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*       Copyright (C) 2019 The FindStatCrew <info@findstat.org>             *
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-----------------------------------------------------------------------------
Statistic identifier: St000338

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

-----------------------------------------------------------------------------
Description: The number of pixed points of a permutation.

For a permutation $\sigma = p \tau_{1} \tau_{2} \cdots \tau_{k}$ in its hook factorization, [1] defines

$$\textrm{pix} \, \sigma = \textrm{length} (p)$$.

-----------------------------------------------------------------------------
References: [1]   Foata, D., Han, G.-N. Fix-Mahonian Calculus III; a Quadruple Distribution [[arXiv:math/0703454]]

-----------------------------------------------------------------------------
Code:
def hook_factorization(w):
    """
    sage: w=[1,2,4,5,6,4,5,6,4,1,3,6,5,5,4,6,1,1,4,5,1,1]
    sage: hook_factorization(w)
    [[1, 2, 4, 5],
    [6, 4, 5, 6],
    [4, 1, 3],
    [6, 5],
    [5, 4],
    [6, 1, 1, 4],
    [5, 1, 1]]

    sage: w=[1,3,4,14,12,2,5,11,15,8,6,7,13,9,10]
    sage: hook_factorization(w)
    [[1, 3, 4, 14], [12, 2, 5, 11, 15], [8, 6, 7], [13, 9, 10]]
    """
    if len(w) == 0:
        return []
    w1 = w + [max(w)+1]
    i = len(w)-1
    while w1[i] <= w1[i+1]:
        i -= 1
    if i == -1:
        return [w]
    else:
        return hook_factorization(w[:i]) + [w[i:]]
    
def statistic(pi):
    p0 = hook_factorization(pi)[0]
    if len(p0) == 1 or p0[0] < p0[1]:
        return len(p0)
    else:
        return 0


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

[1]           => 1
[1,2]         => 2
[2,1]         => 0
[1,2,3]       => 3
[1,3,2]       => 1
[2,1,3]       => 0
[2,3,1]       => 1
[3,1,2]       => 0
[3,2,1]       => 1
[1,2,3,4]     => 4
[1,2,4,3]     => 2
[1,3,2,4]     => 1
[1,3,4,2]     => 2
[1,4,2,3]     => 1
[1,4,3,2]     => 2
[2,1,3,4]     => 0
[2,1,4,3]     => 0
[2,3,1,4]     => 1
[2,3,4,1]     => 2
[2,4,1,3]     => 1
[2,4,3,1]     => 2
[3,1,2,4]     => 0
[3,1,4,2]     => 0
[3,2,1,4]     => 1
[3,2,4,1]     => 0
[3,4,1,2]     => 1
[3,4,2,1]     => 2
[4,1,2,3]     => 0
[4,1,3,2]     => 0
[4,2,1,3]     => 1
[4,2,3,1]     => 0
