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-----------------------------------------------------------------------------
Statistic identifier: St001094
-----------------------------------------------------------------------------
Collection: Set partitions
-----------------------------------------------------------------------------
Description: The depth index of a set partition.
For a set partition $\Pi$ of $\{1,\dots,n\}$ with arcs $\mathcal A$, this is $$\sum_{i=1}^{|\mathcal A|} (n-i) - \sum_{j=1}^n depth(j) + \sum_{\alpha\in\mathcal A} depth(\alpha),$$
where the depth of an element $i$ is the number of arcs $(k,\ell)$ with $k < i < \ell$, and the depth of an arc $(i,j)$ is the number of arcs $(k,\ell)$ with $k < i$ and $j < \ell$.
-----------------------------------------------------------------------------
References: [1] Bilen Can, M., Cherniavsky, Y. Stirling Posets [[arXiv:1801.08231]]
-----------------------------------------------------------------------------
Code:
def depth_vertex(P, i):
"""
sage: P = SetPartition([{1, 2, 7, 8}, {3, 4, 6}, {5}, {9, 10}])
sage: [depth_vertex(P, i) for i in range(1, P.size()+1)]
[0, 0, 1, 1, 2, 1, 0, 0, 0, 0]
"""
return sum(1 for a in P.arcs() if a[0] < i < a[1])
def depth_arc(P, a):
"""
sage: P = SetPartition([{1, 2, 7, 8}, {3, 4, 6}, {5}, {9, 10}])
sage: [(a, depth_arc(P, a)) for a in P.arcs()]
[((1, 2), 0), ((2, 7), 0), ((7, 8), 0), ((3, 4), 1), ((4, 6), 1), ((9, 10), 0)]
"""
return sum(1 for b in P.arcs() if b[0] < a[0] and a[1] < b[1])
def statistic(P):
"""
sage: P = SetPartition([[1,8], [2,5,6,9], [3,7], [4]])
sage: statistic(P)
21
"""
n = P.size()
A = P.arcs()
return (sum(n-i for i in range(1, len(A)+1)) -
sum(depth_vertex(P, i) for i in range(1, n+1)) +
sum(depth_arc(P, a) for a in A))
-----------------------------------------------------------------------------
Statistic values:
{{1}} => 0
{{1,2}} => 1
{{1},{2}} => 0
{{1,2,3}} => 3
{{1,2},{3}} => 2
{{1,3},{2}} => 1
{{1},{2,3}} => 2
{{1},{2},{3}} => 0
{{1,2,3,4}} => 6
{{1,2,3},{4}} => 5
{{1,2,4},{3}} => 4
{{1,2},{3,4}} => 5
{{1,2},{3},{4}} => 3
{{1,3,4},{2}} => 4
{{1,3},{2,4}} => 3
{{1,3},{2},{4}} => 2
{{1,4},{2,3}} => 4
{{1},{2,3,4}} => 5
{{1},{2,3},{4}} => 3
{{1,4},{2},{3}} => 1
{{1},{2,4},{3}} => 2
{{1},{2},{3,4}} => 3
{{1},{2},{3},{4}} => 0
{{1,2,3,4,5}} => 10
{{1,2,3,4},{5}} => 9
{{1,2,3,5},{4}} => 8
{{1,2,3},{4,5}} => 9
{{1,2,3},{4},{5}} => 7
{{1,2,4,5},{3}} => 8
{{1,2,4},{3,5}} => 7
{{1,2,4},{3},{5}} => 6
{{1,2,5},{3,4}} => 8
{{1,2},{3,4,5}} => 9
{{1,2},{3,4},{5}} => 7
{{1,2,5},{3},{4}} => 5
{{1,2},{3,5},{4}} => 6
{{1,2},{3},{4,5}} => 7
{{1,2},{3},{4},{5}} => 4
{{1,3,4,5},{2}} => 8
{{1,3,4},{2,5}} => 7
{{1,3,4},{2},{5}} => 6
{{1,3,5},{2,4}} => 6
{{1,3},{2,4,5}} => 7
{{1,3},{2,4},{5}} => 5
{{1,3,5},{2},{4}} => 5
{{1,3},{2,5},{4}} => 4
{{1,3},{2},{4,5}} => 6
{{1,3},{2},{4},{5}} => 3
{{1,4,5},{2,3}} => 8
{{1,4},{2,3,5}} => 7
{{1,4},{2,3},{5}} => 6
{{1,5},{2,3,4}} => 8
{{1},{2,3,4,5}} => 9
{{1},{2,3,4},{5}} => 7
{{1,5},{2,3},{4}} => 5
{{1},{2,3,5},{4}} => 6
{{1},{2,3},{4,5}} => 7
{{1},{2,3},{4},{5}} => 4
{{1,4,5},{2},{3}} => 5
{{1,4},{2,5},{3}} => 3
{{1,4},{2},{3,5}} => 4
{{1,4},{2},{3},{5}} => 2
{{1,5},{2,4},{3}} => 4
{{1},{2,4,5},{3}} => 6
{{1},{2,4},{3,5}} => 5
{{1},{2,4},{3},{5}} => 3
{{1,5},{2},{3,4}} => 5
{{1},{2,5},{3,4}} => 6
{{1},{2},{3,4,5}} => 7
{{1},{2},{3,4},{5}} => 4
{{1,5},{2},{3},{4}} => 1
{{1},{2,5},{3},{4}} => 2
{{1},{2},{3,5},{4}} => 3
{{1},{2},{3},{4,5}} => 4
{{1},{2},{3},{4},{5}} => 0
{{1,2,3,4,5,6}} => 15
{{1,2,3,4,5},{6}} => 14
{{1,2,3,4,6},{5}} => 13
{{1,2,3,4},{5,6}} => 14
{{1,2,3,4},{5},{6}} => 12
{{1,2,3,5,6},{4}} => 13
{{1,2,3,5},{4,6}} => 12
{{1,2,3,5},{4},{6}} => 11
{{1,2,3,6},{4,5}} => 13
{{1,2,3},{4,5,6}} => 14
{{1,2,3},{4,5},{6}} => 12
{{1,2,3,6},{4},{5}} => 10
{{1,2,3},{4,6},{5}} => 11
{{1,2,3},{4},{5,6}} => 12
{{1,2,3},{4},{5},{6}} => 9
{{1,2,4,5,6},{3}} => 13
{{1,2,4,5},{3,6}} => 12
{{1,2,4,5},{3},{6}} => 11
{{1,2,4,6},{3,5}} => 11
{{1,2,4},{3,5,6}} => 12
{{1,2,4},{3,5},{6}} => 10
{{1,2,4,6},{3},{5}} => 10
{{1,2,4},{3,6},{5}} => 9
{{1,2,4},{3},{5,6}} => 11
{{1,2,4},{3},{5},{6}} => 8
{{1,2,5,6},{3,4}} => 13
{{1,2,5},{3,4,6}} => 12
{{1,2,5},{3,4},{6}} => 11
{{1,2,6},{3,4,5}} => 13
{{1,2},{3,4,5,6}} => 14
{{1,2},{3,4,5},{6}} => 12
{{1,2,6},{3,4},{5}} => 10
{{1,2},{3,4,6},{5}} => 11
{{1,2},{3,4},{5,6}} => 12
{{1,2},{3,4},{5},{6}} => 9
{{1,2,5,6},{3},{4}} => 10
{{1,2,5},{3,6},{4}} => 8
{{1,2,5},{3},{4,6}} => 9
{{1,2,5},{3},{4},{6}} => 7
{{1,2,6},{3,5},{4}} => 9
{{1,2},{3,5,6},{4}} => 11
{{1,2},{3,5},{4,6}} => 10
{{1,2},{3,5},{4},{6}} => 8
{{1,2,6},{3},{4,5}} => 10
{{1,2},{3,6},{4,5}} => 11
{{1,2},{3},{4,5,6}} => 12
{{1,2},{3},{4,5},{6}} => 9
{{1,2,6},{3},{4},{5}} => 6
{{1,2},{3,6},{4},{5}} => 7
{{1,2},{3},{4,6},{5}} => 8
{{1,2},{3},{4},{5,6}} => 9
{{1,2},{3},{4},{5},{6}} => 5
{{1,3,4,5,6},{2}} => 13
{{1,3,4,5},{2,6}} => 12
{{1,3,4,5},{2},{6}} => 11
{{1,3,4,6},{2,5}} => 11
{{1,3,4},{2,5,6}} => 12
{{1,3,4},{2,5},{6}} => 10
{{1,3,4,6},{2},{5}} => 10
{{1,3,4},{2,6},{5}} => 9
{{1,3,4},{2},{5,6}} => 11
{{1,3,4},{2},{5},{6}} => 8
{{1,3,5,6},{2,4}} => 11
{{1,3,5},{2,4,6}} => 10
{{1,3,5},{2,4},{6}} => 9
{{1,3,6},{2,4,5}} => 11
{{1,3},{2,4,5,6}} => 12
{{1,3},{2,4,5},{6}} => 10
{{1,3,6},{2,4},{5}} => 8
{{1,3},{2,4,6},{5}} => 9
{{1,3},{2,4},{5,6}} => 10
{{1,3},{2,4},{5},{6}} => 7
{{1,3,5,6},{2},{4}} => 10
{{1,3,5},{2,6},{4}} => 8
{{1,3,5},{2},{4,6}} => 9
{{1,3,5},{2},{4},{6}} => 7
{{1,3,6},{2,5},{4}} => 7
{{1,3},{2,5,6},{4}} => 9
{{1,3},{2,5},{4,6}} => 8
{{1,3},{2,5},{4},{6}} => 6
{{1,3,6},{2},{4,5}} => 10
{{1,3},{2,6},{4,5}} => 9
{{1,3},{2},{4,5,6}} => 11
{{1,3},{2},{4,5},{6}} => 8
{{1,3,6},{2},{4},{5}} => 6
{{1,3},{2,6},{4},{5}} => 5
{{1,3},{2},{4,6},{5}} => 7
{{1,3},{2},{4},{5,6}} => 8
{{1,3},{2},{4},{5},{6}} => 4
{{1,4,5,6},{2,3}} => 13
{{1,4,5},{2,3,6}} => 12
{{1,4,5},{2,3},{6}} => 11
{{1,4,6},{2,3,5}} => 11
{{1,4},{2,3,5,6}} => 12
{{1,4},{2,3,5},{6}} => 10
{{1,4,6},{2,3},{5}} => 10
