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* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
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-----------------------------------------------------------------------------
Statistic identifier: St001461
-----------------------------------------------------------------------------
Collection: Permutations
-----------------------------------------------------------------------------
Description: The number of topologically connected components of the chord diagram of a permutation.
The chord diagram of a permutation $\pi\in\mathfrak S_n$ is obtained by placing labels $1,\dots,n$ in cyclic order on a cycle and drawing a (straight) arc from $i$ to $\pi(i)$ for every label $i$.
This statistic records the number of topologically connected components in the chord diagram. In particular, if two arcs cross, all four labels connected by the two arcs are in the same component.
The permutation $\pi\in\mathfrak S_n$ stabilizes an interval $I=\{a,a+1,\dots,b\}$ if $\pi(I)=I$. It is stabilized-interval-free, if the only interval $\pi$ stablizes is $\{1,\dots,n\}$. Thus, this statistic is $1$ if $\pi$ is stabilized-interval-free.
-----------------------------------------------------------------------------
References: [1] Callan, D. Counting Stabilized-Interval-Free Permutations [[arXiv:math/0310157]]
[2] Coefficients of power series A(x) such that n-th term of A(x)^n = n! x^(n-1) for n > 0. [[OEIS:A075834]]
-----------------------------------------------------------------------------
Code:
def factor(pi):
"""
Return smallest i such that pi([1,...,i]) equals [1,...,i]
"""
pi = list(pi)
for i in range(1, len(pi)+1):
A = pi[:i]
if max(A) == i:
return Permutation(A), Permutation([e-i for e in pi[i:]])
def rotate(pi):
r = len(pi)
pi1 = [x % r + 1 for x in pi]
return Permutation(pi1[-1:] + pi1[:-1])
def orbit(pi):
o = [pi]
new_pi = rotate(pi)
while pi != new_pi:
o += [new_pi]
new_pi = rotate(new_pi)
return o
@cached_function
def statistic(pi):
o = orbit(pi)
for pi in o:
A, B = factor(pi)
if len(B) > 0:
return statistic(A) + statistic(B)
return 1
-----------------------------------------------------------------------------
Statistic values:
[1] => 1
[1,2] => 2
[2,1] => 1
[1,2,3] => 3
[1,3,2] => 2
[2,1,3] => 2
[2,3,1] => 1
[3,1,2] => 1
[3,2,1] => 2
[1,2,3,4] => 4
[1,2,4,3] => 3
[1,3,2,4] => 3
[1,3,4,2] => 2
[1,4,2,3] => 2
[1,4,3,2] => 3
[2,1,3,4] => 3
[2,1,4,3] => 2
[2,3,1,4] => 2
[2,3,4,1] => 1
[2,4,1,3] => 1
[2,4,3,1] => 2
[3,1,2,4] => 2
[3,1,4,2] => 1
[3,2,1,4] => 3
[3,2,4,1] => 2
[3,4,1,2] => 1
[3,4,2,1] => 1
[4,1,2,3] => 1
[4,1,3,2] => 2
[4,2,1,3] => 2
[4,2,3,1] => 3
[4,3,1,2] => 1
[4,3,2,1] => 2
[1,2,3,4,5] => 5
[1,2,3,5,4] => 4
[1,2,4,3,5] => 4
[1,2,4,5,3] => 3
[1,2,5,3,4] => 3
[1,2,5,4,3] => 4
[1,3,2,4,5] => 4
[1,3,2,5,4] => 3
[1,3,4,2,5] => 3
[1,3,4,5,2] => 2
[1,3,5,2,4] => 2
[1,3,5,4,2] => 3
[1,4,2,3,5] => 3
[1,4,2,5,3] => 2
[1,4,3,2,5] => 4
[1,4,3,5,2] => 3
[1,4,5,2,3] => 2
