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*       Copyright (C) 2019 The FindStatCrew <info@findstat.org>             *
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-----------------------------------------------------------------------------
Statistic identifier: St000339

-----------------------------------------------------------------------------
Collection: Permutations

-----------------------------------------------------------------------------
Description: The maf index of a permutation.

Let $\sigma$ be a permutation with fixed point set $\operatorname{FIX}(\sigma)$, and let $\operatorname{Der}(\sigma)$ be the derangement obtained from $\sigma$ by removing the fixed points.
Then
$$\operatorname{maj}(\sigma) = \sum_{i \in \operatorname{FIX}(\sigma)} i - \binom{|\operatorname{FIX}(\sigma)|+1}{2} + \operatorname{maj}(\operatorname{Der}(\sigma)),$$
where $\operatorname{maj}(\operatorname{Der}(\sigma))$ is the major index of the derangement of $\sigma$.

-----------------------------------------------------------------------------
References: [1]   Foata, D., Han, G.-N. Fix-Mahonian Calculus, II: further statistics [[arXiv:math/0703101]]
[2]   Han, G.-N., Xin, G. Permutations with Extremal number of Fixed Points [[arXiv:0706.1738]]

-----------------------------------------------------------------------------
Code:
def statistic(x):
    f = len(x.fixed_points())
    return sum(x.fixed_points()) - ((f+1)*f)//2 + Der(x).major_index()

def Der(x):
    return Word([i for i in sz(x) if i != 0]).standard_permutation()

#Returns the word (as a list) where fixed points of x are changed to zero (see [2])
def sz(x):
    l = list(x)
    for i in x.fixed_points():
            l[i-1] = 0
    return l

-----------------------------------------------------------------------------
Statistic values:

[1]           => 0
[1,2]         => 0
[2,1]         => 1
[1,2,3]       => 0
[1,3,2]       => 1
[2,1,3]       => 3
[2,3,1]       => 2
[3,1,2]       => 1
[3,2,1]       => 2
[1,2,3,4]     => 0
[1,2,4,3]     => 1
[1,3,2,4]     => 3
[1,3,4,2]     => 2
[1,4,2,3]     => 1
[1,4,3,2]     => 2
[2,1,3,4]     => 5
[2,1,4,3]     => 4
[2,3,1,4]     => 5
[2,3,4,1]     => 3
[2,4,1,3]     => 2
[2,4,3,1]     => 4
[3,1,2,4]     => 4
[3,1,4,2]     => 4
[3,2,1,4]     => 4
[3,2,4,1]     => 3
[3,4,1,2]     => 2
[3,4,2,1]     => 5