{{1,4},{2,3,6},{5}} => 9
{{1,4},{2,3},{5,6}} => 11
{{1,4},{2,3},{5},{6}} => 8
{{1,5,6},{2,3,4}} => 13
{{1,5},{2,3,4,6}} => 12
{{1,5},{2,3,4},{6}} => 11
{{1,6},{2,3,4,5}} => 13
{{1},{2,3,4,5,6}} => 14
{{1},{2,3,4,5},{6}} => 12
{{1,6},{2,3,4},{5}} => 10
{{1},{2,3,4,6},{5}} => 11
{{1},{2,3,4},{5,6}} => 12
{{1},{2,3,4},{5},{6}} => 9
{{1,5,6},{2,3},{4}} => 10
{{1,5},{2,3,6},{4}} => 8
{{1,5},{2,3},{4,6}} => 9
{{1,5},{2,3},{4},{6}} => 7
{{1,6},{2,3,5},{4}} => 9
{{1},{2,3,5,6},{4}} => 11
{{1},{2,3,5},{4,6}} => 10
{{1},{2,3,5},{4},{6}} => 8
{{1,6},{2,3},{4,5}} => 10
{{1},{2,3,6},{4,5}} => 11
{{1},{2,3},{4,5,6}} => 12
{{1},{2,3},{4,5},{6}} => 9
{{1,6},{2,3},{4},{5}} => 6
{{1},{2,3,6},{4},{5}} => 7
{{1},{2,3},{4,6},{5}} => 8
{{1},{2,3},{4},{5,6}} => 9
{{1},{2,3},{4},{5},{6}} => 5
{{1,4,5,6},{2},{3}} => 10
{{1,4,5},{2,6},{3}} => 8
{{1,4,5},{2},{3,6}} => 9
{{1,4,5},{2},{3},{6}} => 7
{{1,4,6},{2,5},{3}} => 7
{{1,4},{2,5,6},{3}} => 8
{{1,4},{2,5},{3,6}} => 6
{{1,4},{2,5},{3},{6}} => 5
{{1,4,6},{2},{3,5}} => 8
{{1,4},{2,6},{3,5}} => 7
{{1,4},{2},{3,5,6}} => 9
{{1,4},{2},{3,5},{6}} => 6
{{1,4,6},{2},{3},{5}} => 6
{{1,4},{2,6},{3},{5}} => 4
{{1,4},{2},{3,6},{5}} => 5
{{1,4},{2},{3},{5,6}} => 7
{{1,4},{2},{3},{5},{6}} => 3
{{1,5,6},{2,4},{3}} => 9
{{1,5},{2,4,6},{3}} => 8
{{1,5},{2,4},{3,6}} => 7
{{1,5},{2,4},{3},{6}} => 6
{{1,6},{2,4,5},{3}} => 9
{{1},{2,4,5,6},{3}} => 11
{{1},{2,4,5},{3,6}} => 10
{{1},{2,4,5},{3},{6}} => 8
{{1,6},{2,4},{3,5}} => 8
{{1},{2,4,6},{3,5}} => 9
{{1},{2,4},{3,5,6}} => 10
{{1},{2,4},{3,5},{6}} => 7
{{1,6},{2,4},{3},{5}} => 5
{{1},{2,4,6},{3},{5}} => 7
{{1},{2,4},{3,6},{5}} => 6
{{1},{2,4},{3},{5,6}} => 8
{{1},{2,4},{3},{5},{6}} => 4
{{1,5,6},{2},{3,4}} => 10
{{1,5},{2,6},{3,4}} => 8
{{1,5},{2},{3,4,6}} => 9
{{1,5},{2},{3,4},{6}} => 7
{{1,6},{2,5},{3,4}} => 9
{{1},{2,5,6},{3,4}} => 11
{{1},{2,5},{3,4,6}} => 10
{{1},{2,5},{3,4},{6}} => 8
{{1,6},{2},{3,4,5}} => 10
{{1},{2,6},{3,4,5}} => 11
{{1},{2},{3,4,5,6}} => 12
{{1},{2},{3,4,5},{6}} => 9
{{1,6},{2},{3,4},{5}} => 6
{{1},{2,6},{3,4},{5}} => 7
{{1},{2},{3,4,6},{5}} => 8
{{1},{2},{3,4},{5,6}} => 9
{{1},{2},{3,4},{5},{6}} => 5
{{1,5,6},{2},{3},{4}} => 6
{{1,5},{2,6},{3},{4}} => 3
{{1,5},{2},{3,6},{4}} => 4
{{1,5},{2},{3},{4,6}} => 5
{{1,5},{2},{3},{4},{6}} => 2
{{1,6},{2,5},{3},{4}} => 4
{{1},{2,5,6},{3},{4}} => 7
{{1},{2,5},{3,6},{4}} => 5
{{1},{2,5},{3},{4,6}} => 6
{{1},{2,5},{3},{4},{6}} => 3
{{1,6},{2},{3,5},{4}} => 5
{{1},{2,6},{3,5},{4}} => 6
{{1},{2},{3,5,6},{4}} => 8
{{1},{2},{3,5},{4,6}} => 7
{{1},{2},{3,5},{4},{6}} => 4
{{1,6},{2},{3},{4,5}} => 6
{{1},{2,6},{3},{4,5}} => 7
{{1},{2},{3,6},{4,5}} => 8
{{1},{2},{3},{4,5,6}} => 9
{{1},{2},{3},{4,5},{6}} => 5
{{1,6},{2},{3},{4},{5}} => 1
{{1},{2,6},{3},{4},{5}} => 2
{{1},{2},{3,6},{4},{5}} => 3
{{1},{2},{3},{4,6},{5}} => 4
{{1},{2},{3},{4},{5,6}} => 5
{{1},{2},{3},{4},{5},{6}} => 0
{{1,2,3,4,5,6,7}} => 21
{{1,2,3,4,5,6},{7}} => 20
{{1,2,3,4,5,7},{6}} => 19
{{1,2,3,4,5},{6,7}} => 20
{{1,2,3,4,5},{6},{7}} => 18
{{1,2,3,4,6,7},{5}} => 19
{{1,2,3,4,6},{5,7}} => 18
{{1,2,3,4,6},{5},{7}} => 17
{{1,2,3,4,7},{5,6}} => 19
{{1,2,3,4},{5,6,7}} => 20
{{1,2,3,4},{5,6},{7}} => 18
{{1,2,3,4,7},{5},{6}} => 16
{{1,2,3,4},{5,7},{6}} => 17
{{1,2,3,4},{5},{6,7}} => 18
{{1,2,3,4},{5},{6},{7}} => 15
{{1,2,3,5,6,7},{4}} => 19
{{1,2,3,5,6},{4,7}} => 18
{{1,2,3,5,6},{4},{7}} => 17
{{1,2,3,5,7},{4,6}} => 17
{{1,2,3,5},{4,6,7}} => 18
{{1,2,3,5},{4,6},{7}} => 16
{{1,2,3,5,7},{4},{6}} => 16
{{1,2,3,5},{4,7},{6}} => 15
{{1,2,3,5},{4},{6,7}} => 17
{{1,2,3,5},{4},{6},{7}} => 14
{{1,2,3,6,7},{4,5}} => 19
{{1,2,3,6},{4,5,7}} => 18
{{1,2,3,6},{4,5},{7}} => 17
{{1,2,3,7},{4,5,6}} => 19
{{1,2,3},{4,5,6,7}} => 20
{{1,2,3},{4,5,6},{7}} => 18
{{1,2,3,7},{4,5},{6}} => 16
{{1,2,3},{4,5,7},{6}} => 17
{{1,2,3},{4,5},{6,7}} => 18
{{1,2,3},{4,5},{6},{7}} => 15
{{1,2,3,6,7},{4},{5}} => 16
{{1,2,3,6},{4,7},{5}} => 14
{{1,2,3,6},{4},{5,7}} => 15
{{1,2,3,6},{4},{5},{7}} => 13
{{1,2,3,7},{4,6},{5}} => 15
{{1,2,3},{4,6,7},{5}} => 17
{{1,2,3},{4,6},{5,7}} => 16
{{1,2,3},{4,6},{5},{7}} => 14
{{1,2,3,7},{4},{5,6}} => 16
{{1,2,3},{4,7},{5,6}} => 17
{{1,2,3},{4},{5,6,7}} => 18
{{1,2,3},{4},{5,6},{7}} => 15
{{1,2,3,7},{4},{5},{6}} => 12
{{1,2,3},{4,7},{5},{6}} => 13
{{1,2,3},{4},{5,7},{6}} => 14
{{1,2,3},{4},{5},{6,7}} => 15
{{1,2,3},{4},{5},{6},{7}} => 11
{{1,2,4,5,6,7},{3}} => 19
{{1,2,4,5,6},{3,7}} => 18
{{1,2,4,5,6},{3},{7}} => 17
{{1,2,4,5,7},{3,6}} => 17
{{1,2,4,5},{3,6,7}} => 18
{{1,2,4,5},{3,6},{7}} => 16
{{1,2,4,5,7},{3},{6}} => 16
{{1,2,4,5},{3,7},{6}} => 15
{{1,2,4,5},{3},{6,7}} => 17
{{1,2,4,5},{3},{6},{7}} => 14
{{1,2,4,6,7},{3,5}} => 17
{{1,2,4,6},{3,5,7}} => 16
{{1,2,4,6},{3,5},{7}} => 15
{{1,2,4,7},{3,5,6}} => 17
{{1,2,4},{3,5,6,7}} => 18
{{1,2,4},{3,5,6},{7}} => 16
{{1,2,4,7},{3,5},{6}} => 14
{{1,2,4},{3,5,7},{6}} => 15
{{1,2,4},{3,5},{6,7}} => 16
{{1,2,4},{3,5},{6},{7}} => 13
{{1,2,4,6,7},{3},{5}} => 16
{{1,2,4,6},{3,7},{5}} => 14
{{1,2,4,6},{3},{5,7}} => 15
{{1,2,4,6},{3},{5},{7}} => 13
{{1,2,4,7},{3,6},{5}} => 13
{{1,2,4},{3,6,7},{5}} => 15
{{1,2,4},{3,6},{5,7}} => 14
{{1,2,4},{3,6},{5},{7}} => 12
{{1,2,4,7},{3},{5,6}} => 16
{{1,2,4},{3,7},{5,6}} => 15
{{1,2,4},{3},{5,6,7}} => 17
{{1,2,4},{3},{5,6},{7}} => 14
{{1,2,4,7},{3},{5},{6}} => 12
{{1,2,4},{3,7},{5},{6}} => 11
{{1,2,4},{3},{5,7},{6}} => 13
{{1,2,4},{3},{5},{6,7}} => 14
{{1,2,4},{3},{5},{6},{7}} => 10
{{1,2,5,6,7},{3,4}} => 19
{{1,2,5,6},{3,4,7}} => 18
{{1,2,5,6},{3,4},{7}} => 17
{{1,2,5,7},{3,4,6}} => 17
{{1,2,5},{3,4,6,7}} => 18
{{1,2,5},{3,4,6},{7}} => 16
{{1,2,5,7},{3,4},{6}} => 16
{{1,2,5},{3,4,7},{6}} => 15
{{1,2,5},{3,4},{6,7}} => 17
{{1,2,5},{3,4},{6},{7}} => 14
{{1,2,6,7},{3,4,5}} => 19
{{1,2,6},{3,4,5,7}} => 18
{{1,2,6},{3,4,5},{7}} => 17
{{1,2,7},{3,4,5,6}} => 19
{{1,2},{3,4,5,6,7}} => 20
{{1,2},{3,4,5,6},{7}} => 18
{{1,2,7},{3,4,5},{6}} => 16
{{1,2},{3,4,5,7},{6}} => 17
{{1,2},{3,4,5},{6,7}} => 18
{{1,2},{3,4,5},{6},{7}} => 15
{{1,2,6,7},{3,4},{5}} => 16
{{1,2,6},{3,4,7},{5}} => 14
