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-----------------------------------------------------------------------------
Statistic identifier: St001841
-----------------------------------------------------------------------------
Collection: Set partitions
-----------------------------------------------------------------------------
Description: The number of inversions of a set partition.
The Mahonian representation of a set partition $\{B_1,\dots,B_k\}$ of $\{1,\dots,n\}$ is the restricted growth word $w_1\dots w_n\}$ obtained by sorting the blocks of the set partition according to their maximal element, and setting $w_i$ to the index of the block containing $i$.
A pair $(i,j)$ is an inversion of the word $w$ if $w_i > w_j$.
-----------------------------------------------------------------------------
References: [1] Liu, S.-H. Mahonian and Euler-Mahonian statistics for set partitions [[arXiv:2202.02089]]
-----------------------------------------------------------------------------
Code:
def to_restricted_growth_word_blocks_max(self):
w = [0] * self.size()
for i, B in enumerate(sorted(self, key=lambda B: max(B))):
for j in B:
w[j-1] = i
return w
def statistic(p):
w = to_restricted_growth_word_blocks_max(p)
return sum(1 for j in range(len(w)) for i in range(j) if w[i] > w[j])
-----------------------------------------------------------------------------
Statistic values:
{{1}} => 0
{{1,2}} => 0
{{1},{2}} => 0
{{1,2,3}} => 0
{{1,2},{3}} => 0
{{1,3},{2}} => 1
{{1},{2,3}} => 0
{{1},{2},{3}} => 0
{{1,2,3,4}} => 0
{{1,2,3},{4}} => 0
{{1,2,4},{3}} => 2
{{1,2},{3,4}} => 0
{{1,2},{3},{4}} => 0
{{1,3,4},{2}} => 1
{{1,3},{2,4}} => 1
{{1,3},{2},{4}} => 1
{{1,4},{2,3}} => 2
{{1},{2,3,4}} => 0
{{1},{2,3},{4}} => 0
{{1,4},{2},{3}} => 2
{{1},{2,4},{3}} => 1
{{1},{2},{3,4}} => 0
{{1},{2},{3},{4}} => 0
{{1,2,3,4,5}} => 0
{{1,2,3,4},{5}} => 0
{{1,2,3,5},{4}} => 3
{{1,2,3},{4,5}} => 0
{{1,2,3},{4},{5}} => 0
{{1,2,4,5},{3}} => 2
{{1,2,4},{3,5}} => 1
{{1,2,4},{3},{5}} => 2
{{1,2,5},{3,4}} => 4
{{1,2},{3,4,5}} => 0
{{1,2},{3,4},{5}} => 0
{{1,2,5},{3},{4}} => 4
{{1,2},{3,5},{4}} => 1
{{1,2},{3},{4,5}} => 0
{{1,2},{3},{4},{5}} => 0
{{1,3,4,5},{2}} => 1
{{1,3,4},{2,5}} => 2
{{1,3,4},{2},{5}} => 1
{{1,3,5},{2,4}} => 3
{{1,3},{2,4,5}} => 1
{{1,3},{2,4},{5}} => 1
{{1,3,5},{2},{4}} => 3
{{1,3},{2,5},{4}} => 2
{{1,3},{2},{4,5}} => 1
{{1,3},{2},{4},{5}} => 1
{{1,4,5},{2,3}} => 2
{{1,4},{2,3,5}} => 2
{{1,4},{2,3},{5}} => 2
{{1,5},{2,3,4}} => 3
{{1},{2,3,4,5}} => 0
{{1},{2,3,4},{5}} => 0
{{1,5},{2,3},{4}} => 3
{{1},{2,3,5},{4}} => 2
{{1},{2,3},{4,5}} => 0
{{1},{2,3},{4},{5}} => 0
{{1,4,5},{2},{3}} => 2
{{1,4},{2,5},{3}} => 3
{{1,4},{2},{3,5}} => 2
{{1,4},{2},{3},{5}} => 2
{{1,5},{2,4},{3}} => 4
{{1},{2,4,5},{3}} => 1
{{1},{2,4},{3,5}} => 1
{{1},{2,4},{3},{5}} => 1
{{1,5},{2},{3,4}} => 3
{{1},{2,5},{3,4}} => 2
{{1},{2},{3,4,5}} => 0
{{1},{2},{3,4},{5}} => 0
{{1,5},{2},{3},{4}} => 3
{{1},{2,5},{3},{4}} => 2
{{1},{2},{3,5},{4}} => 1
{{1},{2},{3},{4,5}} => 0
{{1},{2},{3},{4},{5}} => 0
{{1,2,3,4,5,6}} => 0
{{1,2,3,4,5},{6}} => 0
{{1,2,3,4,6},{5}} => 4
{{1,2,3,4},{5,6}} => 0
{{1,2,3,4},{5},{6}} => 0
{{1,2,3,5,6},{4}} => 3
{{1,2,3,5},{4,6}} => 1
{{1,2,3,5},{4},{6}} => 3
{{1,2,3,6},{4,5}} => 6
{{1,2,3},{4,5,6}} => 0
{{1,2,3},{4,5},{6}} => 0
{{1,2,3,6},{4},{5}} => 6
{{1,2,3},{4,6},{5}} => 1
{{1,2,3},{4},{5,6}} => 0
{{1,2,3},{4},{5},{6}} => 0
{{1,2,4,5,6},{3}} => 2
{{1,2,4,5},{3,6}} => 2
{{1,2,4,5},{3},{6}} => 2
{{1,2,4,6},{3,5}} => 5
{{1,2,4},{3,5,6}} => 1
{{1,2,4},{3,5},{6}} => 1
{{1,2,4,6},{3},{5}} => 5
{{1,2,4},{3,6},{5}} => 2
{{1,2,4},{3},{5,6}} => 2
{{1,2,4},{3},{5},{6}} => 2
{{1,2,5,6},{3,4}} => 4
{{1,2,5},{3,4,6}} => 2
{{1,2,5},{3,4},{6}} => 4
{{1,2,6},{3,4,5}} => 6
{{1,2},{3,4,5,6}} => 0
{{1,2},{3,4,5},{6}} => 0
{{1,2,6},{3,4},{5}} => 6
{{1,2},{3,4,6},{5}} => 2
{{1,2},{3,4},{5,6}} => 0
{{1,2},{3,4},{5},{6}} => 0
{{1,2,5,6},{3},{4}} => 4
{{1,2,5},{3,6},{4}} => 4
{{1,2,5},{3},{4,6}} => 3
{{1,2,5},{3},{4},{6}} => 4
{{1,2,6},{3,5},{4}} => 7
{{1,2},{3,5,6},{4}} => 1
{{1,2},{3,5},{4,6}} => 1
{{1,2},{3,5},{4},{6}} => 1
{{1,2,6},{3},{4,5}} => 6
{{1,2},{3,6},{4,5}} => 2
{{1,2},{3},{4,5,6}} => 0
{{1,2},{3},{4,5},{6}} => 0