[1,4,5,3,2] => 2
[1,5,2,3,4] => 2
[1,5,2,4,3] => 3
[1,5,3,2,4] => 3
[1,5,3,4,2] => 4
[1,5,4,2,3] => 2
[1,5,4,3,2] => 3
[2,1,3,4,5] => 4
[2,1,3,5,4] => 3
[2,1,4,3,5] => 3
[2,1,4,5,3] => 2
[2,1,5,3,4] => 2
[2,1,5,4,3] => 3
[2,3,1,4,5] => 3
[2,3,1,5,4] => 2
[2,3,4,1,5] => 2
[2,3,4,5,1] => 1
[2,3,5,1,4] => 1
[2,3,5,4,1] => 2
[2,4,1,3,5] => 2
[2,4,1,5,3] => 1
[2,4,3,1,5] => 3
[2,4,3,5,1] => 2
[2,4,5,1,3] => 1
[2,4,5,3,1] => 1
[2,5,1,3,4] => 1
[2,5,1,4,3] => 2
[2,5,3,1,4] => 2
[2,5,3,4,1] => 3
[2,5,4,1,3] => 1
[2,5,4,3,1] => 2
[3,1,2,4,5] => 3
[3,1,2,5,4] => 2
[3,1,4,2,5] => 2
[3,1,4,5,2] => 1
[3,1,5,2,4] => 1
[3,1,5,4,2] => 2
[3,2,1,4,5] => 4
[3,2,1,5,4] => 3
[3,2,4,1,5] => 3
[3,2,4,5,1] => 2
[3,2,5,1,4] => 2
[3,2,5,4,1] => 3
[3,4,1,2,5] => 2
[3,4,1,5,2] => 1
[3,4,2,1,5] => 2
[3,4,2,5,1] => 1
[3,4,5,1,2] => 1
[3,4,5,2,1] => 1
[3,5,1,2,4] => 1
[3,5,1,4,2] => 2
[3,5,2,1,4] => 1
[3,5,2,4,1] => 2
[3,5,4,1,2] => 1
[3,5,4,2,1] => 1
[4,1,2,3,5] => 2
[4,1,2,5,3] => 1
[4,1,3,2,5] => 3
[4,1,3,5,2] => 2
[4,1,5,2,3] => 1
[4,1,5,3,2] => 1
[4,2,1,3,5] => 3
[4,2,1,5,3] => 2
[4,2,3,1,5] => 4
[4,2,3,5,1] => 3
[4,2,5,1,3] => 2
[4,2,5,3,1] => 2
[4,3,1,2,5] => 2
[4,3,1,5,2] => 1
[4,3,2,1,5] => 3
[4,3,2,5,1] => 2
[4,3,5,1,2] => 1
[4,3,5,2,1] => 1
[4,5,1,2,3] => 1
[4,5,1,3,2] => 1
[4,5,2,1,3] => 1
[4,5,2,3,1] => 1
[4,5,3,1,2] => 2
[4,5,3,2,1] => 2
[5,1,2,3,4] => 1
[5,1,2,4,3] => 2
[5,1,3,2,4] => 2
[5,1,3,4,2] => 3
[5,1,4,2,3] => 1
[5,1,4,3,2] => 2
[5,2,1,3,4] => 2
[5,2,1,4,3] => 3
[5,2,3,1,4] => 3
[5,2,3,4,1] => 4
[5,2,4,1,3] => 2
[5,2,4,3,1] => 3
[5,3,1,2,4] => 1
[5,3,1,4,2] => 2
[5,3,2,1,4] => 2
[5,3,2,4,1] => 3
[5,3,4,1,2] => 1
[5,3,4,2,1] => 2
[5,4,1,2,3] => 1
[5,4,1,3,2] => 1
[5,4,2,1,3] => 1
[5,4,2,3,1] => 2
[5,4,3,1,2] => 2
[5,4,3,2,1] => 3
[1,2,3,4,5,6] => 6
[1,2,3,4,6,5] => 5
[1,2,3,5,4,6] => 5
[1,2,3,5,6,4] => 4
[1,2,3,6,4,5] => 4
[1,2,3,6,5,4] => 5
[1,2,4,3,5,6] => 5
[1,2,4,3,6,5] => 4
[1,2,4,5,3,6] => 4
[1,2,4,5,6,3] => 3
[1,2,4,6,3,5] => 3
[1,2,4,6,5,3] => 4
[1,2,5,3,4,6] => 4
[1,2,5,3,6,4] => 3
[1,2,5,4,3,6] => 5
[1,2,5,4,6,3] => 4
[1,2,5,6,3,4] => 3
[1,2,5,6,4,3] => 3
[1,2,6,3,4,5] => 3
[1,2,6,3,5,4] => 4
[1,2,6,4,3,5] => 4
[1,2,6,4,5,3] => 5
[1,2,6,5,3,4] => 3
[1,2,6,5,4,3] => 4
[1,3,2,4,5,6] => 5
[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] => 4
[1,3,4,2,5,6] => 4
[1,3,4,2,6,5] => 3
[1,3,4,5,2,6] => 3
[1,3,4,5,6,2] => 2
[1,3,4,6,2,5] => 2
[1,3,4,6,5,2] => 3
[1,3,5,2,4,6] => 3
[1,3,5,2,6,4] => 2
[1,3,5,4,2,6] => 4
[1,3,5,4,6,2] => 3
[1,3,5,6,2,4] => 2
[1,3,5,6,4,2] => 2
[1,3,6,2,4,5] => 2
[1,3,6,2,5,4] => 3
[1,3,6,4,2,5] => 3
[1,3,6,4,5,2] => 4
[1,3,6,5,2,4] => 2
[1,3,6,5,4,2] => 3
[1,4,2,3,5,6] => 4
[1,4,2,3,6,5] => 3
[1,4,2,5,3,6] => 3
[1,4,2,5,6,3] => 2
[1,4,2,6,3,5] => 2
[1,4,2,6,5,3] => 3
[1,4,3,2,5,6] => 5
[1,4,3,2,6,5] => 4
[1,4,3,5,2,6] => 4
[1,4,3,5,6,2] => 3
[1,4,3,6,2,5] => 3
[1,4,3,6,5,2] => 4
[1,4,5,2,3,6] => 3
[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] => 2
[1,4,5,6,3,2] => 2
[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] => 3