[4,3,1,2]     => 1
[4,3,2,1]     => 0
[1,2,3,4,5]   => 5
[1,2,3,5,4]   => 3
[1,2,4,3,5]   => 2
[1,2,4,5,3]   => 3
[1,2,5,3,4]   => 2
[1,2,5,4,3]   => 3
[1,3,2,4,5]   => 1
[1,3,2,5,4]   => 1
[1,3,4,2,5]   => 2
[1,3,4,5,2]   => 3
[1,3,5,2,4]   => 2
[1,3,5,4,2]   => 3
[1,4,2,3,5]   => 1
[1,4,2,5,3]   => 1
[1,4,3,2,5]   => 2
[1,4,3,5,2]   => 1
[1,4,5,2,3]   => 2
[1,4,5,3,2]   => 3
[1,5,2,3,4]   => 1
[1,5,2,4,3]   => 1
[1,5,3,2,4]   => 2
[1,5,3,4,2]   => 1
[1,5,4,2,3]   => 2
[1,5,4,3,2]   => 1
[2,1,3,4,5]   => 0
[2,1,3,5,4]   => 0
[2,1,4,3,5]   => 0
[2,1,4,5,3]   => 0
[2,1,5,3,4]   => 0
[2,1,5,4,3]   => 0
[2,3,1,4,5]   => 1
[2,3,1,5,4]   => 1
[2,3,4,1,5]   => 2
[2,3,4,5,1]   => 3
[2,3,5,1,4]   => 2
[2,3,5,4,1]   => 3
[2,4,1,3,5]   => 1
[2,4,1,5,3]   => 1
[2,4,3,1,5]   => 2
[2,4,3,5,1]   => 1
[2,4,5,1,3]   => 2
[2,4,5,3,1]   => 3
[2,5,1,3,4]   => 1
[2,5,1,4,3]   => 1
[2,5,3,1,4]   => 2
[2,5,3,4,1]   => 1
[2,5,4,1,3]   => 2
[2,5,4,3,1]   => 1
[3,1,2,4,5]   => 0
[3,1,2,5,4]   => 0
[3,1,4,2,5]   => 0
[3,1,4,5,2]   => 0
[3,1,5,2,4]   => 0
[3,1,5,4,2]   => 0
[3,2,1,4,5]   => 1
[3,2,1,5,4]   => 1
[3,2,4,1,5]   => 0
[3,2,4,5,1]   => 0
[3,2,5,1,4]   => 0
[3,2,5,4,1]   => 0
[3,4,1,2,5]   => 1
[3,4,1,5,2]   => 1
[3,4,2,1,5]   => 2
[3,4,2,5,1]   => 1
[3,4,5,1,2]   => 2
[3,4,5,2,1]   => 3
[3,5,1,2,4]   => 1
[3,5,1,4,2]   => 1
[3,5,2,1,4]   => 2
[3,5,2,4,1]   => 1
[3,5,4,1,2]   => 2
[3,5,4,2,1]   => 1
[4,1,2,3,5]   => 0
[4,1,2,5,3]   => 0
[4,1,3,2,5]   => 0
[4,1,3,5,2]   => 0
[4,1,5,2,3]   => 0
[4,1,5,3,2]   => 0
[4,2,1,3,5]   => 1
[4,2,1,5,3]   => 1
[4,2,3,1,5]   => 0
[4,2,3,5,1]   => 0
[4,2,5,1,3]   => 0
[4,2,5,3,1]   => 0
[4,3,1,2,5]   => 1
[4,3,1,5,2]   => 1
[4,3,2,1,5]   => 0
[4,3,2,5,1]   => 1
[4,3,5,1,2]   => 0
[4,3,5,2,1]   => 0
[4,5,1,2,3]   => 1
[4,5,1,3,2]   => 1
[4,5,2,1,3]   => 2
[4,5,2,3,1]   => 1
[4,5,3,1,2]   => 2
[4,5,3,2,1]   => 1
[5,1,2,3,4]   => 0
[5,1,2,4,3]   => 0
[5,1,3,2,4]   => 0
[5,1,3,4,2]   => 0
[5,1,4,2,3]   => 0
[5,1,4,3,2]   => 0
[5,2,1,3,4]   => 1
[5,2,1,4,3]   => 1
[5,2,3,1,4]   => 0
[5,2,3,4,1]   => 0
[5,2,4,1,3]   => 0
[5,2,4,3,1]   => 0
[5,3,1,2,4]   => 1
[5,3,1,4,2]   => 1
[5,3,2,1,4]   => 0
[5,3,2,4,1]   => 1
[5,3,4,1,2]   => 0
[5,3,4,2,1]   => 0
[5,4,1,2,3]   => 1
[5,4,1,3,2]   => 1
[5,4,2,1,3]   => 0
[5,4,2,3,1]   => 1
[5,4,3,1,2]   => 0
[5,4,3,2,1]   => 1
