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* www.FindStat.org - The Combinatorial Statistic Finder *
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* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
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* This information is distributed in the hope that it will be useful, *
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. *
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-----------------------------------------------------------------------------
Statistic identifier: St001402
-----------------------------------------------------------------------------
Collection: Permutations
-----------------------------------------------------------------------------
Description: The number of separators in a permutation.
Let $\sigma$ be a permutation. Then $\sigma_i$ is a vertical separator if $|\sigma_{i-1} - \sigma_{i+1}| = 1$, and $i$ is a horizontal separator, if it is a vertical separator of $\sigma^{-1}$. The set of separators is the union of the set of the vertical and the set of the horizontal separators.
-----------------------------------------------------------------------------
References: [1] Bagno, E., Eisenberg, E., Reches, S., Sigron, M. Separators - a new statistic for permutations [[arXiv:1905.12364]]
-----------------------------------------------------------------------------
Code:
def statistic(pi):
"""
sage: oeis([sum(1 for pi in Permutations(n) if not statistic(pi)) for n in range(1,7)])
0: A137774: Number of ways to place n nonattacking empresses on an n X n board.
"""
return len(separators(pi))
def vertical_separators(sigma):
"""
sage: list(vertical_separators(sigma))
[3, 2, 6, 7]
"""
n = len(sigma)
for i in range(n):
if 0 < i < n-1 and abs(sigma[i-1]-sigma[i+1]) == 1:
yield sigma[i]
def horizontal_separators(sigma):
"""
sage: list(horizontal_separators(sigma))
[2, 3, 5, 8]
"""
sigma_inv = sigma.inverse()
for i in vertical_separators(sigma_inv):
yield sigma_inv(i)
def separators(sigma):
"""
sage: separators(sigma)
[2, 3, 5, 6, 7, 8]
"""
return list(set(horizontal_separators(sigma)).union(set(vertical_separators(sigma))))
-----------------------------------------------------------------------------
Statistic values:
[1] => 0
[1,2] => 0
[2,1] => 0
[1,2,3] => 0
[1,3,2] => 2
[2,1,3] => 2
[2,3,1] => 1
[3,1,2] => 1
[3,2,1] => 0
[1,2,3,4] => 0
[1,2,4,3] => 2
[1,3,2,4] => 2
[1,3,4,2] => 2
[1,4,2,3] => 2
[1,4,3,2] => 0
[2,1,3,4] => 2
[2,1,4,3] => 0
[2,3,1,4] => 2
[2,3,4,1] => 0
[2,4,1,3] => 4
[2,4,3,1] => 2
[3,1,2,4] => 2
[3,1,4,2] => 4
[3,2,1,4] => 0
[3,2,4,1] => 2
[3,4,1,2] => 0
[3,4,2,1] => 1
[4,1,2,3] => 0
[4,1,3,2] => 2
[4,2,1,3] => 2
[4,2,3,1] => 2
[4,3,1,2] => 1
[4,3,2,1] => 0
[1,2,3,4,5] => 0
[1,2,3,5,4] => 2
[1,2,4,3,5] => 2
[1,2,4,5,3] => 2
[1,2,5,3,4] => 2
[1,2,5,4,3] => 0
[1,3,2,4,5] => 2
[1,3,2,5,4] => 2
[1,3,4,2,5] => 3
[1,3,4,5,2] => 1
[1,3,5,2,4] => 4
[1,3,5,4,2] => 3
[1,4,2,3,5] => 3
[1,4,2,5,3] => 4
[1,4,3,2,5] => 0
[1,4,3,5,2] => 2
[1,4,5,2,3] => 0
[1,4,5,3,2] => 1
[1,5,2,3,4] => 1
[1,5,2,4,3] => 3
[1,5,3,2,4] => 2
[1,5,3,4,2] => 2
[1,5,4,2,3] => 1
[1,5,4,3,2] => 0
[2,1,3,4,5] => 2
[2,1,3,5,4] => 4
[2,1,4,3,5] => 2
[2,1,4,5,3] => 1