[1,5,2,3,6,4] => 2
[1,5,2,4,3,6] => 4
[1,5,2,4,6,3] => 3
[1,5,2,6,3,4] => 2
[1,5,2,6,4,3] => 2
[1,5,3,2,4,6] => 4
[1,5,3,2,6,4] => 3
[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] => 3
[1,5,4,2,3,6] => 3
[1,5,4,2,6,3] => 2
[1,5,4,3,2,6] => 4
[1,5,4,3,6,2] => 3
[1,5,4,6,2,3] => 2
[1,5,4,6,3,2] => 2
[1,5,6,2,3,4] => 2
[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] => 3
[1,5,6,4,3,2] => 3
[1,6,2,3,4,5] => 2
[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] => 2
[1,6,2,5,4,3] => 3
[1,6,3,2,4,5] => 3
[1,6,3,2,5,4] => 4
[1,6,3,4,2,5] => 4
[1,6,3,4,5,2] => 5
[1,6,3,5,2,4] => 3
[1,6,3,5,4,2] => 4
[1,6,4,2,3,5] => 2
[1,6,4,2,5,3] => 3
[1,6,4,3,2,5] => 3
[1,6,4,3,5,2] => 4
[1,6,4,5,2,3] => 2
[1,6,4,5,3,2] => 3
[1,6,5,2,3,4] => 2
[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] => 3
[1,6,5,4,3,2] => 4
[2,1,3,4,5,6] => 5
[2,1,3,4,6,5] => 4
[2,1,3,5,4,6] => 4
[2,1,3,5,6,4] => 3
[2,1,3,6,4,5] => 3
[2,1,3,6,5,4] => 4
[2,1,4,3,5,6] => 4
[2,1,4,3,6,5] => 3
[2,1,4,5,3,6] => 3
[2,1,4,5,6,3] => 2
[2,1,4,6,3,5] => 2
[2,1,4,6,5,3] => 3
[2,1,5,3,4,6] => 3
[2,1,5,3,6,4] => 2
[2,1,5,4,3,6] => 4
[2,1,5,4,6,3] => 3
[2,1,5,6,3,4] => 2
[2,1,5,6,4,3] => 2
[2,1,6,3,4,5] => 2
[2,1,6,3,5,4] => 3
[2,1,6,4,3,5] => 3
[2,1,6,4,5,3] => 4
[2,1,6,5,3,4] => 2
[2,1,6,5,4,3] => 3
[2,3,1,4,5,6] => 4
[2,3,1,4,6,5] => 3
[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] => 3
[2,3,4,1,5,6] => 3
[2,3,4,1,6,5] => 2
[2,3,4,5,1,6] => 2
[2,3,4,5,6,1] => 1
[2,3,4,6,1,5] => 1
[2,3,4,6,5,1] => 2
[2,3,5,1,4,6] => 2
[2,3,5,1,6,4] => 1
[2,3,5,4,1,6] => 3
[2,3,5,4,6,1] => 2
[2,3,5,6,1,4] => 1
[2,3,5,6,4,1] => 1
[2,3,6,1,4,5] => 1
[2,3,6,1,5,4] => 2
[2,3,6,4,1,5] => 2
[2,3,6,4,5,1] => 3
[2,3,6,5,1,4] => 1
[2,3,6,5,4,1] => 2
[2,4,1,3,5,6] => 3
[2,4,1,3,6,5] => 2
[2,4,1,5,3,6] => 2
[2,4,1,5,6,3] => 1
[2,4,1,6,3,5] => 1
[2,4,1,6,5,3] => 2
[2,4,3,1,5,6] => 4
[2,4,3,1,6,5] => 3
[2,4,3,5,1,6] => 3
[2,4,3,5,6,1] => 2
[2,4,3,6,1,5] => 2
[2,4,3,6,5,1] => 3
[2,4,5,1,3,6] => 2
[2,4,5,1,6,3] => 1
[2,4,5,3,1,6] => 2
[2,4,5,3,6,1] => 1
[2,4,5,6,1,3] => 1
[2,4,5,6,3,1] => 1
[2,4,6,1,3,5] => 1
[2,4,6,1,5,3] => 2
[2,4,6,3,1,5] => 1
[2,4,6,3,5,1] => 2
[2,4,6,5,1,3] => 1
[2,4,6,5,3,1] => 1
[2,5,1,3,4,6] => 2
[2,5,1,3,6,4] => 1
[2,5,1,4,3,6] => 3
[2,5,1,4,6,3] => 2
[2,5,1,6,3,4] => 1
[2,5,1,6,4,3] => 1
[2,5,3,1,4,6] => 3
[2,5,3,1,6,4] => 2
[2,5,3,4,1,6] => 4
[2,5,3,4,6,1] => 3
[2,5,3,6,1,4] => 2
[2,5,3,6,4,1] => 2
[2,5,4,1,3,6] => 2
[2,5,4,1,6,3] => 1
[2,5,4,3,1,6] => 3
[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] => 1
[2,5,6,1,4,3] => 1
[2,5,6,3,1,4] => 1
[2,5,6,3,4,1] => 1
[2,5,6,4,1,3] => 2
[2,5,6,4,3,1] => 2
[2,6,1,3,4,5] => 1
[2,6,1,3,5,4] => 2
[2,6,1,4,3,5] => 2
[2,6,1,4,5,3] => 3
[2,6,1,5,3,4] => 1
[2,6,1,5,4,3] => 2
[2,6,3,1,4,5] => 2
[2,6,3,1,5,4] => 3
[2,6,3,4,1,5] => 3
[2,6,3,4,5,1] => 4
[2,6,3,5,1,4] => 2
[2,6,3,5,4,1] => 3
[2,6,4,1,3,5] => 1
[2,6,4,1,5,3] => 2
[2,6,4,3,1,5] => 2
[2,6,4,3,5,1] => 3
[2,6,4,5,1,3] => 1