[1,2,3,4,5,6] => 6
[1,2,3,4,6,5] => 4
[1,2,3,5,4,6] => 3
[1,2,3,5,6,4] => 4
[1,2,3,6,4,5] => 3
[1,2,3,6,5,4] => 4
[1,2,4,3,5,6] => 2
[1,2,4,3,6,5] => 2
[1,2,4,5,3,6] => 3
[1,2,4,5,6,3] => 4
[1,2,4,6,3,5] => 3
[1,2,4,6,5,3] => 4
[1,2,5,3,4,6] => 2
[1,2,5,3,6,4] => 2
[1,2,5,4,3,6] => 3
[1,2,5,4,6,3] => 2
[1,2,5,6,3,4] => 3
[1,2,5,6,4,3] => 4
[1,2,6,3,4,5] => 2
[1,2,6,3,5,4] => 2
[1,2,6,4,3,5] => 3
[1,2,6,4,5,3] => 2
[1,2,6,5,3,4] => 3
[1,2,6,5,4,3] => 2
[1,3,2,4,5,6] => 1
[1,3,2,4,6,5] => 1
[1,3,2,5,4,6] => 1
[1,3,2,5,6,4] => 1
[1,3,2,6,4,5] => 1
[1,3,2,6,5,4] => 1
[1,3,4,2,5,6] => 2
[1,3,4,2,6,5] => 2
[1,3,4,5,2,6] => 3
[1,3,4,5,6,2] => 4
[1,3,4,6,2,5] => 3
[1,3,4,6,5,2] => 4
[1,3,5,2,4,6] => 2
[1,3,5,2,6,4] => 2
[1,3,5,4,2,6] => 3
[1,3,5,4,6,2] => 2
[1,3,5,6,2,4] => 3
[1,3,5,6,4,2] => 4
[1,3,6,2,4,5] => 2
[1,3,6,2,5,4] => 2
[1,3,6,4,2,5] => 3
[1,3,6,4,5,2] => 2
[1,3,6,5,2,4] => 3
[1,3,6,5,4,2] => 2
[1,4,2,3,5,6] => 1
[1,4,2,3,6,5] => 1
[1,4,2,5,3,6] => 1
[1,4,2,5,6,3] => 1
[1,4,2,6,3,5] => 1
[1,4,2,6,5,3] => 1
[1,4,3,2,5,6] => 2
[1,4,3,2,6,5] => 2
[1,4,3,5,2,6] => 1
[1,4,3,5,6,2] => 1
[1,4,3,6,2,5] => 1
[1,4,3,6,5,2] => 1
[1,4,5,2,3,6] => 2
[1,4,5,2,6,3] => 2
[1,4,5,3,2,6] => 3
[1,4,5,3,6,2] => 2
[1,4,5,6,2,3] => 3
[1,4,5,6,3,2] => 4
[1,4,6,2,3,5] => 2
[1,4,6,2,5,3] => 2
[1,4,6,3,2,5] => 3
[1,4,6,3,5,2] => 2
[1,4,6,5,2,3] => 3
[1,4,6,5,3,2] => 2
[1,5,2,3,4,6] => 1
[1,5,2,3,6,4] => 1
[1,5,2,4,3,6] => 1
[1,5,2,4,6,3] => 1
[1,5,2,6,3,4] => 1
[1,5,2,6,4,3] => 1
[1,5,3,2,4,6] => 2
[1,5,3,2,6,4] => 2
[1,5,3,4,2,6] => 1
[1,5,3,4,6,2] => 1
[1,5,3,6,2,4] => 1
[1,5,3,6,4,2] => 1
[1,5,4,2,3,6] => 2
[1,5,4,2,6,3] => 2
[1,5,4,3,2,6] => 1
[1,5,4,3,6,2] => 2
[1,5,4,6,2,3] => 1
[1,5,4,6,3,2] => 1
[1,5,6,2,3,4] => 2
[1,5,6,2,4,3] => 2
[1,5,6,3,2,4] => 3
[1,5,6,3,4,2] => 2
[1,5,6,4,2,3] => 3
[1,5,6,4,3,2] => 2
[1,6,2,3,4,5] => 1
[1,6,2,3,5,4] => 1
[1,6,2,4,3,5] => 1
[1,6,2,4,5,3] => 1
[1,6,2,5,3,4] => 1
[1,6,2,5,4,3] => 1
[1,6,3,2,4,5] => 2
[1,6,3,2,5,4] => 2
[1,6,3,4,2,5] => 1
[1,6,3,4,5,2] => 1
[1,6,3,5,2,4] => 1
[1,6,3,5,4,2] => 1
[1,6,4,2,3,5] => 2
[1,6,4,2,5,3] => 2
[1,6,4,3,2,5] => 1
[1,6,4,3,5,2] => 2
[1,6,4,5,2,3] => 1
[1,6,4,5,3,2] => 1
[1,6,5,2,3,4] => 2
[1,6,5,2,4,3] => 2
[1,6,5,3,2,4] => 1
[1,6,5,3,4,2] => 2
[1,6,5,4,2,3] => 1
[1,6,5,4,3,2] => 2
[2,1,3,4,5,6] => 0
[2,1,3,4,6,5] => 0
[2,1,3,5,4,6] => 0