{{1,2,6},{3},{4},{5}} => 6
{{1,2},{3,6},{4},{5}} => 2
{{1,2},{3},{4,6},{5}} => 1
{{1,2},{3},{4},{5,6}} => 0
{{1,2},{3},{4},{5},{6}} => 0
{{1,3,4,5,6},{2}} => 1
{{1,3,4,5},{2,6}} => 3
{{1,3,4,5},{2},{6}} => 1
{{1,3,4,6},{2,5}} => 4
{{1,3,4},{2,5,6}} => 2
{{1,3,4},{2,5},{6}} => 2
{{1,3,4,6},{2},{5}} => 4
{{1,3,4},{2,6},{5}} => 3
{{1,3,4},{2},{5,6}} => 1
{{1,3,4},{2},{5},{6}} => 1
{{1,3,5,6},{2,4}} => 3
{{1,3,5},{2,4,6}} => 3
{{1,3,5},{2,4},{6}} => 3
{{1,3,6},{2,4,5}} => 5
{{1,3},{2,4,5,6}} => 1
{{1,3},{2,4,5},{6}} => 1
{{1,3,6},{2,4},{5}} => 5
{{1,3},{2,4,6},{5}} => 3
{{1,3},{2,4},{5,6}} => 1
{{1,3},{2,4},{5},{6}} => 1
{{1,3,5,6},{2},{4}} => 3
{{1,3,5},{2,6},{4}} => 5
{{1,3,5},{2},{4,6}} => 2
{{1,3,5},{2},{4},{6}} => 3
{{1,3,6},{2,5},{4}} => 6
{{1,3},{2,5,6},{4}} => 2
{{1,3},{2,5},{4,6}} => 2
{{1,3},{2,5},{4},{6}} => 2
{{1,3,6},{2},{4,5}} => 5
{{1,3},{2,6},{4,5}} => 3
{{1,3},{2},{4,5,6}} => 1
{{1,3},{2},{4,5},{6}} => 1
{{1,3,6},{2},{4},{5}} => 5
{{1,3},{2,6},{4},{5}} => 3
{{1,3},{2},{4,6},{5}} => 2
{{1,3},{2},{4},{5,6}} => 1
{{1,3},{2},{4},{5},{6}} => 1
{{1,4,5,6},{2,3}} => 2
{{1,4,5},{2,3,6}} => 4
{{1,4,5},{2,3},{6}} => 2
{{1,4,6},{2,3,5}} => 4
{{1,4},{2,3,5,6}} => 2
{{1,4},{2,3,5},{6}} => 2
{{1,4,6},{2,3},{5}} => 4
{{1,4},{2,3,6},{5}} => 4
{{1,4},{2,3},{5,6}} => 2
{{1,4},{2,3},{5},{6}} => 2
{{1,5,6},{2,3,4}} => 3
{{1,5},{2,3,4,6}} => 3
{{1,5},{2,3,4},{6}} => 3
{{1,6},{2,3,4,5}} => 4
{{1},{2,3,4,5,6}} => 0
{{1},{2,3,4,5},{6}} => 0
{{1,6},{2,3,4},{5}} => 4
{{1},{2,3,4,6},{5}} => 3
{{1},{2,3,4},{5,6}} => 0
{{1},{2,3,4},{5},{6}} => 0
{{1,5,6},{2,3},{4}} => 3
{{1,5},{2,3,6},{4}} => 5
{{1,5},{2,3},{4,6}} => 3
{{1,5},{2,3},{4},{6}} => 3
{{1,6},{2,3,5},{4}} => 6
{{1},{2,3,5,6},{4}} => 2
{{1},{2,3,5},{4,6}} => 1
{{1},{2,3,5},{4},{6}} => 2
{{1,6},{2,3},{4,5}} => 4
{{1},{2,3,6},{4,5}} => 4
{{1},{2,3},{4,5,6}} => 0
{{1},{2,3},{4,5},{6}} => 0
{{1,6},{2,3},{4},{5}} => 4
{{1},{2,3,6},{4},{5}} => 4
{{1},{2,3},{4,6},{5}} => 1
{{1},{2,3},{4},{5,6}} => 0
{{1},{2,3},{4},{5},{6}} => 0
{{1,4,5,6},{2},{3}} => 2
{{1,4,5},{2,6},{3}} => 4
{{1,4,5},{2},{3,6}} => 3
{{1,4,5},{2},{3},{6}} => 2
{{1,4,6},{2,5},{3}} => 5
{{1,4},{2,5,6},{3}} => 3
{{1,4},{2,5},{3,6}} => 3
{{1,4},{2,5},{3},{6}} => 3
{{1,4,6},{2},{3,5}} => 4
{{1,4},{2,6},{3,5}} => 4
{{1,4},{2},{3,5,6}} => 2
{{1,4},{2},{3,5},{6}} => 2
{{1,4,6},{2},{3},{5}} => 4
{{1,4},{2,6},{3},{5}} => 4
{{1,4},{2},{3,6},{5}} => 3
{{1,4},{2},{3},{5,6}} => 2
{{1,4},{2},{3},{5},{6}} => 2
{{1,5,6},{2,4},{3}} => 4
{{1,5},{2,4,6},{3}} => 4
{{1,5},{2,4},{3,6}} => 4
{{1,5},{2,4},{3},{6}} => 4
{{1,6},{2,4,5},{3}} => 5
{{1},{2,4,5,6},{3}} => 1
{{1},{2,4,5},{3,6}} => 2
{{1},{2,4,5},{3},{6}} => 1
{{1,6},{2,4},{3,5}} => 5
{{1},{2,4,6},{3,5}} => 3
{{1},{2,4},{3,5,6}} => 1
{{1},{2,4},{3,5},{6}} => 1
{{1,6},{2,4},{3},{5}} => 5
{{1},{2,4,6},{3},{5}} => 3
{{1},{2,4},{3,6},{5}} => 2
{{1},{2,4},{3},{5,6}} => 1
{{1},{2,4},{3},{5},{6}} => 1
{{1,5,6},{2},{3,4}} => 3
{{1,5},{2,6},{3,4}} => 5
{{1,5},{2},{3,4,6}} => 3
{{1,5},{2},{3,4},{6}} => 3
{{1,6},{2,5},{3,4}} => 6
{{1},{2,5,6},{3,4}} => 2
{{1},{2,5},{3,4,6}} => 2
{{1},{2,5},{3,4},{6}} => 2
{{1,6},{2},{3,4,5}} => 4
{{1},{2,6},{3,4,5}} => 3
{{1},{2},{3,4,5,6}} => 0
{{1},{2},{3,4,5},{6}} => 0
{{1,6},{2},{3,4},{5}} => 4
{{1},{2,6},{3,4},{5}} => 3
{{1},{2},{3,4,6},{5}} => 2
{{1},{2},{3,4},{5,6}} => 0
{{1},{2},{3,4},{5},{6}} => 0
{{1,5,6},{2},{3},{4}} => 3
{{1,5},{2,6},{3},{4}} => 5
{{1,5},{2},{3,6},{4}} => 4
{{1,5},{2},{3},{4,6}} => 3
{{1,5},{2},{3},{4},{6}} => 3
{{1,6},{2,5},{3},{4}} => 6
{{1},{2,5,6},{3},{4}} => 2
{{1},{2,5},{3,6},{4}} => 3
{{1},{2,5},{3},{4,6}} => 2
{{1},{2,5},{3},{4},{6}} => 2
{{1,6},{2},{3,5},{4}} => 5
{{1},{2,6},{3,5},{4}} => 4
{{1},{2},{3,5,6},{4}} => 1
{{1},{2},{3,5},{4,6}} => 1
{{1},{2},{3,5},{4},{6}} => 1
{{1,6},{2},{3},{4,5}} => 4
{{1},{2,6},{3},{4,5}} => 3
{{1},{2},{3,6},{4,5}} => 2
{{1},{2},{3},{4,5,6}} => 0
{{1},{2},{3},{4,5},{6}} => 0
{{1,6},{2},{3},{4},{5}} => 4
{{1},{2,6},{3},{4},{5}} => 3
{{1},{2},{3,6},{4},{5}} => 2
{{1},{2},{3},{4,6},{5}} => 1
{{1},{2},{3},{4},{5,6}} => 0
{{1},{2},{3},{4},{5},{6}} => 0
{{1,2,3,4,5,6,7}} => 0
{{1,2,3,4,5,6},{7}} => 0
{{1,2,3,4,5,7},{6}} => 5
{{1,2,3,4,5},{6,7}} => 0
{{1,2,3,4,5},{6},{7}} => 0
