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-----------------------------------------------------------------------------
Statistic identifier: St000577
-----------------------------------------------------------------------------
Collection: Set partitions
-----------------------------------------------------------------------------
Description: The number of occurrences of the pattern {{1},{2}} such that 1 is a maximal element.
This is the number of pairs $i\lt j$ in different blocks such that $i$ is the maximal element of a block.
-----------------------------------------------------------------------------
References: [1] Chern, B., Diaconis, P., Kane, D. M., Rhoades, R. C. Closed expressions for averages of set partition statistics [[MathSciNet:3338726]] [[arXiv:1304.4309]]
-----------------------------------------------------------------------------
Code:
def statistic(pi):
return len(pattern_occurrences(pi, [[1],[2]], [], [1], [], []))
def pattern_occurrences(pi, P, First, Last, Arcs, Consecutives):
"""We assume that pi is a SetPartition of {1,2,...,n} and P is a
SetPartition of {1,2,...,k}.
"""
occurrences = []
pi = SetPartition(pi)
P = SetPartition(P)
openers = [min(B) for B in pi]
closers = [max(B) for B in pi]
pi_sorted = sorted([sorted(b) for b in pi])
edges = [(a,b) for B in pi_sorted for (a,b) in zip(B, B[1:])]
for s in Subsets(pi.base_set(), P.size()):
s = sorted(s)
pi_r = pi.restriction(s)
if pi_r.standardization() != P:
continue
X = pi_r.base_set()
if any(X[i-1] not in openers for i in First):
continue
if any(X[i-1] not in closers for i in Last):
continue
if any((X[i-1], X[j-1]) not in edges for (i,j) in Arcs):
continue
if any(abs(X[i-1]-X[j-1]) != 1 for (i,j) in Consecutives):
continue
occurrences += [s]
return occurrences
-----------------------------------------------------------------------------
Statistic values:
{{1,2}} => 0
{{1},{2}} => 1
{{1,2,3}} => 0
{{1,2},{3}} => 1
{{1,3},{2}} => 1
{{1},{2,3}} => 2
{{1},{2},{3}} => 3
{{1,2,3,4}} => 0
{{1,2,3},{4}} => 1
{{1,2,4},{3}} => 1
{{1,2},{3,4}} => 2
{{1,2},{3},{4}} => 3
{{1,3,4},{2}} => 2
{{1,3},{2,4}} => 1
{{1,3},{2},{4}} => 3
{{1,4},{2,3}} => 1
{{1},{2,3,4}} => 3
{{1},{2,3},{4}} => 4
{{1,4},{2},{3}} => 3
{{1},{2,4},{3}} => 4
{{1},{2},{3,4}} => 5
{{1},{2},{3},{4}} => 6
{{1,2,3,4,5}} => 0
{{1,2,3,4},{5}} => 1
{{1,2,3,5},{4}} => 1
{{1,2,3},{4,5}} => 2
{{1,2,3},{4},{5}} => 3
{{1,2,4,5},{3}} => 2
{{1,2,4},{3,5}} => 1
{{1,2,4},{3},{5}} => 3
{{1,2,5},{3,4}} => 1
{{1,2},{3,4,5}} => 3
{{1,2},{3,4},{5}} => 4
{{1,2,5},{3},{4}} => 3
{{1,2},{3,5},{4}} => 4
{{1,2},{3},{4,5}} => 5
{{1,2},{3},{4},{5}} => 6
{{1,3,4,5},{2}} => 3
{{1,3,4},{2,5}} => 1
{{1,3,4},{2},{5}} => 4
{{1,3,5},{2,4}} => 1
{{1,3},{2,4,5}} => 2
{{1,3},{2,4},{5}} => 3
{{1,3,5},{2},{4}} => 4
{{1,3},{2,5},{4}} => 3
{{1,3},{2},{4,5}} => 5
{{1,3},{2},{4},{5}} => 6
{{1,4,5},{2,3}} => 2
{{1,4},{2,3,5}} => 1
{{1,4},{2,3},{5}} => 3
{{1,5},{2,3,4}} => 1
{{1},{2,3,4,5}} => 4
{{1},{2,3,4},{5}} => 5
{{1,5},{2,3},{4}} => 3
{{1},{2,3,5},{4}} => 5
{{1},{2,3},{4,5}} => 6
{{1},{2,3},{4},{5}} => 7
{{1,4,5},{2},{3}} => 5
{{1,4},{2,5},{3}} => 3
{{1,4},{2},{3,5}} => 4
{{1,4},{2},{3},{5}} => 6
{{1,5},{2,4},{3}} => 3
{{1},{2,4,5},{3}} => 6
{{1},{2,4},{3,5}} => 5
{{1},{2,4},{3},{5}} => 7
{{1,5},{2},{3,4}} => 4
{{1},{2,5},{3,4}} => 5
{{1},{2},{3,4,5}} => 7
{{1},{2},{3,4},{5}} => 8
{{1,5},{2},{3},{4}} => 6
{{1},{2,5},{3},{4}} => 7
{{1},{2},{3,5},{4}} => 8
{{1},{2},{3},{4,5}} => 9
{{1},{2},{3},{4},{5}} => 10
{{1,2,3,4,5,6}} => 0
{{1,2,3,4,5},{6}} => 1
{{1,2,3,4,6},{5}} => 1
{{1,2,3,4},{5,6}} => 2
{{1,2,3,4},{5},{6}} => 3
{{1,2,3,5,6},{4}} => 2
{{1,2,3,5},{4,6}} => 1
{{1,2,3,5},{4},{6}} => 3
{{1,2,3,6},{4,5}} => 1
{{1,2,3},{4,5,6}} => 3
{{1,2,3},{4,5},{6}} => 4
{{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}} => 6
{{1,2,4,5,6},{3}} => 3
{{1,2,4,5},{3,6}} => 1
{{1,2,4,5},{3},{6}} => 4
{{1,2,4,6},{3,5}} => 1
{{1,2,4},{3,5,6}} => 2
{{1,2,4},{3,5},{6}} => 3
{{1,2,4,6},{3},{5}} => 4
{{1,2,4},{3,6},{5}} => 3
{{1,2,4},{3},{5,6}} => 5
{{1,2,4},{3},{5},{6}} => 6
{{1,2,5,6},{3,4}} => 2
{{1,2,5},{3,4,6}} => 1
{{1,2,5},{3,4},{6}} => 3
{{1,2,6},{3,4,5}} => 1
{{1,2},{3,4,5,6}} => 4
{{1,2},{3,4,5},{6}} => 5
{{1,2,6},{3,4},{5}} => 3
{{1,2},{3,4,6},{5}} => 5
{{1,2},{3,4},{5,6}} => 6
{{1,2},{3,4},{5},{6}} => 7
{{1,2,5,6},{3},{4}} => 5
