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-----------------------------------------------------------------------------
Statistic identifier: St000565
-----------------------------------------------------------------------------
Collection: Set partitions
-----------------------------------------------------------------------------
Description: The major index of a set partition.
Let $\pi=B_1/B_2/\dots/B_k$ with $\min B_1<\min B_2<\dots<\min B_k$ a set partition. Let $d_i$ be the number of elements in $B_i$ larger than $\min B_{i+1}$. Then the major index of $\pi$ is $1d_1+2d_2+\dots+(k-1)d_{k-1}$.
-----------------------------------------------------------------------------
References: [1] Sagan, B. E. A maj statistic for set partitions [[MathSciNet:1087650]]
-----------------------------------------------------------------------------
Code:
def statistic(pi):
"""
sage: statistic([[1,3,8],[2],[4,6,7],[5,9]])
8
"""
pi_sorted = sorted([sorted(b) for b in pi])
l = len(pi_sorted)-1
des = [0]*l
for i in range(l):
min_next = min(pi_sorted[i+1])
des[i] = len([e for e in pi_sorted[i] if e > min_next])
return sum(i*d for i, d in enumerate(des, 1))
-----------------------------------------------------------------------------
Statistic values:
{{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}} => 1
{{1,2},{3,4}} => 0
{{1,2},{3},{4}} => 0
{{1,3,4},{2}} => 2
{{1,3},{2,4}} => 1
{{1,3},{2},{4}} => 1
{{1,4},{2,3}} => 1
{{1},{2,3,4}} => 0
{{1},{2,3},{4}} => 0
{{1,4},{2},{3}} => 1
{{1},{2,4},{3}} => 2
{{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}} => 1
{{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}} => 1
{{1,2,5},{3,4}} => 1
{{1,2},{3,4,5}} => 0
{{1,2},{3,4},{5}} => 0
{{1,2,5},{3},{4}} => 1
{{1,2},{3,5},{4}} => 2
{{1,2},{3},{4,5}} => 0
{{1,2},{3},{4},{5}} => 0
{{1,3,4,5},{2}} => 3
{{1,3,4},{2,5}} => 2
{{1,3,4},{2},{5}} => 2
{{1,3,5},{2,4}} => 2
{{1,3},{2,4,5}} => 1
{{1,3},{2,4},{5}} => 1
{{1,3,5},{2},{4}} => 2
{{1,3},{2,5},{4}} => 3
{{1,3},{2},{4,5}} => 1
{{1,3},{2},{4},{5}} => 1
{{1,4,5},{2,3}} => 2
{{1,4},{2,3,5}} => 1
{{1,4},{2,3},{5}} => 1
{{1,5},{2,3,4}} => 1
{{1},{2,3,4,5}} => 0
{{1},{2,3,4},{5}} => 0
{{1,5},{2,3},{4}} => 1
{{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}} => 1
{{1,4},{2},{3},{5}} => 1
{{1,5},{2,4},{3}} => 3
{{1},{2,4,5},{3}} => 4
{{1},{2,4},{3,5}} => 2
{{1},{2,4},{3},{5}} => 2
{{1,5},{2},{3,4}} => 1
{{1},{2,5},{3,4}} => 2
{{1},{2},{3,4,5}} => 0
{{1},{2},{3,4},{5}} => 0
{{1,5},{2},{3},{4}} => 1
{{1},{2,5},{3},{4}} => 2
{{1},{2},{3,5},{4}} => 3
{{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}} => 1
{{1,2,3,4},{5,6}} => 0
{{1,2,3,4},{5},{6}} => 0
{{1,2,3,5,6},{4}} => 2
{{1,2,3,5},{4,6}} => 1
{{1,2,3,5},{4},{6}} => 1
{{1,2,3,6},{4,5}} => 1
{{1,2,3},{4,5,6}} => 0
{{1,2,3},{4,5},{6}} => 0
{{1,2,3,6},{4},{5}} => 1
{{1,2,3},{4,6},{5}} => 2
{{1,2,3},{4},{5,6}} => 0
{{1,2,3},{4},{5},{6}} => 0
{{1,2,4,5,6},{3}} => 3
{{1,2,4,5},{3,6}} => 2
{{1,2,4,5},{3},{6}} => 2
{{1,2,4,6},{3,5}} => 2
{{1,2,4},{3,5,6}} => 1
{{1,2,4},{3,5},{6}} => 1
{{1,2,4,6},{3},{5}} => 2
{{1,2,4},{3,6},{5}} => 3
{{1,2,4},{3},{5,6}} => 1
{{1,2,4},{3},{5},{6}} => 1
{{1,2,5,6},{3,4}} => 2
{{1,2,5},{3,4,6}} => 1
{{1,2,5},{3,4},{6}} => 1
{{1,2,6},{3,4,5}} => 1
{{1,2},{3,4,5,6}} => 0
{{1,2},{3,4,5},{6}} => 0
{{1,2,6},{3,4},{5}} => 1
{{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}} => 2
{{1,2,5},{3,6},{4}} => 3
{{1,2,5},{3},{4,6}} => 1
{{1,2,5},{3},{4},{6}} => 1
{{1,2,6},{3,5},{4}} => 3
{{1,2},{3,5,6},{4}} => 4
{{1,2},{3,5},{4,6}} => 2
{{1,2},{3,5},{4},{6}} => 2
{{1,2,6},{3},{4,5}} => 1
{{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}} => 1
{{1,2},{3,6},{4},{5}} => 2
{{1,2},{3},{4,6},{5}} => 3
{{1,2},{3},{4},{5,6}} => 0
{{1,2},{3},{4},{5},{6}} => 0
{{1,3,4,5,6},{2}} => 4
{{1,3,4,5},{2,6}} => 3
{{1,3,4,5},{2},{6}} => 3
{{1,3,4,6},{2,5}} => 3
{{1,3,4},{2,5,6}} => 2
{{1,3,4},{2,5},{6}} => 2
{{1,3,4,6},{2},{5}} => 3
{{1,3,4},{2,6},{5}} => 4
{{1,3,4},{2},{5,6}} => 2
{{1,3,4},{2},{5},{6}} => 2