[4,1,2,3]     => 1
[4,1,3,2]     => 3
[4,2,1,3]     => 2
[4,2,3,1]     => 3
[4,3,1,2]     => 3
[4,3,2,1]     => 6
[1,2,3,4,5]   => 0
[1,2,3,5,4]   => 1
[1,2,4,3,5]   => 3
[1,2,4,5,3]   => 2
[1,2,5,3,4]   => 1
[1,2,5,4,3]   => 2
[1,3,2,4,5]   => 5
[1,3,2,5,4]   => 4
[1,3,4,2,5]   => 5
[1,3,4,5,2]   => 3
[1,3,5,2,4]   => 2
[1,3,5,4,2]   => 4
[1,4,2,3,5]   => 4
[1,4,2,5,3]   => 4
[1,4,3,2,5]   => 4
[1,4,3,5,2]   => 3
[1,4,5,2,3]   => 2
[1,4,5,3,2]   => 5
[1,5,2,3,4]   => 1
[1,5,2,4,3]   => 3
[1,5,3,2,4]   => 2
[1,5,3,4,2]   => 3
[1,5,4,2,3]   => 3
[1,5,4,3,2]   => 6
[2,1,3,4,5]   => 7
[2,1,3,5,4]   => 6
[2,1,4,3,5]   => 8
[2,1,4,5,3]   => 5
[2,1,5,3,4]   => 4
[2,1,5,4,3]   => 7
[2,3,1,4,5]   => 8
[2,3,1,5,4]   => 6
[2,3,4,1,5]   => 7
[2,3,4,5,1]   => 4
[2,3,5,1,4]   => 3
[2,3,5,4,1]   => 6
[2,4,1,3,5]   => 6
[2,4,1,5,3]   => 6
[2,4,3,1,5]   => 7
[2,4,3,5,1]   => 5
[2,4,5,1,3]   => 3
[2,4,5,3,1]   => 7
[2,5,1,3,4]   => 2
[2,5,1,4,3]   => 5
[2,5,3,1,4]   => 4
[2,5,3,4,1]   => 6
[2,5,4,1,3]   => 5
[2,5,4,3,1]   => 9
[3,1,2,4,5]   => 7
[3,1,2,5,4]   => 5
[3,1,4,2,5]   => 8
[3,1,4,5,2]   => 5
[3,1,5,2,4]   => 4
[3,1,5,4,2]   => 7
[3,2,1,4,5]   => 6
[3,2,1,5,4]   => 5
[3,2,4,1,5]   => 6
[3,2,4,5,1]   => 4
[3,2,5,1,4]   => 3
[3,2,5,4,1]   => 5
[3,4,1,2,5]   => 6
[3,4,1,5,2]   => 6
[3,4,2,1,5]   => 9
[3,4,2,5,1]   => 6
[3,4,5,1,2]   => 3
[3,4,5,2,1]   => 7
[3,5,1,2,4]   => 2
[3,5,1,4,2]   => 5
[3,5,2,1,4]   => 5
[3,5,2,4,1]   => 8
[3,5,4,1,2]   => 5
[3,5,4,2,1]   => 9
[4,1,2,3,5]   => 5
[4,1,2,5,3]   => 5
[4,1,3,2,5]   => 6
[4,1,3,5,2]   => 6
[4,1,5,2,3]   => 4
[4,1,5,3,2]   => 8
[4,2,1,3,5]   => 5
[4,2,1,5,3]   => 5
[4,2,3,1,5]   => 5
[4,2,3,5,1]   => 4
[4,2,5,1,3]   => 3
[4,2,5,3,1]   => 6
[4,3,1,2,5]   => 7
[4,3,1,5,2]   => 7
[4,3,2,1,5]   => 10
[4,3,2,5,1]   => 7
[4,3,5,1,2]   => 4
[4,3,5,2,1]   => 8
[4,5,1,2,3]   => 2
[4,5,1,3,2]   => 6
[4,5,2,1,3]   => 5
[4,5,2,3,1]   => 6
[4,5,3,1,2]   => 4
[4,5,3,2,1]   => 7
[5,1,2,3,4]   => 1
[5,1,2,4,3]   => 4
[5,1,3,2,4]   => 3
[5,1,3,4,2]   => 5
[5,1,4,2,3]   => 4
[5,1,4,3,2]   => 8
[5,2,1,3,4]   => 2
[5,2,1,4,3]   => 4
[5,2,3,1,4]   => 3
[5,2,3,4,1]   => 4
[5,2,4,1,3]   => 4
[5,2,4,3,1]   => 7
[5,3,1,2,4]   => 3
[5,3,1,4,2]   => 6
[5,3,2,1,4]   => 6
[5,3,2,4,1]   => 9
[5,3,4,1,2]   => 4
[5,3,4,2,1]   => 8
[5,4,1,2,3]   => 3
[5,4,1,3,2]   => 7
[5,4,2,1,3]   => 6
[5,4,2,3,1]   => 7