{{1,2,5},{3,6},{4}} => 3
{{1,2,5},{3},{4,6}} => 4
{{1,2,5},{3},{4},{6}} => 6
{{1,2,6},{3,5},{4}} => 3
{{1,2},{3,5,6},{4}} => 6
{{1,2},{3,5},{4,6}} => 5
{{1,2},{3,5},{4},{6}} => 7
{{1,2,6},{3},{4,5}} => 4
{{1,2},{3,6},{4,5}} => 5
{{1,2},{3},{4,5,6}} => 7
{{1,2},{3},{4,5},{6}} => 8
{{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}} => 10
{{1,3,4,5,6},{2}} => 4
{{1,3,4,5},{2,6}} => 1
{{1,3,4,5},{2},{6}} => 5
{{1,3,4,6},{2,5}} => 1
{{1,3,4},{2,5,6}} => 2
{{1,3,4},{2,5},{6}} => 3
{{1,3,4,6},{2},{5}} => 5
{{1,3,4},{2,6},{5}} => 3
{{1,3,4},{2},{5,6}} => 6
{{1,3,4},{2},{5},{6}} => 7
{{1,3,5,6},{2,4}} => 2
{{1,3,5},{2,4,6}} => 1
{{1,3,5},{2,4},{6}} => 3
{{1,3,6},{2,4,5}} => 1
{{1,3},{2,4,5,6}} => 3
{{1,3},{2,4,5},{6}} => 4
{{1,3,6},{2,4},{5}} => 3
{{1,3},{2,4,6},{5}} => 4
{{1,3},{2,4},{5,6}} => 5
{{1,3},{2,4},{5},{6}} => 6
{{1,3,5,6},{2},{4}} => 6
{{1,3,5},{2,6},{4}} => 3
{{1,3,5},{2},{4,6}} => 5
{{1,3,5},{2},{4},{6}} => 7
{{1,3,6},{2,5},{4}} => 3
{{1,3},{2,5,6},{4}} => 5
{{1,3},{2,5},{4,6}} => 4
{{1,3},{2,5},{4},{6}} => 6
{{1,3,6},{2},{4,5}} => 5
{{1,3},{2,6},{4,5}} => 4
{{1,3},{2},{4,5,6}} => 7
{{1,3},{2},{4,5},{6}} => 8
{{1,3,6},{2},{4},{5}} => 7
{{1,3},{2,6},{4},{5}} => 6
{{1,3},{2},{4,6},{5}} => 8
{{1,3},{2},{4},{5,6}} => 9
{{1,3},{2},{4},{5},{6}} => 10
{{1,4,5,6},{2,3}} => 3
{{1,4,5},{2,3,6}} => 1
{{1,4,5},{2,3},{6}} => 4
{{1,4,6},{2,3,5}} => 1
{{1,4},{2,3,5,6}} => 2
{{1,4},{2,3,5},{6}} => 3
{{1,4,6},{2,3},{5}} => 4
{{1,4},{2,3,6},{5}} => 3
{{1,4},{2,3},{5,6}} => 5
{{1,4},{2,3},{5},{6}} => 6
{{1,5,6},{2,3,4}} => 2
{{1,5},{2,3,4,6}} => 1
{{1,5},{2,3,4},{6}} => 3
{{1,6},{2,3,4,5}} => 1
{{1},{2,3,4,5,6}} => 5
{{1},{2,3,4,5},{6}} => 6
{{1,6},{2,3,4},{5}} => 3
{{1},{2,3,4,6},{5}} => 6
{{1},{2,3,4},{5,6}} => 7
{{1},{2,3,4},{5},{6}} => 8
{{1,5,6},{2,3},{4}} => 5
{{1,5},{2,3,6},{4}} => 3
{{1,5},{2,3},{4,6}} => 4
{{1,5},{2,3},{4},{6}} => 6
{{1,6},{2,3,5},{4}} => 3
{{1},{2,3,5,6},{4}} => 7
{{1},{2,3,5},{4,6}} => 6
{{1},{2,3,5},{4},{6}} => 8
{{1,6},{2,3},{4,5}} => 4
{{1},{2,3,6},{4,5}} => 6
{{1},{2,3},{4,5,6}} => 8
{{1},{2,3},{4,5},{6}} => 9
{{1,6},{2,3},{4},{5}} => 6
{{1},{2,3,6},{4},{5}} => 8
{{1},{2,3},{4,6},{5}} => 9
{{1},{2,3},{4},{5,6}} => 10
{{1},{2,3},{4},{5},{6}} => 11
{{1,4,5,6},{2},{3}} => 7
{{1,4,5},{2,6},{3}} => 4
{{1,4,5},{2},{3,6}} => 5
{{1,4,5},{2},{3},{6}} => 8
{{1,4,6},{2,5},{3}} => 4
{{1,4},{2,5,6},{3}} => 5
{{1,4},{2,5},{3,6}} => 3
{{1,4},{2,5},{3},{6}} => 6
{{1,4,6},{2},{3,5}} => 5
{{1,4},{2,6},{3,5}} => 3
{{1,4},{2},{3,5,6}} => 6
{{1,4},{2},{3,5},{6}} => 7
{{1,4,6},{2},{3},{5}} => 8
{{1,4},{2,6},{3},{5}} => 6
{{1,4},{2},{3,6},{5}} => 7
{{1,4},{2},{3},{5,6}} => 9
{{1,4},{2},{3},{5},{6}} => 10
{{1,5,6},{2,4},{3}} => 5
{{1,5},{2,4,6},{3}} => 4
{{1,5},{2,4},{3,6}} => 3
{{1,5},{2,4},{3},{6}} => 6
{{1,6},{2,4,5},{3}} => 4
{{1},{2,4,5,6},{3}} => 8
{{1},{2,4,5},{3,6}} => 6
{{1},{2,4,5},{3},{6}} => 9
{{1,6},{2,4},{3,5}} => 3
{{1},{2,4,6},{3,5}} => 6
{{1},{2,4},{3,5,6}} => 7
{{1},{2,4},{3,5},{6}} => 8
{{1,6},{2,4},{3},{5}} => 6
{{1},{2,4,6},{3},{5}} => 9
{{1},{2,4},{3,6},{5}} => 8
{{1},{2,4},{3},{5,6}} => 10
{{1},{2,4},{3},{5},{6}} => 11
{{1,5,6},{2},{3,4}} => 6
{{1,5},{2,6},{3,4}} => 3
{{1,5},{2},{3,4,6}} => 5
{{1,5},{2},{3,4},{6}} => 7
{{1,6},{2,5},{3,4}} => 3
{{1},{2,5,6},{3,4}} => 7
{{1},{2,5},{3,4,6}} => 6
{{1},{2,5},{3,4},{6}} => 8
{{1,6},{2},{3,4,5}} => 5
{{1},{2,6},{3,4,5}} => 6
{{1},{2},{3,4,5,6}} => 9
{{1},{2},{3,4,5},{6}} => 10
{{1,6},{2},{3,4},{5}} => 7
{{1},{2,6},{3,4},{5}} => 8
{{1},{2},{3,4,6},{5}} => 10
{{1},{2},{3,4},{5,6}} => 11
{{1},{2},{3,4},{5},{6}} => 12
{{1,5,6},{2},{3},{4}} => 9
{{1,5},{2,6},{3},{4}} => 6
{{1,5},{2},{3,6},{4}} => 7
{{1,5},{2},{3},{4,6}} => 8
{{1,5},{2},{3},{4},{6}} => 10
{{1,6},{2,5},{3},{4}} => 6
{{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}} => 11
{{1,6},{2},{3,5},{4}} => 7
{{1},{2,6},{3,5},{4}} => 8
{{1},{2},{3,5,6},{4}} => 11
{{1},{2},{3,5},{4,6}} => 10
{{1},{2},{3,5},{4},{6}} => 12
{{1,6},{2},{3},{4,5}} => 8
{{1},{2,6},{3},{4,5}} => 9
{{1},{2},{3,6},{4,5}} => 10
{{1},{2},{3},{4,5,6}} => 12
{{1},{2},{3},{4,5},{6}} => 13
{{1,6},{2},{3},{4},{5}} => 10
{{1},{2,6},{3},{4},{5}} => 11
{{1},{2},{3,6},{4},{5}} => 12
{{1},{2},{3},{4,6},{5}} => 13
{{1},{2},{3},{4},{5,6}} => 14
{{1},{2},{3},{4},{5},{6}} => 15
{{1,2,3,4,5,6,7}} => 0
{{1,2,3,4,5,6},{7}} => 1
{{1,2,3,4,5,7},{6}} => 1