[2,1,5,3,4] => 1
[2,1,5,4,3] => 0
[2,3,1,4,5] => 2
[2,3,1,5,4] => 1
[2,3,4,1,5] => 1
[2,3,4,5,1] => 0
[2,3,5,1,4] => 2
[2,3,5,4,1] => 2
[2,4,1,3,5] => 4
[2,4,1,5,3] => 2
[2,4,3,1,5] => 2
[2,4,3,5,1] => 3
[2,4,5,1,3] => 2
[2,4,5,3,1] => 3
[2,5,1,3,4] => 2
[2,5,1,4,3] => 2
[2,5,3,1,4] => 4
[2,5,3,4,1] => 3
[2,5,4,1,3] => 2
[2,5,4,3,1] => 1
[3,1,2,4,5] => 2
[3,1,2,5,4] => 1
[3,1,4,2,5] => 4
[3,1,4,5,2] => 2
[3,1,5,2,4] => 2
[3,1,5,4,2] => 2
[3,2,1,4,5] => 0
[3,2,1,5,4] => 0
[3,2,4,1,5] => 3
[3,2,4,5,1] => 2
[3,2,5,1,4] => 2
[3,2,5,4,1] => 0
[3,4,1,2,5] => 0
[3,4,1,5,2] => 2
[3,4,2,1,5] => 1
[3,4,2,5,1] => 3
[3,4,5,1,2] => 0
[3,4,5,2,1] => 0
[3,5,1,2,4] => 2
[3,5,1,4,2] => 3
[3,5,2,1,4] => 2
[3,5,2,4,1] => 3
[3,5,4,1,2] => 2
[3,5,4,2,1] => 2
[4,1,2,3,5] => 1
[4,1,2,5,3] => 2
[4,1,3,2,5] => 2
[4,1,3,5,2] => 4
[4,1,5,2,3] => 2
[4,1,5,3,2] => 2
[4,2,1,3,5] => 3
[4,2,1,5,3] => 2
[4,2,3,1,5] => 2
[4,2,3,5,1] => 3
[4,2,5,1,3] => 3
[4,2,5,3,1] => 3
[4,3,1,2,5] => 1
[4,3,1,5,2] => 2
[4,3,2,1,5] => 0
[4,3,2,5,1] => 1
[4,3,5,1,2] => 2
[4,3,5,2,1] => 2
[4,5,1,2,3] => 0
[4,5,1,3,2] => 2
[4,5,2,1,3] => 2
[4,5,2,3,1] => 2
[4,5,3,1,2] => 4
[4,5,3,2,1] => 1
[5,1,2,3,4] => 0
[5,1,2,4,3] => 2
[5,1,3,2,4] => 3
[5,1,3,4,2] => 3
[5,1,4,2,3] => 3
[5,1,4,3,2] => 1
[5,2,1,3,4] => 2
[5,2,1,4,3] => 0
[5,2,3,1,4] => 3
[5,2,3,4,1] => 0
[5,2,4,1,3] => 3
[5,2,4,3,1] => 3
[5,3,1,2,4] => 3
[5,3,1,4,2] => 3
[5,3,2,1,4] => 1
[5,3,2,4,1] => 3
[5,3,4,1,2] => 2
[5,3,4,2,1] => 3
[5,4,1,2,3] => 0
[5,4,1,3,2] => 2
[5,4,2,1,3] => 2
[5,4,2,3,1] => 3
[5,4,3,1,2] => 1
[5,4,3,2,1] => 0
[1,2,3,4,5,6] => 0
[1,2,3,4,6,5] => 2
[1,2,3,5,4,6] => 2
[1,2,3,5,6,4] => 2
[1,2,3,6,4,5] => 2
[1,2,3,6,5,4] => 0
[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] => 1
[1,2,4,6,3,5] => 4
[1,2,4,6,5,3] => 3
[1,2,5,3,4,6] => 3
[1,2,5,3,6,4] => 4
[1,2,5,4,3,6] => 0
[1,2,5,4,6,3] => 2
[1,2,5,6,3,4] => 0
[1,2,5,6,4,3] => 1
[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] => 2
[1,2,6,5,3,4] => 1
[1,2,6,5,4,3] => 0
[1,3,2,4,5,6] => 2
[1,3,2,4,6,5] => 4
[1,3,2,5,4,6] => 4
[1,3,2,5,6,4] => 3
[1,3,2,6,4,5] => 3
[1,3,2,6,5,4] => 2
[1,3,4,2,5,6] => 3
[1,3,4,2,6,5] => 2
[1,3,4,5,2,6] => 2
[1,3,4,5,6,2] => 1
[1,3,4,6,2,5] => 3
[1,3,4,6,5,2] => 3
[1,3,5,2,4,6] => 4
[1,3,5,2,6,4] => 3
[1,3,5,4,2,6] => 3
[1,3,5,4,6,2] => 3
[1,3,5,6,2,4] => 3
[1,3,5,6,4,2] => 4
[1,3,6,2,4,5] => 3
[1,3,6,2,5,4] => 2
[1,3,6,4,2,5] => 4
[1,3,6,4,5,2] => 4
[1,3,6,5,2,4] => 3
[1,3,6,5,4,2] => 2
[1,4,2,3,5,6] => 3
[1,4,2,3,6,5] => 2
[1,4,2,5,3,6] => 4
[1,4,2,5,6,3] => 3
[1,4,2,6,3,5] => 3
[1,4,2,6,5,3] => 2
[1,4,3,2,5,6] => 0
[1,4,3,2,6,5] => 0
[1,4,3,5,2,6] => 3
[1,4,3,5,6,2] => 2
[1,4,3,6,2,5] => 2
[1,4,3,6,5,2] => 0
[1,4,5,2,3,6] => 0
[1,4,5,2,6,3] => 2
[1,4,5,3,2,6] => 1
[1,4,5,3,6,2] => 3
[1,4,5,6,2,3] => 0
[1,4,5,6,3,2] => 0
[1,4,6,2,3,5] => 2
[1,4,6,2,5,3] => 3
[1,4,6,3,2,5] => 2
[1,4,6,3,5,2] => 3
[1,4,6,5,2,3] => 2
[1,4,6,5,3,2] => 2
[1,5,2,3,4,6] => 2
[1,5,2,3,6,4] => 3
[1,5,2,4,3,6] => 3
[1,5,2,4,6,3] => 4
[1,5,2,6,3,4] => 3
[1,5,2,6,4,3] => 3
[1,5,3,2,4,6] => 3
[1,5,3,2,6,4] => 2
[1,5,3,4,2,6] => 2
[1,5,3,4,6,2] => 3
[1,5,3,6,2,4] => 3
[1,5,3,6,4,2] => 3
[1,5,4,2,3,6] => 1
[1,5,4,2,6,3] => 2
[1,5,4,3,2,6] => 0