[2,1,3,5,6,4] => 0
[2,1,3,6,4,5] => 0
[2,1,3,6,5,4] => 0
[2,1,4,3,5,6] => 0
[2,1,4,3,6,5] => 0
[2,1,4,5,3,6] => 0
[2,1,4,5,6,3] => 0
[2,1,4,6,3,5] => 0
[2,1,4,6,5,3] => 0
[2,1,5,3,4,6] => 0
[2,1,5,3,6,4] => 0
[2,1,5,4,3,6] => 0
[2,1,5,4,6,3] => 0
[2,1,5,6,3,4] => 0
[2,1,5,6,4,3] => 0
[2,1,6,3,4,5] => 0
[2,1,6,3,5,4] => 0
[2,1,6,4,3,5] => 0
[2,1,6,4,5,3] => 0
[2,1,6,5,3,4] => 0
[2,1,6,5,4,3] => 0
[2,3,1,4,5,6] => 1
[2,3,1,4,6,5] => 1
[2,3,1,5,4,6] => 1
[2,3,1,5,6,4] => 1
[2,3,1,6,4,5] => 1
[2,3,1,6,5,4] => 1
[2,3,4,1,5,6] => 2
[2,3,4,1,6,5] => 2
[2,3,4,5,1,6] => 3
[2,3,4,5,6,1] => 4
[2,3,4,6,1,5] => 3
[2,3,4,6,5,1] => 4
[2,3,5,1,4,6] => 2
[2,3,5,1,6,4] => 2
[2,3,5,4,1,6] => 3
[2,3,5,4,6,1] => 2
[2,3,5,6,1,4] => 3
[2,3,5,6,4,1] => 4
[2,3,6,1,4,5] => 2
[2,3,6,1,5,4] => 2
[2,3,6,4,1,5] => 3
[2,3,6,4,5,1] => 2
[2,3,6,5,1,4] => 3
[2,3,6,5,4,1] => 2
[2,4,1,3,5,6] => 1
[2,4,1,3,6,5] => 1
[2,4,1,5,3,6] => 1
[2,4,1,5,6,3] => 1
[2,4,1,6,3,5] => 1
[2,4,1,6,5,3] => 1
[2,4,3,1,5,6] => 2
[2,4,3,1,6,5] => 2
[2,4,3,5,1,6] => 1
[2,4,3,5,6,1] => 1
[2,4,3,6,1,5] => 1
[2,4,3,6,5,1] => 1
[2,4,5,1,3,6] => 2
[2,4,5,1,6,3] => 2
[2,4,5,3,1,6] => 3
[2,4,5,3,6,1] => 2
[2,4,5,6,1,3] => 3
[2,4,5,6,3,1] => 4
[2,4,6,1,3,5] => 2
[2,4,6,1,5,3] => 2
[2,4,6,3,1,5] => 3
[2,4,6,3,5,1] => 2
[2,4,6,5,1,3] => 3
[2,4,6,5,3,1] => 2
[2,5,1,3,4,6] => 1
[2,5,1,3,6,4] => 1
[2,5,1,4,3,6] => 1
[2,5,1,4,6,3] => 1
[2,5,1,6,3,4] => 1
[2,5,1,6,4,3] => 1
[2,5,3,1,4,6] => 2
[2,5,3,1,6,4] => 2
[2,5,3,4,1,6] => 1
[2,5,3,4,6,1] => 1
[2,5,3,6,1,4] => 1
[2,5,3,6,4,1] => 1
[2,5,4,1,3,6] => 2
[2,5,4,1,6,3] => 2
[2,5,4,3,1,6] => 1
[2,5,4,3,6,1] => 2
[2,5,4,6,1,3] => 1
[2,5,4,6,3,1] => 1
[2,5,6,1,3,4] => 2
[2,5,6,1,4,3] => 2
[2,5,6,3,1,4] => 3
[2,5,6,3,4,1] => 2
[2,5,6,4,1,3] => 3
[2,5,6,4,3,1] => 2
[2,6,1,3,4,5] => 1
[2,6,1,3,5,4] => 1
[2,6,1,4,3,5] => 1
[2,6,1,4,5,3] => 1
[2,6,1,5,3,4] => 1
[2,6,1,5,4,3] => 1
[2,6,3,1,4,5] => 2
[2,6,3,1,5,4] => 2
[2,6,3,4,1,5] => 1
[2,6,3,4,5,1] => 1
[2,6,3,5,1,4] => 1
[2,6,3,5,4,1] => 1
[2,6,4,1,3,5] => 2
[2,6,4,1,5,3] => 2
[2,6,4,3,1,5] => 1
[2,6,4,3,5,1] => 2
[2,6,4,5,1,3] => 1
[2,6,4,5,3,1] => 1
[2,6,5,1,3,4] => 2
[2,6,5,1,4,3] => 2
[2,6,5,3,1,4] => 1
[2,6,5,3,4,1] => 2
[2,6,5,4,1,3] => 1
[2,6,5,4,3,1] => 2
[3,1,2,4,5,6] => 0
[3,1,2,4,6,5] => 0
[3,1,2,5,4,6] => 0
[3,1,2,5,6,4] => 0
[3,1,2,6,4,5] => 0