{{1,2,3,4,6,7},{5}} => 4
{{1,2,3,4,6},{5,7}} => 1
{{1,2,3,4,6},{5},{7}} => 4
{{1,2,3,4,7},{5,6}} => 8
{{1,2,3,4},{5,6,7}} => 0
{{1,2,3,4},{5,6},{7}} => 0
{{1,2,3,4,7},{5},{6}} => 8
{{1,2,3,4},{5,7},{6}} => 1
{{1,2,3,4},{5},{6,7}} => 0
{{1,2,3,4},{5},{6},{7}} => 0
{{1,2,3,5,6,7},{4}} => 3
{{1,2,3,5,6},{4,7}} => 2
{{1,2,3,5,6},{4},{7}} => 3
{{1,2,3,5,7},{4,6}} => 7
{{1,2,3,5},{4,6,7}} => 1
{{1,2,3,5},{4,6},{7}} => 1
{{1,2,3,5,7},{4},{6}} => 7
{{1,2,3,5},{4,7},{6}} => 2
{{1,2,3,5},{4},{6,7}} => 3
{{1,2,3,5},{4},{6},{7}} => 3
{{1,2,3,6,7},{4,5}} => 6
{{1,2,3,6},{4,5,7}} => 2
{{1,2,3,6},{4,5},{7}} => 6
{{1,2,3,7},{4,5,6}} => 9
{{1,2,3},{4,5,6,7}} => 0
{{1,2,3},{4,5,6},{7}} => 0
{{1,2,3,7},{4,5},{6}} => 9
{{1,2,3},{4,5,7},{6}} => 2
{{1,2,3},{4,5},{6,7}} => 0
{{1,2,3},{4,5},{6},{7}} => 0
{{1,2,3,6,7},{4},{5}} => 6
{{1,2,3,6},{4,7},{5}} => 5
{{1,2,3,6},{4},{5,7}} => 4
{{1,2,3,6},{4},{5},{7}} => 6
{{1,2,3,7},{4,6},{5}} => 10
{{1,2,3},{4,6,7},{5}} => 1
{{1,2,3},{4,6},{5,7}} => 1
{{1,2,3},{4,6},{5},{7}} => 1
{{1,2,3,7},{4},{5,6}} => 9
{{1,2,3},{4,7},{5,6}} => 2
{{1,2,3},{4},{5,6,7}} => 0
{{1,2,3},{4},{5,6},{7}} => 0
{{1,2,3,7},{4},{5},{6}} => 9
{{1,2,3},{4,7},{5},{6}} => 2
{{1,2,3},{4},{5,7},{6}} => 1
{{1,2,3},{4},{5},{6,7}} => 0
{{1,2,3},{4},{5},{6},{7}} => 0
{{1,2,4,5,6,7},{3}} => 2
{{1,2,4,5,6},{3,7}} => 3
{{1,2,4,5,6},{3},{7}} => 2
{{1,2,4,5,7},{3,6}} => 6
{{1,2,4,5},{3,6,7}} => 2
{{1,2,4,5},{3,6},{7}} => 2
{{1,2,4,5,7},{3},{6}} => 6
{{1,2,4,5},{3,7},{6}} => 3
{{1,2,4,5},{3},{6,7}} => 2
{{1,2,4,5},{3},{6},{7}} => 2
{{1,2,4,6,7},{3,5}} => 5
{{1,2,4,6},{3,5,7}} => 3
{{1,2,4,6},{3,5},{7}} => 5
{{1,2,4,7},{3,5,6}} => 8
{{1,2,4},{3,5,6,7}} => 1
{{1,2,4},{3,5,6},{7}} => 1
{{1,2,4,7},{3,5},{6}} => 8
{{1,2,4},{3,5,7},{6}} => 3
{{1,2,4},{3,5},{6,7}} => 1
{{1,2,4},{3,5},{6},{7}} => 1
{{1,2,4,6,7},{3},{5}} => 5
{{1,2,4,6},{3,7},{5}} => 6
{{1,2,4,6},{3},{5,7}} => 3
{{1,2,4,6},{3},{5},{7}} => 5
{{1,2,4,7},{3,6},{5}} => 9
{{1,2,4},{3,6,7},{5}} => 2
{{1,2,4},{3,6},{5,7}} => 2
{{1,2,4},{3,6},{5},{7}} => 2
{{1,2,4,7},{3},{5,6}} => 8
{{1,2,4},{3,7},{5,6}} => 3
{{1,2,4},{3},{5,6,7}} => 2
{{1,2,4},{3},{5,6},{7}} => 2
{{1,2,4,7},{3},{5},{6}} => 8
{{1,2,4},{3,7},{5},{6}} => 3
{{1,2,4},{3},{5,7},{6}} => 3
{{1,2,4},{3},{5},{6,7}} => 2
{{1,2,4},{3},{5},{6},{7}} => 2
{{1,2,5,6,7},{3,4}} => 4
{{1,2,5,6},{3,4,7}} => 4
{{1,2,5,6},{3,4},{7}} => 4
{{1,2,5,7},{3,4,6}} => 7
{{1,2,5},{3,4,6,7}} => 2
{{1,2,5},{3,4,6},{7}} => 2
{{1,2,5,7},{3,4},{6}} => 7
{{1,2,5},{3,4,7},{6}} => 4
{{1,2,5},{3,4},{6,7}} => 4
{{1,2,5},{3,4},{6},{7}} => 4
{{1,2,6,7},{3,4,5}} => 6
{{1,2,6},{3,4,5,7}} => 3
{{1,2,6},{3,4,5},{7}} => 6
{{1,2,7},{3,4,5,6}} => 8
{{1,2},{3,4,5,6,7}} => 0
{{1,2},{3,4,5,6},{7}} => 0
{{1,2,7},{3,4,5},{6}} => 8
{{1,2},{3,4,5,7},{6}} => 3
{{1,2},{3,4,5},{6,7}} => 0
{{1,2},{3,4,5},{6},{7}} => 0
{{1,2,6,7},{3,4},{5}} => 6
{{1,2,6},{3,4,7},{5}} => 6
{{1,2,6},{3,4},{5,7}} => 5
{{1,2,6},{3,4},{5},{7}} => 6
{{1,2,7},{3,4,6},{5}} => 10
{{1,2},{3,4,6,7},{5}} => 2
{{1,2},{3,4,6},{5,7}} => 1
{{1,2},{3,4,6},{5},{7}} => 2
{{1,2,7},{3,4},{5,6}} => 8
{{1,2},{3,4,7},{5,6}} => 4
{{1,2},{3,4},{5,6,7}} => 0
{{1,2},{3,4},{5,6},{7}} => 0
{{1,2,7},{3,4},{5},{6}} => 8
{{1,2},{3,4,7},{5},{6}} => 4
{{1,2},{3,4},{5,7},{6}} => 1
{{1,2},{3,4},{5},{6,7}} => 0
{{1,2},{3,4},{5},{6},{7}} => 0
{{1,2,5,6,7},{3},{4}} => 4
{{1,2,5,6},{3,7},{4}} => 5
{{1,2,5,6},{3},{4,7}} => 4
{{1,2,5,6},{3},{4},{7}} => 4
{{1,2,5,7},{3,6},{4}} => 8
{{1,2,5},{3,6,7},{4}} => 4
{{1,2,5},{3,6},{4,7}} => 3
{{1,2,5},{3,6},{4},{7}} => 4
{{1,2,5,7},{3},{4,6}} => 7
{{1,2,5},{3,7},{4,6}} => 4
{{1,2,5},{3},{4,6,7}} => 3
{{1,2,5},{3},{4,6},{7}} => 3
{{1,2,5,7},{3},{4},{6}} => 7
{{1,2,5},{3,7},{4},{6}} => 5
{{1,2,5},{3},{4,7},{6}} => 4
{{1,2,5},{3},{4},{6,7}} => 4
{{1,2,5},{3},{4},{6},{7}} => 4
{{1,2,6,7},{3,5},{4}} => 7
{{1,2,6},{3,5,7},{4}} => 5
{{1,2,6},{3,5},{4,7}} => 6
{{1,2,6},{3,5},{4},{7}} => 7
{{1,2,7},{3,5,6},{4}} => 9
{{1,2},{3,5,6,7},{4}} => 1
{{1,2},{3,5,6},{4,7}} => 2
{{1,2},{3,5,6},{4},{7}} => 1
{{1,2,7},{3,5},{4,6}} => 9
{{1,2},{3,5,7},{4,6}} => 3
{{1,2},{3,5},{4,6,7}} => 1
{{1,2},{3,5},{4,6},{7}} => 1
{{1,2,7},{3,5},{4},{6}} => 9
{{1,2},{3,5,7},{4},{6}} => 3
{{1,2},{3,5},{4,7},{6}} => 2