{{1,2,6},{3,4},{5,7}} => 15
{{1,2,6},{3,4},{5},{7}} => 13
{{1,2,7},{3,4,6},{5}} => 15
{{1,2},{3,4,6,7},{5}} => 17
{{1,2},{3,4,6},{5,7}} => 16
{{1,2},{3,4,6},{5},{7}} => 14
{{1,2,7},{3,4},{5,6}} => 16
{{1,2},{3,4,7},{5,6}} => 17
{{1,2},{3,4},{5,6,7}} => 18
{{1,2},{3,4},{5,6},{7}} => 15
{{1,2,7},{3,4},{5},{6}} => 12
{{1,2},{3,4,7},{5},{6}} => 13
{{1,2},{3,4},{5,7},{6}} => 14
{{1,2},{3,4},{5},{6,7}} => 15
{{1,2},{3,4},{5},{6},{7}} => 11
{{1,2,5,6,7},{3},{4}} => 16
{{1,2,5,6},{3,7},{4}} => 14
{{1,2,5,6},{3},{4,7}} => 15
{{1,2,5,6},{3},{4},{7}} => 13
{{1,2,5,7},{3,6},{4}} => 13
{{1,2,5},{3,6,7},{4}} => 14
{{1,2,5},{3,6},{4,7}} => 12
{{1,2,5},{3,6},{4},{7}} => 11
{{1,2,5,7},{3},{4,6}} => 14
{{1,2,5},{3,7},{4,6}} => 13
{{1,2,5},{3},{4,6,7}} => 15
{{1,2,5},{3},{4,6},{7}} => 12
{{1,2,5,7},{3},{4},{6}} => 12
{{1,2,5},{3,7},{4},{6}} => 10
{{1,2,5},{3},{4,7},{6}} => 11
{{1,2,5},{3},{4},{6,7}} => 13
{{1,2,5},{3},{4},{6},{7}} => 9
{{1,2,6,7},{3,5},{4}} => 15
{{1,2,6},{3,5,7},{4}} => 14
{{1,2,6},{3,5},{4,7}} => 13
{{1,2,6},{3,5},{4},{7}} => 12
{{1,2,7},{3,5,6},{4}} => 15
{{1,2},{3,5,6,7},{4}} => 17
{{1,2},{3,5,6},{4,7}} => 16
{{1,2},{3,5,6},{4},{7}} => 14
{{1,2,7},{3,5},{4,6}} => 14
{{1,2},{3,5,7},{4,6}} => 15
{{1,2},{3,5},{4,6,7}} => 16
{{1,2},{3,5},{4,6},{7}} => 13
{{1,2,7},{3,5},{4},{6}} => 11
{{1,2},{3,5,7},{4},{6}} => 13
{{1,2},{3,5},{4,7},{6}} => 12
{{1,2},{3,5},{4},{6,7}} => 14
{{1,2},{3,5},{4},{6},{7}} => 10
{{1,2,6,7},{3},{4,5}} => 16
{{1,2,6},{3,7},{4,5}} => 14
{{1,2,6},{3},{4,5,7}} => 15
{{1,2,6},{3},{4,5},{7}} => 13
{{1,2,7},{3,6},{4,5}} => 15
{{1,2},{3,6,7},{4,5}} => 17
{{1,2},{3,6},{4,5,7}} => 16
{{1,2},{3,6},{4,5},{7}} => 14
{{1,2,7},{3},{4,5,6}} => 16
{{1,2},{3,7},{4,5,6}} => 17
{{1,2},{3},{4,5,6,7}} => 18
{{1,2},{3},{4,5,6},{7}} => 15
{{1,2,7},{3},{4,5},{6}} => 12
{{1,2},{3,7},{4,5},{6}} => 13
{{1,2},{3},{4,5,7},{6}} => 14
{{1,2},{3},{4,5},{6,7}} => 15
{{1,2},{3},{4,5},{6},{7}} => 11
{{1,2,6,7},{3},{4},{5}} => 12
{{1,2,6},{3,7},{4},{5}} => 9
{{1,2,6},{3},{4,7},{5}} => 10
{{1,2,6},{3},{4},{5,7}} => 11
{{1,2,6},{3},{4},{5},{7}} => 8
{{1,2,7},{3,6},{4},{5}} => 10
{{1,2},{3,6,7},{4},{5}} => 13
{{1,2},{3,6},{4,7},{5}} => 11
{{1,2},{3,6},{4},{5,7}} => 12
{{1,2},{3,6},{4},{5},{7}} => 9
{{1,2,7},{3},{4,6},{5}} => 11
{{1,2},{3,7},{4,6},{5}} => 12
{{1,2},{3},{4,6,7},{5}} => 14
{{1,2},{3},{4,6},{5,7}} => 13
{{1,2},{3},{4,6},{5},{7}} => 10
{{1,2,7},{3},{4},{5,6}} => 12
{{1,2},{3,7},{4},{5,6}} => 13
{{1,2},{3},{4,7},{5,6}} => 14
{{1,2},{3},{4},{5,6,7}} => 15
{{1,2},{3},{4},{5,6},{7}} => 11
{{1,2,7},{3},{4},{5},{6}} => 7
{{1,2},{3,7},{4},{5},{6}} => 8
{{1,2},{3},{4,7},{5},{6}} => 9
{{1,2},{3},{4},{5,7},{6}} => 10
{{1,2},{3},{4},{5},{6,7}} => 11
{{1,2},{3},{4},{5},{6},{7}} => 6
{{1,3,4,5,6,7},{2}} => 19
{{1,3,4,5,6},{2,7}} => 18
{{1,3,4,5,6},{2},{7}} => 17
{{1,3,4,5,7},{2,6}} => 17
{{1,3,4,5},{2,6,7}} => 18
{{1,3,4,5},{2,6},{7}} => 16
{{1,3,4,5,7},{2},{6}} => 16
{{1,3,4,5},{2,7},{6}} => 15
{{1,3,4,5},{2},{6,7}} => 17
{{1,3,4,5},{2},{6},{7}} => 14
{{1,3,4,6,7},{2,5}} => 17
{{1,3,4,6},{2,5,7}} => 16
{{1,3,4,6},{2,5},{7}} => 15
{{1,3,4,7},{2,5,6}} => 17
{{1,3,4},{2,5,6,7}} => 18
{{1,3,4},{2,5,6},{7}} => 16
{{1,3,4,7},{2,5},{6}} => 14
{{1,3,4},{2,5,7},{6}} => 15
{{1,3,4},{2,5},{6,7}} => 16
{{1,3,4},{2,5},{6},{7}} => 13
{{1,3,4,6,7},{2},{5}} => 16
{{1,3,4,6},{2,7},{5}} => 14
{{1,3,4,6},{2},{5,7}} => 15
{{1,3,4,6},{2},{5},{7}} => 13
{{1,3,4,7},{2,6},{5}} => 13
{{1,3,4},{2,6,7},{5}} => 15
{{1,3,4},{2,6},{5,7}} => 14
{{1,3,4},{2,6},{5},{7}} => 12
{{1,3,4,7},{2},{5,6}} => 16
{{1,3,4},{2,7},{5,6}} => 15
{{1,3,4},{2},{5,6,7}} => 17
{{1,3,4},{2},{5,6},{7}} => 14
{{1,3,4,7},{2},{5},{6}} => 12
{{1,3,4},{2,7},{5},{6}} => 11
{{1,3,4},{2},{5,7},{6}} => 13
{{1,3,4},{2},{5},{6,7}} => 14
{{1,3,4},{2},{5},{6},{7}} => 10
{{1,3,5,6,7},{2,4}} => 17
{{1,3,5,6},{2,4,7}} => 16
{{1,3,5,6},{2,4},{7}} => 15
{{1,3,5,7},{2,4,6}} => 15
{{1,3,5},{2,4,6,7}} => 16
{{1,3,5},{2,4,6},{7}} => 14
{{1,3,5,7},{2,4},{6}} => 14
{{1,3,5},{2,4,7},{6}} => 13
{{1,3,5},{2,4},{6,7}} => 15
{{1,3,5},{2,4},{6},{7}} => 12
{{1,3,6,7},{2,4,5}} => 17
{{1,3,6},{2,4,5,7}} => 16
{{1,3,6},{2,4,5},{7}} => 15
{{1,3,7},{2,4,5,6}} => 17
{{1,3},{2,4,5,6,7}} => 18
{{1,3},{2,4,5,6},{7}} => 16
{{1,3,7},{2,4,5},{6}} => 14
{{1,3},{2,4,5,7},{6}} => 15
{{1,3},{2,4,5},{6,7}} => 16
{{1,3},{2,4,5},{6},{7}} => 13
{{1,3,6,7},{2,4},{5}} => 14
{{1,3,6},{2,4,7},{5}} => 12
{{1,3,6},{2,4},{5,7}} => 13
{{1,3,6},{2,4},{5},{7}} => 11
{{1,3,7},{2,4,6},{5}} => 13
{{1,3},{2,4,6,7},{5}} => 15
{{1,3},{2,4,6},{5,7}} => 14
{{1,3},{2,4,6},{5},{7}} => 12
{{1,3,7},{2,4},{5,6}} => 14
{{1,3},{2,4,7},{5,6}} => 15
{{1,3},{2,4},{5,6,7}} => 16
{{1,3},{2,4},{5,6},{7}} => 13
{{1,3,7},{2,4},{5},{6}} => 10
{{1,3},{2,4,7},{5},{6}} => 11
{{1,3},{2,4},{5,7},{6}} => 12
{{1,3},{2,4},{5},{6,7}} => 13
{{1,3},{2,4},{5},{6},{7}} => 9
{{1,3,5,6,7},{2},{4}} => 16
{{1,3,5,6},{2,7},{4}} => 14
{{1,3,5,6},{2},{4,7}} => 15
{{1,3,5,6},{2},{4},{7}} => 13
{{1,3,5,7},{2,6},{4}} => 13
{{1,3,5},{2,6,7},{4}} => 14
{{1,3,5},{2,6},{4,7}} => 12
{{1,3,5},{2,6},{4},{7}} => 11
{{1,3,5,7},{2},{4,6}} => 14
{{1,3,5},{2,7},{4,6}} => 13
{{1,3,5},{2},{4,6,7}} => 15
{{1,3,5},{2},{4,6},{7}} => 12
{{1,3,5,7},{2},{4},{6}} => 12
{{1,3,5},{2,7},{4},{6}} => 10
{{1,3,5},{2},{4,7},{6}} => 11
{{1,3,5},{2},{4},{6,7}} => 13
{{1,3,5},{2},{4},{6},{7}} => 9
{{1,3,6,7},{2,5},{4}} => 13
{{1,3,6},{2,5,7},{4}} => 12
{{1,3,6},{2,5},{4,7}} => 11
{{1,3,6},{2,5},{4},{7}} => 10
{{1,3,7},{2,5,6},{4}} => 13
{{1,3},{2,5,6,7},{4}} => 15
{{1,3},{2,5,6},{4,7}} => 14
{{1,3},{2,5,6},{4},{7}} => 12
{{1,3,7},{2,5},{4,6}} => 12
{{1,3},{2,5,7},{4,6}} => 13
{{1,3},{2,5},{4,6,7}} => 14
{{1,3},{2,5},{4,6},{7}} => 11
{{1,3,7},{2,5},{4},{6}} => 9
{{1,3},{2,5,7},{4},{6}} => 11
{{1,3},{2,5},{4,7},{6}} => 10
{{1,3},{2,5},{4},{6,7}} => 12
{{1,3},{2,5},{4},{6},{7}} => 8
{{1,3,6,7},{2},{4,5}} => 16
{{1,3,6},{2,7},{4,5}} => 14
{{1,3,6},{2},{4,5,7}} => 15
{{1,3,6},{2},{4,5},{7}} => 13
{{1,3,7},{2,6},{4,5}} => 13