[3,1,2,6,5,4] => 0
[3,1,4,2,5,6] => 0
[3,1,4,2,6,5] => 0
[3,1,4,5,2,6] => 0
[3,1,4,5,6,2] => 0
[3,1,4,6,2,5] => 0
[3,1,4,6,5,2] => 0
[3,1,5,2,4,6] => 0
[3,1,5,2,6,4] => 0
[3,1,5,4,2,6] => 0
[3,1,5,4,6,2] => 0
[3,1,5,6,2,4] => 0
[3,1,5,6,4,2] => 0
[3,1,6,2,4,5] => 0
[3,1,6,2,5,4] => 0
[3,1,6,4,2,5] => 0
[3,1,6,4,5,2] => 0
[3,1,6,5,2,4] => 0
[3,1,6,5,4,2] => 0
[3,2,1,4,5,6] => 1
[3,2,1,4,6,5] => 1
[3,2,1,5,4,6] => 1
[3,2,1,5,6,4] => 1
[3,2,1,6,4,5] => 1
[3,2,1,6,5,4] => 1
[3,2,4,1,5,6] => 0
[3,2,4,1,6,5] => 0
[3,2,4,5,1,6] => 0
[3,2,4,5,6,1] => 0
[3,2,4,6,1,5] => 0
[3,2,4,6,5,1] => 0
[3,2,5,1,4,6] => 0
[3,2,5,1,6,4] => 0
[3,2,5,4,1,6] => 0
[3,2,5,4,6,1] => 0
[3,2,5,6,1,4] => 0
[3,2,5,6,4,1] => 0
[3,2,6,1,4,5] => 0
[3,2,6,1,5,4] => 0
[3,2,6,4,1,5] => 0
[3,2,6,4,5,1] => 0
[3,2,6,5,1,4] => 0
[3,2,6,5,4,1] => 0
[3,4,1,2,5,6] => 1
[3,4,1,2,6,5] => 1
[3,4,1,5,2,6] => 1
[3,4,1,5,6,2] => 1
[3,4,1,6,2,5] => 1
[3,4,1,6,5,2] => 1
[3,4,2,1,5,6] => 2
[3,4,2,1,6,5] => 2
[3,4,2,5,1,6] => 1
[3,4,2,5,6,1] => 1
[3,4,2,6,1,5] => 1
[3,4,2,6,5,1] => 1
[3,4,5,1,2,6] => 2
[3,4,5,1,6,2] => 2
[3,4,5,2,1,6] => 3
[3,4,5,2,6,1] => 2
[3,4,5,6,1,2] => 3
[3,4,5,6,2,1] => 4
[3,4,6,1,2,5] => 2
[3,4,6,1,5,2] => 2
[3,4,6,2,1,5] => 3
[3,4,6,2,5,1] => 2
[3,4,6,5,1,2] => 3
[3,4,6,5,2,1] => 2
[3,5,1,2,4,6] => 1
[3,5,1,2,6,4] => 1
[3,5,1,4,2,6] => 1
[3,5,1,4,6,2] => 1
[3,5,1,6,2,4] => 1
[3,5,1,6,4,2] => 1
[3,5,2,1,4,6] => 2
[3,5,2,1,6,4] => 2
[3,5,2,4,1,6] => 1
[3,5,2,4,6,1] => 1
[3,5,2,6,1,4] => 1
[3,5,2,6,4,1] => 1
[3,5,4,1,2,6] => 2
[3,5,4,1,6,2] => 2
[3,5,4,2,1,6] => 1
[3,5,4,2,6,1] => 2
[3,5,4,6,1,2] => 1
[3,5,4,6,2,1] => 1
[3,5,6,1,2,4] => 2
[3,5,6,1,4,2] => 2
[3,5,6,2,1,4] => 3
[3,5,6,2,4,1] => 2
[3,5,6,4,1,2] => 3
[3,5,6,4,2,1] => 2
[3,6,1,2,4,5] => 1
[3,6,1,2,5,4] => 1
[3,6,1,4,2,5] => 1
[3,6,1,4,5,2] => 1
[3,6,1,5,2,4] => 1
[3,6,1,5,4,2] => 1
[3,6,2,1,4,5] => 2
[3,6,2,1,5,4] => 2
[3,6,2,4,1,5] => 1
[3,6,2,4,5,1] => 1
[3,6,2,5,1,4] => 1
[3,6,2,5,4,1] => 1
[3,6,4,1,2,5] => 2
[3,6,4,1,5,2] => 2
[3,6,4,2,1,5] => 1
[3,6,4,2,5,1] => 2
[3,6,4,5,1,2] => 1
[3,6,4,5,2,1] => 1
[3,6,5,1,2,4] => 2
[3,6,5,1,4,2] => 2
[3,6,5,2,1,4] => 1
[3,6,5,2,4,1] => 2
[3,6,5,4,1,2] => 1
[3,6,5,4,2,1] => 2
[4,1,2,3,5,6] => 0
[4,1,2,3,6,5] => 0
[4,1,2,5,3,6] => 0
[4,1,2,5,6,3] => 0
[4,1,2,6,3,5] => 0
[4,1,2,6,5,3] => 0
[4,1,3,2,5,6] => 0