[1,5,4,3,6,2] => 1
[1,5,4,6,2,3] => 2
[1,5,4,6,3,2] => 2
[1,5,6,2,3,4] => 0
[1,5,6,2,4,3] => 2
[1,5,6,3,2,4] => 2
[1,5,6,3,4,2] => 2
[1,5,6,4,2,3] => 4
[1,5,6,4,3,2] => 1
[1,6,2,3,4,5] => 1
[1,6,2,3,5,4] => 3
[1,6,2,4,3,5] => 3
[1,6,2,4,5,3] => 4
[1,6,2,5,3,4] => 4
[1,6,2,5,4,3] => 2
[1,6,3,2,4,5] => 2
[1,6,3,2,5,4] => 0
[1,6,3,4,2,5] => 3
[1,6,3,4,5,2] => 0
[1,6,3,5,2,4] => 3
[1,6,3,5,4,2] => 3
[1,6,4,2,3,5] => 3
[1,6,4,2,5,3] => 3
[1,6,4,3,2,5] => 1
[1,6,4,3,5,2] => 3
[1,6,4,5,2,3] => 2
[1,6,4,5,3,2] => 3
[1,6,5,2,3,4] => 0
[1,6,5,2,4,3] => 2
[1,6,5,3,2,4] => 2
[1,6,5,3,4,2] => 3
[1,6,5,4,2,3] => 1
[1,6,5,4,3,2] => 0
[2,1,3,4,5,6] => 2
[2,1,3,4,6,5] => 4
[2,1,3,5,4,6] => 4
[2,1,3,5,6,4] => 4
[2,1,3,6,4,5] => 4
[2,1,3,6,5,4] => 2
[2,1,4,3,5,6] => 2
[2,1,4,3,6,5] => 0
[2,1,4,5,3,6] => 2
[2,1,4,5,6,3] => 0
[2,1,4,6,3,5] => 4
[2,1,4,6,5,3] => 2
[2,1,5,3,4,6] => 2
[2,1,5,3,6,4] => 4
[2,1,5,4,3,6] => 0
[2,1,5,4,6,3] => 2
[2,1,5,6,3,4] => 0
[2,1,5,6,4,3] => 1
[2,1,6,3,4,5] => 0
[2,1,6,3,5,4] => 2
[2,1,6,4,3,5] => 2
[2,1,6,4,5,3] => 2
[2,1,6,5,3,4] => 1
[2,1,6,5,4,3] => 0
[2,3,1,4,5,6] => 2
[2,3,1,4,6,5] => 4
[2,3,1,5,4,6] => 3
[2,3,1,5,6,4] => 2
[2,3,1,6,4,5] => 2
[2,3,1,6,5,4] => 1
[2,3,4,1,5,6] => 1
[2,3,4,1,6,5] => 0
[2,3,4,5,1,6] => 1
[2,3,4,5,6,1] => 0
[2,3,4,6,1,5] => 2
[2,3,4,6,5,1] => 2
[2,3,5,1,4,6] => 3
[2,3,5,1,6,4] => 3
[2,3,5,4,1,6] => 2
[2,3,5,4,6,1] => 3
[2,3,5,6,1,4] => 1
[2,3,5,6,4,1] => 3
[2,3,6,1,4,5] => 0
[2,3,6,1,5,4] => 1
[2,3,6,4,1,5] => 3
[2,3,6,4,5,1] => 3
[2,3,6,5,1,4] => 1
[2,3,6,5,4,1] => 0
[2,4,1,3,5,6] => 4
[2,4,1,3,6,5] => 4
[2,4,1,5,3,6] => 3
[2,4,1,5,6,3] => 3
[2,4,1,6,3,5] => 4
[2,4,1,6,5,3] => 2
[2,4,3,1,5,6] => 2
[2,4,3,1,6,5] => 2
[2,4,3,5,1,6] => 3
[2,4,3,5,6,1] => 3
[2,4,3,6,1,5] => 3
[2,4,3,6,5,1] => 2
[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] => 4
[2,4,5,6,1,3] => 2
[2,4,5,6,3,1] => 2
[2,4,6,1,3,5] => 4
[2,4,6,1,5,3] => 3
[2,4,6,3,1,5] => 4
[2,4,6,3,5,1] => 5
[2,4,6,5,1,3] => 4
[2,4,6,5,3,1] => 4
[2,5,1,3,4,6] => 3
[2,5,1,3,6,4] => 4
[2,5,1,4,3,6] => 2
[2,5,1,4,6,3] => 3
[2,5,1,6,3,4] => 2
[2,5,1,6,4,3] => 2
[2,5,3,1,4,6] => 4
[2,5,3,1,6,4] => 3
[2,5,3,4,1,6] => 3
[2,5,3,4,6,1] => 4
[2,5,3,6,1,4] => 3
[2,5,3,6,4,1] => 5
[2,5,4,1,3,6] => 2
[2,5,4,1,6,3] => 0
[2,5,4,3,1,6] => 1
[2,5,4,3,6,1] => 0
[2,5,4,6,1,3] => 3
[2,5,4,6,3,1] => 3
[2,5,6,1,3,4] => 1
[2,5,6,1,4,3] => 0
[2,5,6,3,1,4] => 2
[2,5,6,3,4,1] => 0
[2,5,6,4,1,3] => 3
[2,5,6,4,3,1] => 2
[2,6,1,3,4,5] => 2
[2,6,1,3,5,4] => 4
[2,6,1,4,3,5] => 3
[2,6,1,4,5,3] => 3
[2,6,1,5,3,4] => 4
[2,6,1,5,4,3] => 2
[2,6,3,1,4,5] => 3
[2,6,3,1,5,4] => 2
[2,6,3,4,1,5] => 2
[2,6,3,4,5,1] => 1
[2,6,3,5,1,4] => 4
[2,6,3,5,4,1] => 4
[2,6,4,1,3,5] => 4
[2,6,4,1,5,3] => 3
[2,6,4,3,1,5] => 2
[2,6,4,3,5,1] => 3
[2,6,4,5,1,3] => 3
[2,6,4,5,3,1] => 4
[2,6,5,1,3,4] => 1
[2,6,5,1,4,3] => 1
[2,6,5,3,1,4] => 3
[2,6,5,3,4,1] => 1
[2,6,5,4,1,3] => 2
[2,6,5,4,3,1] => 1
[3,1,2,4,5,6] => 2
[3,1,2,4,6,5] => 4
[3,1,2,5,4,6] => 3
[3,1,2,5,6,4] => 2
[3,1,2,6,4,5] => 2
[3,1,2,6,5,4] => 1
[3,1,4,2,5,6] => 4
[3,1,4,2,6,5] => 4
[3,1,4,5,2,6] => 3
[3,1,4,5,6,2] => 2
[3,1,4,6,2,5] => 4
[3,1,4,6,5,2] => 4
[3,1,5,2,4,6] => 3
[3,1,5,2,6,4] => 4
[3,1,5,4,2,6] => 2