{{1,3},{2,6,7},{4,5}} => 15
{{1,3},{2,6},{4,5,7}} => 14
{{1,3},{2,6},{4,5},{7}} => 12
{{1,3,7},{2},{4,5,6}} => 16
{{1,3},{2,7},{4,5,6}} => 15
{{1,3},{2},{4,5,6,7}} => 17
{{1,3},{2},{4,5,6},{7}} => 14
{{1,3,7},{2},{4,5},{6}} => 12
{{1,3},{2,7},{4,5},{6}} => 11
{{1,3},{2},{4,5,7},{6}} => 13
{{1,3},{2},{4,5},{6,7}} => 14
{{1,3},{2},{4,5},{6},{7}} => 10
{{1,3,6,7},{2},{4},{5}} => 12
{{1,3,6},{2,7},{4},{5}} => 9
{{1,3,6},{2},{4,7},{5}} => 10
{{1,3,6},{2},{4},{5,7}} => 11
{{1,3,6},{2},{4},{5},{7}} => 8
{{1,3,7},{2,6},{4},{5}} => 8
{{1,3},{2,6,7},{4},{5}} => 11
{{1,3},{2,6},{4,7},{5}} => 9
{{1,3},{2,6},{4},{5,7}} => 10
{{1,3},{2,6},{4},{5},{7}} => 7
{{1,3,7},{2},{4,6},{5}} => 11
{{1,3},{2,7},{4,6},{5}} => 10
{{1,3},{2},{4,6,7},{5}} => 13
{{1,3},{2},{4,6},{5,7}} => 12
{{1,3},{2},{4,6},{5},{7}} => 9
{{1,3,7},{2},{4},{5,6}} => 12
{{1,3},{2,7},{4},{5,6}} => 11
{{1,3},{2},{4,7},{5,6}} => 13
{{1,3},{2},{4},{5,6,7}} => 14
{{1,3},{2},{4},{5,6},{7}} => 10
{{1,3,7},{2},{4},{5},{6}} => 7
{{1,3},{2,7},{4},{5},{6}} => 6
{{1,3},{2},{4,7},{5},{6}} => 8
{{1,3},{2},{4},{5,7},{6}} => 9
{{1,3},{2},{4},{5},{6,7}} => 10
{{1,3},{2},{4},{5},{6},{7}} => 5
{{1,4,5,6,7},{2,3}} => 19
{{1,4,5,6},{2,3,7}} => 18
{{1,4,5,6},{2,3},{7}} => 17
{{1,4,5,7},{2,3,6}} => 17
{{1,4,5},{2,3,6,7}} => 18
{{1,4,5},{2,3,6},{7}} => 16
{{1,4,5,7},{2,3},{6}} => 16
{{1,4,5},{2,3,7},{6}} => 15
{{1,4,5},{2,3},{6,7}} => 17
{{1,4,5},{2,3},{6},{7}} => 14
{{1,4,6,7},{2,3,5}} => 17
{{1,4,6},{2,3,5,7}} => 16
{{1,4,6},{2,3,5},{7}} => 15
{{1,4,7},{2,3,5,6}} => 17
{{1,4},{2,3,5,6,7}} => 18
{{1,4},{2,3,5,6},{7}} => 16
{{1,4,7},{2,3,5},{6}} => 14
{{1,4},{2,3,5,7},{6}} => 15
{{1,4},{2,3,5},{6,7}} => 16
{{1,4},{2,3,5},{6},{7}} => 13
{{1,4,6,7},{2,3},{5}} => 16
{{1,4,6},{2,3,7},{5}} => 14
{{1,4,6},{2,3},{5,7}} => 15
{{1,4,6},{2,3},{5},{7}} => 13
{{1,4,7},{2,3,6},{5}} => 13
{{1,4},{2,3,6,7},{5}} => 15
{{1,4},{2,3,6},{5,7}} => 14
{{1,4},{2,3,6},{5},{7}} => 12
{{1,4,7},{2,3},{5,6}} => 16
{{1,4},{2,3,7},{5,6}} => 15
{{1,4},{2,3},{5,6,7}} => 17
{{1,4},{2,3},{5,6},{7}} => 14
{{1,4,7},{2,3},{5},{6}} => 12
{{1,4},{2,3,7},{5},{6}} => 11
{{1,4},{2,3},{5,7},{6}} => 13
{{1,4},{2,3},{5},{6,7}} => 14
{{1,4},{2,3},{5},{6},{7}} => 10
{{1,5,6,7},{2,3,4}} => 19
{{1,5,6},{2,3,4,7}} => 18
{{1,5,6},{2,3,4},{7}} => 17
{{1,5,7},{2,3,4,6}} => 17
{{1,5},{2,3,4,6,7}} => 18
{{1,5},{2,3,4,6},{7}} => 16
{{1,5,7},{2,3,4},{6}} => 16
{{1,5},{2,3,4,7},{6}} => 15
{{1,5},{2,3,4},{6,7}} => 17
{{1,5},{2,3,4},{6},{7}} => 14
{{1,6,7},{2,3,4,5}} => 19
{{1,6},{2,3,4,5,7}} => 18
{{1,6},{2,3,4,5},{7}} => 17
{{1,7},{2,3,4,5,6}} => 19
{{1},{2,3,4,5,6,7}} => 20
{{1},{2,3,4,5,6},{7}} => 18
{{1,7},{2,3,4,5},{6}} => 16
{{1},{2,3,4,5,7},{6}} => 17
{{1},{2,3,4,5},{6,7}} => 18
{{1},{2,3,4,5},{6},{7}} => 15
{{1,6,7},{2,3,4},{5}} => 16
{{1,6},{2,3,4,7},{5}} => 14
{{1,6},{2,3,4},{5,7}} => 15
{{1,6},{2,3,4},{5},{7}} => 13
{{1,7},{2,3,4,6},{5}} => 15
{{1},{2,3,4,6,7},{5}} => 17
{{1},{2,3,4,6},{5,7}} => 16
{{1},{2,3,4,6},{5},{7}} => 14
{{1,7},{2,3,4},{5,6}} => 16
{{1},{2,3,4,7},{5,6}} => 17
{{1},{2,3,4},{5,6,7}} => 18
{{1},{2,3,4},{5,6},{7}} => 15
{{1,7},{2,3,4},{5},{6}} => 12
{{1},{2,3,4,7},{5},{6}} => 13
{{1},{2,3,4},{5,7},{6}} => 14
{{1},{2,3,4},{5},{6,7}} => 15
{{1},{2,3,4},{5},{6},{7}} => 11
{{1,5,6,7},{2,3},{4}} => 16
{{1,5,6},{2,3,7},{4}} => 14
{{1,5,6},{2,3},{4,7}} => 15
{{1,5,6},{2,3},{4},{7}} => 13
{{1,5,7},{2,3,6},{4}} => 13
{{1,5},{2,3,6,7},{4}} => 14
{{1,5},{2,3,6},{4,7}} => 12
{{1,5},{2,3,6},{4},{7}} => 11
{{1,5,7},{2,3},{4,6}} => 14
{{1,5},{2,3,7},{4,6}} => 13
{{1,5},{2,3},{4,6,7}} => 15
{{1,5},{2,3},{4,6},{7}} => 12
{{1,5,7},{2,3},{4},{6}} => 12
{{1,5},{2,3,7},{4},{6}} => 10
{{1,5},{2,3},{4,7},{6}} => 11
{{1,5},{2,3},{4},{6,7}} => 13
{{1,5},{2,3},{4},{6},{7}} => 9
{{1,6,7},{2,3,5},{4}} => 15
{{1,6},{2,3,5,7},{4}} => 14
{{1,6},{2,3,5},{4,7}} => 13
{{1,6},{2,3,5},{4},{7}} => 12
{{1,7},{2,3,5,6},{4}} => 15
{{1},{2,3,5,6,7},{4}} => 17
{{1},{2,3,5,6},{4,7}} => 16
{{1},{2,3,5,6},{4},{7}} => 14
{{1,7},{2,3,5},{4,6}} => 14
{{1},{2,3,5,7},{4,6}} => 15
{{1},{2,3,5},{4,6,7}} => 16
{{1},{2,3,5},{4,6},{7}} => 13
{{1,7},{2,3,5},{4},{6}} => 11
{{1},{2,3,5,7},{4},{6}} => 13
{{1},{2,3,5},{4,7},{6}} => 12
{{1},{2,3,5},{4},{6,7}} => 14
{{1},{2,3,5},{4},{6},{7}} => 10
{{1,6,7},{2,3},{4,5}} => 16
{{1,6},{2,3,7},{4,5}} => 14
{{1,6},{2,3},{4,5,7}} => 15
{{1,6},{2,3},{4,5},{7}} => 13
{{1,7},{2,3,6},{4,5}} => 15
{{1},{2,3,6,7},{4,5}} => 17
{{1},{2,3,6},{4,5,7}} => 16
{{1},{2,3,6},{4,5},{7}} => 14
{{1,7},{2,3},{4,5,6}} => 16
{{1},{2,3,7},{4,5,6}} => 17
{{1},{2,3},{4,5,6,7}} => 18
{{1},{2,3},{4,5,6},{7}} => 15
{{1,7},{2,3},{4,5},{6}} => 12
{{1},{2,3,7},{4,5},{6}} => 13
{{1},{2,3},{4,5,7},{6}} => 14
{{1},{2,3},{4,5},{6,7}} => 15
{{1},{2,3},{4,5},{6},{7}} => 11
{{1,6,7},{2,3},{4},{5}} => 12
{{1,6},{2,3,7},{4},{5}} => 9
{{1,6},{2,3},{4,7},{5}} => 10
{{1,6},{2,3},{4},{5,7}} => 11
{{1,6},{2,3},{4},{5},{7}} => 8
{{1,7},{2,3,6},{4},{5}} => 10
{{1},{2,3,6,7},{4},{5}} => 13
{{1},{2,3,6},{4,7},{5}} => 11
{{1},{2,3,6},{4},{5,7}} => 12
{{1},{2,3,6},{4},{5},{7}} => 9
{{1,7},{2,3},{4,6},{5}} => 11
{{1},{2,3,7},{4,6},{5}} => 12
{{1},{2,3},{4,6,7},{5}} => 14
{{1},{2,3},{4,6},{5,7}} => 13
{{1},{2,3},{4,6},{5},{7}} => 10
{{1,7},{2,3},{4},{5,6}} => 12
{{1},{2,3,7},{4},{5,6}} => 13
{{1},{2,3},{4,7},{5,6}} => 14
{{1},{2,3},{4},{5,6,7}} => 15
{{1},{2,3},{4},{5,6},{7}} => 11
{{1,7},{2,3},{4},{5},{6}} => 7
{{1},{2,3,7},{4},{5},{6}} => 8
{{1},{2,3},{4,7},{5},{6}} => 9
{{1},{2,3},{4},{5,7},{6}} => 10
{{1},{2,3},{4},{5},{6,7}} => 11
{{1},{2,3},{4},{5},{6},{7}} => 6
{{1,4,5,6,7},{2},{3}} => 16
{{1,4,5,6},{2,7},{3}} => 14
{{1,4,5,6},{2},{3,7}} => 15
{{1,4,5,6},{2},{3},{7}} => 13
{{1,4,5,7},{2,6},{3}} => 13
{{1,4,5},{2,6,7},{3}} => 14
{{1,4,5},{2,6},{3,7}} => 12
{{1,4,5},{2,6},{3},{7}} => 11
{{1,4,5,7},{2},{3,6}} => 14
{{1,4,5},{2,7},{3,6}} => 13
{{1,4,5},{2},{3,6,7}} => 15
{{1,4,5},{2},{3,6},{7}} => 12
{{1,4,5,7},{2},{3},{6}} => 12
{{1,4,5},{2,7},{3},{6}} => 10
{{1,4,5},{2},{3,7},{6}} => 11