[4,1,3,2,6,5] => 0
[4,1,3,5,2,6] => 0
[4,1,3,5,6,2] => 0
[4,1,3,6,2,5] => 0
[4,1,3,6,5,2] => 0
[4,1,5,2,3,6] => 0
[4,1,5,2,6,3] => 0
[4,1,5,3,2,6] => 0
[4,1,5,3,6,2] => 0
[4,1,5,6,2,3] => 0
[4,1,5,6,3,2] => 0
[4,1,6,2,3,5] => 0
[4,1,6,2,5,3] => 0
[4,1,6,3,2,5] => 0
[4,1,6,3,5,2] => 0
[4,1,6,5,2,3] => 0
[4,1,6,5,3,2] => 0
[4,2,1,3,5,6] => 1
[4,2,1,3,6,5] => 1
[4,2,1,5,3,6] => 1
[4,2,1,5,6,3] => 1
[4,2,1,6,3,5] => 1
[4,2,1,6,5,3] => 1
[4,2,3,1,5,6] => 0
[4,2,3,1,6,5] => 0
[4,2,3,5,1,6] => 0
[4,2,3,5,6,1] => 0
[4,2,3,6,1,5] => 0
[4,2,3,6,5,1] => 0
[4,2,5,1,3,6] => 0
[4,2,5,1,6,3] => 0
[4,2,5,3,1,6] => 0
[4,2,5,3,6,1] => 0
[4,2,5,6,1,3] => 0
[4,2,5,6,3,1] => 0
[4,2,6,1,3,5] => 0
[4,2,6,1,5,3] => 0
[4,2,6,3,1,5] => 0
[4,2,6,3,5,1] => 0
[4,2,6,5,1,3] => 0
[4,2,6,5,3,1] => 0
[4,3,1,2,5,6] => 1
[4,3,1,2,6,5] => 1
[4,3,1,5,2,6] => 1
[4,3,1,5,6,2] => 1
[4,3,1,6,2,5] => 1
[4,3,1,6,5,2] => 1
[4,3,2,1,5,6] => 0
[4,3,2,1,6,5] => 0
[4,3,2,5,1,6] => 1
[4,3,2,5,6,1] => 1
[4,3,2,6,1,5] => 1
[4,3,2,6,5,1] => 1
[4,3,5,1,2,6] => 0
[4,3,5,1,6,2] => 0
[4,3,5,2,1,6] => 0
[4,3,5,2,6,1] => 0
[4,3,5,6,1,2] => 0
[4,3,5,6,2,1] => 0
[4,3,6,1,2,5] => 0
[4,3,6,1,5,2] => 0
[4,3,6,2,1,5] => 0
[4,3,6,2,5,1] => 0
[4,3,6,5,1,2] => 0
[4,3,6,5,2,1] => 0
[4,5,1,2,3,6] => 1
[4,5,1,2,6,3] => 1
[4,5,1,3,2,6] => 1
[4,5,1,3,6,2] => 1
[4,5,1,6,2,3] => 1
[4,5,1,6,3,2] => 1
[4,5,2,1,3,6] => 2
[4,5,2,1,6,3] => 2
[4,5,2,3,1,6] => 1
[4,5,2,3,6,1] => 1
[4,5,2,6,1,3] => 1
[4,5,2,6,3,1] => 1
[4,5,3,1,2,6] => 2
[4,5,3,1,6,2] => 2
[4,5,3,2,1,6] => 1
[4,5,3,2,6,1] => 2
[4,5,3,6,1,2] => 1
[4,5,3,6,2,1] => 1
[4,5,6,1,2,3] => 2
[4,5,6,1,3,2] => 2
[4,5,6,2,1,3] => 3
[4,5,6,2,3,1] => 2
[4,5,6,3,1,2] => 3
[4,5,6,3,2,1] => 2
[4,6,1,2,3,5] => 1
[4,6,1,2,5,3] => 1
[4,6,1,3,2,5] => 1
[4,6,1,3,5,2] => 1
[4,6,1,5,2,3] => 1
[4,6,1,5,3,2] => 1
[4,6,2,1,3,5] => 2
[4,6,2,1,5,3] => 2
[4,6,2,3,1,5] => 1
[4,6,2,3,5,1] => 1
[4,6,2,5,1,3] => 1
[4,6,2,5,3,1] => 1
[4,6,3,1,2,5] => 2
[4,6,3,1,5,2] => 2
[4,6,3,2,1,5] => 1
[4,6,3,2,5,1] => 2
[4,6,3,5,1,2] => 1
[4,6,3,5,2,1] => 1
[4,6,5,1,2,3] => 2
[4,6,5,1,3,2] => 2
[4,6,5,2,1,3] => 1
[4,6,5,2,3,1] => 2
[4,6,5,3,1,2] => 1
[4,6,5,3,2,1] => 2
[5,1,2,3,4,6] => 0
[5,1,2,3,6,4] => 0
[5,1,2,4,3,6] => 0
[5,1,2,4,6,3] => 0
[5,1,2,6,3,4] => 0
[5,1,2,6,4,3] => 0
[5,1,3,2,4,6] => 0
[5,1,3,2,6,4] => 0
[5,1,3,4,2,6] => 0