{{1,3,5,6},{2,4}} => 3
{{1,3,5},{2,4,6}} => 2
{{1,3,5},{2,4},{6}} => 2
{{1,3,6},{2,4,5}} => 2
{{1,3},{2,4,5,6}} => 1
{{1,3},{2,4,5},{6}} => 1
{{1,3,6},{2,4},{5}} => 2
{{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}} => 4
{{1,3,5},{2},{4,6}} => 2
{{1,3,5},{2},{4},{6}} => 2
{{1,3,6},{2,5},{4}} => 4
{{1,3},{2,5,6},{4}} => 5
{{1,3},{2,5},{4,6}} => 3
{{1,3},{2,5},{4},{6}} => 3
{{1,3,6},{2},{4,5}} => 2
{{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}} => 2
{{1,3},{2,6},{4},{5}} => 3
{{1,3},{2},{4,6},{5}} => 4
{{1,3},{2},{4},{5,6}} => 1
{{1,3},{2},{4},{5},{6}} => 1
{{1,4,5,6},{2,3}} => 3
{{1,4,5},{2,3,6}} => 2
{{1,4,5},{2,3},{6}} => 2
{{1,4,6},{2,3,5}} => 2
{{1,4},{2,3,5,6}} => 1
{{1,4},{2,3,5},{6}} => 1
{{1,4,6},{2,3},{5}} => 2
{{1,4},{2,3,6},{5}} => 3
{{1,4},{2,3},{5,6}} => 1
{{1,4},{2,3},{5},{6}} => 1
{{1,5,6},{2,3,4}} => 2
{{1,5},{2,3,4,6}} => 1
{{1,5},{2,3,4},{6}} => 1
{{1,6},{2,3,4,5}} => 1
{{1},{2,3,4,5,6}} => 0
{{1},{2,3,4,5},{6}} => 0
{{1,6},{2,3,4},{5}} => 1
{{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}} => 2
{{1,5},{2,3,6},{4}} => 3
{{1,5},{2,3},{4,6}} => 1
{{1,5},{2,3},{4},{6}} => 1
{{1,6},{2,3,5},{4}} => 3
{{1},{2,3,5,6},{4}} => 4
{{1},{2,3,5},{4,6}} => 2
{{1},{2,3,5},{4},{6}} => 2
{{1,6},{2,3},{4,5}} => 1
{{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}} => 1
{{1},{2,3,6},{4},{5}} => 2
{{1},{2,3},{4,6},{5}} => 3
{{1},{2,3},{4},{5,6}} => 0
{{1},{2,3},{4},{5},{6}} => 0
{{1,4,5,6},{2},{3}} => 3
{{1,4,5},{2,6},{3}} => 4
{{1,4,5},{2},{3,6}} => 2
{{1,4,5},{2},{3},{6}} => 2
{{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}} => 3
{{1,4,6},{2},{3,5}} => 2
{{1,4},{2,6},{3,5}} => 3
{{1,4},{2},{3,5,6}} => 1
{{1,4},{2},{3,5},{6}} => 1
{{1,4,6},{2},{3},{5}} => 2
{{1,4},{2,6},{3},{5}} => 3
{{1,4},{2},{3,6},{5}} => 4
{{1,4},{2},{3},{5,6}} => 1
{{1,4},{2},{3},{5},{6}} => 1
{{1,5,6},{2,4},{3}} => 4
{{1,5},{2,4,6},{3}} => 5
{{1,5},{2,4},{3,6}} => 3
{{1,5},{2,4},{3},{6}} => 3
{{1,6},{2,4,5},{3}} => 5
{{1},{2,4,5,6},{3}} => 6
{{1},{2,4,5},{3,6}} => 4
{{1},{2,4,5},{3},{6}} => 4
{{1,6},{2,4},{3,5}} => 3
{{1},{2,4,6},{3,5}} => 4
{{1},{2,4},{3,5,6}} => 2
{{1},{2,4},{3,5},{6}} => 2
{{1,6},{2,4},{3},{5}} => 3
{{1},{2,4,6},{3},{5}} => 4
{{1},{2,4},{3,6},{5}} => 5
{{1},{2,4},{3},{5,6}} => 2
{{1},{2,4},{3},{5},{6}} => 2
{{1,5,6},{2},{3,4}} => 2
{{1,5},{2,6},{3,4}} => 3
{{1,5},{2},{3,4,6}} => 1
{{1,5},{2},{3,4},{6}} => 1
{{1,6},{2,5},{3,4}} => 3
{{1},{2,5,6},{3,4}} => 4
{{1},{2,5},{3,4,6}} => 2
{{1},{2,5},{3,4},{6}} => 2
{{1,6},{2},{3,4,5}} => 1
{{1},{2,6},{3,4,5}} => 2
{{1},{2},{3,4,5,6}} => 0
{{1},{2},{3,4,5},{6}} => 0
{{1,6},{2},{3,4},{5}} => 1
{{1},{2,6},{3,4},{5}} => 2
{{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}} => 2
{{1,5},{2,6},{3},{4}} => 3
{{1,5},{2},{3,6},{4}} => 4
{{1,5},{2},{3},{4,6}} => 1
{{1,5},{2},{3},{4},{6}} => 1
{{1,6},{2,5},{3},{4}} => 3
{{1},{2,5,6},{3},{4}} => 4
{{1},{2,5},{3,6},{4}} => 5
{{1},{2,5},{3},{4,6}} => 2
{{1},{2,5},{3},{4},{6}} => 2
{{1,6},{2},{3,5},{4}} => 4
{{1},{2,6},{3,5},{4}} => 5
{{1},{2},{3,5,6},{4}} => 6
{{1},{2},{3,5},{4,6}} => 3
{{1},{2},{3,5},{4},{6}} => 3
{{1,6},{2},{3},{4,5}} => 1
{{1},{2,6},{3},{4,5}} => 2
{{1},{2},{3,6},{4,5}} => 3
{{1},{2},{3},{4,5,6}} => 0
{{1},{2},{3},{4,5},{6}} => 0
{{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}} => 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}} => 1
{{1,2,3,4,5},{6,7}} => 0
{{1,2,3,4,5},{6},{7}} => 0
{{1,2,3,4,6,7},{5}} => 2
{{1,2,3,4,6},{5,7}} => 1
{{1,2,3,4,6},{5},{7}} => 1
{{1,2,3,4,7},{5,6}} => 1
{{1,2,3,4},{5,6,7}} => 0
{{1,2,3,4},{5,6},{7}} => 0
{{1,2,3,4,7},{5},{6}} => 1
{{1,2,3,4},{5,7},{6}} => 2
{{1,2,3,4},{5},{6,7}} => 0
{{1,2,3,4},{5},{6},{7}} => 0
{{1,2,3,5,6,7},{4}} => 3
{{1,2,3,5,6},{4,7}} => 2
{{1,2,3,5,6},{4},{7}} => 2
{{1,2,3,5,7},{4,6}} => 2
{{1,2,3,5},{4,6,7}} => 1
{{1,2,3,5},{4,6},{7}} => 1
{{1,2,3,5,7},{4},{6}} => 2
{{1,2,3,5},{4,7},{6}} => 3
{{1,2,3,5},{4},{6,7}} => 1
{{1,2,3,5},{4},{6},{7}} => 1
{{1,2,3,6,7},{4,5}} => 2
{{1,2,3,6},{4,5,7}} => 1
{{1,2,3,6},{4,5},{7}} => 1