{{1,4,5},{2},{3},{6,7}} => 13
{{1,4,5},{2},{3},{6},{7}} => 9
{{1,4,6,7},{2,5},{3}} => 13
{{1,4,6},{2,5,7},{3}} => 12
{{1,4,6},{2,5},{3,7}} => 11
{{1,4,6},{2,5},{3},{7}} => 10
{{1,4,7},{2,5,6},{3}} => 13
{{1,4},{2,5,6,7},{3}} => 14
{{1,4},{2,5,6},{3,7}} => 12
{{1,4},{2,5,6},{3},{7}} => 11
{{1,4,7},{2,5},{3,6}} => 10
{{1,4},{2,5,7},{3,6}} => 11
{{1,4},{2,5},{3,6,7}} => 12
{{1,4},{2,5},{3,6},{7}} => 9
{{1,4,7},{2,5},{3},{6}} => 9
{{1,4},{2,5,7},{3},{6}} => 10
{{1,4},{2,5},{3,7},{6}} => 8
{{1,4},{2,5},{3},{6,7}} => 11
{{1,4},{2,5},{3},{6},{7}} => 7
{{1,4,6,7},{2},{3,5}} => 14
{{1,4,6},{2,7},{3,5}} => 12
{{1,4,6},{2},{3,5,7}} => 13
{{1,4,6},{2},{3,5},{7}} => 11
{{1,4,7},{2,6},{3,5}} => 11
{{1,4},{2,6,7},{3,5}} => 13
{{1,4},{2,6},{3,5,7}} => 12
{{1,4},{2,6},{3,5},{7}} => 10
{{1,4,7},{2},{3,5,6}} => 14
{{1,4},{2,7},{3,5,6}} => 13
{{1,4},{2},{3,5,6,7}} => 15
{{1,4},{2},{3,5,6},{7}} => 12
{{1,4,7},{2},{3,5},{6}} => 10
{{1,4},{2,7},{3,5},{6}} => 9
{{1,4},{2},{3,5,7},{6}} => 11
{{1,4},{2},{3,5},{6,7}} => 12
{{1,4},{2},{3,5},{6},{7}} => 8
{{1,4,6,7},{2},{3},{5}} => 12
{{1,4,6},{2,7},{3},{5}} => 9
{{1,4,6},{2},{3,7},{5}} => 10
{{1,4,6},{2},{3},{5,7}} => 11
{{1,4,6},{2},{3},{5},{7}} => 8
{{1,4,7},{2,6},{3},{5}} => 8
{{1,4},{2,6,7},{3},{5}} => 10
{{1,4},{2,6},{3,7},{5}} => 7
{{1,4},{2,6},{3},{5,7}} => 9
{{1,4},{2,6},{3},{5},{7}} => 6
{{1,4,7},{2},{3,6},{5}} => 9
{{1,4},{2,7},{3,6},{5}} => 8
{{1,4},{2},{3,6,7},{5}} => 11
{{1,4},{2},{3,6},{5,7}} => 10
{{1,4},{2},{3,6},{5},{7}} => 7
{{1,4,7},{2},{3},{5,6}} => 12
{{1,4},{2,7},{3},{5,6}} => 10
{{1,4},{2},{3,7},{5,6}} => 11
{{1,4},{2},{3},{5,6,7}} => 13
{{1,4},{2},{3},{5,6},{7}} => 9
{{1,4,7},{2},{3},{5},{6}} => 7
{{1,4},{2,7},{3},{5},{6}} => 5
{{1,4},{2},{3,7},{5},{6}} => 6
{{1,4},{2},{3},{5,7},{6}} => 8
{{1,4},{2},{3},{5},{6,7}} => 9
{{1,4},{2},{3},{5},{6},{7}} => 4
{{1,5,6,7},{2,4},{3}} => 15
{{1,5,6},{2,4,7},{3}} => 14
{{1,5,6},{2,4},{3,7}} => 13
{{1,5,6},{2,4},{3},{7}} => 12
{{1,5,7},{2,4,6},{3}} => 13
{{1,5},{2,4,6,7},{3}} => 14
{{1,5},{2,4,6},{3,7}} => 12
{{1,5},{2,4,6},{3},{7}} => 11
{{1,5,7},{2,4},{3,6}} => 12
{{1,5},{2,4,7},{3,6}} => 11
{{1,5},{2,4},{3,6,7}} => 13
{{1,5},{2,4},{3,6},{7}} => 10
{{1,5,7},{2,4},{3},{6}} => 11
{{1,5},{2,4,7},{3},{6}} => 10
{{1,5},{2,4},{3,7},{6}} => 9
{{1,5},{2,4},{3},{6,7}} => 12
{{1,5},{2,4},{3},{6},{7}} => 8
{{1,6,7},{2,4,5},{3}} => 15
{{1,6},{2,4,5,7},{3}} => 14
{{1,6},{2,4,5},{3,7}} => 13
{{1,6},{2,4,5},{3},{7}} => 12
{{1,7},{2,4,5,6},{3}} => 15
{{1},{2,4,5,6,7},{3}} => 17
{{1},{2,4,5,6},{3,7}} => 16
{{1},{2,4,5,6},{3},{7}} => 14
{{1,7},{2,4,5},{3,6}} => 14
{{1},{2,4,5,7},{3,6}} => 15
{{1},{2,4,5},{3,6,7}} => 16
{{1},{2,4,5},{3,6},{7}} => 13
{{1,7},{2,4,5},{3},{6}} => 11
{{1},{2,4,5,7},{3},{6}} => 13
{{1},{2,4,5},{3,7},{6}} => 12
{{1},{2,4,5},{3},{6,7}} => 14
{{1},{2,4,5},{3},{6},{7}} => 10
{{1,6,7},{2,4},{3,5}} => 14
{{1,6},{2,4,7},{3,5}} => 12
{{1,6},{2,4},{3,5,7}} => 13
{{1,6},{2,4},{3,5},{7}} => 11
{{1,7},{2,4,6},{3,5}} => 13
{{1},{2,4,6,7},{3,5}} => 15
{{1},{2,4,6},{3,5,7}} => 14
{{1},{2,4,6},{3,5},{7}} => 12
{{1,7},{2,4},{3,5,6}} => 14
{{1},{2,4,7},{3,5,6}} => 15
{{1},{2,4},{3,5,6,7}} => 16
{{1},{2,4},{3,5,6},{7}} => 13
{{1,7},{2,4},{3,5},{6}} => 10
{{1},{2,4,7},{3,5},{6}} => 11
{{1},{2,4},{3,5,7},{6}} => 12
{{1},{2,4},{3,5},{6,7}} => 13
{{1},{2,4},{3,5},{6},{7}} => 9
{{1,6,7},{2,4},{3},{5}} => 11
{{1,6},{2,4,7},{3},{5}} => 9
{{1,6},{2,4},{3,7},{5}} => 8
{{1,6},{2,4},{3},{5,7}} => 10
{{1,6},{2,4},{3},{5},{7}} => 7
{{1,7},{2,4,6},{3},{5}} => 10
{{1},{2,4,6,7},{3},{5}} => 13
{{1},{2,4,6},{3,7},{5}} => 11
{{1},{2,4,6},{3},{5,7}} => 12
{{1},{2,4,6},{3},{5},{7}} => 9
{{1,7},{2,4},{3,6},{5}} => 9
{{1},{2,4,7},{3,6},{5}} => 10
{{1},{2,4},{3,6,7},{5}} => 12
{{1},{2,4},{3,6},{5,7}} => 11
{{1},{2,4},{3,6},{5},{7}} => 8
{{1,7},{2,4},{3},{5,6}} => 11
{{1},{2,4,7},{3},{5,6}} => 13
{{1},{2,4},{3,7},{5,6}} => 12
{{1},{2,4},{3},{5,6,7}} => 14
{{1},{2,4},{3},{5,6},{7}} => 10
{{1,7},{2,4},{3},{5},{6}} => 6
{{1},{2,4,7},{3},{5},{6}} => 8
{{1},{2,4},{3,7},{5},{6}} => 7
{{1},{2,4},{3},{5,7},{6}} => 9
{{1},{2,4},{3},{5},{6,7}} => 10
{{1},{2,4},{3},{5},{6},{7}} => 5
{{1,5,6,7},{2},{3,4}} => 16
{{1,5,6},{2,7},{3,4}} => 14
{{1,5,6},{2},{3,4,7}} => 15
{{1,5,6},{2},{3,4},{7}} => 13
{{1,5,7},{2,6},{3,4}} => 13
{{1,5},{2,6,7},{3,4}} => 14
{{1,5},{2,6},{3,4,7}} => 12
{{1,5},{2,6},{3,4},{7}} => 11
{{1,5,7},{2},{3,4,6}} => 14
{{1,5},{2,7},{3,4,6}} => 13
{{1,5},{2},{3,4,6,7}} => 15
{{1,5},{2},{3,4,6},{7}} => 12
{{1,5,7},{2},{3,4},{6}} => 12
{{1,5},{2,7},{3,4},{6}} => 10
{{1,5},{2},{3,4,7},{6}} => 11
{{1,5},{2},{3,4},{6,7}} => 13
{{1,5},{2},{3,4},{6},{7}} => 9
{{1,6,7},{2,5},{3,4}} => 15
{{1,6},{2,5,7},{3,4}} => 14
{{1,6},{2,5},{3,4,7}} => 13
{{1,6},{2,5},{3,4},{7}} => 12
{{1,7},{2,5,6},{3,4}} => 15
{{1},{2,5,6,7},{3,4}} => 17
{{1},{2,5,6},{3,4,7}} => 16
{{1},{2,5,6},{3,4},{7}} => 14
{{1,7},{2,5},{3,4,6}} => 14
{{1},{2,5,7},{3,4,6}} => 15
{{1},{2,5},{3,4,6,7}} => 16
{{1},{2,5},{3,4,6},{7}} => 13
{{1,7},{2,5},{3,4},{6}} => 11
{{1},{2,5,7},{3,4},{6}} => 13
{{1},{2,5},{3,4,7},{6}} => 12
{{1},{2,5},{3,4},{6,7}} => 14
{{1},{2,5},{3,4},{6},{7}} => 10
{{1,6,7},{2},{3,4,5}} => 16
{{1,6},{2,7},{3,4,5}} => 14
{{1,6},{2},{3,4,5,7}} => 15
{{1,6},{2},{3,4,5},{7}} => 13
{{1,7},{2,6},{3,4,5}} => 15
{{1},{2,6,7},{3,4,5}} => 17
{{1},{2,6},{3,4,5,7}} => 16
{{1},{2,6},{3,4,5},{7}} => 14
{{1,7},{2},{3,4,5,6}} => 16
{{1},{2,7},{3,4,5,6}} => 17
{{1},{2},{3,4,5,6,7}} => 18
{{1},{2},{3,4,5,6},{7}} => 15
{{1,7},{2},{3,4,5},{6}} => 12
{{1},{2,7},{3,4,5},{6}} => 13
{{1},{2},{3,4,5,7},{6}} => 14
{{1},{2},{3,4,5},{6,7}} => 15
{{1},{2},{3,4,5},{6},{7}} => 11
{{1,6,7},{2},{3,4},{5}} => 12
{{1,6},{2,7},{3,4},{5}} => 9
{{1,6},{2},{3,4,7},{5}} => 10
{{1,6},{2},{3,4},{5,7}} => 11
{{1,6},{2},{3,4},{5},{7}} => 8
{{1,7},{2,6},{3,4},{5}} => 10
{{1},{2,6,7},{3,4},{5}} => 13
{{1},{2,6},{3,4,7},{5}} => 11
{{1},{2,6},{3,4},{5,7}} => 12
{{1},{2,6},{3,4},{5},{7}} => 9
{{1,7},{2},{3,4,6},{5}} => 11