[3,1,5,4,6,2] => 3
[3,1,5,6,2,4] => 2
[3,1,5,6,4,2] => 4
[3,1,6,2,4,5] => 3
[3,1,6,2,5,4] => 2
[3,1,6,4,2,5] => 3
[3,1,6,4,5,2] => 3
[3,1,6,5,2,4] => 2
[3,1,6,5,4,2] => 2
[3,2,1,4,5,6] => 0
[3,2,1,4,6,5] => 2
[3,2,1,5,4,6] => 2
[3,2,1,5,6,4] => 1
[3,2,1,6,4,5] => 1
[3,2,1,6,5,4] => 0
[3,2,4,1,5,6] => 3
[3,2,4,1,6,5] => 2
[3,2,4,5,1,6] => 3
[3,2,4,5,6,1] => 2
[3,2,4,6,1,5] => 4
[3,2,4,6,5,1] => 3
[3,2,5,1,4,6] => 2
[3,2,5,1,6,4] => 2
[3,2,5,4,1,6] => 0
[3,2,5,4,6,1] => 2
[3,2,5,6,1,4] => 0
[3,2,5,6,4,1] => 2
[3,2,6,1,4,5] => 1
[3,2,6,1,5,4] => 2
[3,2,6,4,1,5] => 2
[3,2,6,4,5,1] => 2
[3,2,6,5,1,4] => 1
[3,2,6,5,4,1] => 0
[3,4,1,2,5,6] => 0
[3,4,1,2,6,5] => 0
[3,4,1,5,2,6] => 3
[3,4,1,5,6,2] => 1
[3,4,1,6,2,5] => 2
[3,4,1,6,5,2] => 0
[3,4,2,1,5,6] => 1
[3,4,2,1,6,5] => 1
[3,4,2,5,1,6] => 4
[3,4,2,5,6,1] => 3
[3,4,2,6,1,5] => 4
[3,4,2,6,5,1] => 2
[3,4,5,1,2,6] => 0
[3,4,5,1,6,2] => 2
[3,4,5,2,1,6] => 0
[3,4,5,2,6,1] => 2
[3,4,5,6,1,2] => 0
[3,4,5,6,2,1] => 0
[3,4,6,1,2,5] => 1
[3,4,6,1,5,2] => 2
[3,4,6,2,1,5] => 1
[3,4,6,2,5,1] => 2
[3,4,6,5,1,2] => 2
[3,4,6,5,2,1] => 2
[3,5,1,2,4,6] => 3
[3,5,1,2,6,4] => 2
[3,5,1,4,2,6] => 3
[3,5,1,4,6,2] => 3
[3,5,1,6,2,4] => 4
[3,5,1,6,4,2] => 4
[3,5,2,1,4,6] => 3
[3,5,2,1,6,4] => 2
[3,5,2,4,1,6] => 3
[3,5,2,4,6,1] => 5
[3,5,2,6,1,4] => 4
[3,5,2,6,4,1] => 3
[3,5,4,1,2,6] => 2
[3,5,4,1,6,2] => 3
[3,5,4,2,1,6] => 2
[3,5,4,2,6,1] => 3
[3,5,4,6,1,2] => 4
[3,5,4,6,2,1] => 3
[3,5,6,1,2,4] => 2
[3,5,6,1,4,2] => 2
[3,5,6,2,1,4] => 1
[3,5,6,2,4,1] => 3
[3,5,6,4,1,2] => 2
[3,5,6,4,2,1] => 3
[3,6,1,2,4,5] => 1
[3,6,1,2,5,4] => 0
[3,6,1,4,2,5] => 3
[3,6,1,4,5,2] => 0
[3,6,1,5,2,4] => 4
[3,6,1,5,4,2] => 2
[3,6,2,1,4,5] => 1
[3,6,2,1,5,4] => 1
[3,6,2,4,1,5] => 4
[3,6,2,4,5,1] => 1
[3,6,2,5,1,4] => 4
[3,6,2,5,4,1] => 2
[3,6,4,1,2,5] => 2
[3,6,4,1,5,2] => 3
[3,6,4,2,1,5] => 3
[3,6,4,2,5,1] => 3
[3,6,4,5,1,2] => 3
[3,6,4,5,2,1] => 3
[3,6,5,1,2,4] => 1
[3,6,5,1,4,2] => 2
[3,6,5,2,1,4] => 0
[3,6,5,2,4,1] => 3
[3,6,5,4,1,2] => 0
[3,6,5,4,2,1] => 1
[4,1,2,3,5,6] => 1
[4,1,2,3,6,5] => 0
[4,1,2,5,3,6] => 3
[4,1,2,5,6,3] => 0
[4,1,2,6,3,5] => 3
[4,1,2,6,5,3] => 1
[4,1,3,2,5,6] => 2
[4,1,3,2,6,5] => 2
[4,1,3,5,2,6] => 4
[4,1,3,5,6,2] => 3
[4,1,3,6,2,5] => 3
[4,1,3,6,5,2] => 2
[4,1,5,2,3,6] => 2
[4,1,5,2,6,3] => 4
[4,1,5,3,2,6] => 2
[4,1,5,3,6,2] => 4
[4,1,5,6,2,3] => 1
[4,1,5,6,3,2] => 1
[4,1,6,2,3,5] => 2
[4,1,6,2,5,3] => 3
[4,1,6,3,2,5] => 0
[4,1,6,3,5,2] => 3
[4,1,6,5,2,3] => 0
[4,1,6,5,3,2] => 1
[4,2,1,3,5,6] => 3
[4,2,1,3,6,5] => 2
[4,2,1,5,3,6] => 2
[4,2,1,5,6,3] => 1
[4,2,1,6,3,5] => 2
[4,2,1,6,5,3] => 2
[4,2,3,1,5,6] => 2
[4,2,3,1,6,5] => 2
[4,2,3,5,1,6] => 4
[4,2,3,5,6,1] => 3
[4,2,3,6,1,5] => 3
[4,2,3,6,5,1] => 2
[4,2,5,1,3,6] => 3
[4,2,5,1,6,3] => 3
[4,2,5,3,1,6] => 3
[4,2,5,3,6,1] => 5
[4,2,5,6,1,3] => 2
[4,2,5,6,3,1] => 2
[4,2,6,1,3,5] => 3
[4,2,6,1,5,3] => 4
[4,2,6,3,1,5] => 3
[4,2,6,3,5,1] => 3
[4,2,6,5,1,3] => 2
[4,2,6,5,3,1] => 3
[4,3,1,2,5,6] => 1
[4,3,1,2,6,5] => 1
[4,3,1,5,2,6] => 3
[4,3,1,5,6,2] => 1
[4,3,1,6,2,5] => 2
[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] => 2
[4,3,2,5,6,1] => 0
[4,3,2,6,1,5] => 2
[4,3,2,6,5,1] => 0
[4,3,5,1,2,6] => 2
[4,3,5,1,6,2] => 4
[4,3,5,2,1,6] => 2
[4,3,5,2,6,1] => 4