[5,1,3,4,6,2] => 0
[5,1,3,6,2,4] => 0
[5,1,3,6,4,2] => 0
[5,1,4,2,3,6] => 0
[5,1,4,2,6,3] => 0
[5,1,4,3,2,6] => 0
[5,1,4,3,6,2] => 0
[5,1,4,6,2,3] => 0
[5,1,4,6,3,2] => 0
[5,1,6,2,3,4] => 0
[5,1,6,2,4,3] => 0
[5,1,6,3,2,4] => 0
[5,1,6,3,4,2] => 0
[5,1,6,4,2,3] => 0
[5,1,6,4,3,2] => 0
[5,2,1,3,4,6] => 1
[5,2,1,3,6,4] => 1
[5,2,1,4,3,6] => 1
[5,2,1,4,6,3] => 1
[5,2,1,6,3,4] => 1
[5,2,1,6,4,3] => 1
[5,2,3,1,4,6] => 0
[5,2,3,1,6,4] => 0
[5,2,3,4,1,6] => 0
[5,2,3,4,6,1] => 0
[5,2,3,6,1,4] => 0
[5,2,3,6,4,1] => 0
[5,2,4,1,3,6] => 0
[5,2,4,1,6,3] => 0
[5,2,4,3,1,6] => 0
[5,2,4,3,6,1] => 0
[5,2,4,6,1,3] => 0
[5,2,4,6,3,1] => 0
[5,2,6,1,3,4] => 0
[5,2,6,1,4,3] => 0
[5,2,6,3,1,4] => 0
[5,2,6,3,4,1] => 0
[5,2,6,4,1,3] => 0
[5,2,6,4,3,1] => 0
[5,3,1,2,4,6] => 1
[5,3,1,2,6,4] => 1
[5,3,1,4,2,6] => 1
[5,3,1,4,6,2] => 1
[5,3,1,6,2,4] => 1
[5,3,1,6,4,2] => 1
[5,3,2,1,4,6] => 0
[5,3,2,1,6,4] => 0
[5,3,2,4,1,6] => 1
[5,3,2,4,6,1] => 1
[5,3,2,6,1,4] => 1
[5,3,2,6,4,1] => 1
[5,3,4,1,2,6] => 0
[5,3,4,1,6,2] => 0
[5,3,4,2,1,6] => 0
[5,3,4,2,6,1] => 0
[5,3,4,6,1,2] => 0
[5,3,4,6,2,1] => 0
[5,3,6,1,2,4] => 0
[5,3,6,1,4,2] => 0
[5,3,6,2,1,4] => 0
[5,3,6,2,4,1] => 0
[5,3,6,4,1,2] => 0
[5,3,6,4,2,1] => 0
[5,4,1,2,3,6] => 1
[5,4,1,2,6,3] => 1
[5,4,1,3,2,6] => 1
[5,4,1,3,6,2] => 1
[5,4,1,6,2,3] => 1
[5,4,1,6,3,2] => 1
[5,4,2,1,3,6] => 0
[5,4,2,1,6,3] => 0
[5,4,2,3,1,6] => 1
[5,4,2,3,6,1] => 1
[5,4,2,6,1,3] => 1
[5,4,2,6,3,1] => 1
[5,4,3,1,2,6] => 0
[5,4,3,1,6,2] => 0
[5,4,3,2,1,6] => 1
[5,4,3,2,6,1] => 0
[5,4,3,6,1,2] => 1
[5,4,3,6,2,1] => 1
[5,4,6,1,2,3] => 0
[5,4,6,1,3,2] => 0
[5,4,6,2,1,3] => 0
[5,4,6,2,3,1] => 0
[5,4,6,3,1,2] => 0
[5,4,6,3,2,1] => 0
[5,6,1,2,3,4] => 1
[5,6,1,2,4,3] => 1
[5,6,1,3,2,4] => 1
[5,6,1,3,4,2] => 1
[5,6,1,4,2,3] => 1
[5,6,1,4,3,2] => 1
[5,6,2,1,3,4] => 2
[5,6,2,1,4,3] => 2
[5,6,2,3,1,4] => 1
[5,6,2,3,4,1] => 1
[5,6,2,4,1,3] => 1
[5,6,2,4,3,1] => 1
[5,6,3,1,2,4] => 2
[5,6,3,1,4,2] => 2
[5,6,3,2,1,4] => 1
[5,6,3,2,4,1] => 2
[5,6,3,4,1,2] => 1
[5,6,3,4,2,1] => 1
[5,6,4,1,2,3] => 2
[5,6,4,1,3,2] => 2
[5,6,4,2,1,3] => 1
[5,6,4,2,3,1] => 2
[5,6,4,3,1,2] => 1
[5,6,4,3,2,1] => 2
[6,1,2,3,4,5] => 0
[6,1,2,3,5,4] => 0
[6,1,2,4,3,5] => 0
[6,1,2,4,5,3] => 0
[6,1,2,5,3,4] => 0
[6,1,2,5,4,3] => 0
[6,1,3,2,4,5] => 0
[6,1,3,2,5,4] => 0
[6,1,3,4,2,5] => 0
[6,1,3,4,5,2] => 0
[6,1,3,5,2,4] => 0