{{1,2,3,7},{4,5,6}} => 1
{{1,2,3},{4,5,6,7}} => 0
{{1,2,3},{4,5,6},{7}} => 0
{{1,2,3,7},{4,5},{6}} => 1
{{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}} => 2
{{1,2,3,6},{4,7},{5}} => 3
{{1,2,3,6},{4},{5,7}} => 1
{{1,2,3,6},{4},{5},{7}} => 1
{{1,2,3,7},{4,6},{5}} => 3
{{1,2,3},{4,6,7},{5}} => 4
{{1,2,3},{4,6},{5,7}} => 2
{{1,2,3},{4,6},{5},{7}} => 2
{{1,2,3,7},{4},{5,6}} => 1
{{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}} => 1
{{1,2,3},{4,7},{5},{6}} => 2
{{1,2,3},{4},{5,7},{6}} => 3
{{1,2,3},{4},{5},{6,7}} => 0
{{1,2,3},{4},{5},{6},{7}} => 0
{{1,2,4,5,6,7},{3}} => 4
{{1,2,4,5,6},{3,7}} => 3
{{1,2,4,5,6},{3},{7}} => 3
{{1,2,4,5,7},{3,6}} => 3
{{1,2,4,5},{3,6,7}} => 2
{{1,2,4,5},{3,6},{7}} => 2
{{1,2,4,5,7},{3},{6}} => 3
{{1,2,4,5},{3,7},{6}} => 4
{{1,2,4,5},{3},{6,7}} => 2
{{1,2,4,5},{3},{6},{7}} => 2
{{1,2,4,6,7},{3,5}} => 3
{{1,2,4,6},{3,5,7}} => 2
{{1,2,4,6},{3,5},{7}} => 2
{{1,2,4,7},{3,5,6}} => 2
{{1,2,4},{3,5,6,7}} => 1
{{1,2,4},{3,5,6},{7}} => 1
{{1,2,4,7},{3,5},{6}} => 2
{{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}} => 3
{{1,2,4,6},{3,7},{5}} => 4
{{1,2,4,6},{3},{5,7}} => 2
{{1,2,4,6},{3},{5},{7}} => 2
{{1,2,4,7},{3,6},{5}} => 4
{{1,2,4},{3,6,7},{5}} => 5
{{1,2,4},{3,6},{5,7}} => 3
{{1,2,4},{3,6},{5},{7}} => 3
{{1,2,4,7},{3},{5,6}} => 2
{{1,2,4},{3,7},{5,6}} => 3
{{1,2,4},{3},{5,6,7}} => 1
{{1,2,4},{3},{5,6},{7}} => 1
{{1,2,4,7},{3},{5},{6}} => 2
{{1,2,4},{3,7},{5},{6}} => 3
{{1,2,4},{3},{5,7},{6}} => 4
{{1,2,4},{3},{5},{6,7}} => 1
{{1,2,4},{3},{5},{6},{7}} => 1
{{1,2,5,6,7},{3,4}} => 3
{{1,2,5,6},{3,4,7}} => 2
{{1,2,5,6},{3,4},{7}} => 2
{{1,2,5,7},{3,4,6}} => 2
{{1,2,5},{3,4,6,7}} => 1
{{1,2,5},{3,4,6},{7}} => 1
{{1,2,5,7},{3,4},{6}} => 2
{{1,2,5},{3,4,7},{6}} => 3
{{1,2,5},{3,4},{6,7}} => 1
{{1,2,5},{3,4},{6},{7}} => 1
{{1,2,6,7},{3,4,5}} => 2
{{1,2,6},{3,4,5,7}} => 1
{{1,2,6},{3,4,5},{7}} => 1
{{1,2,7},{3,4,5,6}} => 1
{{1,2},{3,4,5,6,7}} => 0
{{1,2},{3,4,5,6},{7}} => 0
{{1,2,7},{3,4,5},{6}} => 1
{{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}} => 2
{{1,2,6},{3,4,7},{5}} => 3
{{1,2,6},{3,4},{5,7}} => 1
{{1,2,6},{3,4},{5},{7}} => 1
{{1,2,7},{3,4,6},{5}} => 3
{{1,2},{3,4,6,7},{5}} => 4
{{1,2},{3,4,6},{5,7}} => 2
{{1,2},{3,4,6},{5},{7}} => 2
{{1,2,7},{3,4},{5,6}} => 1
{{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}} => 1
{{1,2},{3,4,7},{5},{6}} => 2
{{1,2},{3,4},{5,7},{6}} => 3
{{1,2},{3,4},{5},{6,7}} => 0
{{1,2},{3,4},{5},{6},{7}} => 0
{{1,2,5,6,7},{3},{4}} => 3
{{1,2,5,6},{3,7},{4}} => 4
{{1,2,5,6},{3},{4,7}} => 2
{{1,2,5,6},{3},{4},{7}} => 2
{{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}} => 3
{{1,2,5,7},{3},{4,6}} => 2
{{1,2,5},{3,7},{4,6}} => 3
{{1,2,5},{3},{4,6,7}} => 1
{{1,2,5},{3},{4,6},{7}} => 1
{{1,2,5,7},{3},{4},{6}} => 2
{{1,2,5},{3,7},{4},{6}} => 3
{{1,2,5},{3},{4,7},{6}} => 4
{{1,2,5},{3},{4},{6,7}} => 1
{{1,2,5},{3},{4},{6},{7}} => 1
{{1,2,6,7},{3,5},{4}} => 4
{{1,2,6},{3,5,7},{4}} => 5
{{1,2,6},{3,5},{4,7}} => 3
{{1,2,6},{3,5},{4},{7}} => 3
{{1,2,7},{3,5,6},{4}} => 5
{{1,2},{3,5,6,7},{4}} => 6
{{1,2},{3,5,6},{4,7}} => 4
{{1,2},{3,5,6},{4},{7}} => 4
{{1,2,7},{3,5},{4,6}} => 3
{{1,2},{3,5,7},{4,6}} => 4
{{1,2},{3,5},{4,6,7}} => 2
{{1,2},{3,5},{4,6},{7}} => 2
{{1,2,7},{3,5},{4},{6}} => 3
{{1,2},{3,5,7},{4},{6}} => 4
{{1,2},{3,5},{4,7},{6}} => 5
{{1,2},{3,5},{4},{6,7}} => 2
{{1,2},{3,5},{4},{6},{7}} => 2
{{1,2,6,7},{3},{4,5}} => 2
{{1,2,6},{3,7},{4,5}} => 3
{{1,2,6},{3},{4,5,7}} => 1
{{1,2,6},{3},{4,5},{7}} => 1
{{1,2,7},{3,6},{4,5}} => 3
{{1,2},{3,6,7},{4,5}} => 4
{{1,2},{3,6},{4,5,7}} => 2
{{1,2},{3,6},{4,5},{7}} => 2
{{1,2,7},{3},{4,5,6}} => 1
{{1,2},{3,7},{4,5,6}} => 2
{{1,2},{3},{4,5,6,7}} => 0
{{1,2},{3},{4,5,6},{7}} => 0
{{1,2,7},{3},{4,5},{6}} => 1
{{1,2},{3,7},{4,5},{6}} => 2
{{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}} => 2
{{1,2,6},{3,7},{4},{5}} => 3
{{1,2,6},{3},{4,7},{5}} => 4
{{1,2,6},{3},{4},{5,7}} => 1
{{1,2,6},{3},{4},{5},{7}} => 1
{{1,2,7},{3,6},{4},{5}} => 3
{{1,2},{3,6,7},{4},{5}} => 4
{{1,2},{3,6},{4,7},{5}} => 5