{{1},{2,7},{3,4,6},{5}} => 12
{{1},{2},{3,4,6,7},{5}} => 14
{{1},{2},{3,4,6},{5,7}} => 13
{{1},{2},{3,4,6},{5},{7}} => 10
{{1,7},{2},{3,4},{5,6}} => 12
{{1},{2,7},{3,4},{5,6}} => 13
{{1},{2},{3,4,7},{5,6}} => 14
{{1},{2},{3,4},{5,6,7}} => 15
{{1},{2},{3,4},{5,6},{7}} => 11
{{1,7},{2},{3,4},{5},{6}} => 7
{{1},{2,7},{3,4},{5},{6}} => 8
{{1},{2},{3,4,7},{5},{6}} => 9
{{1},{2},{3,4},{5,7},{6}} => 10
{{1},{2},{3,4},{5},{6,7}} => 11
{{1},{2},{3,4},{5},{6},{7}} => 6
{{1,5,6,7},{2},{3},{4}} => 12
{{1,5,6},{2,7},{3},{4}} => 9
{{1,5,6},{2},{3,7},{4}} => 10
{{1,5,6},{2},{3},{4,7}} => 11
{{1,5,6},{2},{3},{4},{7}} => 8
{{1,5,7},{2,6},{3},{4}} => 8
{{1,5},{2,6,7},{3},{4}} => 9
{{1,5},{2,6},{3,7},{4}} => 6
{{1,5},{2,6},{3},{4,7}} => 7
{{1,5},{2,6},{3},{4},{7}} => 5
{{1,5,7},{2},{3,6},{4}} => 9
{{1,5},{2,7},{3,6},{4}} => 7
{{1,5},{2},{3,6,7},{4}} => 10
{{1,5},{2},{3,6},{4,7}} => 8
{{1,5},{2},{3,6},{4},{7}} => 6
{{1,5,7},{2},{3},{4,6}} => 10
{{1,5},{2,7},{3},{4,6}} => 8
{{1,5},{2},{3,7},{4,6}} => 9
{{1,5},{2},{3},{4,6,7}} => 11
{{1,5},{2},{3},{4,6},{7}} => 7
{{1,5,7},{2},{3},{4},{6}} => 7
{{1,5},{2,7},{3},{4},{6}} => 4
{{1,5},{2},{3,7},{4},{6}} => 5
{{1,5},{2},{3},{4,7},{6}} => 6
{{1,5},{2},{3},{4},{6,7}} => 8
{{1,5},{2},{3},{4},{6},{7}} => 3
{{1,6,7},{2,5},{3},{4}} => 10
{{1,6},{2,5,7},{3},{4}} => 9
{{1,6},{2,5},{3,7},{4}} => 7
{{1,6},{2,5},{3},{4,7}} => 8
{{1,6},{2,5},{3},{4},{7}} => 6
{{1,7},{2,5,6},{3},{4}} => 10
{{1},{2,5,6,7},{3},{4}} => 13
{{1},{2,5,6},{3,7},{4}} => 11
{{1},{2,5,6},{3},{4,7}} => 12
{{1},{2,5,6},{3},{4},{7}} => 9
{{1,7},{2,5},{3,6},{4}} => 8
{{1},{2,5,7},{3,6},{4}} => 10
{{1},{2,5},{3,6,7},{4}} => 11
{{1},{2,5},{3,6},{4,7}} => 9
{{1},{2,5},{3,6},{4},{7}} => 7
{{1,7},{2,5},{3},{4,6}} => 9
{{1},{2,5,7},{3},{4,6}} => 11
{{1},{2,5},{3,7},{4,6}} => 10
{{1},{2,5},{3},{4,6,7}} => 12
{{1},{2,5},{3},{4,6},{7}} => 8
{{1,7},{2,5},{3},{4},{6}} => 5
{{1},{2,5,7},{3},{4},{6}} => 8
{{1},{2,5},{3,7},{4},{6}} => 6
{{1},{2,5},{3},{4,7},{6}} => 7
{{1},{2,5},{3},{4},{6,7}} => 9
{{1},{2,5},{3},{4},{6},{7}} => 4
{{1,6,7},{2},{3,5},{4}} => 11
{{1,6},{2,7},{3,5},{4}} => 8
{{1,6},{2},{3,5,7},{4}} => 10
{{1,6},{2},{3,5},{4,7}} => 9
{{1,6},{2},{3,5},{4},{7}} => 7
{{1,7},{2,6},{3,5},{4}} => 9
{{1},{2,6,7},{3,5},{4}} => 12
{{1},{2,6},{3,5,7},{4}} => 11
{{1},{2,6},{3,5},{4,7}} => 10
{{1},{2,6},{3,5},{4},{7}} => 8
{{1,7},{2},{3,5,6},{4}} => 11
{{1},{2,7},{3,5,6},{4}} => 12
{{1},{2},{3,5,6,7},{4}} => 14
{{1},{2},{3,5,6},{4,7}} => 13
{{1},{2},{3,5,6},{4},{7}} => 10
{{1,7},{2},{3,5},{4,6}} => 10
{{1},{2,7},{3,5},{4,6}} => 11
{{1},{2},{3,5,7},{4,6}} => 12
{{1},{2},{3,5},{4,6,7}} => 13
{{1},{2},{3,5},{4,6},{7}} => 9
{{1,7},{2},{3,5},{4},{6}} => 6
{{1},{2,7},{3,5},{4},{6}} => 7
{{1},{2},{3,5,7},{4},{6}} => 9
{{1},{2},{3,5},{4,7},{6}} => 8
{{1},{2},{3,5},{4},{6,7}} => 10
{{1},{2},{3,5},{4},{6},{7}} => 5
{{1,6,7},{2},{3},{4,5}} => 12
{{1,6},{2,7},{3},{4,5}} => 9
{{1,6},{2},{3,7},{4,5}} => 10
{{1,6},{2},{3},{4,5,7}} => 11
{{1,6},{2},{3},{4,5},{7}} => 8
{{1,7},{2,6},{3},{4,5}} => 10
{{1},{2,6,7},{3},{4,5}} => 13
{{1},{2,6},{3,7},{4,5}} => 11
{{1},{2,6},{3},{4,5,7}} => 12
{{1},{2,6},{3},{4,5},{7}} => 9
{{1,7},{2},{3,6},{4,5}} => 11
{{1},{2,7},{3,6},{4,5}} => 12
{{1},{2},{3,6,7},{4,5}} => 14
{{1},{2},{3,6},{4,5,7}} => 13
{{1},{2},{3,6},{4,5},{7}} => 10
{{1,7},{2},{3},{4,5,6}} => 12
{{1},{2,7},{3},{4,5,6}} => 13
{{1},{2},{3,7},{4,5,6}} => 14
{{1},{2},{3},{4,5,6,7}} => 15
{{1},{2},{3},{4,5,6},{7}} => 11
{{1,7},{2},{3},{4,5},{6}} => 7
{{1},{2,7},{3},{4,5},{6}} => 8
{{1},{2},{3,7},{4,5},{6}} => 9
{{1},{2},{3},{4,5,7},{6}} => 10
{{1},{2},{3},{4,5},{6,7}} => 11
{{1},{2},{3},{4,5},{6},{7}} => 6
{{1,6,7},{2},{3},{4},{5}} => 7
{{1,6},{2,7},{3},{4},{5}} => 3
{{1,6},{2},{3,7},{4},{5}} => 4
{{1,6},{2},{3},{4,7},{5}} => 5
{{1,6},{2},{3},{4},{5,7}} => 6
{{1,6},{2},{3},{4},{5},{7}} => 2
{{1,7},{2,6},{3},{4},{5}} => 4
{{1},{2,6,7},{3},{4},{5}} => 8
{{1},{2,6},{3,7},{4},{5}} => 5
{{1},{2,6},{3},{4,7},{5}} => 6
{{1},{2,6},{3},{4},{5,7}} => 7
{{1},{2,6},{3},{4},{5},{7}} => 3
{{1,7},{2},{3,6},{4},{5}} => 5
{{1},{2,7},{3,6},{4},{5}} => 6
{{1},{2},{3,6,7},{4},{5}} => 9
{{1},{2},{3,6},{4,7},{5}} => 7
{{1},{2},{3,6},{4},{5,7}} => 8
{{1},{2},{3,6},{4},{5},{7}} => 4
{{1,7},{2},{3},{4,6},{5}} => 6
{{1},{2,7},{3},{4,6},{5}} => 7
{{1},{2},{3,7},{4,6},{5}} => 8
{{1},{2},{3},{4,6,7},{5}} => 10
{{1},{2},{3},{4,6},{5,7}} => 9
{{1},{2},{3},{4,6},{5},{7}} => 5
{{1,7},{2},{3},{4},{5,6}} => 7
{{1},{2,7},{3},{4},{5,6}} => 8
{{1},{2},{3,7},{4},{5,6}} => 9
{{1},{2},{3},{4,7},{5,6}} => 10
{{1},{2},{3},{4},{5,6,7}} => 11
{{1},{2},{3},{4},{5,6},{7}} => 6
{{1,7},{2},{3},{4},{5},{6}} => 1
{{1},{2,7},{3},{4},{5},{6}} => 2
{{1},{2},{3,7},{4},{5},{6}} => 3
{{1},{2},{3},{4,7},{5},{6}} => 4
{{1},{2},{3},{4},{5,7},{6}} => 5
{{1},{2},{3},{4},{5},{6,7}} => 6
{{1},{2},{3},{4},{5},{6},{7}} => 0
{{1,2},{3,4},{5,6},{7,8}} => 22
{{1,3},{2,4},{5,6},{7,8}} => 20
{{1,4},{2,3},{5,6},{7,8}} => 21
{{1,5},{2,3},{4,6},{7,8}} => 19
{{1,6},{2,3},{4,5},{7,8}} => 20
{{1,7},{2,3},{4,5},{6,8}} => 18
{{1,8},{2,3},{4,5},{6,7}} => 19
{{1,8},{2,4},{3,5},{6,7}} => 17
{{1,7},{2,4},{3,5},{6,8}} => 16
{{1,6},{2,4},{3,5},{7,8}} => 18
{{1,5},{2,4},{3,6},{7,8}} => 17
{{1,4},{2,5},{3,6},{7,8}} => 16
{{1,3},{2,5},{4,6},{7,8}} => 18
{{1,2},{3,5},{4,6},{7,8}} => 20
{{1,2},{3,6},{4,5},{7,8}} => 21
{{1,3},{2,6},{4,5},{7,8}} => 19
{{1,4},{2,6},{3,5},{7,8}} => 17
{{1,5},{2,6},{3,4},{7,8}} => 18
{{1,6},{2,5},{3,4},{7,8}} => 19
{{1,7},{2,5},{3,4},{6,8}} => 17
{{1,8},{2,5},{3,4},{6,7}} => 18
{{1,8},{2,6},{3,4},{5,7}} => 16
{{1,7},{2,6},{3,4},{5,8}} => 15
{{1,6},{2,7},{3,4},{5,8}} => 14
{{1,5},{2,7},{3,4},{6,8}} => 16
{{1,4},{2,7},{3,5},{6,8}} => 15
{{1,3},{2,7},{4,5},{6,8}} => 17
{{1,2},{3,7},{4,5},{6,8}} => 19
{{1,2},{3,8},{4,5},{6,7}} => 20
{{1,3},{2,8},{4,5},{6,7}} => 18
{{1,4},{2,8},{3,5},{6,7}} => 16
{{1,5},{2,8},{3,4},{6,7}} => 17
{{1,6},{2,8},{3,4},{5,7}} => 15
{{1,7},{2,8},{3,4},{5,6}} => 16
{{1,8},{2,7},{3,4},{5,6}} => 17
{{1,8},{2,7},{3,5},{4,6}} => 15