{{1,2,3,4,5},{6,7}} => 2
{{1,2,3,4,5},{6},{7}} => 3
{{1,2,3,4,6,7},{5}} => 2
{{1,2,3,4,6},{5,7}} => 1
{{1,2,3,4,6},{5},{7}} => 3
{{1,2,3,4,7},{5,6}} => 1
{{1,2,3,4},{5,6,7}} => 3
{{1,2,3,4},{5,6},{7}} => 4
{{1,2,3,4,7},{5},{6}} => 3
{{1,2,3,4},{5,7},{6}} => 4
{{1,2,3,4},{5},{6,7}} => 5
{{1,2,3,4},{5},{6},{7}} => 6
{{1,2,3,5,6,7},{4}} => 3
{{1,2,3,5,6},{4,7}} => 1
{{1,2,3,5,6},{4},{7}} => 4
{{1,2,3,5,7},{4,6}} => 1
{{1,2,3,5},{4,6,7}} => 2
{{1,2,3,5},{4,6},{7}} => 3
{{1,2,3,5,7},{4},{6}} => 4
{{1,2,3,5},{4,7},{6}} => 3
{{1,2,3,5},{4},{6,7}} => 5
{{1,2,3,5},{4},{6},{7}} => 6
{{1,2,3,6,7},{4,5}} => 2
{{1,2,3,6},{4,5,7}} => 1
{{1,2,3,6},{4,5},{7}} => 3
{{1,2,3,7},{4,5,6}} => 1
{{1,2,3},{4,5,6,7}} => 4
{{1,2,3},{4,5,6},{7}} => 5
{{1,2,3,7},{4,5},{6}} => 3
{{1,2,3},{4,5,7},{6}} => 5
{{1,2,3},{4,5},{6,7}} => 6
{{1,2,3},{4,5},{6},{7}} => 7
{{1,2,3,6,7},{4},{5}} => 5
{{1,2,3,6},{4,7},{5}} => 3
{{1,2,3,6},{4},{5,7}} => 4
{{1,2,3,6},{4},{5},{7}} => 6
{{1,2,3,7},{4,6},{5}} => 3
{{1,2,3},{4,6,7},{5}} => 6
{{1,2,3},{4,6},{5,7}} => 5
{{1,2,3},{4,6},{5},{7}} => 7
{{1,2,3,7},{4},{5,6}} => 4
{{1,2,3},{4,7},{5,6}} => 5
{{1,2,3},{4},{5,6,7}} => 7
{{1,2,3},{4},{5,6},{7}} => 8
{{1,2,3,7},{4},{5},{6}} => 6
{{1,2,3},{4,7},{5},{6}} => 7
{{1,2,3},{4},{5,7},{6}} => 8
{{1,2,3},{4},{5},{6,7}} => 9
{{1,2,3},{4},{5},{6},{7}} => 10
{{1,2,4,5,6,7},{3}} => 4
{{1,2,4,5,6},{3,7}} => 1
{{1,2,4,5,6},{3},{7}} => 5
{{1,2,4,5,7},{3,6}} => 1
{{1,2,4,5},{3,6,7}} => 2
{{1,2,4,5},{3,6},{7}} => 3
{{1,2,4,5,7},{3},{6}} => 5
{{1,2,4,5},{3,7},{6}} => 3
{{1,2,4,5},{3},{6,7}} => 6
{{1,2,4,5},{3},{6},{7}} => 7
{{1,2,4,6,7},{3,5}} => 2
{{1,2,4,6},{3,5,7}} => 1
{{1,2,4,6},{3,5},{7}} => 3
{{1,2,4,7},{3,5,6}} => 1
{{1,2,4},{3,5,6,7}} => 3
{{1,2,4},{3,5,6},{7}} => 4
{{1,2,4,7},{3,5},{6}} => 3
{{1,2,4},{3,5,7},{6}} => 4
{{1,2,4},{3,5},{6,7}} => 5
{{1,2,4},{3,5},{6},{7}} => 6
{{1,2,4,6,7},{3},{5}} => 6
{{1,2,4,6},{3,7},{5}} => 3
{{1,2,4,6},{3},{5,7}} => 5
{{1,2,4,6},{3},{5},{7}} => 7
{{1,2,4,7},{3,6},{5}} => 3
{{1,2,4},{3,6,7},{5}} => 5
{{1,2,4},{3,6},{5,7}} => 4
{{1,2,4},{3,6},{5},{7}} => 6
{{1,2,4,7},{3},{5,6}} => 5
{{1,2,4},{3,7},{5,6}} => 4
{{1,2,4},{3},{5,6,7}} => 7
{{1,2,4},{3},{5,6},{7}} => 8
{{1,2,4,7},{3},{5},{6}} => 7
{{1,2,4},{3,7},{5},{6}} => 6
{{1,2,4},{3},{5,7},{6}} => 8
{{1,2,4},{3},{5},{6,7}} => 9
{{1,2,4},{3},{5},{6},{7}} => 10
{{1,2,5,6,7},{3,4}} => 3
{{1,2,5,6},{3,4,7}} => 1
{{1,2,5,6},{3,4},{7}} => 4
{{1,2,5,7},{3,4,6}} => 1
{{1,2,5},{3,4,6,7}} => 2
{{1,2,5},{3,4,6},{7}} => 3
{{1,2,5,7},{3,4},{6}} => 4
{{1,2,5},{3,4,7},{6}} => 3
{{1,2,5},{3,4},{6,7}} => 5
{{1,2,5},{3,4},{6},{7}} => 6
{{1,2,6,7},{3,4,5}} => 2
{{1,2,6},{3,4,5,7}} => 1
{{1,2,6},{3,4,5},{7}} => 3
{{1,2,7},{3,4,5,6}} => 1
{{1,2},{3,4,5,6,7}} => 5
{{1,2},{3,4,5,6},{7}} => 6
{{1,2,7},{3,4,5},{6}} => 3
{{1,2},{3,4,5,7},{6}} => 6
{{1,2},{3,4,5},{6,7}} => 7
{{1,2},{3,4,5},{6},{7}} => 8
{{1,2,6,7},{3,4},{5}} => 5
{{1,2,6},{3,4,7},{5}} => 3
{{1,2,6},{3,4},{5,7}} => 4
{{1,2,6},{3,4},{5},{7}} => 6
{{1,2,7},{3,4,6},{5}} => 3
{{1,2},{3,4,6,7},{5}} => 7
{{1,2},{3,4,6},{5,7}} => 6
{{1,2},{3,4,6},{5},{7}} => 8
{{1,2,7},{3,4},{5,6}} => 4
{{1,2},{3,4,7},{5,6}} => 6
{{1,2},{3,4},{5,6,7}} => 8
{{1,2},{3,4},{5,6},{7}} => 9
{{1,2,7},{3,4},{5},{6}} => 6
{{1,2},{3,4,7},{5},{6}} => 8
{{1,2},{3,4},{5,7},{6}} => 9
{{1,2},{3,4},{5},{6,7}} => 10
{{1,2},{3,4},{5},{6},{7}} => 11
{{1,2,5,6,7},{3},{4}} => 7
{{1,2,5,6},{3,7},{4}} => 4
{{1,2,5,6},{3},{4,7}} => 5
{{1,2,5,6},{3},{4},{7}} => 8
{{1,2,5,7},{3,6},{4}} => 4
{{1,2,5},{3,6,7},{4}} => 5
{{1,2,5},{3,6},{4,7}} => 3
{{1,2,5},{3,6},{4},{7}} => 6
{{1,2,5,7},{3},{4,6}} => 5
{{1,2,5},{3,7},{4,6}} => 3
{{1,2,5},{3},{4,6,7}} => 6
{{1,2,5},{3},{4,6},{7}} => 7
{{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}} => 10
{{1,2,6,7},{3,5},{4}} => 5
{{1,2,6},{3,5,7},{4}} => 4
{{1,2,6},{3,5},{4,7}} => 3
{{1,2,6},{3,5},{4},{7}} => 6
{{1,2,7},{3,5,6},{4}} => 4
{{1,2},{3,5,6,7},{4}} => 8
{{1,2},{3,5,6},{4,7}} => 6
{{1,2},{3,5,6},{4},{7}} => 9
{{1,2,7},{3,5},{4,6}} => 3
{{1,2},{3,5,7},{4,6}} => 6
{{1,2},{3,5},{4,6,7}} => 7
{{1,2},{3,5},{4,6},{7}} => 8
{{1,2,7},{3,5},{4},{6}} => 6
{{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}} => 11
{{1,2,6,7},{3},{4,5}} => 6
{{1,2,6},{3,7},{4,5}} => 3
{{1,2,6},{3},{4,5,7}} => 5
{{1,2,6},{3},{4,5},{7}} => 7
{{1,2,7},{3,6},{4,5}} => 3
{{1,2},{3,6,7},{4,5}} => 7