{{1,2},{3,6},{4},{5,7}} => 2
{{1,2},{3,6},{4},{5},{7}} => 2
{{1,2,7},{3},{4,6},{5}} => 4
{{1,2},{3,7},{4,6},{5}} => 5
{{1,2},{3},{4,6,7},{5}} => 6
{{1,2},{3},{4,6},{5,7}} => 3
{{1,2},{3},{4,6},{5},{7}} => 3
{{1,2,7},{3},{4},{5,6}} => 1
{{1,2},{3,7},{4},{5,6}} => 2
{{1,2},{3},{4,7},{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}} => 1
{{1,2},{3,7},{4},{5},{6}} => 2
{{1,2},{3},{4,7},{5},{6}} => 3
{{1,2},{3},{4},{5,7},{6}} => 4
{{1,2},{3},{4},{5},{6,7}} => 0
{{1,2},{3},{4},{5},{6},{7}} => 0
{{1,3,4,5,6,7},{2}} => 5
{{1,3,4,5,6},{2,7}} => 4
{{1,3,4,5,6},{2},{7}} => 4
{{1,3,4,5,7},{2,6}} => 4
{{1,3,4,5},{2,6,7}} => 3
{{1,3,4,5},{2,6},{7}} => 3
{{1,3,4,5,7},{2},{6}} => 4
{{1,3,4,5},{2,7},{6}} => 5
{{1,3,4,5},{2},{6,7}} => 3
{{1,3,4,5},{2},{6},{7}} => 3
{{1,3,4,6,7},{2,5}} => 4
{{1,3,4,6},{2,5,7}} => 3
{{1,3,4,6},{2,5},{7}} => 3
{{1,3,4,7},{2,5,6}} => 3
{{1,3,4},{2,5,6,7}} => 2
{{1,3,4},{2,5,6},{7}} => 2
{{1,3,4,7},{2,5},{6}} => 3
{{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}} => 5
{{1,3,4,6},{2},{5,7}} => 3
{{1,3,4,6},{2},{5},{7}} => 3
{{1,3,4,7},{2,6},{5}} => 5
{{1,3,4},{2,6,7},{5}} => 6
{{1,3,4},{2,6},{5,7}} => 4
{{1,3,4},{2,6},{5},{7}} => 4
{{1,3,4,7},{2},{5,6}} => 3
{{1,3,4},{2,7},{5,6}} => 4
{{1,3,4},{2},{5,6,7}} => 2
{{1,3,4},{2},{5,6},{7}} => 2
{{1,3,4,7},{2},{5},{6}} => 3
{{1,3,4},{2,7},{5},{6}} => 4
{{1,3,4},{2},{5,7},{6}} => 5
{{1,3,4},{2},{5},{6,7}} => 2
{{1,3,4},{2},{5},{6},{7}} => 2
{{1,3,5,6,7},{2,4}} => 4
{{1,3,5,6},{2,4,7}} => 3
{{1,3,5,6},{2,4},{7}} => 3
{{1,3,5,7},{2,4,6}} => 3
{{1,3,5},{2,4,6,7}} => 2
{{1,3,5},{2,4,6},{7}} => 2
{{1,3,5,7},{2,4},{6}} => 3
{{1,3,5},{2,4,7},{6}} => 4
{{1,3,5},{2,4},{6,7}} => 2
{{1,3,5},{2,4},{6},{7}} => 2
{{1,3,6,7},{2,4,5}} => 3
{{1,3,6},{2,4,5,7}} => 2
{{1,3,6},{2,4,5},{7}} => 2
{{1,3,7},{2,4,5,6}} => 2
{{1,3},{2,4,5,6,7}} => 1
{{1,3},{2,4,5,6},{7}} => 1
{{1,3,7},{2,4,5},{6}} => 2
{{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}} => 3
{{1,3,6},{2,4,7},{5}} => 4
{{1,3,6},{2,4},{5,7}} => 2
{{1,3,6},{2,4},{5},{7}} => 2
{{1,3,7},{2,4,6},{5}} => 4
{{1,3},{2,4,6,7},{5}} => 5
{{1,3},{2,4,6},{5,7}} => 3
{{1,3},{2,4,6},{5},{7}} => 3
{{1,3,7},{2,4},{5,6}} => 2
{{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}} => 2
{{1,3},{2,4,7},{5},{6}} => 3
{{1,3},{2,4},{5,7},{6}} => 4
{{1,3},{2,4},{5},{6,7}} => 1
{{1,3},{2,4},{5},{6},{7}} => 1
{{1,3,5,6,7},{2},{4}} => 4
{{1,3,5,6},{2,7},{4}} => 5
{{1,3,5,6},{2},{4,7}} => 3
{{1,3,5,6},{2},{4},{7}} => 3
{{1,3,5,7},{2,6},{4}} => 5
{{1,3,5},{2,6,7},{4}} => 6
{{1,3,5},{2,6},{4,7}} => 4
{{1,3,5},{2,6},{4},{7}} => 4
{{1,3,5,7},{2},{4,6}} => 3
{{1,3,5},{2,7},{4,6}} => 4
{{1,3,5},{2},{4,6,7}} => 2
{{1,3,5},{2},{4,6},{7}} => 2
{{1,3,5,7},{2},{4},{6}} => 3
{{1,3,5},{2,7},{4},{6}} => 4
{{1,3,5},{2},{4,7},{6}} => 5
{{1,3,5},{2},{4},{6,7}} => 2
{{1,3,5},{2},{4},{6},{7}} => 2
{{1,3,6,7},{2,5},{4}} => 5
{{1,3,6},{2,5,7},{4}} => 6
{{1,3,6},{2,5},{4,7}} => 4
{{1,3,6},{2,5},{4},{7}} => 4
{{1,3,7},{2,5,6},{4}} => 6
{{1,3},{2,5,6,7},{4}} => 7
{{1,3},{2,5,6},{4,7}} => 5
{{1,3},{2,5,6},{4},{7}} => 5
{{1,3,7},{2,5},{4,6}} => 4
{{1,3},{2,5,7},{4,6}} => 5
{{1,3},{2,5},{4,6,7}} => 3
{{1,3},{2,5},{4,6},{7}} => 3
{{1,3,7},{2,5},{4},{6}} => 4
{{1,3},{2,5,7},{4},{6}} => 5
{{1,3},{2,5},{4,7},{6}} => 6
{{1,3},{2,5},{4},{6,7}} => 3
{{1,3},{2,5},{4},{6},{7}} => 3
{{1,3,6,7},{2},{4,5}} => 3
{{1,3,6},{2,7},{4,5}} => 4
{{1,3,6},{2},{4,5,7}} => 2
{{1,3,6},{2},{4,5},{7}} => 2
{{1,3,7},{2,6},{4,5}} => 4
{{1,3},{2,6,7},{4,5}} => 5
{{1,3},{2,6},{4,5,7}} => 3
{{1,3},{2,6},{4,5},{7}} => 3
{{1,3,7},{2},{4,5,6}} => 2
{{1,3},{2,7},{4,5,6}} => 3
{{1,3},{2},{4,5,6,7}} => 1
{{1,3},{2},{4,5,6},{7}} => 1
{{1,3,7},{2},{4,5},{6}} => 2
{{1,3},{2,7},{4,5},{6}} => 3
{{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}} => 3
{{1,3,6},{2,7},{4},{5}} => 4
{{1,3,6},{2},{4,7},{5}} => 5
{{1,3,6},{2},{4},{5,7}} => 2
{{1,3,6},{2},{4},{5},{7}} => 2
{{1,3,7},{2,6},{4},{5}} => 4
{{1,3},{2,6,7},{4},{5}} => 5
{{1,3},{2,6},{4,7},{5}} => 6
{{1,3},{2,6},{4},{5,7}} => 3
{{1,3},{2,6},{4},{5},{7}} => 3