[2,6,4,5,3,1] => 2
[2,6,5,1,3,4] => 1
[2,6,5,1,4,3] => 1
[2,6,5,3,1,4] => 1
[2,6,5,3,4,1] => 2
[2,6,5,4,1,3] => 2
[2,6,5,4,3,1] => 3
[3,1,2,4,5,6] => 4
[3,1,2,4,6,5] => 3
[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] => 3
[3,1,4,2,5,6] => 3
[3,1,4,2,6,5] => 2
[3,1,4,5,2,6] => 2
[3,1,4,5,6,2] => 1
[3,1,4,6,2,5] => 1
[3,1,4,6,5,2] => 2
[3,1,5,2,4,6] => 2
[3,1,5,2,6,4] => 1
[3,1,5,4,2,6] => 3
[3,1,5,4,6,2] => 2
[3,1,5,6,2,4] => 1
[3,1,5,6,4,2] => 1
[3,1,6,2,4,5] => 1
[3,1,6,2,5,4] => 2
[3,1,6,4,2,5] => 2
[3,1,6,4,5,2] => 3
[3,1,6,5,2,4] => 1
[3,1,6,5,4,2] => 2
[3,2,1,4,5,6] => 5
[3,2,1,4,6,5] => 4
[3,2,1,5,4,6] => 4
[3,2,1,5,6,4] => 3
[3,2,1,6,4,5] => 3
[3,2,1,6,5,4] => 4
[3,2,4,1,5,6] => 4
[3,2,4,1,6,5] => 3
[3,2,4,5,1,6] => 3
[3,2,4,5,6,1] => 2
[3,2,4,6,1,5] => 2
[3,2,4,6,5,1] => 3
[3,2,5,1,4,6] => 3
[3,2,5,1,6,4] => 2
[3,2,5,4,1,6] => 4
[3,2,5,4,6,1] => 3
[3,2,5,6,1,4] => 2
[3,2,5,6,4,1] => 2
[3,2,6,1,4,5] => 2
[3,2,6,1,5,4] => 3
[3,2,6,4,1,5] => 3
[3,2,6,4,5,1] => 4
[3,2,6,5,1,4] => 2
[3,2,6,5,4,1] => 3
[3,4,1,2,5,6] => 3
[3,4,1,2,6,5] => 2
[3,4,1,5,2,6] => 2
[3,4,1,5,6,2] => 1
[3,4,1,6,2,5] => 1
[3,4,1,6,5,2] => 2
[3,4,2,1,5,6] => 3
[3,4,2,1,6,5] => 2
[3,4,2,5,1,6] => 2
[3,4,2,5,6,1] => 1
[3,4,2,6,1,5] => 1
[3,4,2,6,5,1] => 2
[3,4,5,1,2,6] => 2
[3,4,5,1,6,2] => 1
[3,4,5,2,1,6] => 2
[3,4,5,2,6,1] => 1
[3,4,5,6,1,2] => 1
[3,4,5,6,2,1] => 1
[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] => 1
[3,4,6,5,2,1] => 1
[3,5,1,2,4,6] => 2
[3,5,1,2,6,4] => 1
[3,5,1,4,2,6] => 3
[3,5,1,4,6,2] => 2
[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] => 1
[3,5,2,4,1,6] => 3
[3,5,2,4,6,1] => 2
[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] => 1
[3,5,4,2,1,6] => 2
[3,5,4,2,6,1] => 1
[3,5,4,6,1,2] => 1
[3,5,4,6,2,1] => 1
[3,5,6,1,2,4] => 1
[3,5,6,1,4,2] => 1
[3,5,6,2,1,4] => 1
[3,5,6,2,4,1] => 1
[3,5,6,4,1,2] => 2
[3,5,6,4,2,1] => 2
[3,6,1,2,4,5] => 1
[3,6,1,2,5,4] => 2
[3,6,1,4,2,5] => 2
[3,6,1,4,5,2] => 3
[3,6,1,5,2,4] => 1
[3,6,1,5,4,2] => 2
[3,6,2,1,4,5] => 1
[3,6,2,1,5,4] => 2
[3,6,2,4,1,5] => 2
[3,6,2,4,5,1] => 3
[3,6,2,5,1,4] => 1
[3,6,2,5,4,1] => 2
[3,6,4,1,2,5] => 1
[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] => 1
[3,6,5,1,4,2] => 1
[3,6,5,2,1,4] => 1
[3,6,5,2,4,1] => 1
[3,6,5,4,1,2] => 2
[3,6,5,4,2,1] => 2
[4,1,2,3,5,6] => 3
[4,1,2,3,6,5] => 2
[4,1,2,5,3,6] => 2
[4,1,2,5,6,3] => 1
[4,1,2,6,3,5] => 1
[4,1,2,6,5,3] => 2
[4,1,3,2,5,6] => 4
[4,1,3,2,6,5] => 3
[4,1,3,5,2,6] => 3
[4,1,3,5,6,2] => 2
[4,1,3,6,2,5] => 2
[4,1,3,6,5,2] => 3
[4,1,5,2,3,6] => 2
[4,1,5,2,6,3] => 1
[4,1,5,3,2,6] => 2
[4,1,5,3,6,2] => 1
[4,1,5,6,2,3] => 1
[4,1,5,6,3,2] => 1
[4,1,6,2,3,5] => 1
[4,1,6,2,5,3] => 2
[4,1,6,3,2,5] => 1
[4,1,6,3,5,2] => 2
[4,1,6,5,2,3] => 1
[4,1,6,5,3,2] => 1
[4,2,1,3,5,6] => 4
[4,2,1,3,6,5] => 3
[4,2,1,5,3,6] => 3
[4,2,1,5,6,3] => 2
[4,2,1,6,3,5] => 2
[4,2,1,6,5,3] => 3
[4,2,3,1,5,6] => 5
[4,2,3,1,6,5] => 4
[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] => 4
[4,2,5,1,3,6] => 3
[4,2,5,1,6,3] => 2