[5,4,3,1,2]   => 5
[5,4,3,2,1]   => 8
[1,2,3,4,5,6] => 0
[1,2,3,4,6,5] => 1
[1,2,3,5,4,6] => 3
[1,2,3,5,6,4] => 2
[1,2,3,6,4,5] => 1
[1,2,3,6,5,4] => 2
[1,2,4,3,5,6] => 5
[1,2,4,3,6,5] => 4
[1,2,4,5,3,6] => 5
[1,2,4,5,6,3] => 3
[1,2,4,6,3,5] => 2
[1,2,4,6,5,3] => 4
[1,2,5,3,4,6] => 4
[1,2,5,3,6,4] => 4
[1,2,5,4,3,6] => 4
[1,2,5,4,6,3] => 3
[1,2,5,6,3,4] => 2
[1,2,5,6,4,3] => 5
[1,2,6,3,4,5] => 1
[1,2,6,3,5,4] => 3
[1,2,6,4,3,5] => 2
[1,2,6,4,5,3] => 3
[1,2,6,5,3,4] => 3
[1,2,6,5,4,3] => 6
[1,3,2,4,5,6] => 7
[1,3,2,4,6,5] => 6
[1,3,2,5,4,6] => 8
[1,3,2,5,6,4] => 5
[1,3,2,6,4,5] => 4
[1,3,2,6,5,4] => 7
[1,3,4,2,5,6] => 8
[1,3,4,2,6,5] => 6
[1,3,4,5,2,6] => 7
[1,3,4,5,6,2] => 4
[1,3,4,6,2,5] => 3
[1,3,4,6,5,2] => 6
[1,3,5,2,4,6] => 6
[1,3,5,2,6,4] => 6
[1,3,5,4,2,6] => 7
[1,3,5,4,6,2] => 5
[1,3,5,6,2,4] => 3
[1,3,5,6,4,2] => 7
[1,3,6,2,4,5] => 2
[1,3,6,2,5,4] => 5
[1,3,6,4,2,5] => 4
[1,3,6,4,5,2] => 6
[1,3,6,5,2,4] => 5
[1,3,6,5,4,2] => 9
[1,4,2,3,5,6] => 7
[1,4,2,3,6,5] => 5
[1,4,2,5,3,6] => 8
[1,4,2,5,6,3] => 5
[1,4,2,6,3,5] => 4
[1,4,2,6,5,3] => 7
[1,4,3,2,5,6] => 6
[1,4,3,2,6,5] => 5
[1,4,3,5,2,6] => 6
[1,4,3,5,6,2] => 4
[1,4,3,6,2,5] => 3
[1,4,3,6,5,2] => 5
[1,4,5,2,3,6] => 6
[1,4,5,2,6,3] => 6
[1,4,5,3,2,6] => 9
[1,4,5,3,6,2] => 6
[1,4,5,6,2,3] => 3
[1,4,5,6,3,2] => 7
[1,4,6,2,3,5] => 2
[1,4,6,2,5,3] => 5
[1,4,6,3,2,5] => 5
[1,4,6,3,5,2] => 8
[1,4,6,5,2,3] => 5
[1,4,6,5,3,2] => 9
[1,5,2,3,4,6] => 5
[1,5,2,3,6,4] => 5
[1,5,2,4,3,6] => 6
[1,5,2,4,6,3] => 6
[1,5,2,6,3,4] => 4
[1,5,2,6,4,3] => 8
[1,5,3,2,4,6] => 5
[1,5,3,2,6,4] => 5
[1,5,3,4,2,6] => 5
[1,5,3,4,6,2] => 4
[1,5,3,6,2,4] => 3
[1,5,3,6,4,2] => 6
[1,5,4,2,3,6] => 7
[1,5,4,2,6,3] => 7
[1,5,4,3,2,6] => 10
[1,5,4,3,6,2] => 7
[1,5,4,6,2,3] => 4
[1,5,4,6,3,2] => 8
[1,5,6,2,3,4] => 2
[1,5,6,2,4,3] => 6
[1,5,6,3,2,4] => 5
[1,5,6,3,4,2] => 6
[1,5,6,4,2,3] => 4
[1,5,6,4,3,2] => 7
[1,6,2,3,4,5] => 1
[1,6,2,3,5,4] => 4
[1,6,2,4,3,5] => 3
[1,6,2,4,5,3] => 5
[1,6,2,5,3,4] => 4
[1,6,2,5,4,3] => 8
[1,6,3,2,4,5] => 2
[1,6,3,2,5,4] => 4
[1,6,3,4,2,5] => 3
[1,6,3,4,5,2] => 4
[1,6,3,5,2,4] => 4
[1,6,3,5,4,2] => 7
[1,6,4,2,3,5] => 3
[1,6,4,2,5,3] => 6
[1,6,4,3,2,5] => 6
[1,6,4,3,5,2] => 9
[1,6,4,5,2,3] => 4
[1,6,4,5,3,2] => 8
[1,6,5,2,3,4] => 3
[1,6,5,2,4,3] => 7
[1,6,5,3,2,4] => 6
[1,6,5,3,4,2] => 7
[1,6,5,4,2,3] => 5
[1,6,5,4,3,2] => 8
[2,1,3,4,5,6] => 9
