => 4
[(1,2),(3,4),(5,9),(6,12),(7,11),(8,10)] => 6
[(1,2),(3,4),(5,9),(6,12),(7,10),(8,11)] => 6
[(1,2),(3,4),(5,9),(6,12),(7,8),(10,11)] => 6
[(1,2),(3,4),(5,10),(6,7),(8,11),(9,12)] => 5
[(1,2),(3,4),(5,10),(6,7),(8,12),(9,11)] => 2
[(1,2),(3,4),(5,10),(6,8),(7,12),(9,11)] => 6
[(1,2),(3,4),(5,10),(6,8),(7,11),(9,12)] => 5
[(1,2),(3,4),(5,10),(6,8),(7,9),(11,12)] => 4
[(1,2),(3,4),(5,10),(6,9),(7,12),(8,11)] => 6
[(1,2),(3,4),(5,10),(6,9),(7,11),(8,12)] => 2
[(1,2),(3,4),(5,10),(6,11),(7,12),(8,9)] => 6
[(1,2),(3,4),(5,10),(6,11),(7,9),(8,12)] => 2
[(1,2),(3,4),(5,10),(6,11),(7,8),(9,12)] => 5
[(1,2),(3,4),(5,10),(6,12),(7,11),(8,9)] => 6
[(1,2),(3,4),(5,10),(6,12),(7,9),(8,11)] => 6
[(1,2),(3,4),(5,10),(6,12),(7,8),(9,11)] => 6
[(1,2),(3,4),(5,11),(6,7),(8,9),(10,12)] => 5
[(1,2),(3,4),(5,11),(6,7),(8,10),(9,12)] => 5
[(1,2),(3,4),(5,11),(6,7),(8,12),(9,10)] => 2
[(1,2),(3,4),(5,11),(6,8),(7,12),(9,10)] => 6
[(1,2),(3,4),(5,11),(6,8),(7,10),(9,12)] => 5
[(1,2),(3,4),(5,11),(6,8),(7,9),(10,12)] => 3
[(1,2),(3,4),(5,11),(6,9),(7,12),(8,10)] => 6
[(1,2),(3,4),(5,11),(6,9),(7,10),(8,12)] => 2
[(1,2),(3,4),(5,11),(6,9),(7,8),(10,12)] => 4
[(1,2),(3,4),(5,11),(6,10),(7,12),(8,9)] => 6
[(1,2),(3,4),(5,11),(6,10),(7,9),(8,12)] => 2
[(1,2),(3,4),(5,11),(6,10),(7,8),(9,12)] => 5
[(1,2),(3,4),(5,11),(6,12),(7,10),(8,9)] => 6
[(1,2),(3,4),(5,11),(6,12),(7,9),(8,10)] => 6
[(1,2),(3,4),(5,11),(6,12),(7,8),(9,10)] => 6
[(1,2),(3,4),(5,12),(6,7),(8,10),(9,11)] => 6
[(1,2),(3,4),(5,12),(6,8),(7,11),(9,10)] => 6
[(1,2),(3,4),(5,12),(6,8),(7,10),(9,11)] => 6
[(1,2),(3,4),(5,12),(6,8),(7,9),(10,11)] => 6
[(1,2),(3,4),(5,12),(6,9),(7,11),(8,10)] => 6
[(1,2),(3,4),(5,12),(6,9),(7,10),(8,11)] => 6
[(1,2),(3,4),(5,12),(6,10),(7,11),(8,9)] => 6
[(1,2),(3,4),(5,12),(6,10),(7,9),(8,11)] => 6
[(1,2),(3,4),(5,12),(6,10),(7,8),(9,11)] => 6
[(1,2),(3,4),(5,12),(6,11),(7,9),(8,10)] => 6
[(1,2),(3,5),(4,6),(7,8),(9,12),(10,11)] => 5
[(1,2),(3,5),(4,6),(7,9),(8,12),(10,11)] => 2
[(1,2),(3,5),(4,6),(7,10),(8,9),(11,12)] => 4
[(1,2),(3,5),(4,6),(7,10),(8,12),(9,11)] => 2
[(1,2),(3,5),(4,6),(7,11),(8,9),(10,12)] => 5
[(1,2),(3,5),(4,6),(7,11),(8,10),(9,12)] => 5
[(1,2),(3,5),(4,6),(7,11),(8,12),(9,10)] => 2
[(1,2),(3,5),(4,6),(7,12),(8,9),(10,11)] => 6
[(1,2),(3,5),(4,6),(7,12),(8,10),(9,11)] => 6
[(1,2),(3,5),(4,6),(7,12),(8,11),(9,10)] => 6
[(1,2),(3,5),(4,7),(6,8),(9,12),(10,11)] => 5
[(1,2),(3,5),(4,7),(6,9),(8,12),(10,11)] => 2
[(1,2),(3,5),(4,7),(6,10),(8,9),(11,12)] => 4
[(1,2),(3,5),(4,7),(6,10),(8,12),(9,11)] => 2
[(1,2),(3,5),(4,7),(6,11),(8,9),(10,12)] => 5
[(1,2),(3,5),(4,7),(6,11),(8,10),(9,12)] => 5
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Created: Nov 13, 2017 at 11:27 by Martin Rubey
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Last Updated: Apr 01, 2018 at 22:50 by Martin Rubey