[4,2,5,3,1,6] => 3
[4,2,5,3,6,1] => 2
[4,2,5,6,1,3] => 2
[4,2,5,6,3,1] => 2
[4,2,6,1,3,5] => 2
[4,2,6,1,5,3] => 3
[4,2,6,3,1,5] => 2
[4,2,6,3,5,1] => 3
[4,2,6,5,1,3] => 2
[4,2,6,5,3,1] => 2
[4,3,1,2,5,6] => 3
[4,3,1,2,6,5] => 2
[4,3,1,5,2,6] => 2
[4,3,1,5,6,2] => 1
[4,3,1,6,2,5] => 1
[4,3,1,6,5,2] => 2
[4,3,2,1,5,6] => 4
[4,3,2,1,6,5] => 3
[4,3,2,5,1,6] => 3
[4,3,2,5,6,1] => 2
[4,3,2,6,1,5] => 2
[4,3,2,6,5,1] => 3
[4,3,5,1,2,6] => 2
[4,3,5,1,6,2] => 1
[4,3,5,2,1,6] => 2
[4,3,5,2,6,1] => 1
[4,3,5,6,1,2] => 1
[4,3,5,6,2,1] => 1
[4,3,6,1,2,5] => 1
[4,3,6,1,5,2] => 2
[4,3,6,2,1,5] => 1
[4,3,6,2,5,1] => 2
[4,3,6,5,1,2] => 1
[4,3,6,5,2,1] => 1
[4,5,1,2,3,6] => 2
[4,5,1,2,6,3] => 1
[4,5,1,3,2,6] => 2
[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] => 1
[4,5,2,3,1,6] => 2
[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] => 3
[4,5,3,1,6,2] => 2
[4,5,3,2,1,6] => 3
[4,5,3,2,6,1] => 2
[4,5,3,6,1,2] => 2
[4,5,3,6,2,1] => 2
[4,5,6,1,2,3] => 1
[4,5,6,1,3,2] => 1
[4,5,6,2,1,3] => 1
[4,5,6,2,3,1] => 1
[4,5,6,3,1,2] => 1
[4,5,6,3,2,1] => 1
[4,6,1,2,3,5] => 1
[4,6,1,2,5,3] => 2
[4,6,1,3,2,5] => 1
[4,6,1,3,5,2] => 2
[4,6,1,5,2,3] => 1
[4,6,1,5,3,2] => 1
[4,6,2,1,3,5] => 1
[4,6,2,1,5,3] => 2
[4,6,2,3,1,5] => 1
[4,6,2,3,5,1] => 2
[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] => 3
[4,6,3,2,1,5] => 2
[4,6,3,2,5,1] => 3
[4,6,3,5,1,2] => 2
[4,6,3,5,2,1] => 2
[4,6,5,1,2,3] => 1
[4,6,5,1,3,2] => 1
[4,6,5,2,1,3] => 1
[4,6,5,2,3,1] => 1
[4,6,5,3,1,2] => 1
[4,6,5,3,2,1] => 1
[5,1,2,3,4,6] => 2
[5,1,2,3,6,4] => 1
[5,1,2,4,3,6] => 3
[5,1,2,4,6,3] => 2
[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] => 2
[5,1,3,4,2,6] => 4
[5,1,3,4,6,2] => 3
[5,1,3,6,2,4] => 2
[5,1,3,6,4,2] => 2
[5,1,4,2,3,6] => 2
[5,1,4,2,6,3] => 1
[5,1,4,3,2,6] => 3
[5,1,4,3,6,2] => 2
[5,1,4,6,2,3] => 1
[5,1,4,6,3,2] => 1
[5,1,6,2,3,4] => 1
[5,1,6,2,4,3] => 1
[5,1,6,3,2,4] => 1
[5,1,6,3,4,2] => 1
[5,1,6,4,2,3] => 2
[5,1,6,4,3,2] => 2
[5,2,1,3,4,6] => 3
[5,2,1,3,6,4] => 2
[5,2,1,4,3,6] => 4
[5,2,1,4,6,3] => 3
[5,2,1,6,3,4] => 2
[5,2,1,6,4,3] => 2
[5,2,3,1,4,6] => 4
[5,2,3,1,6,4] => 3
[5,2,3,4,1,6] => 5
[5,2,3,4,6,1] => 4
[5,2,3,6,1,4] => 3
[5,2,3,6,4,1] => 3
[5,2,4,1,3,6] => 3
[5,2,4,1,6,3] => 2
[5,2,4,3,1,6] => 4
[5,2,4,3,6,1] => 3
[5,2,4,6,1,3] => 2
[5,2,4,6,3,1] => 2
[5,2,6,1,3,4] => 2
[5,2,6,1,4,3] => 2
[5,2,6,3,1,4] => 2
[5,2,6,3,4,1] => 2
[5,2,6,4,1,3] => 3
[5,2,6,4,3,1] => 3
[5,3,1,2,4,6] => 2
[5,3,1,2,6,4] => 1
[5,3,1,4,2,6] => 3
[5,3,1,4,6,2] => 2
[5,3,1,6,2,4] => 1
[5,3,1,6,4,2] => 1
[5,3,2,1,4,6] => 3
[5,3,2,1,6,4] => 2
[5,3,2,4,1,6] => 4
[5,3,2,4,6,1] => 3
[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] => 1
[5,3,4,2,1,6] => 3
[5,3,4,2,6,1] => 2
[5,3,4,6,1,2] => 1
[5,3,4,6,2,1] => 1
[5,3,6,1,2,4] => 1
[5,3,6,1,4,2] => 1
[5,3,6,2,1,4] => 1
[5,3,6,2,4,1] => 1
[5,3,6,4,1,2] => 2
[5,3,6,4,2,1] => 2
[5,4,1,2,3,6] => 2
[5,4,1,2,6,3] => 1
[5,4,1,3,2,6] => 2
[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] => 2
[5,4,2,1,6,3] => 1
[5,4,2,3,1,6] => 3