[4,3,5,6,1,2] => 2
[4,3,5,6,2,1] => 2
[4,3,6,1,2,5] => 0
[4,3,6,1,5,2] => 2
[4,3,6,2,1,5] => 1
[4,3,6,2,5,1] => 3
[4,3,6,5,1,2] => 0
[4,3,6,5,2,1] => 0
[4,5,1,2,3,6] => 0
[4,5,1,2,6,3] => 1
[4,5,1,3,2,6] => 2
[4,5,1,3,6,2] => 2
[4,5,1,6,2,3] => 2
[4,5,1,6,3,2] => 1
[4,5,2,1,3,6] => 2
[4,5,2,1,6,3] => 0
[4,5,2,3,1,6] => 2
[4,5,2,3,6,1] => 0
[4,5,2,6,1,3] => 2
[4,5,2,6,3,1] => 3
[4,5,3,1,2,6] => 4
[4,5,3,1,6,2] => 3
[4,5,3,2,1,6] => 1
[4,5,3,2,6,1] => 2
[4,5,3,6,1,2] => 2
[4,5,3,6,2,1] => 3
[4,5,6,1,2,3] => 0
[4,5,6,1,3,2] => 1
[4,5,6,2,1,3] => 1
[4,5,6,2,3,1] => 2
[4,5,6,3,1,2] => 2
[4,5,6,3,2,1] => 0
[4,6,1,2,3,5] => 2
[4,6,1,2,5,3] => 2
[4,6,1,3,2,5] => 3
[4,6,1,3,5,2] => 3
[4,6,1,5,2,3] => 2
[4,6,1,5,3,2] => 2
[4,6,2,1,3,5] => 4
[4,6,2,1,5,3] => 2
[4,6,2,3,1,5] => 3
[4,6,2,3,5,1] => 2
[4,6,2,5,1,3] => 4
[4,6,2,5,3,1] => 4
[4,6,3,1,2,5] => 3
[4,6,3,1,5,2] => 3
[4,6,3,2,1,5] => 2
[4,6,3,2,5,1] => 2
[4,6,3,5,1,2] => 4
[4,6,3,5,2,1] => 4
[4,6,5,1,2,3] => 1
[4,6,5,1,3,2] => 4
[4,6,5,2,1,3] => 2
[4,6,5,2,3,1] => 4
[4,6,5,3,1,2] => 5
[4,6,5,3,2,1] => 2
[5,1,2,3,4,6] => 1
[5,1,2,3,6,4] => 2
[5,1,2,4,3,6] => 2
[5,1,2,4,6,3] => 3
[5,1,2,6,3,4] => 1
[5,1,2,6,4,3] => 1
[5,1,3,2,4,6] => 3
[5,1,3,2,6,4] => 3
[5,1,3,4,2,6] => 3
[5,1,3,4,6,2] => 2
[5,1,3,6,2,4] => 3
[5,1,3,6,4,2] => 4
[5,1,4,2,3,6] => 3
[5,1,4,2,6,3] => 4
[5,1,4,3,2,6] => 1
[5,1,4,3,6,2] => 2
[5,1,4,6,2,3] => 2
[5,1,4,6,3,2] => 3
[5,1,6,2,3,4] => 2
[5,1,6,2,4,3] => 4
[5,1,6,3,2,4] => 3
[5,1,6,3,4,2] => 3
[5,1,6,4,2,3] => 3
[5,1,6,4,3,2] => 2
[5,2,1,3,4,6] => 3
[5,2,1,3,6,4] => 4
[5,2,1,4,3,6] => 0
[5,2,1,4,6,3] => 2
[5,2,1,6,3,4] => 0
[5,2,1,6,4,3] => 1
[5,2,3,1,4,6] => 4
[5,2,3,1,6,4] => 3
[5,2,3,4,1,6] => 0
[5,2,3,4,6,1] => 1
[5,2,3,6,1,4] => 0
[5,2,3,6,4,1] => 1
[5,2,4,1,3,6] => 3
[5,2,4,1,6,3] => 3
[5,2,4,3,1,6] => 3
[5,2,4,3,6,1] => 3
[5,2,4,6,1,3] => 3
[5,2,4,6,3,1] => 3
[5,2,6,1,3,4] => 2
[5,2,6,1,4,3] => 2
[5,2,6,3,1,4] => 3
[5,2,6,3,4,1] => 2
[5,2,6,4,1,3] => 3
[5,2,6,4,3,1] => 2
[5,3,1,2,4,6] => 4
[5,3,1,2,6,4] => 4
[5,3,1,4,2,6] => 3
[5,3,1,4,6,2] => 4
[5,3,1,6,2,4] => 4
[5,3,1,6,4,2] => 4
[5,3,2,1,4,6] => 2
[5,3,2,1,6,4] => 2
[5,3,2,4,1,6] => 3
[5,3,2,4,6,1] => 4
[5,3,2,6,1,4] => 2
[5,3,2,6,4,1] => 2
[5,3,4,1,2,6] => 2
[5,3,4,1,6,2] => 3
[5,3,4,2,1,6] => 3
[5,3,4,2,6,1] => 4
[5,3,4,6,1,2] => 3
[5,3,4,6,2,1] => 3
[5,3,6,1,2,4] => 2
[5,3,6,1,4,2] => 4
[5,3,6,2,1,4] => 2
[5,3,6,2,4,1] => 4
[5,3,6,4,1,2] => 4
[5,3,6,4,2,1] => 4
[5,4,1,2,3,6] => 0
[5,4,1,2,6,3] => 1
[5,4,1,3,2,6] => 2
[5,4,1,3,6,2] => 3
[5,4,1,6,2,3] => 1
[5,4,1,6,3,2] => 0
[5,4,2,1,3,6] => 2
[5,4,2,1,6,3] => 1
[5,4,2,3,1,6] => 3
[5,4,2,3,6,1] => 1
[5,4,2,6,1,3] => 2
[5,4,2,6,3,1] => 3
[5,4,3,1,2,6] => 1
[5,4,3,1,6,2] => 2
[5,4,3,2,1,6] => 0
[5,4,3,2,6,1] => 1
[5,4,3,6,1,2] => 0
[5,4,3,6,2,1] => 1
[5,4,6,1,2,3] => 1
[5,4,6,1,3,2] => 2
[5,4,6,2,1,3] => 4
[5,4,6,2,3,1] => 4
[5,4,6,3,1,2] => 5
[5,4,6,3,2,1] => 2
[5,6,1,2,3,4] => 0
[5,6,1,2,4,3] => 2
[5,6,1,3,2,4] => 4
[5,6,1,3,4,2] => 3
[5,6,1,4,2,3] => 2
[5,6,1,4,3,2] => 0
[5,6,2,1,3,4] => 2
[5,6,2,1,4,3] => 0
[5,6,2,3,1,4] => 3
[5,6,2,3,4,1] => 0
[5,6,2,4,1,3] => 4
[5,6,2,4,3,1] => 3
[5,6,3,1,2,4] => 2
[5,6,3,1,4,2] => 4
[5,6,3,2,1,4] => 0
[5,6,3,2,4,1] => 3