[2,1,3,4,6,5] => 8
[2,1,3,5,4,6] => 10
[2,1,3,5,6,4] => 7
[2,1,3,6,4,5] => 6
[2,1,3,6,5,4] => 9
[2,1,4,3,5,6] => 12
[2,1,4,3,6,5] => 9
[2,1,4,5,3,6] => 10
[2,1,4,5,6,3] => 6
[2,1,4,6,3,5] => 5
[2,1,4,6,5,3] => 9
[2,1,5,3,4,6] => 9
[2,1,5,3,6,4] => 9
[2,1,5,4,3,6] => 11
[2,1,5,4,6,3] => 8
[2,1,5,6,3,4] => 5
[2,1,5,6,4,3] => 10
[2,1,6,3,4,5] => 4
[2,1,6,3,5,4] => 8
[2,1,6,4,3,5] => 7
[2,1,6,4,5,3] => 10
[2,1,6,5,3,4] => 8
[2,1,6,5,4,3] => 13
[2,3,1,4,5,6] => 11
[2,3,1,4,6,5] => 9
[2,3,1,5,4,6] => 11
[2,3,1,5,6,4] => 7
[2,3,1,6,4,5] => 6
[2,3,1,6,5,4] => 10
[2,3,4,1,5,6] => 11
[2,3,4,1,6,5] => 8
[2,3,4,5,1,6] => 9
[2,3,4,5,6,1] => 5
[2,3,4,6,1,5] => 4
[2,3,4,6,5,1] => 8
[2,3,5,1,4,6] => 8
[2,3,5,1,6,4] => 8
[2,3,5,4,1,6] => 10
[2,3,5,4,6,1] => 7
[2,3,5,6,1,4] => 4
[2,3,5,6,4,1] => 9
[2,3,6,1,4,5] => 3
[2,3,6,1,5,4] => 7
[2,3,6,4,1,5] => 6
[2,3,6,4,5,1] => 9
[2,3,6,5,1,4] => 7
[2,3,6,5,4,1] => 12
[2,4,1,3,5,6] => 10
[2,4,1,3,6,5] => 7
[2,4,1,5,3,6] => 11
[2,4,1,5,6,3] => 7
[2,4,1,6,3,5] => 6
[2,4,1,6,5,3] => 10
[2,4,3,1,5,6] => 10
[2,4,3,1,6,5] => 8
[2,4,3,5,1,6] => 9
[2,4,3,5,6,1] => 6
[2,4,3,6,1,5] => 5
[2,4,3,6,5,1] => 8
[2,4,5,1,3,6] => 8
[2,4,5,1,6,3] => 8
[2,4,5,3,1,6] => 12
[2,4,5,3,6,1] => 8
[2,4,5,6,1,3] => 4
[2,4,5,6,3,1] => 9
[2,4,6,1,3,5] => 3
[2,4,6,1,5,3] => 7
[2,4,6,3,1,5] => 7
[2,4,6,3,5,1] => 11
[2,4,6,5,1,3] => 7
[2,4,6,5,3,1] => 12
[2,5,1,3,4,6] => 7
[2,5,1,3,6,4] => 7
[2,5,1,4,3,6] => 9
[2,5,1,4,6,3] => 9
[2,5,1,6,3,4] => 6
[2,5,1,6,4,3] => 11
[2,5,3,1,4,6] => 8
[2,5,3,1,6,4] => 8
[2,5,3,4,1,6] => 9
[2,5,3,4,6,1] => 7
[2,5,3,6,1,4] => 5
[2,5,3,6,4,1] => 9
[2,5,4,1,3,6] => 10
[2,5,4,1,6,3] => 10
[2,5,4,3,1,6] => 14
[2,5,4,3,6,1] => 10
[2,5,4,6,1,3] => 6
[2,5,4,6,3,1] => 11
[2,5,6,1,3,4] => 3
[2,5,6,1,4,3] => 8
[2,5,6,3,1,4] => 7
[2,5,6,3,4,1] => 8
[2,5,6,4,1,3] => 6
[2,5,6,4,3,1] => 10
[2,6,1,3,4,5] => 2
[2,6,1,3,5,4] => 6
[2,6,1,4,3,5] => 5
[2,6,1,4,5,3] => 8
[2,6,1,5,3,4] => 6
[2,6,1,5,4,3] => 11
[2,6,3,1,4,5] => 4
[2,6,3,1,5,4] => 7
[2,6,3,4,1,5] => 6
[2,6,3,4,5,1] => 8
[2,6,3,5,1,4] => 7
[2,6,3,5,4,1] => 11
[2,6,4,1,3,5] => 5
[2,6,4,1,5,3] => 9
[2,6,4,3,1,5] => 9
[2,6,4,3,5,1] => 13
[2,6,4,5,1,3] => 6
[2,6,4,5,3,1] => 11
[2,6,5,1,3,4] => 5
[2,6,5,1,4,3] => 10
[2,6,5,3,1,4] => 9
[2,6,5,3,4,1] => 10
[2,6,5,4,1,3] => 8
[2,6,5,4,3,1] => 12
[3,1,2,4,5,6] => 10
[3,1,2,4,6,5] => 8
[3,1,2,5,4,6] => 10