[5,4,2,3,6,1] => 2
[5,4,2,6,1,3] => 1
[5,4,2,6,3,1] => 1
[5,4,3,1,2,6] => 3
[5,4,3,1,6,2] => 2
[5,4,3,2,1,6] => 4
[5,4,3,2,6,1] => 3
[5,4,3,6,1,2] => 2
[5,4,3,6,2,1] => 2
[5,4,6,1,2,3] => 1
[5,4,6,1,3,2] => 1
[5,4,6,2,1,3] => 1
[5,4,6,2,3,1] => 1
[5,4,6,3,1,2] => 1
[5,4,6,3,2,1] => 1
[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] => 2
[5,6,1,4,3,2] => 2
[5,6,2,1,3,4] => 1
[5,6,2,1,4,3] => 1
[5,6,2,3,1,4] => 1
[5,6,2,3,4,1] => 1
[5,6,2,4,1,3] => 2
[5,6,2,4,3,1] => 2
[5,6,3,1,2,4] => 2
[5,6,3,1,4,2] => 2
[5,6,3,2,1,4] => 2
[5,6,3,2,4,1] => 2
[5,6,3,4,1,2] => 3
[5,6,3,4,2,1] => 3
[5,6,4,1,2,3] => 1
[5,6,4,1,3,2] => 1
[5,6,4,2,1,3] => 1
[5,6,4,2,3,1] => 1
[5,6,4,3,1,2] => 2
[5,6,4,3,2,1] => 2
[6,1,2,3,4,5] => 1
[6,1,2,3,5,4] => 2
[6,1,2,4,3,5] => 2
[6,1,2,4,5,3] => 3
[6,1,2,5,3,4] => 1
[6,1,2,5,4,3] => 2
[6,1,3,2,4,5] => 2
[6,1,3,2,5,4] => 3
[6,1,3,4,2,5] => 3
[6,1,3,4,5,2] => 4
[6,1,3,5,2,4] => 2
[6,1,3,5,4,2] => 3
[6,1,4,2,3,5] => 1
[6,1,4,2,5,3] => 2
[6,1,4,3,2,5] => 2
[6,1,4,3,5,2] => 3
[6,1,4,5,2,3] => 1
[6,1,4,5,3,2] => 2
[6,1,5,2,3,4] => 1
[6,1,5,2,4,3] => 1
[6,1,5,3,2,4] => 1
[6,1,5,3,4,2] => 2
[6,1,5,4,2,3] => 2
[6,1,5,4,3,2] => 3
[6,2,1,3,4,5] => 2
[6,2,1,3,5,4] => 3
[6,2,1,4,3,5] => 3
[6,2,1,4,5,3] => 4
[6,2,1,5,3,4] => 2
[6,2,1,5,4,3] => 3
[6,2,3,1,4,5] => 3
[6,2,3,1,5,4] => 4
[6,2,3,4,1,5] => 4
[6,2,3,4,5,1] => 5
[6,2,3,5,1,4] => 3
[6,2,3,5,4,1] => 4
[6,2,4,1,3,5] => 2
[6,2,4,1,5,3] => 3
[6,2,4,3,1,5] => 3
[6,2,4,3,5,1] => 4
[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] => 2
[6,2,5,3,1,4] => 2
[6,2,5,3,4,1] => 3
[6,2,5,4,1,3] => 3
[6,2,5,4,3,1] => 4
[6,3,1,2,4,5] => 1
[6,3,1,2,5,4] => 2
[6,3,1,4,2,5] => 2
[6,3,1,4,5,2] => 3
[6,3,1,5,2,4] => 1
[6,3,1,5,4,2] => 2
[6,3,2,1,4,5] => 2
[6,3,2,1,5,4] => 3
[6,3,2,4,1,5] => 3
[6,3,2,4,5,1] => 4
[6,3,2,5,1,4] => 2
[6,3,2,5,4,1] => 3
[6,3,4,1,2,5] => 1
[6,3,4,1,5,2] => 2
[6,3,4,2,1,5] => 2
[6,3,4,2,5,1] => 3
[6,3,4,5,1,2] => 1
[6,3,4,5,2,1] => 2
[6,3,5,1,2,4] => 1
[6,3,5,1,4,2] => 1
[6,3,5,2,1,4] => 1
[6,3,5,2,4,1] => 2
[6,3,5,4,1,2] => 2
[6,3,5,4,2,1] => 3
[6,4,1,2,3,5] => 1
[6,4,1,2,5,3] => 2
[6,4,1,3,2,5] => 1
[6,4,1,3,5,2] => 2
[6,4,1,5,2,3] => 1
[6,4,1,5,3,2] => 1
[6,4,2,1,3,5] => 1
[6,4,2,1,5,3] => 2
[6,4,2,3,1,5] => 2
[6,4,2,3,5,1] => 3
[6,4,2,5,1,3] => 1
[6,4,2,5,3,1] => 2
[6,4,3,1,2,5] => 2
[6,4,3,1,5,2] => 3
[6,4,3,2,1,5] => 3
[6,4,3,2,5,1] => 4
[6,4,3,5,1,2] => 2
[6,4,3,5,2,1] => 3
[6,4,5,1,2,3] => 1
[6,4,5,1,3,2] => 1
[6,4,5,2,1,3] => 1
[6,4,5,2,3,1] => 2
[6,4,5,3,1,2] => 1
[6,4,5,3,2,1] => 2
[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] => 2
[6,5,1,4,3,2] => 2
[6,5,2,1,3,4] => 1
[6,5,2,1,4,3] => 1
[6,5,2,3,1,4] => 1
[6,5,2,3,4,1] => 2
[6,5,2,4,1,3] => 2
[6,5,2,4,3,1] => 3
[6,5,3,1,2,4] => 2
[6,5,3,1,4,2] => 2
[6,5,3,2,1,4] => 2
[6,5,3,2,4,1] => 3
[6,5,3,4,1,2] => 3
[6,5,3,4,2,1] => 4
[6,5,4,1,2,3] => 1
[6,5,4,1,3,2] => 1
[6,5,4,2,1,3] => 1
[6,5,4,2,3,1] => 2
[6,5,4,3,1,2] => 2
[6,5,4,3,2,1] => 3
[1,2,3,4,5,6,7] => 7
[1,2,3,4,5,7,6] => 6