{{1,7},{2,8},{3,5},{4,6}} => 14
{{1,6},{2,8},{3,5},{4,7}} => 13
{{1,5},{2,8},{3,6},{4,7}} => 12
{{1,4},{2,8},{3,6},{5,7}} => 14
{{1,3},{2,8},{4,6},{5,7}} => 16
{{1,2},{3,8},{4,6},{5,7}} => 18
{{1,2},{3,7},{4,6},{5,8}} => 17
{{1,3},{2,7},{4,6},{5,8}} => 15
{{1,4},{2,7},{3,6},{5,8}} => 13
{{1,5},{2,7},{3,6},{4,8}} => 11
{{1,6},{2,7},{3,5},{4,8}} => 12
{{1,7},{2,6},{3,5},{4,8}} => 13
{{1,8},{2,6},{3,5},{4,7}} => 14
{{1,8},{2,5},{3,6},{4,7}} => 13
{{1,7},{2,5},{3,6},{4,8}} => 12
{{1,6},{2,5},{3,7},{4,8}} => 11
{{1,5},{2,6},{3,7},{4,8}} => 10
{{1,4},{2,6},{3,7},{5,8}} => 12
{{1,3},{2,6},{4,7},{5,8}} => 14
{{1,2},{3,6},{4,7},{5,8}} => 16
{{1,2},{3,5},{4,7},{6,8}} => 18
{{1,3},{2,5},{4,7},{6,8}} => 16
{{1,4},{2,5},{3,7},{6,8}} => 14
{{1,5},{2,4},{3,7},{6,8}} => 15
{{1,6},{2,4},{3,7},{5,8}} => 13
{{1,7},{2,4},{3,6},{5,8}} => 14
{{1,8},{2,4},{3,6},{5,7}} => 15
{{1,8},{2,3},{4,6},{5,7}} => 17
{{1,7},{2,3},{4,6},{5,8}} => 16
{{1,6},{2,3},{4,7},{5,8}} => 15
{{1,5},{2,3},{4,7},{6,8}} => 17
{{1,4},{2,3},{5,7},{6,8}} => 19
{{1,3},{2,4},{5,7},{6,8}} => 18
{{1,2},{3,4},{5,7},{6,8}} => 20
{{1,2},{3,4},{5,8},{6,7}} => 21
{{1,3},{2,4},{5,8},{6,7}} => 19
{{1,4},{2,3},{5,8},{6,7}} => 20
{{1,5},{2,3},{4,8},{6,7}} => 18
{{1,6},{2,3},{4,8},{5,7}} => 16
{{1,7},{2,3},{4,8},{5,6}} => 17
{{1,8},{2,3},{4,7},{5,6}} => 18
{{1,8},{2,4},{3,7},{5,6}} => 16
{{1,7},{2,4},{3,8},{5,6}} => 15
{{1,6},{2,4},{3,8},{5,7}} => 14
{{1,5},{2,4},{3,8},{6,7}} => 16
{{1,4},{2,5},{3,8},{6,7}} => 15
{{1,3},{2,5},{4,8},{6,7}} => 17
{{1,2},{3,5},{4,8},{6,7}} => 19
{{1,2},{3,6},{4,8},{5,7}} => 17
{{1,3},{2,6},{4,8},{5,7}} => 15
{{1,4},{2,6},{3,8},{5,7}} => 13
{{1,5},{2,6},{3,8},{4,7}} => 11
{{1,6},{2,5},{3,8},{4,7}} => 12
{{1,7},{2,5},{3,8},{4,6}} => 13
{{1,8},{2,5},{3,7},{4,6}} => 14
{{1,8},{2,6},{3,7},{4,5}} => 15
{{1,7},{2,6},{3,8},{4,5}} => 14
{{1,6},{2,7},{3,8},{4,5}} => 13
{{1,5},{2,7},{3,8},{4,6}} => 12
{{1,4},{2,7},{3,8},{5,6}} => 14
{{1,3},{2,7},{4,8},{5,6}} => 16
{{1,2},{3,7},{4,8},{5,6}} => 18
{{1,2},{3,8},{4,7},{5,6}} => 19
{{1,3},{2,8},{4,7},{5,6}} => 17
{{1,4},{2,8},{3,7},{5,6}} => 15
{{1,5},{2,8},{3,7},{4,6}} => 13
{{1,6},{2,8},{3,7},{4,5}} => 14
{{1,7},{2,8},{3,6},{4,5}} => 15
{{1,8},{2,7},{3,6},{4,5}} => 16
{{1},{2},{3,4,5,6,7,8}} => 25
{{1},{2,4,5,6,7,8},{3}} => 24
{{1},{2,3,5,6,7,8},{4}} => 24
{{1},{2,3,4,6,7,8},{5}} => 24
{{1},{2,3,4,5,8},{6},{7}} => 20
{{1},{2,3,4,5,7,8},{6}} => 24
{{1},{2,3,4,5,6,7},{8}} => 25
{{1},{2,3,4,8},{5,6,7}} => 24
{{1},{2,3,4,5,8},{6,7}} => 24
{{1},{2,3,4,5,6,8},{7}} => 24
{{1},{2,3,4,5,6,7,8}} => 27
{{1,2},{3,4,5,6,7,8}} => 27
{{1,4,5,6,7,8},{2},{3}} => 23
{{1,3,5,6,7,8},{2},{4}} => 23
{{1,3,4,5,6,7,8},{2}} => 26
{{1,4,5,6,7,8},{2,3}} => 26
{{1,2,4,5,6,7,8},{3}} => 26
{{1,2,5,6,7,8},{3,4}} => 26
{{1,2,3,5,6,7},{4},{8}} => 24
{{1,2,3,5,6,7,8},{4}} => 26
{{1,2,3,6,7,8},{4,5}} => 26
{{1,2,3,4,7},{5},{6},{8}} => 20
{{1,2,3,4,6,7},{5},{8}} => 24
{{1,2,3,4,6,7,8},{5}} => 26
{{1,2,3,4,5,6},{7,8}} => 27
{{1,2,3,7},{4,5,6},{8}} => 24
{{1,2,3,4,7},{5,6},{8}} => 24
{{1,2,3,4,7,8},{5,6}} => 26
{{1,2,3,4,5,7},{6},{8}} => 24
{{1,2,3,4,5,7,8},{6}} => 26
{{1,2,3,4,5,6,7},{8}} => 27
{{1,8},{2,3,4,5,6,7}} => 26
{{1,2,3,4,5,8},{6,7}} => 26
{{1,2,3,4,5,6,8},{7}} => 26
{{1,2,3,4,5,6,7,8}} => 28
{{1,2,4,6,7,8},{3,5}} => 24
{{1,2,3,5,7,8},{4,6}} => 24
{{1,2,3,4,6,8},{5,7}} => 24
{{1,2,3,4,5,7},{6,8}} => 25
{{1,2,3,4,5,6,7,8},{9}} => 35
{{1},{2,3,4,5,6,7,8,9}} => 35
{{1,2,3,4,5,6,8},{7},{9}} => 32
{{1},{2,3,4,5,6,7,9},{8}} => 32
{{1,2,3,4,5,8},{6,7},{9}} => 32
{{1,2,3,4,5,7,8},{6},{9}} => 32
{{1},{2,3,4,5,6,9},{7,8}} => 32
{{1},{2,3,4,5,6,8,9},{7}} => 32
{{1,2},{3,4},{5,6},{7,8},{9,10}} => 35
{{1,4},{2,3},{5,6},{7,8},{9,10}} => 34
{{1,6},{2,3},{4,5},{7,8},{9,10}} => 33
{{1,8},{2,3},{4,5},{6,7},{9,10}} => 32
{{1,10},{2,3},{4,5},{6,7},{8,9}} => 31
{{1,2},{3,6},{4,5},{7,8},{9,10}} => 34
{{1,6},{2,5},{3,4},{7,8},{9,10}} => 32
{{1,8},{2,5},{3,4},{6,7},{9,10}} => 31
{{1,10},{2,5},{3,4},{6,7},{8,9}} => 30
{{1,2},{3,8},{4,5},{6,7},{9,10}} => 33
{{1,8},{2,7},{3,4},{5,6},{9,10}} => 30
{{1,10},{2,7},{3,4},{5,6},{8,9}} => 29
{{1,2},{3,10},{4,5},{6,7},{8,9}} => 32
{{1,10},{2,9},{3,4},{5,6},{7,8}} => 28
{{1,2},{3,4},{5,8},{6,7},{9,10}} => 34
{{1,4},{2,3},{5,8},{6,7},{9,10}} => 33
{{1,8},{2,3},{4,7},{5,6},{9,10}} => 31
{{1,10},{2,3},{4,7},{5,6},{8,9}} => 30
{{1,2},{3,8},{4,7},{5,6},{9,10}} => 32
{{1,8},{2,7},{3,6},{4,5},{9,10}} => 29
{{1,10},{2,7},{3,6},{4,5},{8,9}} => 28
{{1,2},{3,10},{4,7},{5,6},{8,9}} => 31
{{1,10},{2,9},{3,6},{4,5},{7,8}} => 27
{{1,2},{3,4},{5,10},{6,7},{8,9}} => 33
{{1,4},{2,3},{5,10},{6,7},{8,9}} => 32
{{1,10},{2,3},{4,9},{5,6},{7,8}} => 29
{{1,2},{3,10},{4,9},{5,6},{7,8}} => 30
{{1,10},{2,9},{3,8},{4,5},{6,7}} => 26
{{1,2},{3,4},{5,6},{7,10},{8,9}} => 34
{{1,4},{2,3},{5,6},{7,10},{8,9}} => 33
{{1,6},{2,3},{4,5},{7,10},{8,9}} => 32
{{1,10},{2,3},{4,5},{6,9},{7,8}} => 30
{{1,2},{3,6},{4,5},{7,10},{8,9}} => 33
{{1,6},{2,5},{3,4},{7,10},{8,9}} => 31
{{1,10},{2,5},{3,4},{6,9},{7,8}} => 29
{{1,2},{3,10},{4,5},{6,9},{7,8}} => 31
{{1,10},{2,9},{3,4},{5,8},{6,7}} => 27
{{1,2},{3,4},{5,10},{6,9},{7,8}} => 32
{{1,4},{2,3},{5,10},{6,9},{7,8}} => 31
{{1,10},{2,3},{4,9},{5,8},{6,7}} => 28
{{1,2},{3,10},{4,9},{5,8},{6,7}} => 29
{{1,10},{2,9},{3,8},{4,7},{5,6}} => 25
{{1,2,3,4,5,6,7,8,9},{10}} => 44
{{1},{2,3,4,5,6,7,8,9,10}} => 44
{{1,2,3,4,5,6,7,9},{8},{10}} => 41
{{1},{2,3,4,5,6,7,8,10},{9}} => 41
{{1,2,3,4,5,6,7,8,9,10},{11}} => 54
{{1},{2,3,4,5,6,7,8,9,10,11}} => 54
{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}} => 51
{{1,2},{3,4},{5,6},{7,8},{9,12},{10,11}} => 50
{{1,2},{3,4},{5,6},{7,10},{8,9},{11,12}} => 50
{{1,2},{3,4},{5,6},{7,12},{8,9},{10,11}} => 49
{{1,2},{3,4},{5,6},{7,12},{8,11},{9,10}} => 48
{{1,2},{3,4},{5,8},{6,7},{9,10},{11,12}} => 50
{{1,2},{3,4},{5,8},{6,7},{9,12},{10,11}} => 49
{{1,2},{3,4},{5,10},{6,7},{8,9},{11,12}} => 49
{{1,2},{3,4},{5,12},{6,7},{8,9},{10,11}} => 48
{{1,2},{3,4},{5,12},{6,7},{8,11},{9,10}} => 47