{{1,2},{3,6},{4,5,7}} => 6
{{1,2},{3,6},{4,5},{7}} => 8
{{1,2,7},{3},{4,5,6}} => 5
{{1,2},{3,7},{4,5,6}} => 6
{{1,2},{3},{4,5,6,7}} => 9
{{1,2},{3},{4,5,6},{7}} => 10
{{1,2,7},{3},{4,5},{6}} => 7
{{1,2},{3,7},{4,5},{6}} => 8
{{1,2},{3},{4,5,7},{6}} => 10
{{1,2},{3},{4,5},{6,7}} => 11
{{1,2},{3},{4,5},{6},{7}} => 12
{{1,2,6,7},{3},{4},{5}} => 9
{{1,2,6},{3,7},{4},{5}} => 6
{{1,2,6},{3},{4,7},{5}} => 7
{{1,2,6},{3},{4},{5,7}} => 8
{{1,2,6},{3},{4},{5},{7}} => 10
{{1,2,7},{3,6},{4},{5}} => 6
{{1,2},{3,6,7},{4},{5}} => 10
{{1,2},{3,6},{4,7},{5}} => 8
{{1,2},{3,6},{4},{5,7}} => 9
{{1,2},{3,6},{4},{5},{7}} => 11
{{1,2,7},{3},{4,6},{5}} => 7
{{1,2},{3,7},{4,6},{5}} => 8
{{1,2},{3},{4,6,7},{5}} => 11
{{1,2},{3},{4,6},{5,7}} => 10
{{1,2},{3},{4,6},{5},{7}} => 12
{{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}} => 12
{{1,2},{3},{4},{5,6},{7}} => 13
{{1,2,7},{3},{4},{5},{6}} => 10
{{1,2},{3,7},{4},{5},{6}} => 11
{{1,2},{3},{4,7},{5},{6}} => 12
{{1,2},{3},{4},{5,7},{6}} => 13
{{1,2},{3},{4},{5},{6,7}} => 14
{{1,2},{3},{4},{5},{6},{7}} => 15
{{1,3,4,5,6,7},{2}} => 5
{{1,3,4,5,6},{2,7}} => 1
{{1,3,4,5,6},{2},{7}} => 6
{{1,3,4,5,7},{2,6}} => 1
{{1,3,4,5},{2,6,7}} => 2
{{1,3,4,5},{2,6},{7}} => 3
{{1,3,4,5,7},{2},{6}} => 6
{{1,3,4,5},{2,7},{6}} => 3
{{1,3,4,5},{2},{6,7}} => 7
{{1,3,4,5},{2},{6},{7}} => 8
{{1,3,4,6,7},{2,5}} => 2
{{1,3,4,6},{2,5,7}} => 1
{{1,3,4,6},{2,5},{7}} => 3
{{1,3,4,7},{2,5,6}} => 1
{{1,3,4},{2,5,6,7}} => 3
{{1,3,4},{2,5,6},{7}} => 4
{{1,3,4,7},{2,5},{6}} => 3
{{1,3,4},{2,5,7},{6}} => 4
{{1,3,4},{2,5},{6,7}} => 5
{{1,3,4},{2,5},{6},{7}} => 6
{{1,3,4,6,7},{2},{5}} => 7
{{1,3,4,6},{2,7},{5}} => 3
{{1,3,4,6},{2},{5,7}} => 6
{{1,3,4,6},{2},{5},{7}} => 8
{{1,3,4,7},{2,6},{5}} => 3
{{1,3,4},{2,6,7},{5}} => 5
{{1,3,4},{2,6},{5,7}} => 4
{{1,3,4},{2,6},{5},{7}} => 6
{{1,3,4,7},{2},{5,6}} => 6
{{1,3,4},{2,7},{5,6}} => 4
{{1,3,4},{2},{5,6,7}} => 8
{{1,3,4},{2},{5,6},{7}} => 9
{{1,3,4,7},{2},{5},{6}} => 8
{{1,3,4},{2,7},{5},{6}} => 6
{{1,3,4},{2},{5,7},{6}} => 9
{{1,3,4},{2},{5},{6,7}} => 10
{{1,3,4},{2},{5},{6},{7}} => 11
{{1,3,5,6,7},{2,4}} => 3
{{1,3,5,6},{2,4,7}} => 1
{{1,3,5,6},{2,4},{7}} => 4
{{1,3,5,7},{2,4,6}} => 1
{{1,3,5},{2,4,6,7}} => 2
{{1,3,5},{2,4,6},{7}} => 3
{{1,3,5,7},{2,4},{6}} => 4
{{1,3,5},{2,4,7},{6}} => 3
{{1,3,5},{2,4},{6,7}} => 5
{{1,3,5},{2,4},{6},{7}} => 6
{{1,3,6,7},{2,4,5}} => 2
{{1,3,6},{2,4,5,7}} => 1
{{1,3,6},{2,4,5},{7}} => 3
{{1,3,7},{2,4,5,6}} => 1
{{1,3},{2,4,5,6,7}} => 4
{{1,3},{2,4,5,6},{7}} => 5
{{1,3,7},{2,4,5},{6}} => 3
{{1,3},{2,4,5,7},{6}} => 5
{{1,3},{2,4,5},{6,7}} => 6
{{1,3},{2,4,5},{6},{7}} => 7
{{1,3,6,7},{2,4},{5}} => 5
{{1,3,6},{2,4,7},{5}} => 3
{{1,3,6},{2,4},{5,7}} => 4
{{1,3,6},{2,4},{5},{7}} => 6
{{1,3,7},{2,4,6},{5}} => 3
{{1,3},{2,4,6,7},{5}} => 6
{{1,3},{2,4,6},{5,7}} => 5
{{1,3},{2,4,6},{5},{7}} => 7
{{1,3,7},{2,4},{5,6}} => 4
{{1,3},{2,4,7},{5,6}} => 5
{{1,3},{2,4},{5,6,7}} => 7
{{1,3},{2,4},{5,6},{7}} => 8
{{1,3,7},{2,4},{5},{6}} => 6
{{1,3},{2,4,7},{5},{6}} => 7
{{1,3},{2,4},{5,7},{6}} => 8
{{1,3},{2,4},{5},{6,7}} => 9
{{1,3},{2,4},{5},{6},{7}} => 10
{{1,3,5,6,7},{2},{4}} => 8
{{1,3,5,6},{2,7},{4}} => 4
{{1,3,5,6},{2},{4,7}} => 6
{{1,3,5,6},{2},{4},{7}} => 9
{{1,3,5,7},{2,6},{4}} => 4
{{1,3,5},{2,6,7},{4}} => 5
{{1,3,5},{2,6},{4,7}} => 3
{{1,3,5},{2,6},{4},{7}} => 6
{{1,3,5,7},{2},{4,6}} => 6
{{1,3,5},{2,7},{4,6}} => 3
{{1,3,5},{2},{4,6,7}} => 7
{{1,3,5},{2},{4,6},{7}} => 8
{{1,3,5,7},{2},{4},{6}} => 9
{{1,3,5},{2,7},{4},{6}} => 6
{{1,3,5},{2},{4,7},{6}} => 8
{{1,3,5},{2},{4},{6,7}} => 10
{{1,3,5},{2},{4},{6},{7}} => 11
{{1,3,6,7},{2,5},{4}} => 5
{{1,3,6},{2,5,7},{4}} => 4
{{1,3,6},{2,5},{4,7}} => 3
{{1,3,6},{2,5},{4},{7}} => 6
{{1,3,7},{2,5,6},{4}} => 4
{{1,3},{2,5,6,7},{4}} => 7
{{1,3},{2,5,6},{4,7}} => 5
{{1,3},{2,5,6},{4},{7}} => 8
{{1,3,7},{2,5},{4,6}} => 3
{{1,3},{2,5,7},{4,6}} => 5
{{1,3},{2,5},{4,6,7}} => 6
{{1,3},{2,5},{4,6},{7}} => 7
{{1,3,7},{2,5},{4},{6}} => 6
{{1,3},{2,5,7},{4},{6}} => 8
{{1,3},{2,5},{4,7},{6}} => 7
{{1,3},{2,5},{4},{6,7}} => 9
{{1,3},{2,5},{4},{6},{7}} => 10
{{1,3,6,7},{2},{4,5}} => 7
{{1,3,6},{2,7},{4,5}} => 3
{{1,3,6},{2},{4,5,7}} => 6
{{1,3,6},{2},{4,5},{7}} => 8
{{1,3,7},{2,6},{4,5}} => 3
{{1,3},{2,6,7},{4,5}} => 6
{{1,3},{2,6},{4,5,7}} => 5
{{1,3},{2,6},{4,5},{7}} => 7
{{1,3,7},{2},{4,5,6}} => 6
{{1,3},{2,7},{4,5,6}} => 5
{{1,3},{2},{4,5,6,7}} => 9