[1,2,3,4,6,5,7] => 6
[1,2,3,4,6,7,5] => 5
[1,2,3,4,7,5,6] => 5
[1,2,3,4,7,6,5] => 6
[1,2,3,5,4,6,7] => 6
[1,2,3,5,4,7,6] => 5
[1,2,3,5,6,4,7] => 5
[1,2,3,5,6,7,4] => 4
[1,2,3,5,7,4,6] => 4
[1,2,3,5,7,6,4] => 5
[1,2,3,6,4,5,7] => 5
[1,2,3,6,4,7,5] => 4
[1,2,3,6,5,4,7] => 6
[1,2,3,6,5,7,4] => 5
[1,2,3,6,7,4,5] => 4
[1,2,3,6,7,5,4] => 4
[1,2,3,7,4,5,6] => 4
[1,2,3,7,4,6,5] => 5
[1,2,3,7,5,4,6] => 5
[1,2,3,7,5,6,4] => 6
[1,2,3,7,6,4,5] => 4
[1,2,3,7,6,5,4] => 5
[1,2,4,3,5,6,7] => 6
[1,2,4,3,5,7,6] => 5
[1,2,4,3,6,5,7] => 5
[1,2,4,3,6,7,5] => 4
[1,2,4,3,7,5,6] => 4
[1,2,4,3,7,6,5] => 5
[1,2,4,5,3,6,7] => 5
[1,2,4,5,3,7,6] => 4
[1,2,4,5,6,3,7] => 4
[1,2,4,5,6,7,3] => 3
[1,2,4,5,7,3,6] => 3
[1,2,4,5,7,6,3] => 4
[1,2,4,6,3,5,7] => 4
[1,2,4,6,3,7,5] => 3
[1,2,4,6,5,3,7] => 5
[1,2,4,6,5,7,3] => 4
[1,2,4,6,7,3,5] => 3
[1,2,4,6,7,5,3] => 3
[1,2,4,7,3,5,6] => 3
[1,2,4,7,3,6,5] => 4
[1,2,4,7,5,3,6] => 4
[1,2,4,7,5,6,3] => 5
[1,2,4,7,6,3,5] => 3
[1,2,4,7,6,5,3] => 4
[1,2,5,3,4,6,7] => 5
[1,2,5,3,4,7,6] => 4
[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] => 4
[1,2,5,4,3,6,7] => 6
[1,2,5,4,3,7,6] => 5
[1,2,5,4,6,3,7] => 5
[1,2,5,4,6,7,3] => 4
[1,2,5,4,7,3,6] => 4
[1,2,5,4,7,6,3] => 5
[1,2,5,6,3,4,7] => 4
[1,2,5,6,3,7,4] => 3
[1,2,5,6,4,3,7] => 4
[1,2,5,6,4,7,3] => 3
[1,2,5,6,7,3,4] => 3
[1,2,5,6,7,4,3] => 3
[1,2,5,7,3,4,6] => 3
[1,2,5,7,3,6,4] => 4
[1,2,5,7,4,3,6] => 3
[1,2,5,7,4,6,3] => 4
[1,2,5,7,6,3,4] => 3
[1,2,5,7,6,4,3] => 3
[1,2,6,3,4,5,7] => 4
[1,2,6,3,4,7,5] => 3
[1,2,6,3,5,4,7] => 5
[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] => 5
[1,2,6,4,3,7,5] => 4
[1,2,6,4,5,3,7] => 6
[1,2,6,4,5,7,3] => 5
[1,2,6,4,7,3,5] => 4
[1,2,6,4,7,5,3] => 4
[1,2,6,5,3,4,7] => 4
[1,2,6,5,3,7,4] => 3
[1,2,6,5,4,3,7] => 5
[1,2,6,5,4,7,3] => 4
[1,2,6,5,7,3,4] => 3
[1,2,6,5,7,4,3] => 3
[1,2,6,7,3,4,5] => 3
[1,2,6,7,3,5,4] => 3
[1,2,6,7,4,3,5] => 3
[1,2,6,7,4,5,3] => 3
[1,2,6,7,5,3,4] => 4
[1,2,6,7,5,4,3] => 4
[1,2,7,3,4,5,6] => 3
[1,2,7,3,4,6,5] => 4
[1,2,7,3,5,4,6] => 4
[1,2,7,3,5,6,4] => 5
[1,2,7,3,6,4,5] => 3
[1,2,7,3,6,5,4] => 4
[1,2,7,4,3,5,6] => 4
[1,2,7,4,3,6,5] => 5
[1,2,7,4,5,3,6] => 5
[1,2,7,4,5,6,3] => 6
[1,2,7,4,6,3,5] => 4
[1,2,7,4,6,5,3] => 5
[1,2,7,5,3,4,6] => 3
[1,2,7,5,3,6,4] => 4
[1,2,7,5,4,3,6] => 4
[1,2,7,5,4,6,3] => 5
[1,2,7,5,6,3,4] => 3
[1,2,7,5,6,4,3] => 4
[1,2,7,6,3,4,5] => 3
[1,2,7,6,3,5,4] => 3
[1,2,7,6,4,3,5] => 3
[1,2,7,6,4,5,3] => 4
[1,2,7,6,5,3,4] => 4
[1,2,7,6,5,4,3] => 5
[1,3,2,4,5,6,7] => 6
[1,3,2,4,5,7,6] => 5
[1,3,2,4,6,5,7] => 5
[1,3,2,4,6,7,5] => 4
[1,3,2,4,7,5,6] => 4
[1,3,2,4,7,6,5] => 5
[1,3,2,5,4,6,7] => 5
[1,3,2,5,4,7,6] => 4
[1,3,2,5,6,4,7] => 4
[1,3,2,5,6,7,4] => 3
[1,3,2,5,7,4,6] => 3
[1,3,2,5,7,6,4] => 4
[1,3,2,6,4,5,7] => 4
[1,3,2,6,4,7,5] => 3
[1,3,2,6,5,4,7] => 5
[1,3,2,6,5,7,4] => 4
[1,3,2,6,7,4,5] => 3
[1,3,2,6,7,5,4] => 3
[1,3,2,7,4,5,6] => 3
[1,3,2,7,4,6,5] => 4
[1,3,2,7,5,4,6] => 4
[1,3,2,7,5,6,4] => 5
[1,3,2,7,6,4,5] => 3
[1,3,2,7,6,5,4] => 4
[1,3,4,2,5,6,7] => 5
[1,3,4,2,5,7,6] => 4