[3,1,2,5,6,4] => 6
[3,1,2,6,4,5] => 5
[3,1,2,6,5,4] => 9
[3,1,4,2,5,6] => 12
[3,1,4,2,6,5] => 9
[3,1,4,5,2,6] => 10
[3,1,4,5,6,2] => 6
[3,1,4,6,2,5] => 5
[3,1,4,6,5,2] => 9
[3,1,5,2,4,6] => 9
[3,1,5,2,6,4] => 9
[3,1,5,4,2,6] => 11
[3,1,5,4,6,2] => 8
[3,1,5,6,2,4] => 5
[3,1,5,6,4,2] => 10
[3,1,6,2,4,5] => 4
[3,1,6,2,5,4] => 8
[3,1,6,4,2,5] => 7
[3,1,6,4,5,2] => 10
[3,1,6,5,2,4] => 8
[3,1,6,5,4,2] => 13
[3,2,1,4,5,6] => 8
[3,2,1,4,6,5] => 7
[3,2,1,5,4,6] => 9
[3,2,1,5,6,4] => 6
[3,2,1,6,4,5] => 5
[3,2,1,6,5,4] => 8
[3,2,4,1,5,6] => 9
[3,2,4,1,6,5] => 7
[3,2,4,5,1,6] => 8
[3,2,4,5,6,1] => 5
[3,2,4,6,1,5] => 4
[3,2,4,6,5,1] => 7
[3,2,5,1,4,6] => 7
[3,2,5,1,6,4] => 7
[3,2,5,4,1,6] => 8
[3,2,5,4,6,1] => 6
[3,2,5,6,1,4] => 4
[3,2,5,6,4,1] => 8
[3,2,6,1,4,5] => 3
[3,2,6,1,5,4] => 6
[3,2,6,4,1,5] => 5
[3,2,6,4,5,1] => 7
[3,2,6,5,1,4] => 6
[3,2,6,5,4,1] => 10
[3,4,1,2,5,6] => 10
[3,4,1,2,6,5] => 7
[3,4,1,5,2,6] => 11
[3,4,1,5,6,2] => 7
[3,4,1,6,2,5] => 6
[3,4,1,6,5,2] => 10
[3,4,2,1,5,6] => 13
[3,4,2,1,6,5] => 10
[3,4,2,5,1,6] => 11
[3,4,2,5,6,1] => 7
[3,4,2,6,1,5] => 6
[3,4,2,6,5,1] => 10
[3,4,5,1,2,6] => 8
[3,4,5,1,6,2] => 8
[3,4,5,2,1,6] => 12
[3,4,5,2,6,1] => 8
[3,4,5,6,1,2] => 4
[3,4,5,6,2,1] => 9
[3,4,6,1,2,5] => 3
[3,4,6,1,5,2] => 7
[3,4,6,2,1,5] => 7
[3,4,6,2,5,1] => 11
[3,4,6,5,1,2] => 7
[3,4,6,5,2,1] => 12
[3,5,1,2,4,6] => 7
[3,5,1,2,6,4] => 7
[3,5,1,4,2,6] => 9
[3,5,1,4,6,2] => 9
[3,5,1,6,2,4] => 6
[3,5,1,6,4,2] => 11
[3,5,2,1,4,6] => 10
[3,5,2,1,6,4] => 10
[3,5,2,4,1,6] => 12
[3,5,2,4,6,1] => 9
[3,5,2,6,1,4] => 6
[3,5,2,6,4,1] => 11
[3,5,4,1,2,6] => 10
[3,5,4,1,6,2] => 10
[3,5,4,2,1,6] => 14
[3,5,4,2,6,1] => 10
[3,5,4,6,1,2] => 6
[3,5,4,6,2,1] => 11
[3,5,6,1,2,4] => 3
[3,5,6,1,4,2] => 8
[3,5,6,2,1,4] => 7
[3,5,6,2,4,1] => 8
[3,5,6,4,1,2] => 6
[3,5,6,4,2,1] => 10
[3,6,1,2,4,5] => 2
[3,6,1,2,5,4] => 6
[3,6,1,4,2,5] => 5
[3,6,1,4,5,2] => 8
[3,6,1,5,2,4] => 6
[3,6,1,5,4,2] => 11
[3,6,2,1,4,5] => 5
[3,6,2,1,5,4] => 9
[3,6,2,4,1,5] => 8
[3,6,2,4,5,1] => 11
[3,6,2,5,1,4] => 6
[3,6,2,5,4,1] => 11
[3,6,4,1,2,5] => 5
[3,6,4,1,5,2] => 9
[3,6,4,2,1,5] => 9
[3,6,4,2,5,1] => 13
[3,6,4,5,1,2] => 6
[3,6,4,5,2,1] => 11
[3,6,5,1,2,4] => 5
[3,6,5,1,4,2] => 10
[3,6,5,2,1,4] => 9
[3,6,5,2,4,1] => 10
[3,6,5,4,1,2] => 8
[3,6,5,4,2,1] => 12
[4,1,2,3,5,6] => 9
[4,1,2,3,6,5] => 6
[4,1,2,5,3,6] => 10
[4,1,2,5,6,3] => 6
[4,1,2,6,3,5] => 5