{{1,2},{3,5},{4},{6,7}} => 1
{{1,2},{3,5},{4},{6},{7}} => 1
{{1,2,6,7},{3},{4,5}} => 6
{{1,2,6},{3,7},{4,5}} => 7
{{1,2,6},{3},{4,5,7}} => 4
{{1,2,6},{3},{4,5},{7}} => 6
{{1,2,7},{3,6},{4,5}} => 10
{{1,2},{3,6,7},{4,5}} => 2
{{1,2},{3,6},{4,5,7}} => 2
{{1,2},{3,6},{4,5},{7}} => 2
{{1,2,7},{3},{4,5,6}} => 8
{{1,2},{3,7},{4,5,6}} => 3
{{1,2},{3},{4,5,6,7}} => 0
{{1,2},{3},{4,5,6},{7}} => 0
{{1,2,7},{3},{4,5},{6}} => 8
{{1,2},{3,7},{4,5},{6}} => 3
{{1,2},{3},{4,5,7},{6}} => 2
{{1,2},{3},{4,5},{6,7}} => 0
{{1,2},{3},{4,5},{6},{7}} => 0
{{1,2,6,7},{3},{4},{5}} => 6
{{1,2,6},{3,7},{4},{5}} => 7
{{1,2,6},{3},{4,7},{5}} => 6
{{1,2,6},{3},{4},{5,7}} => 5
{{1,2,6},{3},{4},{5},{7}} => 6
{{1,2,7},{3,6},{4},{5}} => 10
{{1,2},{3,6,7},{4},{5}} => 2
{{1,2},{3,6},{4,7},{5}} => 3
{{1,2},{3,6},{4},{5,7}} => 2
{{1,2},{3,6},{4},{5},{7}} => 2
{{1,2,7},{3},{4,6},{5}} => 9
{{1,2},{3,7},{4,6},{5}} => 4
{{1,2},{3},{4,6,7},{5}} => 1
{{1,2},{3},{4,6},{5,7}} => 1
{{1,2},{3},{4,6},{5},{7}} => 1
{{1,2,7},{3},{4},{5,6}} => 8
{{1,2},{3,7},{4},{5,6}} => 3
{{1,2},{3},{4,7},{5,6}} => 2
{{1,2},{3},{4},{5,6,7}} => 0
{{1,2},{3},{4},{5,6},{7}} => 0
{{1,2,7},{3},{4},{5},{6}} => 8
{{1,2},{3,7},{4},{5},{6}} => 3
{{1,2},{3},{4,7},{5},{6}} => 2
{{1,2},{3},{4},{5,7},{6}} => 1
{{1,2},{3},{4},{5},{6,7}} => 0
{{1,2},{3},{4},{5},{6},{7}} => 0
{{1,3,4,5,6,7},{2}} => 1
{{1,3,4,5,6},{2,7}} => 4
{{1,3,4,5,6},{2},{7}} => 1
{{1,3,4,5,7},{2,6}} => 5
{{1,3,4,5},{2,6,7}} => 3
{{1,3,4,5},{2,6},{7}} => 3
{{1,3,4,5,7},{2},{6}} => 5
{{1,3,4,5},{2,7},{6}} => 4
{{1,3,4,5},{2},{6,7}} => 1
{{1,3,4,5},{2},{6},{7}} => 1
{{1,3,4,6,7},{2,5}} => 4
{{1,3,4,6},{2,5,7}} => 4
{{1,3,4,6},{2,5},{7}} => 4
{{1,3,4,7},{2,5,6}} => 7
{{1,3,4},{2,5,6,7}} => 2
{{1,3,4},{2,5,6},{7}} => 2
{{1,3,4,7},{2,5},{6}} => 7
{{1,3,4},{2,5,7},{6}} => 4
{{1,3,4},{2,5},{6,7}} => 2
{{1,3,4},{2,5},{6},{7}} => 2
{{1,3,4,6,7},{2},{5}} => 4
{{1,3,4,6},{2,7},{5}} => 7
{{1,3,4,6},{2},{5,7}} => 2
{{1,3,4,6},{2},{5},{7}} => 4
{{1,3,4,7},{2,6},{5}} => 8
{{1,3,4},{2,6,7},{5}} => 3
{{1,3,4},{2,6},{5,7}} => 3
{{1,3,4},{2,6},{5},{7}} => 3
{{1,3,4,7},{2},{5,6}} => 7
{{1,3,4},{2,7},{5,6}} => 4
{{1,3,4},{2},{5,6,7}} => 1
{{1,3,4},{2},{5,6},{7}} => 1
{{1,3,4,7},{2},{5},{6}} => 7
{{1,3,4},{2,7},{5},{6}} => 4
{{1,3,4},{2},{5,7},{6}} => 2
{{1,3,4},{2},{5},{6,7}} => 1
{{1,3,4},{2},{5},{6},{7}} => 1
{{1,3,5,6,7},{2,4}} => 3
{{1,3,5,6},{2,4,7}} => 5
{{1,3,5,6},{2,4},{7}} => 3
{{1,3,5,7},{2,4,6}} => 6
{{1,3,5},{2,4,6,7}} => 3
{{1,3,5},{2,4,6},{7}} => 3
{{1,3,5,7},{2,4},{6}} => 6
{{1,3,5},{2,4,7},{6}} => 5
{{1,3,5},{2,4},{6,7}} => 3
{{1,3,5},{2,4},{6},{7}} => 3
{{1,3,6,7},{2,4,5}} => 5
{{1,3,6},{2,4,5,7}} => 4
{{1,3,6},{2,4,5},{7}} => 5
{{1,3,7},{2,4,5,6}} => 7
{{1,3},{2,4,5,6,7}} => 1
{{1,3},{2,4,5,6},{7}} => 1
{{1,3,7},{2,4,5},{6}} => 7
{{1,3},{2,4,5,7},{6}} => 4
{{1,3},{2,4,5},{6,7}} => 1
{{1,3},{2,4,5},{6},{7}} => 1
{{1,3,6,7},{2,4},{5}} => 5
{{1,3,6},{2,4,7},{5}} => 7
{{1,3,6},{2,4},{5,7}} => 4
{{1,3,6},{2,4},{5},{7}} => 5
{{1,3,7},{2,4,6},{5}} => 9
{{1,3},{2,4,6,7},{5}} => 3
{{1,3},{2,4,6},{5,7}} => 2
{{1,3},{2,4,6},{5},{7}} => 3
{{1,3,7},{2,4},{5,6}} => 7
{{1,3},{2,4,7},{5,6}} => 5
{{1,3},{2,4},{5,6,7}} => 1
{{1,3},{2,4},{5,6},{7}} => 1
{{1,3,7},{2,4},{5},{6}} => 7
{{1,3},{2,4,7},{5},{6}} => 5
{{1,3},{2,4},{5,7},{6}} => 2
{{1,3},{2,4},{5},{6,7}} => 1
{{1,3},{2,4},{5},{6},{7}} => 1
{{1,3,5,6,7},{2},{4}} => 3
{{1,3,5,6},{2,7},{4}} => 6
{{1,3,5,6},{2},{4,7}} => 3
{{1,3,5,6},{2},{4},{7}} => 3
{{1,3,5,7},{2,6},{4}} => 7
{{1,3,5},{2,6,7},{4}} => 5
{{1,3,5},{2,6},{4,7}} => 4
{{1,3,5},{2,6},{4},{7}} => 5
{{1,3,5,7},{2},{4,6}} => 6
{{1,3,5},{2,7},{4,6}} => 5
{{1,3,5},{2},{4,6,7}} => 2
{{1,3,5},{2},{4,6},{7}} => 2
{{1,3,5,7},{2},{4},{6}} => 6
{{1,3,5},{2,7},{4},{6}} => 6
{{1,3,5},{2},{4,7},{6}} => 3
{{1,3,5},{2},{4},{6,7}} => 3
{{1,3,5},{2},{4},{6},{7}} => 3
{{1,3,6,7},{2,5},{4}} => 6
{{1,3,6},{2,5,7},{4}} => 6
{{1,3,6},{2,5},{4,7}} => 5
{{1,3,6},{2,5},{4},{7}} => 6
{{1,3,7},{2,5,6},{4}} => 8
{{1,3},{2,5,6,7},{4}} => 2
{{1,3},{2,5,6},{4,7}} => 3
{{1,3},{2,5,6},{4},{7}} => 2
{{1,3,7},{2,5},{4,6}} => 8
{{1,3},{2,5,7},{4,6}} => 4
{{1,3},{2,5},{4,6,7}} => 2
{{1,3},{2,5},{4,6},{7}} => 2
{{1,3,7},{2,5},{4},{6}} => 8
