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Statistic identifier: St000565

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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 $1d_1+2d_2+\dots+(k-1)d_{k-1}$.

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References: [1]   Sagan, B. E. A maj statistic for set partitions [[MathSciNet:1087650]]

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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