[4,1,2,6,5,3] => 9
[4,1,3,2,5,6] => 9
[4,1,3,2,6,5] => 7
[4,1,3,5,2,6] => 10
[4,1,3,5,6,2] => 7
[4,1,3,6,2,5] => 6
[4,1,3,6,5,2] => 9
[4,1,5,2,3,6] => 9
[4,1,5,2,6,3] => 9
[4,1,5,3,2,6] => 13
[4,1,5,3,6,2] => 9
[4,1,5,6,2,3] => 5
[4,1,5,6,3,2] => 10
[4,1,6,2,3,5] => 4
[4,1,6,2,5,3] => 8
[4,1,6,3,2,5] => 8
[4,1,6,3,5,2] => 12
[4,1,6,5,2,3] => 8
[4,1,6,5,3,2] => 13
[4,2,1,3,5,6] => 8
[4,2,1,3,6,5] => 6
[4,2,1,5,3,6] => 9
[4,2,1,5,6,3] => 6
[4,2,1,6,3,5] => 5
[4,2,1,6,5,3] => 8
[4,2,3,1,5,6] => 7
[4,2,3,1,6,5] => 6
[4,2,3,5,1,6] => 7
[4,2,3,5,6,1] => 5
[4,2,3,6,1,5] => 4
[4,2,3,6,5,1] => 6
[4,2,5,1,3,6] => 7
[4,2,5,1,6,3] => 7
[4,2,5,3,1,6] => 10
[4,2,5,3,6,1] => 7
[4,2,5,6,1,3] => 4
[4,2,5,6,3,1] => 8
[4,2,6,1,3,5] => 3
[4,2,6,1,5,3] => 6
[4,2,6,3,1,5] => 6
[4,2,6,3,5,1] => 9
[4,2,6,5,1,3] => 6
[4,2,6,5,3,1] => 10
[4,3,1,2,5,6] => 11
[4,3,1,2,6,5] => 8
[4,3,1,5,2,6] => 12
[4,3,1,5,6,2] => 8
[4,3,1,6,2,5] => 7
[4,3,1,6,5,2] => 11
[4,3,2,1,5,6] => 14
[4,3,2,1,6,5] => 11
[4,3,2,5,1,6] => 12
[4,3,2,5,6,1] => 8
[4,3,2,6,1,5] => 7
[4,3,2,6,5,1] => 11
[4,3,5,1,2,6] => 9
[4,3,5,1,6,2] => 9
[4,3,5,2,1,6] => 13
[4,3,5,2,6,1] => 9
[4,3,5,6,1,2] => 5
[4,3,5,6,2,1] => 10
[4,3,6,1,2,5] => 4
[4,3,6,1,5,2] => 8
[4,3,6,2,1,5] => 8
[4,3,6,2,5,1] => 12
[4,3,6,5,1,2] => 8
[4,3,6,5,2,1] => 13
[4,5,1,2,3,6] => 7
[4,5,1,2,6,3] => 7
[4,5,1,3,2,6] => 11
[4,5,1,3,6,2] => 7
[4,5,1,6,2,3] => 6
[4,5,1,6,3,2] => 11
[4,5,2,1,3,6] => 10
[4,5,2,1,6,3] => 10
[4,5,2,3,1,6] => 11
[4,5,2,3,6,1] => 7
[4,5,2,6,1,3] => 6
[4,5,2,6,3,1] => 11
[4,5,3,1,2,6] => 8
[4,5,3,1,6,2] => 8
[4,5,3,2,1,6] => 11
[4,5,3,2,6,1] => 8
[4,5,3,6,1,2] => 5
[4,5,3,6,2,1] => 9
[4,5,6,1,2,3] => 3
[4,5,6,1,3,2] => 8
[4,5,6,2,1,3] => 7
[4,5,6,2,3,1] => 8
[4,5,6,3,1,2] => 7
[4,5,6,3,2,1] => 12
[4,6,1,2,3,5] => 2
[4,6,1,2,5,3] => 6
[4,6,1,3,2,5] => 6
[4,6,1,3,5,2] => 10
[4,6,1,5,2,3] => 6
[4,6,1,5,3,2] => 11
[4,6,2,1,3,5] => 5
[4,6,2,1,5,3] => 9
[4,6,2,3,1,5] => 6
[4,6,2,3,5,1] => 10
[4,6,2,5,1,3] => 6
[4,6,2,5,3,1] => 11
[4,6,3,1,2,5] => 4
[4,6,3,1,5,2] => 7
[4,6,3,2,1,5] => 7
[4,6,3,2,5,1] => 10
[4,6,3,5,1,2] => 7
[4,6,3,5,2,1] => 11
[4,6,5,1,2,3] => 5
[4,6,5,1,3,2] => 10
[4,6,5,2,1,3] => 9
[4,6,5,2,3,1] => 10
[4,6,5,3,1,2] => 9
[4,6,5,3,2,1] => 14
[5,1,2,3,4,6] => 6
[5,1,2,3,6,4] => 6
[5,1,2,4,3,6] => 8
[5,1,2,4,6,3] => 8
[5,1,2,6,3,4] => 5
[5,1,2,6,4,3] => 10
[5,1,3,2,4,6] => 7