{{1,3,7},{2},{4,6},{5}} => 5
{{1,3},{2,7},{4,6},{5}} => 6
{{1,3},{2},{4,6,7},{5}} => 7
{{1,3},{2},{4,6},{5,7}} => 4
{{1,3},{2},{4,6},{5},{7}} => 4
{{1,3,7},{2},{4},{5,6}} => 2
{{1,3},{2,7},{4},{5,6}} => 3
{{1,3},{2},{4,7},{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}} => 2
{{1,3},{2,7},{4},{5},{6}} => 3
{{1,3},{2},{4,7},{5},{6}} => 4
{{1,3},{2},{4},{5,7},{6}} => 5
{{1,3},{2},{4},{5},{6,7}} => 1
{{1,3},{2},{4},{5},{6},{7}} => 1
{{1,4,5,6,7},{2,3}} => 4
{{1,4,5,6},{2,3,7}} => 3
{{1,4,5,6},{2,3},{7}} => 3
{{1,4,5,7},{2,3,6}} => 3
{{1,4,5},{2,3,6,7}} => 2
{{1,4,5},{2,3,6},{7}} => 2
{{1,4,5,7},{2,3},{6}} => 3
{{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},{2,3,5}} => 3
{{1,4,6},{2,3,5,7}} => 2
{{1,4,6},{2,3,5},{7}} => 2
{{1,4,7},{2,3,5,6}} => 2
{{1,4},{2,3,5,6,7}} => 1
{{1,4},{2,3,5,6},{7}} => 1
{{1,4,7},{2,3,5},{6}} => 2
{{1,4},{2,3,5,7},{6}} => 3
{{1,4},{2,3,5},{6,7}} => 1
{{1,4},{2,3,5},{6},{7}} => 1
{{1,4,6,7},{2,3},{5}} => 3
{{1,4,6},{2,3,7},{5}} => 4
{{1,4,6},{2,3},{5,7}} => 2
{{1,4,6},{2,3},{5},{7}} => 2
{{1,4,7},{2,3,6},{5}} => 4
{{1,4},{2,3,6,7},{5}} => 5
{{1,4},{2,3,6},{5,7}} => 3
{{1,4},{2,3,6},{5},{7}} => 3
{{1,4,7},{2,3},{5,6}} => 2
{{1,4},{2,3,7},{5,6}} => 3
{{1,4},{2,3},{5,6,7}} => 1
{{1,4},{2,3},{5,6},{7}} => 1
{{1,4,7},{2,3},{5},{6}} => 2
{{1,4},{2,3,7},{5},{6}} => 3
{{1,4},{2,3},{5,7},{6}} => 4
{{1,4},{2,3},{5},{6,7}} => 1
{{1,4},{2,3},{5},{6},{7}} => 1
{{1,5,6,7},{2,3,4}} => 3
{{1,5,6},{2,3,4,7}} => 2
{{1,5,6},{2,3,4},{7}} => 2
{{1,5,7},{2,3,4,6}} => 2
{{1,5},{2,3,4,6,7}} => 1
{{1,5},{2,3,4,6},{7}} => 1
{{1,5,7},{2,3,4},{6}} => 2
{{1,5},{2,3,4,7},{6}} => 3
{{1,5},{2,3,4},{6,7}} => 1
{{1,5},{2,3,4},{6},{7}} => 1
{{1,6,7},{2,3,4,5}} => 2
{{1,6},{2,3,4,5,7}} => 1
{{1,6},{2,3,4,5},{7}} => 1
{{1,7},{2,3,4,5,6}} => 1
{{1},{2,3,4,5,6,7}} => 0
{{1},{2,3,4,5,6},{7}} => 0
{{1,7},{2,3,4,5},{6}} => 1
{{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}} => 2
{{1,6},{2,3,4,7},{5}} => 3
{{1,6},{2,3,4},{5,7}} => 1
{{1,6},{2,3,4},{5},{7}} => 1
{{1,7},{2,3,4,6},{5}} => 3
{{1},{2,3,4,6,7},{5}} => 4
{{1},{2,3,4,6},{5,7}} => 2
{{1},{2,3,4,6},{5},{7}} => 2
{{1,7},{2,3,4},{5,6}} => 1
{{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}} => 1
{{1},{2,3,4,7},{5},{6}} => 2
{{1},{2,3,4},{5,7},{6}} => 3
{{1},{2,3,4},{5},{6,7}} => 0
{{1},{2,3,4},{5},{6},{7}} => 0
{{1,5,6,7},{2,3},{4}} => 3
{{1,5,6},{2,3,7},{4}} => 4
{{1,5,6},{2,3},{4,7}} => 2
{{1,5,6},{2,3},{4},{7}} => 2
{{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}} => 3
{{1,5,7},{2,3},{4,6}} => 2
{{1,5},{2,3,7},{4,6}} => 3
{{1,5},{2,3},{4,6,7}} => 1
{{1,5},{2,3},{4,6},{7}} => 1
{{1,5,7},{2,3},{4},{6}} => 2
{{1,5},{2,3,7},{4},{6}} => 3
{{1,5},{2,3},{4,7},{6}} => 4
{{1,5},{2,3},{4},{6,7}} => 1
{{1,5},{2,3},{4},{6},{7}} => 1
{{1,6,7},{2,3,5},{4}} => 4
{{1,6},{2,3,5,7},{4}} => 5
{{1,6},{2,3,5},{4,7}} => 3
{{1,6},{2,3,5},{4},{7}} => 3
{{1,7},{2,3,5,6},{4}} => 5
{{1},{2,3,5,6,7},{4}} => 6
{{1},{2,3,5,6},{4,7}} => 4
{{1},{2,3,5,6},{4},{7}} => 4
{{1,7},{2,3,5},{4,6}} => 3
{{1},{2,3,5,7},{4,6}} => 4
{{1},{2,3,5},{4,6,7}} => 2
{{1},{2,3,5},{4,6},{7}} => 2
{{1,7},{2,3,5},{4},{6}} => 3
{{1},{2,3,5,7},{4},{6}} => 4
{{1},{2,3,5},{4,7},{6}} => 5
{{1},{2,3,5},{4},{6,7}} => 2
{{1},{2,3,5},{4},{6},{7}} => 2
{{1,6,7},{2,3},{4,5}} => 2
{{1,6},{2,3,7},{4,5}} => 3
{{1,6},{2,3},{4,5,7}} => 1
{{1,6},{2,3},{4,5},{7}} => 1
{{1,7},{2,3,6},{4,5}} => 3
{{1},{2,3,6,7},{4,5}} => 4
{{1},{2,3,6},{4,5,7}} => 2
{{1},{2,3,6},{4,5},{7}} => 2
{{1,7},{2,3},{4,5,6}} => 1
{{1},{2,3,7},{4,5,6}} => 2
{{1},{2,3},{4,5,6,7}} => 0
{{1},{2,3},{4,5,6},{7}} => 0
{{1,7},{2,3},{4,5},{6}} => 1
{{1},{2,3,7},{4,5},{6}} => 2
{{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}} => 2
{{1,6},{2,3,7},{4},{5}} => 3
{{1,6},{2,3},{4,7},{5}} => 4
{{1,6},{2,3},{4},{5,7}} => 1
{{1,6},{2,3},{4},{5},{7}} => 1
{{1,7},{2,3,6},{4},{5}} => 3
{{1},{2,3,6,7},{4},{5}} => 4
{{1},{2,3,6},{4,7},{5}} => 5
{{1},{2,3,6},{4},{5,7}} => 2
{{1},{2,3,6},{4},{5},{7}} => 2
{{1,7},{2,3},{4,6},{5}} => 4