[5,6,3,4,1,2] => 0
[5,6,3,4,2,1] => 2
[5,6,4,1,2,3] => 2
[5,6,4,1,3,2] => 5
[5,6,4,2,1,3] => 5
[5,6,4,2,3,1] => 4
[5,6,4,3,1,2] => 4
[5,6,4,3,2,1] => 1
[6,1,2,3,4,5] => 0
[6,1,2,3,5,4] => 2
[6,1,2,4,3,5] => 3
[6,1,2,4,5,3] => 3
[6,1,2,5,3,4] => 3
[6,1,2,5,4,3] => 0
[6,1,3,2,4,5] => 3
[6,1,3,2,5,4] => 2
[6,1,3,4,2,5] => 4
[6,1,3,4,5,2] => 1
[6,1,3,5,2,4] => 5
[6,1,3,5,4,2] => 4
[6,1,4,2,3,5] => 4
[6,1,4,2,5,3] => 5
[6,1,4,3,2,5] => 0
[6,1,4,3,5,2] => 3
[6,1,4,5,2,3] => 0
[6,1,4,5,3,2] => 1
[6,1,5,2,3,4] => 2
[6,1,5,2,4,3] => 4
[6,1,5,3,2,4] => 3
[6,1,5,3,4,2] => 4
[6,1,5,4,2,3] => 2
[6,1,5,4,3,2] => 1
[6,2,1,3,4,5] => 2
[6,2,1,3,5,4] => 3
[6,2,1,4,3,5] => 2
[6,2,1,4,5,3] => 2
[6,2,1,5,3,4] => 2
[6,2,1,5,4,3] => 0
[6,2,3,1,4,5] => 3
[6,2,3,1,5,4] => 2
[6,2,3,4,1,5] => 1
[6,2,3,4,5,1] => 0
[6,2,3,5,1,4] => 1
[6,2,3,5,4,1] => 2
[6,2,4,1,3,5] => 5
[6,2,4,1,5,3] => 3
[6,2,4,3,1,5] => 3
[6,2,4,3,5,1] => 2
[6,2,4,5,1,3] => 2
[6,2,4,5,3,1] => 3
[6,2,5,1,3,4] => 2
[6,2,5,1,4,3] => 3
[6,2,5,3,1,4] => 3
[6,2,5,3,4,1] => 3
[6,2,5,4,1,3] => 2
[6,2,5,4,3,1] => 1
[6,3,1,2,4,5] => 3
[6,3,1,2,5,4] => 2
[6,3,1,4,2,5] => 5
[6,3,1,4,5,2] => 1
[6,3,1,5,2,4] => 3
[6,3,1,5,4,2] => 2
[6,3,2,1,4,5] => 0
[6,3,2,1,5,4] => 0
[6,3,2,4,1,5] => 4
[6,3,2,4,5,1] => 2
[6,3,2,5,1,4] => 2
[6,3,2,5,4,1] => 0
[6,3,4,1,2,5] => 0
[6,3,4,1,5,2] => 2
[6,3,4,2,1,5] => 1
[6,3,4,2,5,1] => 3
[6,3,4,5,1,2] => 0
[6,3,4,5,2,1] => 0
[6,3,5,1,2,4] => 3
[6,3,5,1,4,2] => 4
[6,3,5,2,1,4] => 3
[6,3,5,2,4,1] => 4
[6,3,5,4,1,2] => 3
[6,3,5,4,2,1] => 3
[6,4,1,2,3,5] => 2
[6,4,1,2,5,3] => 2
[6,4,1,3,2,5] => 3
[6,4,1,3,5,2] => 3
[6,4,1,5,2,3] => 3
[6,4,1,5,3,2] => 3
[6,4,2,1,3,5] => 4
[6,4,2,1,5,3] => 3
[6,4,2,3,1,5] => 4
[6,4,2,3,5,1] => 3
[6,4,2,5,1,3] => 4
[6,4,2,5,3,1] => 4
[6,4,3,1,2,5] => 2
[6,4,3,1,5,2] => 2
[6,4,3,2,1,5] => 1
[6,4,3,2,5,1] => 1
[6,4,3,5,1,2] => 3
[6,4,3,5,2,1] => 3
[6,4,5,1,2,3] => 2
[6,4,5,1,3,2] => 4
[6,4,5,2,1,3] => 4
[6,4,5,2,3,1] => 4
[6,4,5,3,1,2] => 4
[6,4,5,3,2,1] => 2
[6,5,1,2,3,4] => 0
[6,5,1,2,4,3] => 2
[6,5,1,3,2,4] => 3
[6,5,1,3,4,2] => 3
[6,5,1,4,2,3] => 3
[6,5,1,4,3,2] => 1
[6,5,2,1,3,4] => 2
[6,5,2,1,4,3] => 0
[6,5,2,3,1,4] => 3
[6,5,2,3,4,1] => 0
[6,5,2,4,1,3] => 4
[6,5,2,4,3,1] => 3
[6,5,3,1,2,4] => 3
[6,5,3,1,4,2] => 4
[6,5,3,2,1,4] => 1
[6,5,3,2,4,1] => 3
[6,5,3,4,1,2] => 2
[6,5,3,4,2,1] => 2
[6,5,4,1,2,3] => 0
[6,5,4,1,3,2] => 2
[6,5,4,2,1,3] => 2
[6,5,4,2,3,1] => 2
[6,5,4,3,1,2] => 1
[6,5,4,3,2,1] => 0
[1,2,3,4,5,6,7] => 0
[1,2,3,4,5,7,6] => 2
[1,2,3,4,6,5,7] => 2
[1,2,3,4,6,7,5] => 2
[1,2,3,4,7,5,6] => 2
[1,2,3,4,7,6,5] => 0
[1,2,3,5,4,6,7] => 2
[1,2,3,5,4,7,6] => 2
[1,2,3,5,6,4,7] => 3
[1,2,3,5,6,7,4] => 1
[1,2,3,5,7,4,6] => 4
[1,2,3,5,7,6,4] => 3
[1,2,3,6,4,5,7] => 3
[1,2,3,6,4,7,5] => 4
[1,2,3,6,5,4,7] => 0
[1,2,3,6,5,7,4] => 2
[1,2,3,6,7,4,5] => 0
[1,2,3,6,7,5,4] => 1
[1,2,3,7,4,5,6] => 1
[1,2,3,7,4,6,5] => 3
[1,2,3,7,5,4,6] => 2
[1,2,3,7,5,6,4] => 2
[1,2,3,7,6,4,5] => 1
[1,2,3,7,6,5,4] => 0
[1,2,4,3,5,6,7] => 2
[1,2,4,3,5,7,6] => 4
[1,2,4,3,6,5,7] => 4
[1,2,4,3,6,7,5] => 3
[1,2,4,3,7,5,6] => 3
[1,2,4,3,7,6,5] => 2
[1,2,4,5,3,6,7] => 3
[1,2,4,5,3,7,6] => 2
[1,2,4,5,6,3,7] => 2
[1,2,4,5,6,7,3] => 1
[1,2,4,5,7,3,6] => 3
[1,2,4,5,7,6,3] => 3