[5,1,3,2,6,4] => 7
[5,1,3,4,2,6] => 8
[5,1,3,4,6,2] => 8
[5,1,3,6,2,4] => 6
[5,1,3,6,4,2] => 10
[5,1,4,2,3,6] => 9
[5,1,4,2,6,3] => 9
[5,1,4,3,2,6] => 13
[5,1,4,3,6,2] => 9
[5,1,4,6,2,3] => 5
[5,1,4,6,3,2] => 10
[5,1,6,2,3,4] => 4
[5,1,6,2,4,3] => 9
[5,1,6,3,2,4] => 8
[5,1,6,3,4,2] => 9
[5,1,6,4,2,3] => 7
[5,1,6,4,3,2] => 11
[5,2,1,3,4,6] => 6
[5,2,1,3,6,4] => 6
[5,2,1,4,3,6] => 7
[5,2,1,4,6,3] => 7
[5,2,1,6,3,4] => 5
[5,2,1,6,4,3] => 9
[5,2,3,1,4,6] => 6
[5,2,3,1,6,4] => 6
[5,2,3,4,1,6] => 6
[5,2,3,4,6,1] => 5
[5,2,3,6,1,4] => 4
[5,2,3,6,4,1] => 7
[5,2,4,1,3,6] => 8
[5,2,4,1,6,3] => 8
[5,2,4,3,1,6] => 11
[5,2,4,3,6,1] => 8
[5,2,4,6,1,3] => 5
[5,2,4,6,3,1] => 9
[5,2,6,1,3,4] => 3
[5,2,6,1,4,3] => 7
[5,2,6,3,1,4] => 6
[5,2,6,3,4,1] => 7
[5,2,6,4,1,3] => 5
[5,2,6,4,3,1] => 8
[5,3,1,2,4,6] => 8
[5,3,1,2,6,4] => 8
[5,3,1,4,2,6] => 10
[5,3,1,4,6,2] => 10
[5,3,1,6,2,4] => 7
[5,3,1,6,4,2] => 12
[5,3,2,1,4,6] => 11
[5,3,2,1,6,4] => 11
[5,3,2,4,1,6] => 13
[5,3,2,4,6,1] => 10
[5,3,2,6,1,4] => 7
[5,3,2,6,4,1] => 12
[5,3,4,1,2,6] => 9
[5,3,4,1,6,2] => 9
[5,3,4,2,1,6] => 13
[5,3,4,2,6,1] => 9
[5,3,4,6,1,2] => 5
[5,3,4,6,2,1] => 10
[5,3,6,1,2,4] => 4
[5,3,6,1,4,2] => 9
[5,3,6,2,1,4] => 8
[5,3,6,2,4,1] => 9
[5,3,6,4,1,2] => 7
[5,3,6,4,2,1] => 11
[5,4,1,2,3,6] => 8
[5,4,1,2,6,3] => 8
[5,4,1,3,2,6] => 12
[5,4,1,3,6,2] => 8
[5,4,1,6,2,3] => 7
[5,4,1,6,3,2] => 12
[5,4,2,1,3,6] => 11
[5,4,2,1,6,3] => 11
[5,4,2,3,1,6] => 12
[5,4,2,3,6,1] => 8
[5,4,2,6,1,3] => 7
[5,4,2,6,3,1] => 12
[5,4,3,1,2,6] => 9
[5,4,3,1,6,2] => 9
[5,4,3,2,1,6] => 12
[5,4,3,2,6,1] => 9
[5,4,3,6,1,2] => 6
[5,4,3,6,2,1] => 10
[5,4,6,1,2,3] => 4
[5,4,6,1,3,2] => 9
[5,4,6,2,1,3] => 8
[5,4,6,2,3,1] => 9
[5,4,6,3,1,2] => 8
[5,4,6,3,2,1] => 13
[5,6,1,2,3,4] => 2
[5,6,1,2,4,3] => 7
[5,6,1,3,2,4] => 6
[5,6,1,3,4,2] => 7
[5,6,1,4,2,3] => 5
[5,6,1,4,3,2] => 9
[5,6,2,1,3,4] => 5
[5,6,2,1,4,3] => 10
[5,6,2,3,1,4] => 6
[5,6,2,3,4,1] => 7
[5,6,2,4,1,3] => 8
[5,6,2,4,3,1] => 9
[5,6,3,1,2,4] => 4
[5,6,3,1,4,2] => 8
[5,6,3,2,1,4] => 7
[5,6,3,2,4,1] => 8
[5,6,3,4,1,2] => 6
[5,6,3,4,2,1] => 9
[5,6,4,1,2,3] => 5
[5,6,4,1,3,2] => 10
[5,6,4,2,1,3] => 9
[5,6,4,2,3,1] => 10
[5,6,4,3,1,2] => 9
[5,6,4,3,2,1] => 14
[6,1,2,3,4,5] => 1
[6,1,2,3,5,4] => 5
[6,1,2,4,3,5] => 4
[6,1,2,4,5,3] => 7
[6,1,2,5,3,4] => 5
[6,1,2,5,4,3] => 10
[6,1,3,2,4,5] => 3
[6,1,3,2,5,4] => 6
[6,1,3,4,2,5] => 5