{{1,2},{3,4},{5,10},{6,9},{7,8},{11,12}} => 48
{{1,2},{3,4},{5,12},{6,9},{7,8},{10,11}} => 47
{{1,2},{3,4},{5,12},{6,11},{7,8},{9,10}} => 46
{{1,2},{3,4},{5,12},{6,11},{7,10},{8,9}} => 45
{{1,2},{3,6},{4,5},{7,8},{9,10},{11,12}} => 50
{{1,2},{3,6},{4,5},{7,8},{9,12},{10,11}} => 49
{{1,2},{3,6},{4,5},{7,10},{8,9},{11,12}} => 49
{{1,2},{3,6},{4,5},{7,12},{8,9},{10,11}} => 48
{{1,2},{3,6},{4,5},{7,12},{8,11},{9,10}} => 47
{{1,2},{3,8},{4,5},{6,7},{9,10},{11,12}} => 49
{{1,2},{3,8},{4,5},{6,7},{9,12},{10,11}} => 48
{{1,2},{3,10},{4,5},{6,7},{8,9},{11,12}} => 48
{{1,2},{3,12},{4,5},{6,7},{8,9},{10,11}} => 47
{{1,2},{3,12},{4,5},{6,7},{8,11},{9,10}} => 46
{{1,2},{3,10},{4,5},{6,9},{7,8},{11,12}} => 47
{{1,2},{3,12},{4,5},{6,9},{7,8},{10,11}} => 46
{{1,2},{3,12},{4,5},{6,11},{7,8},{9,10}} => 45
{{1,2},{3,12},{4,5},{6,11},{7,10},{8,9}} => 44
{{1,2},{3,8},{4,7},{5,6},{9,10},{11,12}} => 48
{{1,2},{3,8},{4,7},{5,6},{9,12},{10,11}} => 47
{{1,2},{3,10},{4,7},{5,6},{8,9},{11,12}} => 47
{{1,2},{3,12},{4,7},{5,6},{8,9},{10,11}} => 46
{{1,2},{3,12},{4,7},{5,6},{8,11},{9,10}} => 45
{{1,2},{3,10},{4,9},{5,6},{7,8},{11,12}} => 46
{{1,2},{3,12},{4,9},{5,6},{7,8},{10,11}} => 45
{{1,2},{3,12},{4,11},{5,6},{7,8},{9,10}} => 44
{{1,2},{3,12},{4,11},{5,6},{7,10},{8,9}} => 43
{{1,2},{3,10},{4,9},{5,8},{6,7},{11,12}} => 45
{{1,2},{3,12},{4,9},{5,8},{6,7},{10,11}} => 44
{{1,2},{3,12},{4,11},{5,8},{6,7},{9,10}} => 43
{{1,2},{3,12},{4,11},{5,10},{6,7},{8,9}} => 42
{{1,2},{3,12},{4,11},{5,10},{6,9},{7,8}} => 41
{{1,4},{2,3},{5,6},{7,8},{9,10},{11,12}} => 50
{{1,4},{2,3},{5,6},{7,8},{9,12},{10,11}} => 49
{{1,4},{2,3},{5,6},{7,10},{8,9},{11,12}} => 49
{{1,4},{2,3},{5,6},{7,12},{8,9},{10,11}} => 48
{{1,4},{2,3},{5,6},{7,12},{8,11},{9,10}} => 47
{{1,4},{2,3},{5,8},{6,7},{9,10},{11,12}} => 49
{{1,4},{2,3},{5,8},{6,7},{9,12},{10,11}} => 48
{{1,4},{2,3},{5,10},{6,7},{8,9},{11,12}} => 48
{{1,4},{2,3},{5,12},{6,7},{8,9},{10,11}} => 47
{{1,4},{2,3},{5,12},{6,7},{8,11},{9,10}} => 46
{{1,4},{2,3},{5,10},{6,9},{7,8},{11,12}} => 47
{{1,4},{2,3},{5,12},{6,9},{7,8},{10,11}} => 46
{{1,4},{2,3},{5,12},{6,11},{7,8},{9,10}} => 45
{{1,4},{2,3},{5,12},{6,11},{7,10},{8,9}} => 44
{{1,6},{2,3},{4,5},{7,8},{9,10},{11,12}} => 49
{{1,6},{2,3},{4,5},{7,8},{9,12},{10,11}} => 48
{{1,6},{2,3},{4,5},{7,10},{8,9},{11,12}} => 48
{{1,6},{2,3},{4,5},{7,12},{8,9},{10,11}} => 47
{{1,6},{2,3},{4,5},{7,12},{8,11},{9,10}} => 46
{{1,8},{2,3},{4,5},{6,7},{9,10},{11,12}} => 48
{{1,8},{2,3},{4,5},{6,7},{9,12},{10,11}} => 47
{{1,10},{2,3},{4,5},{6,7},{8,9},{11,12}} => 47
{{1,12},{2,3},{4,5},{6,7},{8,9},{10,11}} => 46
{{1,12},{2,3},{4,5},{6,7},{8,11},{9,10}} => 45
{{1,10},{2,3},{4,5},{6,9},{7,8},{11,12}} => 46
{{1,12},{2,3},{4,5},{6,9},{7,8},{10,11}} => 45
{{1,12},{2,3},{4,5},{6,11},{7,8},{9,10}} => 44
{{1,12},{2,3},{4,5},{6,11},{7,10},{8,9}} => 43
{{1,8},{2,3},{4,7},{5,6},{9,10},{11,12}} => 47
{{1,8},{2,3},{4,7},{5,6},{9,12},{10,11}} => 46
{{1,10},{2,3},{4,7},{5,6},{8,9},{11,12}} => 46
{{1,12},{2,3},{4,7},{5,6},{8,9},{10,11}} => 45
{{1,12},{2,3},{4,7},{5,6},{8,11},{9,10}} => 44
{{1,10},{2,3},{4,9},{5,6},{7,8},{11,12}} => 45
{{1,12},{2,3},{4,9},{5,6},{7,8},{10,11}} => 44
{{1,12},{2,3},{4,11},{5,6},{7,8},{9,10}} => 43
{{1,12},{2,3},{4,11},{5,6},{7,10},{8,9}} => 42
{{1,10},{2,3},{4,9},{5,8},{6,7},{11,12}} => 44
{{1,12},{2,3},{4,9},{5,8},{6,7},{10,11}} => 43
{{1,12},{2,3},{4,11},{5,8},{6,7},{9,10}} => 42
{{1,12},{2,3},{4,11},{5,10},{6,7},{8,9}} => 41
{{1,12},{2,3},{4,11},{5,10},{6,9},{7,8}} => 40
{{1,6},{2,5},{3,4},{7,8},{9,10},{11,12}} => 48
{{1,6},{2,5},{3,4},{7,8},{9,12},{10,11}} => 47
{{1,6},{2,5},{3,4},{7,10},{8,9},{11,12}} => 47
{{1,6},{2,5},{3,4},{7,12},{8,9},{10,11}} => 46
{{1,6},{2,5},{3,4},{7,12},{8,11},{9,10}} => 45
{{1,8},{2,5},{3,4},{6,7},{9,10},{11,12}} => 47
{{1,8},{2,5},{3,4},{6,7},{9,12},{10,11}} => 46
{{1,10},{2,5},{3,4},{6,7},{8,9},{11,12}} => 46
{{1,12},{2,5},{3,4},{6,7},{8,9},{10,11}} => 45
{{1,12},{2,5},{3,4},{6,7},{8,11},{9,10}} => 44
{{1,10},{2,5},{3,4},{6,9},{7,8},{11,12}} => 45
{{1,12},{2,5},{3,4},{6,9},{7,8},{10,11}} => 44
{{1,12},{2,5},{3,4},{6,11},{7,8},{9,10}} => 43
{{1,12},{2,5},{3,4},{6,11},{7,10},{8,9}} => 42
{{1,8},{2,7},{3,4},{5,6},{9,10},{11,12}} => 46
{{1,8},{2,7},{3,4},{5,6},{9,12},{10,11}} => 45
{{1,10},{2,7},{3,4},{5,6},{8,9},{11,12}} => 45
{{1,12},{2,7},{3,4},{5,6},{8,9},{10,11}} => 44
{{1,12},{2,7},{3,4},{5,6},{8,11},{9,10}} => 43
{{1,10},{2,9},{3,4},{5,6},{7,8},{11,12}} => 44
{{1,12},{2,9},{3,4},{5,6},{7,8},{10,11}} => 43
{{1,12},{2,11},{3,4},{5,6},{7,8},{9,10}} => 42
{{1,12},{2,11},{3,4},{5,6},{7,10},{8,9}} => 41
{{1,10},{2,9},{3,4},{5,8},{6,7},{11,12}} => 43
{{1,12},{2,9},{3,4},{5,8},{6,7},{10,11}} => 42
{{1,12},{2,11},{3,4},{5,8},{6,7},{9,10}} => 41
{{1,12},{2,11},{3,4},{5,10},{6,7},{8,9}} => 40
{{1,12},{2,11},{3,4},{5,10},{6,9},{7,8}} => 39
{{1,8},{2,7},{3,6},{4,5},{9,10},{11,12}} => 45
{{1,8},{2,7},{3,6},{4,5},{9,12},{10,11}} => 44
{{1,10},{2,7},{3,6},{4,5},{8,9},{11,12}} => 44
{{1,12},{2,7},{3,6},{4,5},{8,9},{10,11}} => 43
{{1,12},{2,7},{3,6},{4,5},{8,11},{9,10}} => 42
{{1,10},{2,9},{3,6},{4,5},{7,8},{11,12}} => 43
{{1,12},{2,9},{3,6},{4,5},{7,8},{10,11}} => 42
{{1,12},{2,11},{3,6},{4,5},{7,8},{9,10}} => 41
{{1,12},{2,11},{3,6},{4,5},{7,10},{8,9}} => 40
{{1,10},{2,9},{3,8},{4,5},{6,7},{11,12}} => 42
{{1,12},{2,9},{3,8},{4,5},{6,7},{10,11}} => 41
{{1,12},{2,11},{3,8},{4,5},{6,7},{9,10}} => 40
{{1,12},{2,11},{3,10},{4,5},{6,7},{8,9}} => 39
{{1,12},{2,11},{3,10},{4,5},{6,9},{7,8}} => 38
{{1,10},{2,9},{3,8},{4,7},{5,6},{11,12}} => 41
{{1,12},{2,9},{3,8},{4,7},{5,6},{10,11}} => 40
{{1,12},{2,11},{3,8},{4,7},{5,6},{9,10}} => 39
{{1,12},{2,11},{3,10},{4,7},{5,6},{8,9}} => 38
{{1,12},{2,11},{3,10},{4,9},{5,6},{7,8}} => 37
{{1,12},{2,11},{3,10},{4,9},{5,8},{6,7}} => 36
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Created: Jan 26, 2018 at 08:45 by Martin Rubey
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Last Updated: Feb 01, 2018 at 23:32 by Martin Rubey