{{1,3},{2},{4,5,6},{7}} => 10
{{1,3,7},{2},{4,5},{6}} => 8
{{1,3},{2,7},{4,5},{6}} => 7
{{1,3},{2},{4,5,7},{6}} => 10
{{1,3},{2},{4,5},{6,7}} => 11
{{1,3},{2},{4,5},{6},{7}} => 12
{{1,3,6,7},{2},{4},{5}} => 10
{{1,3,6},{2,7},{4},{5}} => 6
{{1,3,6},{2},{4,7},{5}} => 8
{{1,3,6},{2},{4},{5,7}} => 9
{{1,3,6},{2},{4},{5},{7}} => 11
{{1,3,7},{2,6},{4},{5}} => 6
{{1,3},{2,6,7},{4},{5}} => 9
{{1,3},{2,6},{4,7},{5}} => 7
{{1,3},{2,6},{4},{5,7}} => 8
{{1,3},{2,6},{4},{5},{7}} => 10
{{1,3,7},{2},{4,6},{5}} => 8
{{1,3},{2,7},{4,6},{5}} => 7
{{1,3},{2},{4,6,7},{5}} => 11
{{1,3},{2},{4,6},{5,7}} => 10
{{1,3},{2},{4,6},{5},{7}} => 12
{{1,3,7},{2},{4},{5,6}} => 9
{{1,3},{2,7},{4},{5,6}} => 8
{{1,3},{2},{4,7},{5,6}} => 10
{{1,3},{2},{4},{5,6,7}} => 12
{{1,3},{2},{4},{5,6},{7}} => 13
{{1,3,7},{2},{4},{5},{6}} => 11
{{1,3},{2,7},{4},{5},{6}} => 10
{{1,3},{2},{4,7},{5},{6}} => 12
{{1,3},{2},{4},{5,7},{6}} => 13
{{1,3},{2},{4},{5},{6,7}} => 14
{{1,3},{2},{4},{5},{6},{7}} => 15
{{1,4,5,6,7},{2,3}} => 4
{{1,4,5,6},{2,3,7}} => 1
{{1,4,5,6},{2,3},{7}} => 5
{{1,4,5,7},{2,3,6}} => 1
{{1,4,5},{2,3,6,7}} => 2
{{1,4,5},{2,3,6},{7}} => 3
{{1,4,5,7},{2,3},{6}} => 5
{{1,4,5},{2,3,7},{6}} => 3
{{1,4,5},{2,3},{6,7}} => 6
{{1,4,5},{2,3},{6},{7}} => 7
{{1,4,6,7},{2,3,5}} => 2
{{1,4,6},{2,3,5,7}} => 1
{{1,4,6},{2,3,5},{7}} => 3
{{1,4,7},{2,3,5,6}} => 1
{{1,4},{2,3,5,6,7}} => 3
{{1,4},{2,3,5,6},{7}} => 4
{{1,4,7},{2,3,5},{6}} => 3
{{1,4},{2,3,5,7},{6}} => 4
{{1,4},{2,3,5},{6,7}} => 5
{{1,4},{2,3,5},{6},{7}} => 6
{{1,4,6,7},{2,3},{5}} => 6
{{1,4,6},{2,3,7},{5}} => 3
{{1,4,6},{2,3},{5,7}} => 5
{{1,4,6},{2,3},{5},{7}} => 7
{{1,4,7},{2,3,6},{5}} => 3
{{1,4},{2,3,6,7},{5}} => 5
{{1,4},{2,3,6},{5,7}} => 4
{{1,4},{2,3,6},{5},{7}} => 6
{{1,4,7},{2,3},{5,6}} => 5
{{1,4},{2,3,7},{5,6}} => 4
{{1,4},{2,3},{5,6,7}} => 7
{{1,4},{2,3},{5,6},{7}} => 8
{{1,4,7},{2,3},{5},{6}} => 7
{{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}} => 10
{{1,5,6,7},{2,3,4}} => 3
{{1,5,6},{2,3,4,7}} => 1
{{1,5,6},{2,3,4},{7}} => 4
{{1,5,7},{2,3,4,6}} => 1
{{1,5},{2,3,4,6,7}} => 2
{{1,5},{2,3,4,6},{7}} => 3
{{1,5,7},{2,3,4},{6}} => 4
{{1,5},{2,3,4,7},{6}} => 3
{{1,5},{2,3,4},{6,7}} => 5
{{1,5},{2,3,4},{6},{7}} => 6
{{1,6,7},{2,3,4,5}} => 2
{{1,6},{2,3,4,5,7}} => 1
{{1,6},{2,3,4,5},{7}} => 3
{{1,7},{2,3,4,5,6}} => 1
{{1},{2,3,4,5,6,7}} => 6
{{1},{2,3,4,5,6},{7}} => 7
{{1,7},{2,3,4,5},{6}} => 3
{{1},{2,3,4,5,7},{6}} => 7
{{1},{2,3,4,5},{6,7}} => 8
{{1},{2,3,4,5},{6},{7}} => 9
{{1,6,7},{2,3,4},{5}} => 5
{{1,6},{2,3,4,7},{5}} => 3
{{1,6},{2,3,4},{5,7}} => 4
{{1,6},{2,3,4},{5},{7}} => 6
{{1,7},{2,3,4,6},{5}} => 3
{{1},{2,3,4,6,7},{5}} => 8
{{1},{2,3,4,6},{5,7}} => 7
{{1},{2,3,4,6},{5},{7}} => 9
{{1,7},{2,3,4},{5,6}} => 4
{{1},{2,3,4,7},{5,6}} => 7
{{1},{2,3,4},{5,6,7}} => 9
{{1},{2,3,4},{5,6},{7}} => 10
{{1,7},{2,3,4},{5},{6}} => 6
{{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}} => 12
{{1,5,6,7},{2,3},{4}} => 7
{{1,5,6},{2,3,7},{4}} => 4
{{1,5,6},{2,3},{4,7}} => 5
{{1,5,6},{2,3},{4},{7}} => 8
{{1,5,7},{2,3,6},{4}} => 4
{{1,5},{2,3,6,7},{4}} => 5
{{1,5},{2,3,6},{4,7}} => 3
{{1,5},{2,3,6},{4},{7}} => 6
{{1,5,7},{2,3},{4,6}} => 5
{{1,5},{2,3,7},{4,6}} => 3
{{1,5},{2,3},{4,6,7}} => 6
{{1,5},{2,3},{4,6},{7}} => 7
{{1,5,7},{2,3},{4},{6}} => 8
{{1,5},{2,3,7},{4},{6}} => 6
{{1,5},{2,3},{4,7},{6}} => 7
{{1,5},{2,3},{4},{6,7}} => 9
{{1,5},{2,3},{4},{6},{7}} => 10
{{1,6,7},{2,3,5},{4}} => 5
{{1,6},{2,3,5,7},{4}} => 4
{{1,6},{2,3,5},{4,7}} => 3
{{1,6},{2,3,5},{4},{7}} => 6
{{1,7},{2,3,5,6},{4}} => 4
{{1},{2,3,5,6,7},{4}} => 9
{{1},{2,3,5,6},{4,7}} => 7
{{1},{2,3,5,6},{4},{7}} => 10
{{1,7},{2,3,5},{4,6}} => 3
{{1},{2,3,5,7},{4,6}} => 7
{{1},{2,3,5},{4,6,7}} => 8
{{1},{2,3,5},{4,6},{7}} => 9
{{1,7},{2,3,5},{4},{6}} => 6
{{1},{2,3,5,7},{4},{6}} => 10
{{1},{2,3,5},{4,7},{6}} => 9
{{1},{2,3,5},{4},{6,7}} => 11
{{1},{2,3,5},{4},{6},{7}} => 12
{{1,6,7},{2,3},{4,5}} => 6
{{1,6},{2,3,7},{4,5}} => 3
{{1,6},{2,3},{4,5,7}} => 5
{{1,6},{2,3},{4,5},{7}} => 7
{{1,7},{2,3,6},{4,5}} => 3
{{1},{2,3,6,7},{4,5}} => 8
{{1},{2,3,6},{4,5,7}} => 7
{{1},{2,3,6},{4,5},{7}} => 9
{{1,7},{2,3},{4,5,6}} => 5
{{1},{2,3,7},{4,5,6}} => 7
{{1},{2,3},{4,5,6,7}} => 10
{{1},{2,3},{4,5,6},{7}} => 11
{{1,7},{2,3},{4,5},{6}} => 7
{{1},{2,3,7},{4,5},{6}} => 9
{{1},{2,3},{4,5,7},{6}} => 11
{{1},{2,3},{4,5},{6,7}} => 12
{{1},{2,3},{4,5},{6},{7}} => 13