[6,1,3,5,4,2] => 0
[6,1,4,2,3,5] => 0
[6,1,4,2,5,3] => 0
[6,1,4,3,2,5] => 0
[6,1,4,3,5,2] => 0
[6,1,4,5,2,3] => 0
[6,1,4,5,3,2] => 0
[6,1,5,2,3,4] => 0
[6,1,5,2,4,3] => 0
[6,1,5,3,2,4] => 0
[6,1,5,3,4,2] => 0
[6,1,5,4,2,3] => 0
[6,1,5,4,3,2] => 0
[6,2,1,3,4,5] => 1
[6,2,1,3,5,4] => 1
[6,2,1,4,3,5] => 1
[6,2,1,4,5,3] => 1
[6,2,1,5,3,4] => 1
[6,2,1,5,4,3] => 1
[6,2,3,1,4,5] => 0
[6,2,3,1,5,4] => 0
[6,2,3,4,1,5] => 0
[6,2,3,4,5,1] => 0
[6,2,3,5,1,4] => 0
[6,2,3,5,4,1] => 0
[6,2,4,1,3,5] => 0
[6,2,4,1,5,3] => 0
[6,2,4,3,1,5] => 0
[6,2,4,3,5,1] => 0
[6,2,4,5,1,3] => 0
[6,2,4,5,3,1] => 0
[6,2,5,1,3,4] => 0
[6,2,5,1,4,3] => 0
[6,2,5,3,1,4] => 0
[6,2,5,3,4,1] => 0
[6,2,5,4,1,3] => 0
[6,2,5,4,3,1] => 0
[6,3,1,2,4,5] => 1
[6,3,1,2,5,4] => 1
[6,3,1,4,2,5] => 1
[6,3,1,4,5,2] => 1
[6,3,1,5,2,4] => 1
[6,3,1,5,4,2] => 1
[6,3,2,1,4,5] => 0
[6,3,2,1,5,4] => 0
[6,3,2,4,1,5] => 1
[6,3,2,4,5,1] => 1
[6,3,2,5,1,4] => 1
[6,3,2,5,4,1] => 1
[6,3,4,1,2,5] => 0
[6,3,4,1,5,2] => 0
[6,3,4,2,1,5] => 0
[6,3,4,2,5,1] => 0
[6,3,4,5,1,2] => 0
[6,3,4,5,2,1] => 0
[6,3,5,1,2,4] => 0
[6,3,5,1,4,2] => 0
[6,3,5,2,1,4] => 0
[6,3,5,2,4,1] => 0
[6,3,5,4,1,2] => 0
[6,3,5,4,2,1] => 0
[6,4,1,2,3,5] => 1
[6,4,1,2,5,3] => 1
[6,4,1,3,2,5] => 1
[6,4,1,3,5,2] => 1
[6,4,1,5,2,3] => 1
[6,4,1,5,3,2] => 1
[6,4,2,1,3,5] => 0
[6,4,2,1,5,3] => 0
[6,4,2,3,1,5] => 1
[6,4,2,3,5,1] => 1
[6,4,2,5,1,3] => 1
[6,4,2,5,3,1] => 1
[6,4,3,1,2,5] => 0
[6,4,3,1,5,2] => 0
[6,4,3,2,1,5] => 1
[6,4,3,2,5,1] => 0
[6,4,3,5,1,2] => 1
[6,4,3,5,2,1] => 1
[6,4,5,1,2,3] => 0
[6,4,5,1,3,2] => 0
[6,4,5,2,1,3] => 0
[6,4,5,2,3,1] => 0
[6,4,5,3,1,2] => 0
[6,4,5,3,2,1] => 0
[6,5,1,2,3,4] => 1
[6,5,1,2,4,3] => 1
[6,5,1,3,2,4] => 1
[6,5,1,3,4,2] => 1
[6,5,1,4,2,3] => 1
[6,5,1,4,3,2] => 1
[6,5,2,1,3,4] => 0
[6,5,2,1,4,3] => 0
[6,5,2,3,1,4] => 1
[6,5,2,3,4,1] => 1
[6,5,2,4,1,3] => 1
[6,5,2,4,3,1] => 1
[6,5,3,1,2,4] => 0
[6,5,3,1,4,2] => 0
[6,5,3,2,1,4] => 1
[6,5,3,2,4,1] => 0
[6,5,3,4,1,2] => 1
[6,5,3,4,2,1] => 1
[6,5,4,1,2,3] => 0
[6,5,4,1,3,2] => 0
[6,5,4,2,1,3] => 1
[6,5,4,2,3,1] => 0
[6,5,4,3,1,2] => 1
[6,5,4,3,2,1] => 0

-----------------------------------------------------------------------------
Created: Dec 18, 2015 at 13:44 by Joseph Bernstein

-----------------------------------------------------------------------------
Last Updated: Apr 06, 2016 at 22:50 by Martin Rubey