{{1,3},{2,5,7},{4},{6}} => 4
{{1,3},{2,5},{4,7},{6}} => 3
{{1,3},{2,5},{4},{6,7}} => 2
{{1,3},{2,5},{4},{6},{7}} => 2
{{1,3,6,7},{2},{4,5}} => 5
{{1,3,6},{2,7},{4,5}} => 8
{{1,3,6},{2},{4,5,7}} => 3
{{1,3,6},{2},{4,5},{7}} => 5
{{1,3,7},{2,6},{4,5}} => 9
{{1,3},{2,6,7},{4,5}} => 3
{{1,3},{2,6},{4,5,7}} => 3
{{1,3},{2,6},{4,5},{7}} => 3
{{1,3,7},{2},{4,5,6}} => 7
{{1,3},{2,7},{4,5,6}} => 4
{{1,3},{2},{4,5,6,7}} => 1
{{1,3},{2},{4,5,6},{7}} => 1
{{1,3,7},{2},{4,5},{6}} => 7
{{1,3},{2,7},{4,5},{6}} => 4
{{1,3},{2},{4,5,7},{6}} => 3
{{1,3},{2},{4,5},{6,7}} => 1
{{1,3},{2},{4,5},{6},{7}} => 1
{{1,3,6,7},{2},{4},{5}} => 5
{{1,3,6},{2,7},{4},{5}} => 8
{{1,3,6},{2},{4,7},{5}} => 5
{{1,3,6},{2},{4},{5,7}} => 4
{{1,3,6},{2},{4},{5},{7}} => 5
{{1,3,7},{2,6},{4},{5}} => 9
{{1,3},{2,6,7},{4},{5}} => 3
{{1,3},{2,6},{4,7},{5}} => 4
{{1,3},{2,6},{4},{5,7}} => 3
{{1,3},{2,6},{4},{5},{7}} => 3
{{1,3,7},{2},{4,6},{5}} => 8
{{1,3},{2,7},{4,6},{5}} => 5
{{1,3},{2},{4,6,7},{5}} => 2
{{1,3},{2},{4,6},{5,7}} => 2
{{1,3},{2},{4,6},{5},{7}} => 2
{{1,3,7},{2},{4},{5,6}} => 7
{{1,3},{2,7},{4},{5,6}} => 4
{{1,3},{2},{4,7},{5,6}} => 3
{{1,3},{2},{4},{5,6,7}} => 1
{{1,3},{2},{4},{5,6},{7}} => 1
{{1,3,7},{2},{4},{5},{6}} => 7
{{1,3},{2,7},{4},{5},{6}} => 4
{{1,3},{2},{4,7},{5},{6}} => 3
{{1,3},{2},{4},{5,7},{6}} => 2
{{1,3},{2},{4},{5},{6,7}} => 1
{{1,3},{2},{4},{5},{6},{7}} => 1
{{1,4,5,6,7},{2,3}} => 2
{{1,4,5,6},{2,3,7}} => 6
{{1,4,5,6},{2,3},{7}} => 2
{{1,4,5,7},{2,3,6}} => 5
{{1,4,5},{2,3,6,7}} => 4
{{1,4,5},{2,3,6},{7}} => 4
{{1,4,5,7},{2,3},{6}} => 5
{{1,4,5},{2,3,7},{6}} => 6
{{1,4,5},{2,3},{6,7}} => 2
{{1,4,5},{2,3},{6},{7}} => 2
{{1,4,6,7},{2,3,5}} => 4
{{1,4,6},{2,3,5,7}} => 5
{{1,4,6},{2,3,5},{7}} => 4
{{1,4,7},{2,3,5,6}} => 6
{{1,4},{2,3,5,6,7}} => 2
{{1,4},{2,3,5,6},{7}} => 2
{{1,4,7},{2,3,5},{6}} => 6
{{1,4},{2,3,5,7},{6}} => 5
{{1,4},{2,3,5},{6,7}} => 2
{{1,4},{2,3,5},{6},{7}} => 2
{{1,4,6,7},{2,3},{5}} => 4
{{1,4,6},{2,3,7},{5}} => 8
{{1,4,6},{2,3},{5,7}} => 3
{{1,4,6},{2,3},{5},{7}} => 4
{{1,4,7},{2,3,6},{5}} => 8
{{1,4},{2,3,6,7},{5}} => 4
{{1,4},{2,3,6},{5,7}} => 3
{{1,4},{2,3,6},{5},{7}} => 4
{{1,4,7},{2,3},{5,6}} => 6
{{1,4},{2,3,7},{5,6}} => 6
{{1,4},{2,3},{5,6,7}} => 2
{{1,4},{2,3},{5,6},{7}} => 2
{{1,4,7},{2,3},{5},{6}} => 6
{{1,4},{2,3,7},{5},{6}} => 6
{{1,4},{2,3},{5,7},{6}} => 3
{{1,4},{2,3},{5},{6,7}} => 2
{{1,4},{2,3},{5},{6},{7}} => 2
{{1,5,6,7},{2,3,4}} => 3
{{1,5,6},{2,3,4,7}} => 6
{{1,5,6},{2,3,4},{7}} => 3
{{1,5,7},{2,3,4,6}} => 5
{{1,5},{2,3,4,6,7}} => 3
{{1,5},{2,3,4,6},{7}} => 3
{{1,5,7},{2,3,4},{6}} => 5
{{1,5},{2,3,4,7},{6}} => 6
{{1,5},{2,3,4},{6,7}} => 3
{{1,5},{2,3,4},{6},{7}} => 3
{{1,6,7},{2,3,4,5}} => 4
{{1,6},{2,3,4,5,7}} => 4
{{1,6},{2,3,4,5},{7}} => 4
{{1,7},{2,3,4,5,6}} => 5
{{1},{2,3,4,5,6,7}} => 0
{{1},{2,3,4,5,6},{7}} => 0
{{1,7},{2,3,4,5},{6}} => 5
{{1},{2,3,4,5,7},{6}} => 4
{{1},{2,3,4,5},{6,7}} => 0
{{1},{2,3,4,5},{6},{7}} => 0
{{1,6,7},{2,3,4},{5}} => 4
{{1,6},{2,3,4,7},{5}} => 7
{{1,6},{2,3,4},{5,7}} => 4
{{1,6},{2,3,4},{5},{7}} => 4
{{1,7},{2,3,4,6},{5}} => 8
{{1},{2,3,4,6,7},{5}} => 3
{{1},{2,3,4,6},{5,7}} => 1
{{1},{2,3,4,6},{5},{7}} => 3
{{1,7},{2,3,4},{5,6}} => 5
{{1},{2,3,4,7},{5,6}} => 6
{{1},{2,3,4},{5,6,7}} => 0
{{1},{2,3,4},{5,6},{7}} => 0
{{1,7},{2,3,4},{5},{6}} => 5
{{1},{2,3,4,7},{5},{6}} => 6
{{1},{2,3,4},{5,7},{6}} => 1
{{1},{2,3,4},{5},{6,7}} => 0
{{1},{2,3,4},{5},{6},{7}} => 0
{{1,5,6,7},{2,3},{4}} => 3
{{1,5,6},{2,3,7},{4}} => 7
{{1,5,6},{2,3},{4,7}} => 4
{{1,5,6},{2,3},{4},{7}} => 3
{{1,5,7},{2,3,6},{4}} => 7
{{1,5},{2,3,6,7},{4}} => 5
{{1,5},{2,3,6},{4,7}} => 4
{{1,5},{2,3,6},{4},{7}} => 5
{{1,5,7},{2,3},{4,6}} => 5
{{1,5},{2,3,7},{4,6}} => 7
{{1,5},{2,3},{4,6,7}} => 3
{{1,5},{2,3},{4,6},{7}} => 3
{{1,5,7},{2,3},{4},{6}} => 5
{{1,5},{2,3,7},{4},{6}} => 7
{{1,5},{2,3},{4,7},{6}} => 4
{{1,5},{2,3},{4},{6,7}} => 3
{{1,5},{2,3},{4},{6},{7}} => 3
{{1,6,7},{2,3,5},{4}} => 6
{{1,6},{2,3,5,7},{4}} => 6
{{1,6},{2,3,5},{4,7}} => 5
{{1,6},{2,3,5},{4},{7}} => 6
{{1,7},{2,3,5,6},{4}} => 7
{{1},{2,3,5,6,7},{4}} => 2
{{1},{2,3,5,6},{4,7}} => 2
{{1},{2,3,5,6},{4},{7}} => 2
{{1,7},{2,3,5},{4,6}} => 6
{{1},{2,3,5,7},{4,6}} => 5
{{1},{2,3,5},{4,6,7}} => 1
{{1},{2,3,5},{4,6},{7}} => 1