{{1,6,7},{2,3},{4},{5}} => 9
{{1,6},{2,3,7},{4},{5}} => 6
{{1,6},{2,3},{4,7},{5}} => 7
{{1,6},{2,3},{4},{5,7}} => 8
{{1,6},{2,3},{4},{5},{7}} => 10
{{1,7},{2,3,6},{4},{5}} => 6
{{1},{2,3,6,7},{4},{5}} => 11
{{1},{2,3,6},{4,7},{5}} => 9
{{1},{2,3,6},{4},{5,7}} => 10
{{1},{2,3,6},{4},{5},{7}} => 12
{{1,7},{2,3},{4,6},{5}} => 7
{{1},{2,3,7},{4,6},{5}} => 9
{{1},{2,3},{4,6,7},{5}} => 12
{{1},{2,3},{4,6},{5,7}} => 11
{{1},{2,3},{4,6},{5},{7}} => 13
{{1,7},{2,3},{4},{5,6}} => 8
{{1},{2,3,7},{4},{5,6}} => 10
{{1},{2,3},{4,7},{5,6}} => 11
{{1},{2,3},{4},{5,6,7}} => 13
{{1},{2,3},{4},{5,6},{7}} => 14
{{1,7},{2,3},{4},{5},{6}} => 10
{{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}} => 16
{{1,4,5,6,7},{2},{3}} => 9
{{1,4,5,6},{2,7},{3}} => 5
{{1,4,5,6},{2},{3,7}} => 6
{{1,4,5,6},{2},{3},{7}} => 10
{{1,4,5,7},{2,6},{3}} => 5
{{1,4,5},{2,6,7},{3}} => 6
{{1,4,5},{2,6},{3,7}} => 3
{{1,4,5},{2,6},{3},{7}} => 7
{{1,4,5,7},{2},{3,6}} => 6
{{1,4,5},{2,7},{3,6}} => 3
{{1,4,5},{2},{3,6,7}} => 7
{{1,4,5},{2},{3,6},{7}} => 8
{{1,4,5,7},{2},{3},{6}} => 10
{{1,4,5},{2,7},{3},{6}} => 7
{{1,4,5},{2},{3,7},{6}} => 8
{{1,4,5},{2},{3},{6,7}} => 11
{{1,4,5},{2},{3},{6},{7}} => 12
{{1,4,6,7},{2,5},{3}} => 6
{{1,4,6},{2,5,7},{3}} => 5
{{1,4,6},{2,5},{3,7}} => 3
{{1,4,6},{2,5},{3},{7}} => 7
{{1,4,7},{2,5,6},{3}} => 5
{{1,4},{2,5,6,7},{3}} => 7
{{1,4},{2,5,6},{3,7}} => 4
{{1,4},{2,5,6},{3},{7}} => 8
{{1,4,7},{2,5},{3,6}} => 3
{{1,4},{2,5,7},{3,6}} => 4
{{1,4},{2,5},{3,6,7}} => 5
{{1,4},{2,5},{3,6},{7}} => 6
{{1,4,7},{2,5},{3},{6}} => 7
{{1,4},{2,5,7},{3},{6}} => 8
{{1,4},{2,5},{3,7},{6}} => 6
{{1,4},{2,5},{3},{6,7}} => 9
{{1,4},{2,5},{3},{6},{7}} => 10
{{1,4,6,7},{2},{3,5}} => 7
{{1,4,6},{2,7},{3,5}} => 3
{{1,4,6},{2},{3,5,7}} => 6
{{1,4,6},{2},{3,5},{7}} => 8
{{1,4,7},{2,6},{3,5}} => 3
{{1,4},{2,6,7},{3,5}} => 5
{{1,4},{2,6},{3,5,7}} => 4
{{1,4},{2,6},{3,5},{7}} => 6
{{1,4,7},{2},{3,5,6}} => 6
{{1,4},{2,7},{3,5,6}} => 4
{{1,4},{2},{3,5,6,7}} => 8
{{1,4},{2},{3,5,6},{7}} => 9
{{1,4,7},{2},{3,5},{6}} => 8
{{1,4},{2,7},{3,5},{6}} => 6
{{1,4},{2},{3,5,7},{6}} => 9
{{1,4},{2},{3,5},{6,7}} => 10
{{1,4},{2},{3,5},{6},{7}} => 11
{{1,4,6,7},{2},{3},{5}} => 11
{{1,4,6},{2,7},{3},{5}} => 7
{{1,4,6},{2},{3,7},{5}} => 8
{{1,4,6},{2},{3},{5,7}} => 10
{{1,4,6},{2},{3},{5},{7}} => 12
{{1,4,7},{2,6},{3},{5}} => 7
{{1,4},{2,6,7},{3},{5}} => 9
{{1,4},{2,6},{3,7},{5}} => 6
{{1,4},{2,6},{3},{5,7}} => 8
{{1,4},{2,6},{3},{5},{7}} => 10
{{1,4,7},{2},{3,6},{5}} => 8
{{1,4},{2,7},{3,6},{5}} => 6
{{1,4},{2},{3,6,7},{5}} => 10
{{1,4},{2},{3,6},{5,7}} => 9
{{1,4},{2},{3,6},{5},{7}} => 11
{{1,4,7},{2},{3},{5,6}} => 10
{{1,4},{2,7},{3},{5,6}} => 8
{{1,4},{2},{3,7},{5,6}} => 9
{{1,4},{2},{3},{5,6,7}} => 12
{{1,4},{2},{3},{5,6},{7}} => 13
{{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},{5,7},{6}} => 13
{{1,4},{2},{3},{5},{6,7}} => 14
{{1,4},{2},{3},{5},{6},{7}} => 15
{{1,5,6,7},{2,4},{3}} => 7
{{1,5,6},{2,4,7},{3}} => 5
{{1,5,6},{2,4},{3,7}} => 4
{{1,5,6},{2,4},{3},{7}} => 8
{{1,5,7},{2,4,6},{3}} => 5
{{1,5},{2,4,6,7},{3}} => 6
{{1,5},{2,4,6},{3,7}} => 3
{{1,5},{2,4,6},{3},{7}} => 7
{{1,5,7},{2,4},{3,6}} => 4
{{1,5},{2,4,7},{3,6}} => 3
{{1,5},{2,4},{3,6,7}} => 5
{{1,5},{2,4},{3,6},{7}} => 6
{{1,5,7},{2,4},{3},{6}} => 8
{{1,5},{2,4,7},{3},{6}} => 7
{{1,5},{2,4},{3,7},{6}} => 6
{{1,5},{2,4},{3},{6,7}} => 9
{{1,5},{2,4},{3},{6},{7}} => 10
{{1,6,7},{2,4,5},{3}} => 6
{{1,6},{2,4,5,7},{3}} => 5
{{1,6},{2,4,5},{3,7}} => 3
{{1,6},{2,4,5},{3},{7}} => 7
{{1,7},{2,4,5,6},{3}} => 5
{{1},{2,4,5,6,7},{3}} => 10
{{1},{2,4,5,6},{3,7}} => 7
{{1},{2,4,5,6},{3},{7}} => 11
{{1,7},{2,4,5},{3,6}} => 3
{{1},{2,4,5,7},{3,6}} => 7
{{1},{2,4,5},{3,6,7}} => 8
{{1},{2,4,5},{3,6},{7}} => 9
{{1,7},{2,4,5},{3},{6}} => 7
{{1},{2,4,5,7},{3},{6}} => 11
{{1},{2,4,5},{3,7},{6}} => 9
{{1},{2,4,5},{3},{6,7}} => 12
{{1},{2,4,5},{3},{6},{7}} => 13
{{1,6,7},{2,4},{3,5}} => 5
{{1,6},{2,4,7},{3,5}} => 3
{{1,6},{2,4},{3,5,7}} => 4
{{1,6},{2,4},{3,5},{7}} => 6
{{1,7},{2,4,6},{3,5}} => 3
{{1},{2,4,6,7},{3,5}} => 8
{{1},{2,4,6},{3,5,7}} => 7
{{1},{2,4,6},{3,5},{7}} => 9
{{1,7},{2,4},{3,5,6}} => 4
{{1},{2,4,7},{3,5,6}} => 7
{{1},{2,4},{3,5,6,7}} => 9
{{1},{2,4},{3,5,6},{7}} => 10
{{1,7},{2,4},{3,5},{6}} => 6
{{1},{2,4,7},{3,5},{6}} => 9
{{1},{2,4},{3,5,7},{6}} => 10
{{1},{2,4},{3,5},{6,7}} => 11
{{1},{2,4},{3,5},{6},{7}} => 12