{{1},{2,3,7},{4,6},{5}} => 5
{{1},{2,3},{4,6,7},{5}} => 6
{{1},{2,3},{4,6},{5,7}} => 3
{{1},{2,3},{4,6},{5},{7}} => 3
{{1,7},{2,3},{4},{5,6}} => 1
{{1},{2,3,7},{4},{5,6}} => 2
{{1},{2,3},{4,7},{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}} => 1
{{1},{2,3,7},{4},{5},{6}} => 2
{{1},{2,3},{4,7},{5},{6}} => 3
{{1},{2,3},{4},{5,7},{6}} => 4
{{1},{2,3},{4},{5},{6,7}} => 0
{{1},{2,3},{4},{5},{6},{7}} => 0
{{1,4,5,6,7},{2},{3}} => 4
{{1,4,5,6},{2,7},{3}} => 5
{{1,4,5,6},{2},{3,7}} => 3
{{1,4,5,6},{2},{3},{7}} => 3
{{1,4,5,7},{2,6},{3}} => 5
{{1,4,5},{2,6,7},{3}} => 6
{{1,4,5},{2,6},{3,7}} => 4
{{1,4,5},{2,6},{3},{7}} => 4
{{1,4,5,7},{2},{3,6}} => 3
{{1,4,5},{2,7},{3,6}} => 4
{{1,4,5},{2},{3,6,7}} => 2
{{1,4,5},{2},{3,6},{7}} => 2
{{1,4,5,7},{2},{3},{6}} => 3
{{1,4,5},{2,7},{3},{6}} => 4
{{1,4,5},{2},{3,7},{6}} => 5
{{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}} => 6
{{1,4,6},{2,5},{3,7}} => 4
{{1,4,6},{2,5},{3},{7}} => 4
{{1,4,7},{2,5,6},{3}} => 6
{{1,4},{2,5,6,7},{3}} => 7
{{1,4},{2,5,6},{3,7}} => 5
{{1,4},{2,5,6},{3},{7}} => 5
{{1,4,7},{2,5},{3,6}} => 4
{{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}} => 4
{{1,4},{2,5,7},{3},{6}} => 5
{{1,4},{2,5},{3,7},{6}} => 6
{{1,4},{2,5},{3},{6,7}} => 3
{{1,4},{2,5},{3},{6},{7}} => 3
{{1,4,6,7},{2},{3,5}} => 3
{{1,4,6},{2,7},{3,5}} => 4
{{1,4,6},{2},{3,5,7}} => 2
{{1,4,6},{2},{3,5},{7}} => 2
{{1,4,7},{2,6},{3,5}} => 4
{{1,4},{2,6,7},{3,5}} => 5
{{1,4},{2,6},{3,5,7}} => 3
{{1,4},{2,6},{3,5},{7}} => 3
{{1,4,7},{2},{3,5,6}} => 2
{{1,4},{2,7},{3,5,6}} => 3
{{1,4},{2},{3,5,6,7}} => 1
{{1,4},{2},{3,5,6},{7}} => 1
{{1,4,7},{2},{3,5},{6}} => 2
{{1,4},{2,7},{3,5},{6}} => 3
{{1,4},{2},{3,5,7},{6}} => 4
{{1,4},{2},{3,5},{6,7}} => 1
{{1,4},{2},{3,5},{6},{7}} => 1
{{1,4,6,7},{2},{3},{5}} => 3
{{1,4,6},{2,7},{3},{5}} => 4
{{1,4,6},{2},{3,7},{5}} => 5
{{1,4,6},{2},{3},{5,7}} => 2
{{1,4,6},{2},{3},{5},{7}} => 2
{{1,4,7},{2,6},{3},{5}} => 4
{{1,4},{2,6,7},{3},{5}} => 5
{{1,4},{2,6},{3,7},{5}} => 6
{{1,4},{2,6},{3},{5,7}} => 3
{{1,4},{2,6},{3},{5},{7}} => 3
{{1,4,7},{2},{3,6},{5}} => 5
{{1,4},{2,7},{3,6},{5}} => 6
{{1,4},{2},{3,6,7},{5}} => 7
{{1,4},{2},{3,6},{5,7}} => 4
{{1,4},{2},{3,6},{5},{7}} => 4
{{1,4,7},{2},{3},{5,6}} => 2
{{1,4},{2,7},{3},{5,6}} => 3
{{1,4},{2},{3,7},{5,6}} => 4
{{1,4},{2},{3},{5,6,7}} => 1
{{1,4},{2},{3},{5,6},{7}} => 1
{{1,4,7},{2},{3},{5},{6}} => 2
{{1,4},{2,7},{3},{5},{6}} => 3
{{1,4},{2},{3,7},{5},{6}} => 4
{{1,4},{2},{3},{5,7},{6}} => 5
{{1,4},{2},{3},{5},{6,7}} => 1
{{1,4},{2},{3},{5},{6},{7}} => 1
{{1,5,6,7},{2,4},{3}} => 5
{{1,5,6},{2,4,7},{3}} => 6
{{1,5,6},{2,4},{3,7}} => 4
{{1,5,6},{2,4},{3},{7}} => 4
{{1,5,7},{2,4,6},{3}} => 6
{{1,5},{2,4,6,7},{3}} => 7
{{1,5},{2,4,6},{3,7}} => 5
{{1,5},{2,4,6},{3},{7}} => 5
{{1,5,7},{2,4},{3,6}} => 4
{{1,5},{2,4,7},{3,6}} => 5
{{1,5},{2,4},{3,6,7}} => 3
{{1,5},{2,4},{3,6},{7}} => 3
{{1,5,7},{2,4},{3},{6}} => 4
{{1,5},{2,4,7},{3},{6}} => 5
{{1,5},{2,4},{3,7},{6}} => 6
{{1,5},{2,4},{3},{6,7}} => 3
{{1,5},{2,4},{3},{6},{7}} => 3
{{1,6,7},{2,4,5},{3}} => 6
{{1,6},{2,4,5,7},{3}} => 7
{{1,6},{2,4,5},{3,7}} => 5
{{1,6},{2,4,5},{3},{7}} => 5
{{1,7},{2,4,5,6},{3}} => 7
{{1},{2,4,5,6,7},{3}} => 8
{{1},{2,4,5,6},{3,7}} => 6
{{1},{2,4,5,6},{3},{7}} => 6
{{1,7},{2,4,5},{3,6}} => 5
{{1},{2,4,5,7},{3,6}} => 6
{{1},{2,4,5},{3,6,7}} => 4
{{1},{2,4,5},{3,6},{7}} => 4
{{1,7},{2,4,5},{3},{6}} => 5
{{1},{2,4,5,7},{3},{6}} => 6
{{1},{2,4,5},{3,7},{6}} => 7
{{1},{2,4,5},{3},{6,7}} => 4
{{1},{2,4,5},{3},{6},{7}} => 4
{{1,6,7},{2,4},{3,5}} => 4
{{1,6},{2,4,7},{3,5}} => 5
{{1,6},{2,4},{3,5,7}} => 3
{{1,6},{2,4},{3,5},{7}} => 3
{{1,7},{2,4,6},{3,5}} => 5
{{1},{2,4,6,7},{3,5}} => 6
{{1},{2,4,6},{3,5,7}} => 4
{{1},{2,4,6},{3,5},{7}} => 4
{{1,7},{2,4},{3,5,6}} => 3
{{1},{2,4,7},{3,5,6}} => 4
{{1},{2,4},{3,5,6,7}} => 2
{{1},{2,4},{3,5,6},{7}} => 2
{{1,7},{2,4},{3,5},{6}} => 3
{{1},{2,4,7},{3,5},{6}} => 4
{{1},{2,4},{3,5,7},{6}} => 5
{{1},{2,4},{3,5},{6,7}} => 2
{{1},{2,4},{3,5},{6},{7}} => 2
{{1,6,7},{2,4},{3},{5}} => 4
{{1,6},{2,4,7},{3},{5}} => 5