{{1,7},{2,3,5},{4},{6}} => 7
{{1},{2,3,5,7},{4},{6}} => 5
{{1},{2,3,5},{4,7},{6}} => 2
{{1},{2,3,5},{4},{6,7}} => 2
{{1},{2,3,5},{4},{6},{7}} => 2
{{1,6,7},{2,3},{4,5}} => 4
{{1,6},{2,3,7},{4,5}} => 8
{{1,6},{2,3},{4,5,7}} => 4
{{1,6},{2,3},{4,5},{7}} => 4
{{1,7},{2,3,6},{4,5}} => 9
{{1},{2,3,6,7},{4,5}} => 4
{{1},{2,3,6},{4,5,7}} => 2
{{1},{2,3,6},{4,5},{7}} => 4
{{1,7},{2,3},{4,5,6}} => 5
{{1},{2,3,7},{4,5,6}} => 6
{{1},{2,3},{4,5,6,7}} => 0
{{1},{2,3},{4,5,6},{7}} => 0
{{1,7},{2,3},{4,5},{6}} => 5
{{1},{2,3,7},{4,5},{6}} => 6
{{1},{2,3},{4,5,7},{6}} => 2
{{1},{2,3},{4,5},{6,7}} => 0
{{1},{2,3},{4,5},{6},{7}} => 0
{{1,6,7},{2,3},{4},{5}} => 4
{{1,6},{2,3,7},{4},{5}} => 8
{{1,6},{2,3},{4,7},{5}} => 5
{{1,6},{2,3},{4},{5,7}} => 4
{{1,6},{2,3},{4},{5},{7}} => 4
{{1,7},{2,3,6},{4},{5}} => 9
{{1},{2,3,6,7},{4},{5}} => 4
{{1},{2,3,6},{4,7},{5}} => 4
{{1},{2,3,6},{4},{5,7}} => 3
{{1},{2,3,6},{4},{5},{7}} => 4
{{1,7},{2,3},{4,6},{5}} => 6
{{1},{2,3,7},{4,6},{5}} => 7
{{1},{2,3},{4,6,7},{5}} => 1
{{1},{2,3},{4,6},{5,7}} => 1
{{1},{2,3},{4,6},{5},{7}} => 1
{{1,7},{2,3},{4},{5,6}} => 5
{{1},{2,3,7},{4},{5,6}} => 6
{{1},{2,3},{4,7},{5,6}} => 2
{{1},{2,3},{4},{5,6,7}} => 0
{{1},{2,3},{4},{5,6},{7}} => 0
{{1,7},{2,3},{4},{5},{6}} => 5
{{1},{2,3,7},{4},{5},{6}} => 6
{{1},{2,3},{4,7},{5},{6}} => 2
{{1},{2,3},{4},{5,7},{6}} => 1
{{1},{2,3},{4},{5},{6,7}} => 0
{{1},{2,3},{4},{5},{6},{7}} => 0
{{1,4,5,6,7},{2},{3}} => 2
{{1,4,5,6},{2,7},{3}} => 5
{{1,4,5,6},{2},{3,7}} => 4
{{1,4,5,6},{2},{3},{7}} => 2
{{1,4,5,7},{2,6},{3}} => 6
{{1,4,5},{2,6,7},{3}} => 4
{{1,4,5},{2,6},{3,7}} => 5
{{1,4,5},{2,6},{3},{7}} => 4
{{1,4,5,7},{2},{3,6}} => 5
{{1,4,5},{2,7},{3,6}} => 6
{{1,4,5},{2},{3,6,7}} => 3
{{1,4,5},{2},{3,6},{7}} => 3
{{1,4,5,7},{2},{3},{6}} => 5
{{1,4,5},{2,7},{3},{6}} => 5
{{1,4,5},{2},{3,7},{6}} => 4
{{1,4,5},{2},{3},{6,7}} => 2
{{1,4,5},{2},{3},{6},{7}} => 2
{{1,4,6,7},{2,5},{3}} => 5
{{1,4,6},{2,5,7},{3}} => 5
{{1,4,6},{2,5},{3,7}} => 6
{{1,4,6},{2,5},{3},{7}} => 5
{{1,4,7},{2,5,6},{3}} => 7
{{1,4},{2,5,6,7},{3}} => 3
{{1,4},{2,5,6},{3,7}} => 4
{{1,4},{2,5,6},{3},{7}} => 3
{{1,4,7},{2,5},{3,6}} => 7
{{1,4},{2,5,7},{3,6}} => 5
{{1,4},{2,5},{3,6,7}} => 3
{{1,4},{2,5},{3,6},{7}} => 3
{{1,4,7},{2,5},{3},{6}} => 7
{{1,4},{2,5,7},{3},{6}} => 5
{{1,4},{2,5},{3,7},{6}} => 4
{{1,4},{2,5},{3},{6,7}} => 3
{{1,4},{2,5},{3},{6},{7}} => 3
{{1,4,6,7},{2},{3,5}} => 4
{{1,4,6},{2,7},{3,5}} => 7
{{1,4,6},{2},{3,5,7}} => 4
{{1,4,6},{2},{3,5},{7}} => 4
{{1,4,7},{2,6},{3,5}} => 8
{{1,4},{2,6,7},{3,5}} => 4
{{1,4},{2,6},{3,5,7}} => 4
{{1,4},{2,6},{3,5},{7}} => 4
{{1,4,7},{2},{3,5,6}} => 6
{{1,4},{2,7},{3,5,6}} => 5
{{1,4},{2},{3,5,6,7}} => 2
{{1,4},{2},{3,5,6},{7}} => 2
{{1,4,7},{2},{3,5},{6}} => 6
{{1,4},{2,7},{3,5},{6}} => 5
{{1,4},{2},{3,5,7},{6}} => 4
{{1,4},{2},{3,5},{6,7}} => 2
{{1,4},{2},{3,5},{6},{7}} => 2
{{1,4,6,7},{2},{3},{5}} => 4
{{1,4,6},{2,7},{3},{5}} => 7
{{1,4,6},{2},{3,7},{5}} => 6
{{1,4,6},{2},{3},{5,7}} => 3
{{1,4,6},{2},{3},{5},{7}} => 4
{{1,4,7},{2,6},{3},{5}} => 8
{{1,4},{2,6,7},{3},{5}} => 4
{{1,4},{2,6},{3,7},{5}} => 5
{{1,4},{2,6},{3},{5,7}} => 4
{{1,4},{2,6},{3},{5},{7}} => 4
{{1,4,7},{2},{3,6},{5}} => 7
{{1,4},{2,7},{3,6},{5}} => 6
{{1,4},{2},{3,6,7},{5}} => 3
{{1,4},{2},{3,6},{5,7}} => 3
{{1,4},{2},{3,6},{5},{7}} => 3
{{1,4,7},{2},{3},{5,6}} => 6
{{1,4},{2,7},{3},{5,6}} => 5
{{1,4},{2},{3,7},{5,6}} => 4
{{1,4},{2},{3},{5,6,7}} => 2
{{1,4},{2},{3},{5,6},{7}} => 2
{{1,4,7},{2},{3},{5},{6}} => 6
{{1,4},{2,7},{3},{5},{6}} => 5
{{1,4},{2},{3,7},{5},{6}} => 4
{{1,4},{2},{3},{5,7},{6}} => 3
{{1,4},{2},{3},{5},{6,7}} => 2
{{1,4},{2},{3},{5},{6},{7}} => 2
{{1,5,6,7},{2,4},{3}} => 4
{{1,5,6},{2,4,7},{3}} => 6
{{1,5,6},{2,4},{3,7}} => 5
{{1,5,6},{2,4},{3},{7}} => 4
{{1,5,7},{2,4,6},{3}} => 6
{{1,5},{2,4,6,7},{3}} => 4
{{1,5},{2,4,6},{3,7}} => 5
{{1,5},{2,4,6},{3},{7}} => 4
{{1,5,7},{2,4},{3,6}} => 6
{{1,5},{2,4,7},{3,6}} => 6
{{1,5},{2,4},{3,6,7}} => 4
{{1,5},{2,4},{3,6},{7}} => 4
{{1,5,7},{2,4},{3},{6}} => 6
{{1,5},{2,4,7},{3},{6}} => 6
{{1,5},{2,4},{3,7},{6}} => 5
{{1,5},{2,4},{3},{6,7}} => 4
{{1,5},{2,4},{3},{6},{7}} => 4
{{1,6,7},{2,4,5},{3}} => 5
{{1,6},{2,4,5,7},{3}} => 5
{{1,6},{2,4,5},{3,7}} => 6