[1,2,4,6,3,5,7] => 4
[1,2,4,6,3,7,5] => 3
[1,2,4,6,5,3,7] => 3
[1,2,4,6,5,7,3] => 3
[1,2,4,6,7,3,5] => 3
[1,2,4,6,7,5,3] => 4
[1,2,4,7,3,5,6] => 3
[1,2,4,7,3,6,5] => 2
[1,2,4,7,5,3,6] => 4
[1,2,4,7,5,6,3] => 4
[1,2,4,7,6,3,5] => 3
[1,2,4,7,6,5,3] => 2
[1,2,5,3,4,6,7] => 3
[1,2,5,3,4,7,6] => 2
[1,2,5,3,6,4,7] => 4
[1,2,5,3,6,7,4] => 3
[1,2,5,3,7,4,6] => 3
[1,2,5,3,7,6,4] => 2
[1,2,5,4,3,6,7] => 0
[1,2,5,4,3,7,6] => 0
[1,2,5,4,6,3,7] => 3
[1,2,5,4,6,7,3] => 2
[1,2,5,4,7,3,6] => 2
[1,2,5,4,7,6,3] => 0
[1,2,5,6,3,4,7] => 0
[1,2,5,6,3,7,4] => 2
[1,2,5,6,4,3,7] => 1
[1,2,5,6,4,7,3] => 3
[1,2,5,6,7,3,4] => 0
[1,2,5,6,7,4,3] => 0
[1,2,5,7,3,4,6] => 2
[1,2,5,7,3,6,4] => 3
[1,2,5,7,4,3,6] => 2
[1,2,5,7,4,6,3] => 3
[1,2,5,7,6,3,4] => 2
[1,2,5,7,6,4,3] => 2
[1,2,6,3,4,5,7] => 2
[1,2,6,3,4,7,5] => 3
[1,2,6,3,5,4,7] => 3
[1,2,6,3,5,7,4] => 4
[1,2,6,3,7,4,5] => 3
[1,2,6,3,7,5,4] => 3
[1,2,6,4,3,5,7] => 3
[1,2,6,4,3,7,5] => 2
[1,2,6,4,5,3,7] => 2
[1,2,6,4,5,7,3] => 3
[1,2,6,4,7,3,5] => 3
[1,2,6,4,7,5,3] => 3
[1,2,6,5,3,4,7] => 1
[1,2,6,5,3,7,4] => 2
[1,2,6,5,4,3,7] => 0
[1,2,6,5,4,7,3] => 1
[1,2,6,5,7,3,4] => 2
[1,2,6,5,7,4,3] => 2
[1,2,6,7,3,4,5] => 0
[1,2,6,7,3,5,4] => 2
[1,2,6,7,4,3,5] => 2
[1,2,6,7,4,5,3] => 2
[1,2,6,7,5,3,4] => 4
[1,2,6,7,5,4,3] => 1
[1,2,7,3,4,5,6] => 1
[1,2,7,3,4,6,5] => 3
[1,2,7,3,5,4,6] => 3
[1,2,7,3,5,6,4] => 4
[1,2,7,3,6,4,5] => 4
[1,2,7,3,6,5,4] => 2
[1,2,7,4,3,5,6] => 2
[1,2,7,4,3,6,5] => 0
[1,2,7,4,5,3,6] => 3
[1,2,7,4,5,6,3] => 0
[1,2,7,4,6,3,5] => 3
[1,2,7,4,6,5,3] => 3
[1,2,7,5,3,4,6] => 3
[1,2,7,5,3,6,4] => 3
[1,2,7,5,4,3,6] => 1
[1,2,7,5,4,6,3] => 3
[1,2,7,5,6,3,4] => 2
[1,2,7,5,6,4,3] => 3
[1,2,7,6,3,4,5] => 0
[1,2,7,6,3,5,4] => 2
[1,2,7,6,4,3,5] => 2
[1,2,7,6,4,5,3] => 3
[1,2,7,6,5,3,4] => 1
[1,2,7,6,5,4,3] => 0
[1,3,2,4,5,6,7] => 2
[1,3,2,4,5,7,6] => 4
[1,3,2,4,6,5,7] => 4
[1,3,2,4,6,7,5] => 4
[1,3,2,4,7,5,6] => 4
[1,3,2,4,7,6,5] => 2
[1,3,2,5,4,6,7] => 4
[1,3,2,5,4,7,6] => 2
[1,3,2,5,6,4,7] => 4
[1,3,2,5,6,7,4] => 2
[1,3,2,5,7,4,6] => 6
[1,3,2,5,7,6,4] => 4
[1,3,2,6,4,5,7] => 4
[1,3,2,6,4,7,5] => 6
[1,3,2,6,5,4,7] => 2
[1,3,2,6,5,7,4] => 4
[1,3,2,6,7,4,5] => 2
[1,3,2,6,7,5,4] => 3
[1,3,2,7,4,5,6] => 2
[1,3,2,7,4,6,5] => 4
[1,3,2,7,5,4,6] => 4
[1,3,2,7,5,6,4] => 4
[1,3,2,7,6,4,5] => 3
[1,3,2,7,6,5,4] => 2
[1,3,4,2,5,6,7] => 3
[1,3,4,2,5,7,6] => 5
[1,3,4,2,6,5,7] => 4
[1,3,4,2,6,7,5] => 3
[1,3,4,2,7,5,6] => 3
[1,3,4,2,7,6,5] => 2
[1,3,4,5,2,6,7] => 2
[1,3,4,5,2,7,6] => 1
[1,3,4,5,6,2,7] => 2
[1,3,4,5,6,7,2] => 1
[1,3,4,5,7,2,6] => 3
[1,3,4,5,7,6,2] => 3
[1,3,4,6,2,5,7] => 4
[1,3,4,6,2,7,5] => 4
[1,3,4,6,5,2,7] => 3
[1,3,4,6,5,7,2] => 3
[1,3,4,6,7,2,5] => 2
[1,3,4,6,7,5,2] => 4
[1,3,4,7,2,5,6] => 1
[1,3,4,7,2,6,5] => 2
[1,3,4,7,5,2,6] => 3
[1,3,4,7,5,6,2] => 4
[1,3,4,7,6,2,5] => 2
[1,3,4,7,6,5,2] => 1
[1,3,5,2,4,6,7] => 4
[1,3,5,2,4,7,6] => 4
[1,3,5,2,6,4,7] => 4
[1,3,5,2,6,7,4] => 4
[1,3,5,2,7,4,6] => 5
[1,3,5,2,7,6,4] => 3
[1,3,5,4,2,6,7] => 3
[1,3,5,4,2,7,6] => 3
[1,3,5,4,6,2,7] => 3
[1,3,5,4,6,7,2] => 4
[1,3,5,4,7,2,6] => 4
[1,3,5,4,7,6,2] => 2
[1,3,5,6,2,4,7] => 3
[1,3,5,6,2,7,4] => 3
[1,3,5,6,4,2,7] => 4
[1,3,5,6,4,7,2] => 4
[1,3,5,6,7,2,4] => 3
[1,3,5,6,7,4,2] => 3
[1,3,5,7,2,4,6] => 5