{{1,6,7},{2,4},{3},{5}} => 9
{{1,6},{2,4,7},{3},{5}} => 7
{{1,6},{2,4},{3,7},{5}} => 6
{{1,6},{2,4},{3},{5,7}} => 8
{{1,6},{2,4},{3},{5},{7}} => 10
{{1,7},{2,4,6},{3},{5}} => 7
{{1},{2,4,6,7},{3},{5}} => 12
{{1},{2,4,6},{3,7},{5}} => 9
{{1},{2,4,6},{3},{5,7}} => 11
{{1},{2,4,6},{3},{5},{7}} => 13
{{1,7},{2,4},{3,6},{5}} => 6
{{1},{2,4,7},{3,6},{5}} => 9
{{1},{2,4},{3,6,7},{5}} => 11
{{1},{2,4},{3,6},{5,7}} => 10
{{1},{2,4},{3,6},{5},{7}} => 12
{{1,7},{2,4},{3},{5,6}} => 8
{{1},{2,4,7},{3},{5,6}} => 11
{{1},{2,4},{3,7},{5,6}} => 10
{{1},{2,4},{3},{5,6,7}} => 13
{{1},{2,4},{3},{5,6},{7}} => 14
{{1,7},{2,4},{3},{5},{6}} => 10
{{1},{2,4,7},{3},{5},{6}} => 13
{{1},{2,4},{3,7},{5},{6}} => 12
{{1},{2,4},{3},{5,7},{6}} => 14
{{1},{2,4},{3},{5},{6,7}} => 15
{{1},{2,4},{3},{5},{6},{7}} => 16
{{1,5,6,7},{2},{3,4}} => 8
{{1,5,6},{2,7},{3,4}} => 4
{{1,5,6},{2},{3,4,7}} => 6
{{1,5,6},{2},{3,4},{7}} => 9
{{1,5,7},{2,6},{3,4}} => 4
{{1,5},{2,6,7},{3,4}} => 5
{{1,5},{2,6},{3,4,7}} => 3
{{1,5},{2,6},{3,4},{7}} => 6
{{1,5,7},{2},{3,4,6}} => 6
{{1,5},{2,7},{3,4,6}} => 3
{{1,5},{2},{3,4,6,7}} => 7
{{1,5},{2},{3,4,6},{7}} => 8
{{1,5,7},{2},{3,4},{6}} => 9
{{1,5},{2,7},{3,4},{6}} => 6
{{1,5},{2},{3,4,7},{6}} => 8
{{1,5},{2},{3,4},{6,7}} => 10
{{1,5},{2},{3,4},{6},{7}} => 11
{{1,6,7},{2,5},{3,4}} => 5
{{1,6},{2,5,7},{3,4}} => 4
{{1,6},{2,5},{3,4,7}} => 3
{{1,6},{2,5},{3,4},{7}} => 6
{{1,7},{2,5,6},{3,4}} => 4
{{1},{2,5,6,7},{3,4}} => 9
{{1},{2,5,6},{3,4,7}} => 7
{{1},{2,5,6},{3,4},{7}} => 10
{{1,7},{2,5},{3,4,6}} => 3
{{1},{2,5,7},{3,4,6}} => 7
{{1},{2,5},{3,4,6,7}} => 8
{{1},{2,5},{3,4,6},{7}} => 9
{{1,7},{2,5},{3,4},{6}} => 6
{{1},{2,5,7},{3,4},{6}} => 10
{{1},{2,5},{3,4,7},{6}} => 9
{{1},{2,5},{3,4},{6,7}} => 11
{{1},{2,5},{3,4},{6},{7}} => 12
{{1,6,7},{2},{3,4,5}} => 7
{{1,6},{2,7},{3,4,5}} => 3
{{1,6},{2},{3,4,5,7}} => 6
{{1,6},{2},{3,4,5},{7}} => 8
{{1,7},{2,6},{3,4,5}} => 3
{{1},{2,6,7},{3,4,5}} => 8
{{1},{2,6},{3,4,5,7}} => 7
{{1},{2,6},{3,4,5},{7}} => 9
{{1,7},{2},{3,4,5,6}} => 6
{{1},{2,7},{3,4,5,6}} => 7
{{1},{2},{3,4,5,6,7}} => 11
{{1},{2},{3,4,5,6},{7}} => 12
{{1,7},{2},{3,4,5},{6}} => 8
{{1},{2,7},{3,4,5},{6}} => 9
{{1},{2},{3,4,5,7},{6}} => 12
{{1},{2},{3,4,5},{6,7}} => 13
{{1},{2},{3,4,5},{6},{7}} => 14
{{1,6,7},{2},{3,4},{5}} => 10
{{1,6},{2,7},{3,4},{5}} => 6
{{1,6},{2},{3,4,7},{5}} => 8
{{1,6},{2},{3,4},{5,7}} => 9
{{1,6},{2},{3,4},{5},{7}} => 11
{{1,7},{2,6},{3,4},{5}} => 6
{{1},{2,6,7},{3,4},{5}} => 11
{{1},{2,6},{3,4,7},{5}} => 9
{{1},{2,6},{3,4},{5,7}} => 10
{{1},{2,6},{3,4},{5},{7}} => 12
{{1,7},{2},{3,4,6},{5}} => 8
{{1},{2,7},{3,4,6},{5}} => 9
{{1},{2},{3,4,6,7},{5}} => 13
{{1},{2},{3,4,6},{5,7}} => 12
{{1},{2},{3,4,6},{5},{7}} => 14
{{1,7},{2},{3,4},{5,6}} => 9
{{1},{2,7},{3,4},{5,6}} => 10
{{1},{2},{3,4,7},{5,6}} => 12
{{1},{2},{3,4},{5,6,7}} => 14
{{1},{2},{3,4},{5,6},{7}} => 15
{{1,7},{2},{3,4},{5},{6}} => 11
{{1},{2,7},{3,4},{5},{6}} => 12
{{1},{2},{3,4,7},{5},{6}} => 14
{{1},{2},{3,4},{5,7},{6}} => 15
{{1},{2},{3,4},{5},{6,7}} => 16
{{1},{2},{3,4},{5},{6},{7}} => 17
{{1,5,6,7},{2},{3},{4}} => 12
{{1,5,6},{2,7},{3},{4}} => 8
{{1,5,6},{2},{3,7},{4}} => 9
{{1,5,6},{2},{3},{4,7}} => 10
{{1,5,6},{2},{3},{4},{7}} => 13
{{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}} => 10
{{1,5,7},{2},{3,6},{4}} => 9
{{1,5},{2,7},{3,6},{4}} => 6
{{1,5},{2},{3,6,7},{4}} => 10
{{1,5},{2},{3,6},{4,7}} => 8
{{1,5},{2},{3,6},{4},{7}} => 11
{{1,5,7},{2},{3},{4,6}} => 10
{{1,5},{2,7},{3},{4,6}} => 7
{{1,5},{2},{3,7},{4,6}} => 8
{{1,5},{2},{3},{4,6,7}} => 11
{{1,5},{2},{3},{4,6},{7}} => 12
{{1,5,7},{2},{3},{4},{6}} => 13
{{1,5},{2,7},{3},{4},{6}} => 10
{{1,5},{2},{3,7},{4},{6}} => 11
{{1,5},{2},{3},{4,7},{6}} => 12
{{1,5},{2},{3},{4},{6,7}} => 14
{{1,5},{2},{3},{4},{6},{7}} => 15
{{1,6,7},{2,5},{3},{4}} => 9
{{1,6},{2,5,7},{3},{4}} => 8
{{1,6},{2,5},{3,7},{4}} => 6
{{1,6},{2,5},{3},{4,7}} => 7
{{1,6},{2,5},{3},{4},{7}} => 10
{{1,7},{2,5,6},{3},{4}} => 8
{{1},{2,5,6,7},{3},{4}} => 13
{{1},{2,5,6},{3,7},{4}} => 10
{{1},{2,5,6},{3},{4,7}} => 11
{{1},{2,5,6},{3},{4},{7}} => 14
{{1,7},{2,5},{3,6},{4}} => 6
{{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}} => 12
{{1,7},{2,5},{3},{4,6}} => 7
{{1},{2,5,7},{3},{4,6}} => 11
{{1},{2,5},{3,7},{4,6}} => 9
{{1},{2,5},{3},{4,6,7}} => 12
{{1},{2,5},{3},{4,6},{7}} => 13
{{1,7},{2,5},{3},{4},{6}} => 10