{{1,6},{2,4,5},{3},{7}} => 5
{{1,7},{2,4,5,6},{3}} => 6
{{1},{2,4,5,6,7},{3}} => 1
{{1},{2,4,5,6},{3,7}} => 3
{{1},{2,4,5,6},{3},{7}} => 1
{{1,7},{2,4,5},{3,6}} => 7
{{1},{2,4,5,7},{3,6}} => 4
{{1},{2,4,5},{3,6,7}} => 2
{{1},{2,4,5},{3,6},{7}} => 2
{{1,7},{2,4,5},{3},{6}} => 6
{{1},{2,4,5,7},{3},{6}} => 4
{{1},{2,4,5},{3,7},{6}} => 3
{{1},{2,4,5},{3},{6,7}} => 1
{{1},{2,4,5},{3},{6},{7}} => 1
{{1,6,7},{2,4},{3,5}} => 5
{{1,6},{2,4,7},{3,5}} => 7
{{1,6},{2,4},{3,5,7}} => 5
{{1,6},{2,4},{3,5},{7}} => 5
{{1,7},{2,4,6},{3,5}} => 8
{{1},{2,4,6,7},{3,5}} => 3
{{1},{2,4,6},{3,5,7}} => 3
{{1},{2,4,6},{3,5},{7}} => 3
{{1,7},{2,4},{3,5,6}} => 6
{{1},{2,4,7},{3,5,6}} => 5
{{1},{2,4},{3,5,6,7}} => 1
{{1},{2,4},{3,5,6},{7}} => 1
{{1,7},{2,4},{3,5},{6}} => 6
{{1},{2,4,7},{3,5},{6}} => 5
{{1},{2,4},{3,5,7},{6}} => 3
{{1},{2,4},{3,5},{6,7}} => 1
{{1},{2,4},{3,5},{6},{7}} => 1
{{1,6,7},{2,4},{3},{5}} => 5
{{1,6},{2,4,7},{3},{5}} => 7
{{1,6},{2,4},{3,7},{5}} => 6
{{1,6},{2,4},{3},{5,7}} => 5
{{1,6},{2,4},{3},{5},{7}} => 5
{{1,7},{2,4,6},{3},{5}} => 8
{{1},{2,4,6,7},{3},{5}} => 3
{{1},{2,4,6},{3,7},{5}} => 5
{{1},{2,4,6},{3},{5,7}} => 2
{{1},{2,4,6},{3},{5},{7}} => 3
{{1,7},{2,4},{3,6},{5}} => 7
{{1},{2,4,7},{3,6},{5}} => 6
{{1},{2,4},{3,6,7},{5}} => 2
{{1},{2,4},{3,6},{5,7}} => 2
{{1},{2,4},{3,6},{5},{7}} => 2
{{1,7},{2,4},{3},{5,6}} => 6
{{1},{2,4,7},{3},{5,6}} => 5
{{1},{2,4},{3,7},{5,6}} => 3
{{1},{2,4},{3},{5,6,7}} => 1
{{1},{2,4},{3},{5,6},{7}} => 1
{{1,7},{2,4},{3},{5},{6}} => 6
{{1},{2,4,7},{3},{5},{6}} => 5
{{1},{2,4},{3,7},{5},{6}} => 3
{{1},{2,4},{3},{5,7},{6}} => 2
{{1},{2,4},{3},{5},{6,7}} => 1
{{1},{2,4},{3},{5},{6},{7}} => 1
{{1,5,6,7},{2},{3,4}} => 3
{{1,5,6},{2,7},{3,4}} => 6
{{1,5,6},{2},{3,4,7}} => 5
{{1,5,6},{2},{3,4},{7}} => 3
{{1,5,7},{2,6},{3,4}} => 7
{{1,5},{2,6,7},{3,4}} => 5
{{1,5},{2,6},{3,4,7}} => 5
{{1,5},{2,6},{3,4},{7}} => 5
{{1,5,7},{2},{3,4,6}} => 5
{{1,5},{2,7},{3,4,6}} => 6
{{1,5},{2},{3,4,6,7}} => 3
{{1,5},{2},{3,4,6},{7}} => 3
{{1,5,7},{2},{3,4},{6}} => 5
{{1,5},{2,7},{3,4},{6}} => 6
{{1,5},{2},{3,4,7},{6}} => 5
{{1,5},{2},{3,4},{6,7}} => 3
{{1,5},{2},{3,4},{6},{7}} => 3
{{1,6,7},{2,5},{3,4}} => 6
{{1,6},{2,5,7},{3,4}} => 6
{{1,6},{2,5},{3,4,7}} => 6
{{1,6},{2,5},{3,4},{7}} => 6
{{1,7},{2,5,6},{3,4}} => 7
{{1},{2,5,6,7},{3,4}} => 2
{{1},{2,5,6},{3,4,7}} => 4
{{1},{2,5,6},{3,4},{7}} => 2
{{1,7},{2,5},{3,4,6}} => 7
{{1},{2,5,7},{3,4,6}} => 4
{{1},{2,5},{3,4,6,7}} => 2
{{1},{2,5},{3,4,6},{7}} => 2
{{1,7},{2,5},{3,4},{6}} => 7
{{1},{2,5,7},{3,4},{6}} => 4
{{1},{2,5},{3,4,7},{6}} => 4
{{1},{2,5},{3,4},{6,7}} => 2
{{1},{2,5},{3,4},{6},{7}} => 2
{{1,6,7},{2},{3,4,5}} => 4
{{1,6},{2,7},{3,4,5}} => 7
{{1,6},{2},{3,4,5,7}} => 4
{{1,6},{2},{3,4,5},{7}} => 4
{{1,7},{2,6},{3,4,5}} => 8
{{1},{2,6,7},{3,4,5}} => 3
{{1},{2,6},{3,4,5,7}} => 3
{{1},{2,6},{3,4,5},{7}} => 3
{{1,7},{2},{3,4,5,6}} => 5
{{1},{2,7},{3,4,5,6}} => 4
{{1},{2},{3,4,5,6,7}} => 0
{{1},{2},{3,4,5,6},{7}} => 0
{{1,7},{2},{3,4,5},{6}} => 5
{{1},{2,7},{3,4,5},{6}} => 4
{{1},{2},{3,4,5,7},{6}} => 3
{{1},{2},{3,4,5},{6,7}} => 0
{{1},{2},{3,4,5},{6},{7}} => 0
{{1,6,7},{2},{3,4},{5}} => 4
{{1,6},{2,7},{3,4},{5}} => 7
{{1,6},{2},{3,4,7},{5}} => 6
{{1,6},{2},{3,4},{5,7}} => 4
{{1,6},{2},{3,4},{5},{7}} => 4
{{1,7},{2,6},{3,4},{5}} => 8
{{1},{2,6,7},{3,4},{5}} => 3
{{1},{2,6},{3,4,7},{5}} => 5
{{1},{2,6},{3,4},{5,7}} => 3
{{1},{2,6},{3,4},{5},{7}} => 3
{{1,7},{2},{3,4,6},{5}} => 7
{{1},{2,7},{3,4,6},{5}} => 6
{{1},{2},{3,4,6,7},{5}} => 2
{{1},{2},{3,4,6},{5,7}} => 1
{{1},{2},{3,4,6},{5},{7}} => 2
{{1,7},{2},{3,4},{5,6}} => 5
{{1},{2,7},{3,4},{5,6}} => 4
{{1},{2},{3,4,7},{5,6}} => 4
{{1},{2},{3,4},{5,6,7}} => 0
{{1},{2},{3,4},{5,6},{7}} => 0
{{1,7},{2},{3,4},{5},{6}} => 5
{{1},{2,7},{3,4},{5},{6}} => 4
{{1},{2},{3,4,7},{5},{6}} => 4
{{1},{2},{3,4},{5,7},{6}} => 1
{{1},{2},{3,4},{5},{6,7}} => 0
{{1},{2},{3,4},{5},{6},{7}} => 0
{{1,5,6,7},{2},{3},{4}} => 3
{{1,5,6},{2,7},{3},{4}} => 6
{{1,5,6},{2},{3,7},{4}} => 5
{{1,5,6},{2},{3},{4,7}} => 4
{{1,5,6},{2},{3},{4},{7}} => 3
{{1,5,7},{2,6},{3},{4}} => 7
{{1,5},{2,6,7},{3},{4}} => 5
{{1,5},{2,6},{3,7},{4}} => 6
{{1,5},{2,6},{3},{4,7}} => 5
{{1,5},{2,6},{3},{4},{7}} => 5
{{1,5,7},{2},{3,6},{4}} => 6