{{1,6},{2,4},{3,7},{5}} => 6
{{1,6},{2,4},{3},{5,7}} => 3
{{1,6},{2,4},{3},{5},{7}} => 3
{{1,7},{2,4,6},{3},{5}} => 5
{{1},{2,4,6,7},{3},{5}} => 6
{{1},{2,4,6},{3,7},{5}} => 7
{{1},{2,4,6},{3},{5,7}} => 4
{{1},{2,4,6},{3},{5},{7}} => 4
{{1,7},{2,4},{3,6},{5}} => 6
{{1},{2,4,7},{3,6},{5}} => 7
{{1},{2,4},{3,6,7},{5}} => 8
{{1},{2,4},{3,6},{5,7}} => 5
{{1},{2,4},{3,6},{5},{7}} => 5
{{1,7},{2,4},{3},{5,6}} => 3
{{1},{2,4,7},{3},{5,6}} => 4
{{1},{2,4},{3,7},{5,6}} => 5
{{1},{2,4},{3},{5,6,7}} => 2
{{1},{2,4},{3},{5,6},{7}} => 2
{{1,7},{2,4},{3},{5},{6}} => 3
{{1},{2,4,7},{3},{5},{6}} => 4
{{1},{2,4},{3,7},{5},{6}} => 5
{{1},{2,4},{3},{5,7},{6}} => 6
{{1},{2,4},{3},{5},{6,7}} => 2
{{1},{2,4},{3},{5},{6},{7}} => 2
{{1,5,6,7},{2},{3,4}} => 3
{{1,5,6},{2,7},{3,4}} => 4
{{1,5,6},{2},{3,4,7}} => 2
{{1,5,6},{2},{3,4},{7}} => 2
{{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}} => 3
{{1,5,7},{2},{3,4,6}} => 2
{{1,5},{2,7},{3,4,6}} => 3
{{1,5},{2},{3,4,6,7}} => 1
{{1,5},{2},{3,4,6},{7}} => 1
{{1,5,7},{2},{3,4},{6}} => 2
{{1,5},{2,7},{3,4},{6}} => 3
{{1,5},{2},{3,4,7},{6}} => 4
{{1,5},{2},{3,4},{6,7}} => 1
{{1,5},{2},{3,4},{6},{7}} => 1
{{1,6,7},{2,5},{3,4}} => 4
{{1,6},{2,5,7},{3,4}} => 5
{{1,6},{2,5},{3,4,7}} => 3
{{1,6},{2,5},{3,4},{7}} => 3
{{1,7},{2,5,6},{3,4}} => 5
{{1},{2,5,6,7},{3,4}} => 6
{{1},{2,5,6},{3,4,7}} => 4
{{1},{2,5,6},{3,4},{7}} => 4
{{1,7},{2,5},{3,4,6}} => 3
{{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}} => 3
{{1},{2,5,7},{3,4},{6}} => 4
{{1},{2,5},{3,4,7},{6}} => 5
{{1},{2,5},{3,4},{6,7}} => 2
{{1},{2,5},{3,4},{6},{7}} => 2
{{1,6,7},{2},{3,4,5}} => 2
{{1,6},{2,7},{3,4,5}} => 3
{{1,6},{2},{3,4,5,7}} => 1
{{1,6},{2},{3,4,5},{7}} => 1
{{1,7},{2,6},{3,4,5}} => 3
{{1},{2,6,7},{3,4,5}} => 4
{{1},{2,6},{3,4,5,7}} => 2
{{1},{2,6},{3,4,5},{7}} => 2
{{1,7},{2},{3,4,5,6}} => 1
{{1},{2,7},{3,4,5,6}} => 2
{{1},{2},{3,4,5,6,7}} => 0
{{1},{2},{3,4,5,6},{7}} => 0
{{1,7},{2},{3,4,5},{6}} => 1
{{1},{2,7},{3,4,5},{6}} => 2
{{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}} => 2
{{1,6},{2,7},{3,4},{5}} => 3
{{1,6},{2},{3,4,7},{5}} => 4
{{1,6},{2},{3,4},{5,7}} => 1
{{1,6},{2},{3,4},{5},{7}} => 1
{{1,7},{2,6},{3,4},{5}} => 3
{{1},{2,6,7},{3,4},{5}} => 4
{{1},{2,6},{3,4,7},{5}} => 5
{{1},{2,6},{3,4},{5,7}} => 2
{{1},{2,6},{3,4},{5},{7}} => 2
{{1,7},{2},{3,4,6},{5}} => 4
{{1},{2,7},{3,4,6},{5}} => 5
{{1},{2},{3,4,6,7},{5}} => 6
{{1},{2},{3,4,6},{5,7}} => 3
{{1},{2},{3,4,6},{5},{7}} => 3
{{1,7},{2},{3,4},{5,6}} => 1
{{1},{2,7},{3,4},{5,6}} => 2
{{1},{2},{3,4,7},{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}} => 1
{{1},{2,7},{3,4},{5},{6}} => 2
{{1},{2},{3,4,7},{5},{6}} => 3
{{1},{2},{3,4},{5,7},{6}} => 4
{{1},{2},{3,4},{5},{6,7}} => 0
{{1},{2},{3,4},{5},{6},{7}} => 0
{{1,5,6,7},{2},{3},{4}} => 3
{{1,5,6},{2,7},{3},{4}} => 4
{{1,5,6},{2},{3,7},{4}} => 5
{{1,5,6},{2},{3},{4,7}} => 2
{{1,5,6},{2},{3},{4},{7}} => 2
{{1,5,7},{2,6},{3},{4}} => 4
{{1,5},{2,6,7},{3},{4}} => 5
{{1,5},{2,6},{3,7},{4}} => 6
{{1,5},{2,6},{3},{4,7}} => 3
{{1,5},{2,6},{3},{4},{7}} => 3
{{1,5,7},{2},{3,6},{4}} => 5
{{1,5},{2,7},{3,6},{4}} => 6
{{1,5},{2},{3,6,7},{4}} => 7
{{1,5},{2},{3,6},{4,7}} => 4
{{1,5},{2},{3,6},{4},{7}} => 4
{{1,5,7},{2},{3},{4,6}} => 2
{{1,5},{2,7},{3},{4,6}} => 3
{{1,5},{2},{3,7},{4,6}} => 4
{{1,5},{2},{3},{4,6,7}} => 1
{{1,5},{2},{3},{4,6},{7}} => 1
{{1,5,7},{2},{3},{4},{6}} => 2
{{1,5},{2,7},{3},{4},{6}} => 3
{{1,5},{2},{3,7},{4},{6}} => 4
{{1,5},{2},{3},{4,7},{6}} => 5
{{1,5},{2},{3},{4},{6,7}} => 1
{{1,5},{2},{3},{4},{6},{7}} => 1
{{1,6,7},{2,5},{3},{4}} => 4
{{1,6},{2,5,7},{3},{4}} => 5
{{1,6},{2,5},{3,7},{4}} => 6
{{1,6},{2,5},{3},{4,7}} => 3
{{1,6},{2,5},{3},{4},{7}} => 3
{{1,7},{2,5,6},{3},{4}} => 5
{{1},{2,5,6,7},{3},{4}} => 6
{{1},{2,5,6},{3,7},{4}} => 7
{{1},{2,5,6},{3},{4,7}} => 4
{{1},{2,5,6},{3},{4},{7}} => 4
{{1,7},{2,5},{3,6},{4}} => 6
{{1},{2,5,7},{3,6},{4}} => 7
{{1},{2,5},{3,6,7},{4}} => 8
{{1},{2,5},{3,6},{4,7}} => 5
{{1},{2,5},{3,6},{4},{7}} => 5
{{1,7},{2,5},{3},{4,6}} => 3
{{1},{2,5,7},{3},{4,6}} => 4