[1,3,5,7,2,6,4] => 4
[1,3,5,7,4,2,6] => 4
[1,3,5,7,4,6,2] => 5
[1,3,5,7,6,2,4] => 5
[1,3,5,7,6,4,2] => 5
[1,3,6,2,4,5,7] => 4
[1,3,6,2,4,7,5] => 5
[1,3,6,2,5,4,7] => 2
[1,3,6,2,5,7,4] => 3
[1,3,6,2,7,4,5] => 2
[1,3,6,2,7,5,4] => 3
[1,3,6,4,2,5,7] => 4
[1,3,6,4,2,7,5] => 4
[1,3,6,4,5,2,7] => 4
[1,3,6,4,5,7,2] => 4
[1,3,6,4,7,2,5] => 4
[1,3,6,4,7,5,2] => 6
[1,3,6,5,2,4,7] => 3
[1,3,6,5,2,7,4] => 1
[1,3,6,5,4,2,7] => 2
[1,3,6,5,4,7,2] => 1
[1,3,6,5,7,2,4] => 4
[1,3,6,5,7,4,2] => 3
[1,3,6,7,2,4,5] => 2
[1,3,6,7,2,5,4] => 1
[1,3,6,7,4,2,5] => 3
[1,3,6,7,4,5,2] => 1
[1,3,6,7,5,2,4] => 4
[1,3,6,7,5,4,2] => 3
[1,3,7,2,4,5,6] => 3
[1,3,7,2,4,6,5] => 5
[1,3,7,2,5,4,6] => 4
[1,3,7,2,5,6,4] => 3
[1,3,7,2,6,4,5] => 5
[1,3,7,2,6,5,4] => 2
[1,3,7,4,2,5,6] => 4
[1,3,7,4,2,6,5] => 2
[1,3,7,4,5,2,6] => 2
[1,3,7,4,5,6,2] => 2
[1,3,7,4,6,2,5] => 5
[1,3,7,4,6,5,2] => 5
[1,3,7,5,2,4,6] => 5
[1,3,7,5,2,6,4] => 4
[1,3,7,5,4,2,6] => 3
[1,3,7,5,4,6,2] => 4
[1,3,7,5,6,2,4] => 3
[1,3,7,5,6,4,2] => 5
[1,3,7,6,2,4,5] => 2
[1,3,7,6,2,5,4] => 2
[1,3,7,6,4,2,5] => 4
[1,3,7,6,4,5,2] => 2
[1,3,7,6,5,2,4] => 3
[1,3,7,6,5,4,2] => 2
[1,4,2,3,5,6,7] => 3
[1,4,2,3,5,7,6] => 5
[1,4,2,3,6,5,7] => 4
[1,4,2,3,6,7,5] => 3
[1,4,2,3,7,5,6] => 3
[1,4,2,3,7,6,5] => 2
[1,4,2,5,3,6,7] => 4
[1,4,2,5,3,7,6] => 4
[1,4,2,5,6,3,7] => 4
[1,4,2,5,6,7,3] => 3
[1,4,2,5,7,3,6] => 5
[1,4,2,5,7,6,3] => 5
[1,4,2,6,3,5,7] => 4
[1,4,2,6,3,7,5] => 5
[1,4,2,6,5,3,7] => 2
[1,4,2,6,5,7,3] => 4
[1,4,2,6,7,3,5] => 2
[1,4,2,6,7,5,3] => 5
[1,4,2,7,3,5,6] => 4
[1,4,2,7,3,6,5] => 3
[1,4,2,7,5,3,6] => 3
[1,4,2,7,5,6,3] => 3
[1,4,2,7,6,3,5] => 3
[1,4,2,7,6,5,3] => 2
[1,4,3,2,5,6,7] => 0
[1,4,3,2,5,7,6] => 2
[1,4,3,2,6,5,7] => 2
[1,4,3,2,6,7,5] => 1
[1,4,3,2,7,5,6] => 1
[1,4,3,2,7,6,5] => 0
[1,4,3,5,2,6,7] => 3
[1,4,3,5,2,7,6] => 2
[1,4,3,5,6,2,7] => 3
[1,4,3,5,6,7,2] => 2
[1,4,3,5,7,2,6] => 4
[1,4,3,5,7,6,2] => 3
[1,4,3,6,2,5,7] => 2
[1,4,3,6,2,7,5] => 2
[1,4,3,6,5,2,7] => 0
[1,4,3,6,5,7,2] => 2
[1,4,3,6,7,2,5] => 0
[1,4,3,6,7,5,2] => 2
[1,4,3,7,2,5,6] => 1
[1,4,3,7,2,6,5] => 2
[1,4,3,7,5,2,6] => 2
[1,4,3,7,5,6,2] => 2
[1,4,3,7,6,2,5] => 1
[1,4,3,7,6,5,2] => 0
[1,4,5,2,3,6,7] => 0
[1,4,5,2,3,7,6] => 0
[1,4,5,2,6,3,7] => 3
[1,4,5,2,6,7,3] => 1
[1,4,5,2,7,3,6] => 2
[1,4,5,2,7,6,3] => 0
[1,4,5,3,2,6,7] => 1
[1,4,5,3,2,7,6] => 1
[1,4,5,3,6,2,7] => 4
[1,4,5,3,6,7,2] => 3
[1,4,5,3,7,2,6] => 4
[1,4,5,3,7,6,2] => 2
[1,4,5,6,2,3,7] => 0
[1,4,5,6,2,7,3] => 2
[1,4,5,6,3,2,7] => 0
[1,4,5,6,3,7,2] => 2
[1,4,5,6,7,2,3] => 0
[1,4,5,6,7,3,2] => 0
[1,4,5,7,2,3,6] => 1
[1,4,5,7,2,6,3] => 2
[1,4,5,7,3,2,6] => 1
[1,4,5,7,3,6,2] => 2
[1,4,5,7,6,2,3] => 2
[1,4,5,7,6,3,2] => 2
[1,4,6,2,3,5,7] => 3
[1,4,6,2,3,7,5] => 2
[1,4,6,2,5,3,7] => 3
[1,4,6,2,5,7,3] => 3
[1,4,6,2,7,3,5] => 4
[1,4,6,2,7,5,3] => 4
[1,4,6,3,2,5,7] => 3
[1,4,6,3,2,7,5] => 2
[1,4,6,3,5,2,7] => 3
[1,4,6,3,5,7,2] => 5
[1,4,6,3,7,2,5] => 4
[1,4,6,3,7,5,2] => 3
[1,4,6,5,2,3,7] => 2
[1,4,6,5,2,7,3] => 3
[1,4,6,5,3,2,7] => 2
-----------------------------------------------------------------------------
Created: May 30, 2019 at 14:29 by Martin Rubey
-----------------------------------------------------------------------------
Last Updated: May 30, 2019 at 14:29 by Martin Rubey