{{1},{2,5,7},{3},{4},{6}} => 14
{{1},{2,5},{3,7},{4},{6}} => 12
{{1},{2,5},{3},{4,7},{6}} => 13
{{1},{2,5},{3},{4},{6,7}} => 15
{{1},{2,5},{3},{4},{6},{7}} => 16
{{1,6,7},{2},{3,5},{4}} => 10
{{1,6},{2,7},{3,5},{4}} => 6
{{1,6},{2},{3,5,7},{4}} => 9
{{1,6},{2},{3,5},{4,7}} => 8
{{1,6},{2},{3,5},{4},{7}} => 11
{{1,7},{2,6},{3,5},{4}} => 6
{{1},{2,6,7},{3,5},{4}} => 11
{{1},{2,6},{3,5,7},{4}} => 10
{{1},{2,6},{3,5},{4,7}} => 9
{{1},{2,6},{3,5},{4},{7}} => 12
{{1,7},{2},{3,5,6},{4}} => 9
{{1},{2,7},{3,5,6},{4}} => 10
{{1},{2},{3,5,6,7},{4}} => 14
{{1},{2},{3,5,6},{4,7}} => 12
{{1},{2},{3,5,6},{4},{7}} => 15
{{1,7},{2},{3,5},{4,6}} => 8
{{1},{2,7},{3,5},{4,6}} => 9
{{1},{2},{3,5,7},{4,6}} => 12
{{1},{2},{3,5},{4,6,7}} => 13
{{1},{2},{3,5},{4,6},{7}} => 14
{{1,7},{2},{3,5},{4},{6}} => 11
{{1},{2,7},{3,5},{4},{6}} => 12
{{1},{2},{3,5,7},{4},{6}} => 15
{{1},{2},{3,5},{4,7},{6}} => 14
{{1},{2},{3,5},{4},{6,7}} => 16
{{1},{2},{3,5},{4},{6},{7}} => 17
{{1,6,7},{2},{3},{4,5}} => 11
{{1,6},{2,7},{3},{4,5}} => 7
{{1,6},{2},{3,7},{4,5}} => 8
{{1,6},{2},{3},{4,5,7}} => 10
{{1,6},{2},{3},{4,5},{7}} => 12
{{1,7},{2,6},{3},{4,5}} => 7
{{1},{2,6,7},{3},{4,5}} => 12
{{1},{2,6},{3,7},{4,5}} => 9
{{1},{2,6},{3},{4,5,7}} => 11
{{1},{2,6},{3},{4,5},{7}} => 13
{{1,7},{2},{3,6},{4,5}} => 8
{{1},{2,7},{3,6},{4,5}} => 9
{{1},{2},{3,6,7},{4,5}} => 13
{{1},{2},{3,6},{4,5,7}} => 12
{{1},{2},{3,6},{4,5},{7}} => 14
{{1,7},{2},{3},{4,5,6}} => 10
{{1},{2,7},{3},{4,5,6}} => 11
{{1},{2},{3,7},{4,5,6}} => 12
{{1},{2},{3},{4,5,6,7}} => 15
{{1},{2},{3},{4,5,6},{7}} => 16
{{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},{4,5,7},{6}} => 16
{{1},{2},{3},{4,5},{6,7}} => 17
{{1},{2},{3},{4,5},{6},{7}} => 18
{{1,6,7},{2},{3},{4},{5}} => 14
{{1,6},{2,7},{3},{4},{5}} => 10
{{1,6},{2},{3,7},{4},{5}} => 11
{{1,6},{2},{3},{4,7},{5}} => 12
{{1,6},{2},{3},{4},{5,7}} => 13
{{1,6},{2},{3},{4},{5},{7}} => 15
{{1,7},{2,6},{3},{4},{5}} => 10
{{1},{2,6,7},{3},{4},{5}} => 15
{{1},{2,6},{3,7},{4},{5}} => 12
{{1},{2,6},{3},{4,7},{5}} => 13
{{1},{2,6},{3},{4},{5,7}} => 14
{{1},{2,6},{3},{4},{5},{7}} => 16
{{1,7},{2},{3,6},{4},{5}} => 11
{{1},{2,7},{3,6},{4},{5}} => 12
{{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}} => 17
{{1,7},{2},{3},{4,6},{5}} => 12
{{1},{2,7},{3},{4,6},{5}} => 13
{{1},{2},{3,7},{4,6},{5}} => 14
{{1},{2},{3},{4,6,7},{5}} => 17
{{1},{2},{3},{4,6},{5,7}} => 16
{{1},{2},{3},{4,6},{5},{7}} => 18
{{1,7},{2},{3},{4},{5,6}} => 13
{{1},{2,7},{3},{4},{5,6}} => 14
{{1},{2},{3,7},{4},{5,6}} => 15
{{1},{2},{3},{4,7},{5,6}} => 16
{{1},{2},{3},{4},{5,6,7}} => 18
{{1},{2},{3},{4},{5,6},{7}} => 19
{{1,7},{2},{3},{4},{5},{6}} => 15
{{1},{2,7},{3},{4},{5},{6}} => 16
{{1},{2},{3,7},{4},{5},{6}} => 17
{{1},{2},{3},{4,7},{5},{6}} => 18
{{1},{2},{3},{4},{5,7},{6}} => 19
{{1},{2},{3},{4},{5},{6,7}} => 20
{{1},{2},{3},{4},{5},{6},{7}} => 21
{{1},{2},{3,4,5,6,7,8}} => 13
{{1},{2,4,5,6,7,8},{3}} => 12
{{1},{2,3,5,6,7,8},{4}} => 11
{{1},{2,3,4,6,7,8},{5}} => 10
{{1},{2,3,4,5,7,8},{6}} => 9
{{1},{2,3,4,5,6,7},{8}} => 13
{{1},{2,3,4,5,6,8},{7}} => 8
{{1},{2,3,4,5,6,7,8}} => 7
{{1,2},{3,4,5,6,7,8}} => 7
{{1,4,5,6,7,8},{2},{3}} => 11
{{1,3,5,6,7,8},{2},{4}} => 10
{{1,3,4,5,6,7,8},{2}} => 6
{{1,4,5,6,7,8},{2,3}} => 6
{{1,2,4,5,6,7,8},{3}} => 5
{{1,2,5,6,7,8},{3,4}} => 5
{{1,2,3,5,6,7,8},{4}} => 4
{{1,2,3,6,7,8},{4,5}} => 4
{{1,2,3,4,6,7,8},{5}} => 3
{{1,2,3,4,5,6},{7,8}} => 7
{{1,2,3,4,7,8},{5,6}} => 3
{{1,2,3,4,5,7,8},{6}} => 2
{{1,2,3,4,5,6,7},{8}} => 7
{{1,8},{2,3,4,5,6,7}} => 6
{{1,2,3,4,5,8},{6,7}} => 2
{{1,2,3,4,5,6,8},{7}} => 1
{{1,2,3,4,5,6,7,8}} => 0
{{1,3,5,6,7,8},{2,4}} => 5
{{1,3,4,6,7,8},{2,5}} => 4
{{1,2,4,6,7,8},{3,5}} => 4
{{1,3,4,5,7,8},{2,6}} => 3
{{1,2,4,5,7,8},{3,6}} => 3
{{1,2,3,5,7,8},{4,6}} => 3
{{1,3,4,5,6,8},{2,7}} => 2
{{1,2,4,5,6,8},{3,7}} => 2
{{1,2,3,5,6,8},{4,7}} => 2
{{1,2,3,4,6,8},{5,7}} => 2
{{1,3,4,5,6,7},{2,8}} => 6
{{1,2,4,5,6,7},{3,8}} => 6
{{1,2,3,5,6,7},{4,8}} => 6
{{1,2,3,4,6,7},{5,8}} => 6
{{1,2,3,4,5,7},{6,8}} => 6
{{1,3},{2,4,5,6,7,8}} => 6
{{1,4},{2,3,5,6,7,8}} => 5
{{1,5},{2,3,4,6,7,8}} => 4
{{1,6},{2,3,4,5,7,8}} => 3
{{1,7},{2,3,4,5,6,8}} => 2
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Created: Aug 10, 2016 at 23:16 by Martin Rubey
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Last Updated: Aug 10, 2016 at 23:16 by Martin Rubey