{{1},{2,5},{3,7},{4,6}} => 5
{{1},{2,5},{3},{4,6,7}} => 2
{{1},{2,5},{3},{4,6},{7}} => 2
{{1,7},{2,5},{3},{4},{6}} => 3
{{1},{2,5,7},{3},{4},{6}} => 4
{{1},{2,5},{3,7},{4},{6}} => 5
{{1},{2,5},{3},{4,7},{6}} => 6
{{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}} => 6
{{1,6},{2},{3,5,7},{4}} => 7
{{1,6},{2},{3,5},{4,7}} => 4
{{1,6},{2},{3,5},{4},{7}} => 4
{{1,7},{2,6},{3,5},{4}} => 6
{{1},{2,6,7},{3,5},{4}} => 7
{{1},{2,6},{3,5,7},{4}} => 8
{{1},{2,6},{3,5},{4,7}} => 5
{{1},{2,6},{3,5},{4},{7}} => 5
{{1,7},{2},{3,5,6},{4}} => 7
{{1},{2,7},{3,5,6},{4}} => 8
{{1},{2},{3,5,6,7},{4}} => 9
{{1},{2},{3,5,6},{4,7}} => 6
{{1},{2},{3,5,6},{4},{7}} => 6
{{1,7},{2},{3,5},{4,6}} => 4
{{1},{2,7},{3,5},{4,6}} => 5
{{1},{2},{3,5,7},{4,6}} => 6
{{1},{2},{3,5},{4,6,7}} => 3
{{1},{2},{3,5},{4,6},{7}} => 3
{{1,7},{2},{3,5},{4},{6}} => 4
{{1},{2,7},{3,5},{4},{6}} => 5
{{1},{2},{3,5,7},{4},{6}} => 6
{{1},{2},{3,5},{4,7},{6}} => 7
{{1},{2},{3,5},{4},{6,7}} => 3
{{1},{2},{3,5},{4},{6},{7}} => 3
{{1,6,7},{2},{3},{4,5}} => 2
{{1,6},{2,7},{3},{4,5}} => 3
{{1,6},{2},{3,7},{4,5}} => 4
{{1,6},{2},{3},{4,5,7}} => 1
{{1,6},{2},{3},{4,5},{7}} => 1
{{1,7},{2,6},{3},{4,5}} => 3
{{1},{2,6,7},{3},{4,5}} => 4
{{1},{2,6},{3,7},{4,5}} => 5
{{1},{2,6},{3},{4,5,7}} => 2
{{1},{2,6},{3},{4,5},{7}} => 2
{{1,7},{2},{3,6},{4,5}} => 4
{{1},{2,7},{3,6},{4,5}} => 5
{{1},{2},{3,6,7},{4,5}} => 6
{{1},{2},{3,6},{4,5,7}} => 3
{{1},{2},{3,6},{4,5},{7}} => 3
{{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},{4,5,6,7}} => 0
{{1},{2},{3},{4,5,6},{7}} => 0
{{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},{4,5,7},{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}} => 2
{{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}} => 1
{{1,6},{2},{3},{4},{5},{7}} => 1
{{1,7},{2,6},{3},{4},{5}} => 3
{{1},{2,6,7},{3},{4},{5}} => 4
{{1},{2,6},{3,7},{4},{5}} => 5
{{1},{2,6},{3},{4,7},{5}} => 6
{{1},{2,6},{3},{4},{5,7}} => 2
{{1},{2,6},{3},{4},{5},{7}} => 2
{{1,7},{2},{3,6},{4},{5}} => 4
{{1},{2,7},{3,6},{4},{5}} => 5
{{1},{2},{3,6,7},{4},{5}} => 6
{{1},{2},{3,6},{4,7},{5}} => 7
{{1},{2},{3,6},{4},{5,7}} => 3
{{1},{2},{3,6},{4},{5},{7}} => 3
{{1,7},{2},{3},{4,6},{5}} => 5
{{1},{2,7},{3},{4,6},{5}} => 6
{{1},{2},{3,7},{4,6},{5}} => 7
{{1},{2},{3},{4,6,7},{5}} => 8
{{1},{2},{3},{4,6},{5,7}} => 4
{{1},{2},{3},{4,6},{5},{7}} => 4
{{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},{5,6,7}} => 0
{{1},{2},{3},{4},{5,6},{7}} => 0
{{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}} => 0
{{1},{2},{3},{4},{5},{6},{7}} => 0
{{1},{2},{3,4,5,6,7,8}} => 0
{{1},{2,4,5,6,7,8},{3}} => 10
{{1},{2,3,5,6,7,8},{4}} => 8
{{1},{2,3,4,6,7,8},{5}} => 6
{{1},{2,3,4,5,7,8},{6}} => 4
{{1},{2,3,4,5,6,7},{8}} => 0
{{1},{2,3,4,5,6,8},{7}} => 2
{{1},{2,3,4,5,6,7,8}} => 0
{{1,2},{3,4,5,6,7,8}} => 0
{{1,4,5,6,7,8},{2},{3}} => 5
{{1,3,5,6,7,8},{2},{4}} => 5
{{1,3,4,5,6,7,8},{2}} => 6
{{1,4,5,6,7,8},{2,3}} => 5
{{1,2,4,5,6,7,8},{3}} => 5
{{1,2,5,6,7,8},{3,4}} => 4
{{1,2,3,5,6,7,8},{4}} => 4
{{1,2,3,6,7,8},{4,5}} => 3
{{1,2,3,4,6,7,8},{5}} => 3
{{1,2,3,4,5,6},{7,8}} => 0
{{1,2,3,4,7,8},{5,6}} => 2
{{1,2,3,4,5,7,8},{6}} => 2
{{1,2,3,4,5,6,7},{8}} => 0
{{1,8},{2,3,4,5,6,7}} => 1
{{1,2,3,4,5,8},{6,7}} => 1
{{1,2,3,4,5,6,8},{7}} => 1
{{1,2,3,4,5,6,7,8}} => 0
{{1,3,5,6,7,8},{2,4}} => 5
{{1,3,4,6,7,8},{2,5}} => 5
{{1,2,4,6,7,8},{3,5}} => 4
{{1,3,4,5,7,8},{2,6}} => 5
{{1,2,4,5,7,8},{3,6}} => 4
{{1,2,3,5,7,8},{4,6}} => 3
{{1,3,4,5,6,8},{2,7}} => 5
{{1,2,4,5,6,8},{3,7}} => 4
{{1,2,3,5,6,8},{4,7}} => 3
{{1,2,3,4,6,8},{5,7}} => 2
{{1,3,4,5,6,7},{2,8}} => 5
{{1,2,4,5,6,7},{3,8}} => 4
{{1,2,3,5,6,7},{4,8}} => 3
{{1,2,3,4,6,7},{5,8}} => 2
{{1,2,3,4,5,7},{6,8}} => 1
{{1,3},{2,4,5,6,7,8}} => 1
{{1,4},{2,3,5,6,7,8}} => 1
{{1,5},{2,3,4,6,7,8}} => 1
{{1,6},{2,3,4,5,7,8}} => 1
{{1,7},{2,3,4,5,6,8}} => 1
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Created: Aug 06, 2016 at 15:22 by Martin Rubey
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Last Updated: Aug 06, 2016 at 15:22 by Martin Rubey