[6,1,3,4,5,2] => 7
[6,1,3,5,2,4] => 6
[6,1,3,5,4,2] => 10
[6,1,4,2,3,5] => 4
[6,1,4,2,5,3] => 8
[6,1,4,3,2,5] => 8
[6,1,4,3,5,2] => 12
[6,1,4,5,2,3] => 5
[6,1,4,5,3,2] => 10
[6,1,5,2,3,4] => 4
[6,1,5,2,4,3] => 9
[6,1,5,3,2,4] => 8
[6,1,5,3,4,2] => 9
[6,1,5,4,2,3] => 7
[6,1,5,4,3,2] => 11
[6,2,1,3,4,5] => 2
[6,2,1,3,5,4] => 5
[6,2,1,4,3,5] => 4
[6,2,1,4,5,3] => 6
[6,2,1,5,3,4] => 5
[6,2,1,5,4,3] => 9
[6,2,3,1,4,5] => 3
[6,2,3,1,5,4] => 5
[6,2,3,4,1,5] => 4
[6,2,3,4,5,1] => 5
[6,2,3,5,1,4] => 5
[6,2,3,5,4,1] => 8
[6,2,4,1,3,5] => 4
[6,2,4,1,5,3] => 7
[6,2,4,3,1,5] => 7
[6,2,4,3,5,1] => 10
[6,2,4,5,1,3] => 5
[6,2,4,5,3,1] => 9
[6,2,5,1,3,4] => 4
[6,2,5,1,4,3] => 8
[6,2,5,3,1,4] => 7
[6,2,5,3,4,1] => 8
[6,2,5,4,1,3] => 6
[6,2,5,4,3,1] => 9
[6,3,1,2,4,5] => 3
[6,3,1,2,5,4] => 7
[6,3,1,4,2,5] => 6
[6,3,1,4,5,2] => 9
[6,3,1,5,2,4] => 7
[6,3,1,5,4,2] => 12
[6,3,2,1,4,5] => 6
[6,3,2,1,5,4] => 10
[6,3,2,4,1,5] => 9
[6,3,2,4,5,1] => 12
[6,3,2,5,1,4] => 7
[6,3,2,5,4,1] => 12
[6,3,4,1,2,5] => 4
[6,3,4,1,5,2] => 8
[6,3,4,2,1,5] => 8
[6,3,4,2,5,1] => 12
[6,3,4,5,1,2] => 5
[6,3,4,5,2,1] => 10
[6,3,5,1,2,4] => 4
[6,3,5,1,4,2] => 9
[6,3,5,2,1,4] => 8
[6,3,5,2,4,1] => 9
[6,3,5,4,1,2] => 7
[6,3,5,4,2,1] => 11
[6,4,1,2,3,5] => 3
[6,4,1,2,5,3] => 7
[6,4,1,3,2,5] => 7
[6,4,1,3,5,2] => 11
[6,4,1,5,2,3] => 7
[6,4,1,5,3,2] => 12
[6,4,2,1,3,5] => 6
[6,4,2,1,5,3] => 10
[6,4,2,3,1,5] => 7
[6,4,2,3,5,1] => 11
[6,4,2,5,1,3] => 7
[6,4,2,5,3,1] => 12
[6,4,3,1,2,5] => 5
[6,4,3,1,5,2] => 8
[6,4,3,2,1,5] => 8
[6,4,3,2,5,1] => 11
[6,4,3,5,1,2] => 6
[6,4,3,5,2,1] => 10
[6,4,5,1,2,3] => 4
[6,4,5,1,3,2] => 9
[6,4,5,2,1,3] => 8
[6,4,5,2,3,1] => 9
[6,4,5,3,1,2] => 8
[6,4,5,3,2,1] => 13
[6,5,1,2,3,4] => 3
[6,5,1,2,4,3] => 8
[6,5,1,3,2,4] => 7
[6,5,1,3,4,2] => 8
[6,5,1,4,2,3] => 6
[6,5,1,4,3,2] => 10
[6,5,2,1,3,4] => 6
[6,5,2,1,4,3] => 11
[6,5,2,3,1,4] => 7
[6,5,2,3,4,1] => 8
[6,5,2,4,1,3] => 9
[6,5,2,4,3,1] => 10
[6,5,3,1,2,4] => 5
[6,5,3,1,4,2] => 9
[6,5,3,2,1,4] => 8
[6,5,3,2,4,1] => 9
[6,5,3,4,1,2] => 7
[6,5,3,4,2,1] => 10
[6,5,4,1,2,3] => 6
[6,5,4,1,3,2] => 11
[6,5,4,2,1,3] => 10
[6,5,4,2,3,1] => 11
[6,5,4,3,1,2] => 10
[6,5,4,3,2,1] => 15

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Created: Dec 18, 2015 at 13:45 by Joseph Bernstein

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Last Updated: Feb 23, 2023 at 15:06 by Tilman Möller