{{1,5},{2,7},{3,6},{4}} => 7
{{1,5},{2},{3,6,7},{4}} => 4
{{1,5},{2},{3,6},{4,7}} => 4
{{1,5},{2},{3,6},{4},{7}} => 4
{{1,5,7},{2},{3},{4,6}} => 5
{{1,5},{2,7},{3},{4,6}} => 6
{{1,5},{2},{3,7},{4,6}} => 5
{{1,5},{2},{3},{4,6,7}} => 3
{{1,5},{2},{3},{4,6},{7}} => 3
{{1,5,7},{2},{3},{4},{6}} => 5
{{1,5},{2,7},{3},{4},{6}} => 6
{{1,5},{2},{3,7},{4},{6}} => 5
{{1,5},{2},{3},{4,7},{6}} => 4
{{1,5},{2},{3},{4},{6,7}} => 3
{{1,5},{2},{3},{4},{6},{7}} => 3
{{1,6,7},{2,5},{3},{4}} => 6
{{1,6},{2,5,7},{3},{4}} => 6
{{1,6},{2,5},{3,7},{4}} => 7
{{1,6},{2,5},{3},{4,7}} => 6
{{1,6},{2,5},{3},{4},{7}} => 6
{{1,7},{2,5,6},{3},{4}} => 7
{{1},{2,5,6,7},{3},{4}} => 2
{{1},{2,5,6},{3,7},{4}} => 4
{{1},{2,5,6},{3},{4,7}} => 3
{{1},{2,5,6},{3},{4},{7}} => 2
{{1,7},{2,5},{3,6},{4}} => 8
{{1},{2,5,7},{3,6},{4}} => 5
{{1},{2,5},{3,6,7},{4}} => 3
{{1},{2,5},{3,6},{4,7}} => 3
{{1},{2,5},{3,6},{4},{7}} => 3
{{1,7},{2,5},{3},{4,6}} => 7
{{1},{2,5,7},{3},{4,6}} => 4
{{1},{2,5},{3,7},{4,6}} => 4
{{1},{2,5},{3},{4,6,7}} => 2
{{1},{2,5},{3},{4,6},{7}} => 2
{{1,7},{2,5},{3},{4},{6}} => 7
{{1},{2,5,7},{3},{4},{6}} => 4
{{1},{2,5},{3,7},{4},{6}} => 4
{{1},{2,5},{3},{4,7},{6}} => 3
{{1},{2,5},{3},{4},{6,7}} => 2
{{1},{2,5},{3},{4},{6},{7}} => 2
{{1,6,7},{2},{3,5},{4}} => 5
{{1,6},{2,7},{3,5},{4}} => 8
{{1,6},{2},{3,5,7},{4}} => 5
{{1,6},{2},{3,5},{4,7}} => 5
{{1,6},{2},{3,5},{4},{7}} => 5
{{1,7},{2,6},{3,5},{4}} => 9
{{1},{2,6,7},{3,5},{4}} => 4
{{1},{2,6},{3,5,7},{4}} => 4
{{1},{2,6},{3,5},{4,7}} => 4
{{1},{2,6},{3,5},{4},{7}} => 4
{{1,7},{2},{3,5,6},{4}} => 6
{{1},{2,7},{3,5,6},{4}} => 5
{{1},{2},{3,5,6,7},{4}} => 1
{{1},{2},{3,5,6},{4,7}} => 2
{{1},{2},{3,5,6},{4},{7}} => 1
{{1,7},{2},{3,5},{4,6}} => 6
{{1},{2,7},{3,5},{4,6}} => 5
{{1},{2},{3,5,7},{4,6}} => 3
{{1},{2},{3,5},{4,6,7}} => 1
{{1},{2},{3,5},{4,6},{7}} => 1
{{1,7},{2},{3,5},{4},{6}} => 6
{{1},{2,7},{3,5},{4},{6}} => 5
{{1},{2},{3,5,7},{4},{6}} => 3
{{1},{2},{3,5},{4,7},{6}} => 2
{{1},{2},{3,5},{4},{6,7}} => 1
{{1},{2},{3,5},{4},{6},{7}} => 1
{{1,6,7},{2},{3},{4,5}} => 4
{{1,6},{2,7},{3},{4,5}} => 7
{{1,6},{2},{3,7},{4,5}} => 6
{{1,6},{2},{3},{4,5,7}} => 4
{{1,6},{2},{3},{4,5},{7}} => 4
{{1,7},{2,6},{3},{4,5}} => 8
{{1},{2,6,7},{3},{4,5}} => 3
{{1},{2,6},{3,7},{4,5}} => 5
{{1},{2,6},{3},{4,5,7}} => 3
{{1},{2,6},{3},{4,5},{7}} => 3
{{1,7},{2},{3,6},{4,5}} => 7
{{1},{2,7},{3,6},{4,5}} => 6
{{1},{2},{3,6,7},{4,5}} => 2
{{1},{2},{3,6},{4,5,7}} => 2
{{1},{2},{3,6},{4,5},{7}} => 2
{{1,7},{2},{3},{4,5,6}} => 5
{{1},{2,7},{3},{4,5,6}} => 4
{{1},{2},{3,7},{4,5,6}} => 3
{{1},{2},{3},{4,5,6,7}} => 0
{{1},{2},{3},{4,5,6},{7}} => 0
{{1,7},{2},{3},{4,5},{6}} => 5
{{1},{2,7},{3},{4,5},{6}} => 4
{{1},{2},{3,7},{4,5},{6}} => 3
{{1},{2},{3},{4,5,7},{6}} => 2
{{1},{2},{3},{4,5},{6,7}} => 0
{{1},{2},{3},{4,5},{6},{7}} => 0
{{1,6,7},{2},{3},{4},{5}} => 4
{{1,6},{2,7},{3},{4},{5}} => 7
{{1,6},{2},{3,7},{4},{5}} => 6
{{1,6},{2},{3},{4,7},{5}} => 5
{{1,6},{2},{3},{4},{5,7}} => 4
{{1,6},{2},{3},{4},{5},{7}} => 4
{{1,7},{2,6},{3},{4},{5}} => 8
{{1},{2,6,7},{3},{4},{5}} => 3
{{1},{2,6},{3,7},{4},{5}} => 5
{{1},{2,6},{3},{4,7},{5}} => 4
{{1},{2,6},{3},{4},{5,7}} => 3
{{1},{2,6},{3},{4},{5},{7}} => 3
{{1,7},{2},{3,6},{4},{5}} => 7
{{1},{2,7},{3,6},{4},{5}} => 6
{{1},{2},{3,6,7},{4},{5}} => 2
{{1},{2},{3,6},{4,7},{5}} => 3
{{1},{2},{3,6},{4},{5,7}} => 2
{{1},{2},{3,6},{4},{5},{7}} => 2
{{1,7},{2},{3},{4,6},{5}} => 6
{{1},{2,7},{3},{4,6},{5}} => 5
{{1},{2},{3,7},{4,6},{5}} => 4
{{1},{2},{3},{4,6,7},{5}} => 1
{{1},{2},{3},{4,6},{5,7}} => 1
{{1},{2},{3},{4,6},{5},{7}} => 1
{{1,7},{2},{3},{4},{5,6}} => 5
{{1},{2,7},{3},{4},{5,6}} => 4
{{1},{2},{3,7},{4},{5,6}} => 3
{{1},{2},{3},{4,7},{5,6}} => 2
{{1},{2},{3},{4},{5,6,7}} => 0
{{1},{2},{3},{4},{5,6},{7}} => 0
{{1,7},{2},{3},{4},{5},{6}} => 5
{{1},{2,7},{3},{4},{5},{6}} => 4
{{1},{2},{3,7},{4},{5},{6}} => 3
{{1},{2},{3},{4,7},{5},{6}} => 2
{{1},{2},{3},{4},{5,7},{6}} => 1
{{1},{2},{3},{4},{5},{6,7}} => 0
{{1},{2},{3},{4},{5},{6},{7}} => 0
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Created: Oct 06, 2022 at 15:18 by Martin Rubey
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Last Updated: Oct 06, 2022 at 15:18 by Martin Rubey