[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] => 4
[1,3,4,5,2,6,7] => 4
[1,3,4,5,2,7,6] => 3
[1,3,4,5,6,2,7] => 3
[1,3,4,5,6,7,2] => 2
[1,3,4,5,7,2,6] => 2
[1,3,4,5,7,6,2] => 3
[1,3,4,6,2,5,7] => 3
[1,3,4,6,2,7,5] => 2
[1,3,4,6,5,2,7] => 4
[1,3,4,6,5,7,2] => 3
[1,3,4,6,7,2,5] => 2
[1,3,4,6,7,5,2] => 2
[1,3,4,7,2,5,6] => 2
[1,3,4,7,2,6,5] => 3
[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] => 3
[1,3,5,2,4,6,7] => 4
[1,3,5,2,4,7,6] => 3
[1,3,5,2,6,4,7] => 3
[1,3,5,2,6,7,4] => 2
[1,3,5,2,7,4,6] => 2
[1,3,5,2,7,6,4] => 3
[1,3,5,4,2,6,7] => 5
[1,3,5,4,2,7,6] => 4
[1,3,5,4,6,2,7] => 4
[1,3,5,4,6,7,2] => 3
[1,3,5,4,7,2,6] => 3
[1,3,5,4,7,6,2] => 4
[1,3,5,6,2,4,7] => 3
[1,3,5,6,2,7,4] => 2
[1,3,5,6,4,2,7] => 3
[1,3,5,6,4,7,2] => 2
[1,3,5,6,7,2,4] => 2
[1,3,5,6,7,4,2] => 2
[1,3,5,7,2,4,6] => 2
[1,3,5,7,2,6,4] => 3
[1,3,5,7,4,2,6] => 2
[1,3,5,7,4,6,2] => 3
[1,3,5,7,6,2,4] => 2
[1,3,5,7,6,4,2] => 2
[1,3,6,2,4,5,7] => 3
[1,3,6,2,4,7,5] => 2
[1,3,6,2,5,4,7] => 4
[1,3,6,2,5,7,4] => 3
[1,3,6,2,7,4,5] => 2
[1,3,6,2,7,5,4] => 2
[1,3,6,4,2,5,7] => 4
[1,3,6,4,2,7,5] => 3
[1,3,6,4,5,2,7] => 5
[1,3,6,4,5,7,2] => 4
[1,3,6,4,7,2,5] => 3
[1,3,6,4,7,5,2] => 3
[1,3,6,5,2,4,7] => 3
[1,3,6,5,2,7,4] => 2
[1,3,6,5,4,2,7] => 4
[1,3,6,5,4,7,2] => 3
[1,3,6,5,7,2,4] => 2
[1,3,6,5,7,4,2] => 2
[1,3,6,7,2,4,5] => 2
[1,3,6,7,2,5,4] => 2
[1,3,6,7,4,2,5] => 2
[1,3,6,7,4,5,2] => 2
[1,3,6,7,5,2,4] => 3
[1,3,6,7,5,4,2] => 3
[1,3,7,2,4,5,6] => 2
[1,3,7,2,4,6,5] => 3
[1,3,7,2,5,4,6] => 3
[1,3,7,2,5,6,4] => 4
[1,3,7,2,6,4,5] => 2
[1,3,7,2,6,5,4] => 3
[1,3,7,4,2,5,6] => 3
[1,3,7,4,2,6,5] => 4
[1,3,7,4,5,2,6] => 4
[1,3,7,4,5,6,2] => 5
[1,3,7,4,6,2,5] => 3
[1,3,7,4,6,5,2] => 4
[1,3,7,5,2,4,6] => 2
[1,3,7,5,2,6,4] => 3
[1,3,7,5,4,2,6] => 3
[1,3,7,5,4,6,2] => 4
[1,3,7,5,6,2,4] => 2
[1,3,7,5,6,4,2] => 3
[1,3,7,6,2,4,5] => 2
[1,3,7,6,2,5,4] => 2
[1,3,7,6,4,2,5] => 2
[1,3,7,6,4,5,2] => 3
[1,3,7,6,5,2,4] => 3
[1,3,7,6,5,4,2] => 4
[1,4,2,3,5,6,7] => 5
[1,4,2,3,5,7,6] => 4
[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] => 4
[1,4,2,5,3,6,7] => 4
[1,4,2,5,3,7,6] => 3
[1,4,2,5,6,3,7] => 3
[1,4,2,5,6,7,3] => 2
[1,4,2,5,7,3,6] => 2
[1,4,2,5,7,6,3] => 3
[1,4,2,6,3,5,7] => 3
[1,4,2,6,3,7,5] => 2
[1,4,2,6,5,3,7] => 4
[1,4,2,6,5,7,3] => 3
[1,4,2,6,7,3,5] => 2
[1,4,2,6,7,5,3] => 2
[1,4,2,7,3,5,6] => 2
[1,4,2,7,3,6,5] => 3
[1,4,2,7,5,3,6] => 3
[1,4,2,7,5,6,3] => 4
[1,4,2,7,6,3,5] => 2
[1,4,2,7,6,5,3] => 3
[1,4,3,2,5,6,7] => 6
[1,4,3,2,5,7,6] => 5
[1,4,3,2,6,5,7] => 5
[1,4,3,2,6,7,5] => 4
[1,4,3,2,7,5,6] => 4
[1,4,3,2,7,6,5] => 5
[1,4,3,5,2,6,7] => 5
[1,4,3,5,2,7,6] => 4
[1,4,3,5,6,2,7] => 4
[1,4,3,5,6,7,2] => 3
[1,4,3,5,7,2,6] => 3
[1,4,3,5,7,6,2] => 4
[1,4,3,6,2,5,7] => 4
[1,4,3,6,2,7,5] => 3
[1,4,3,6,5,2,7] => 5
[1,4,3,6,5,7,2] => 4
[1,4,3,6,7,2,5] => 3
[1,4,3,6,7,5,2] => 3
[1,4,3,7,2,5,6] => 3
[1,4,3,7,2,6,5] => 4
[1,4,3,7,5,2,6] => 4
[1,4,3,7,5,6,2] => 5
[1,4,3,7,6,2,5] => 3
[1,4,3,7,6,5,2] => 4
[1,4,5,2,3,6,7] => 4
[1,4,5,2,3,7,6] => 3
[1,4,5,2,6,3,7] => 3
[1,4,5,2,6,7,3] => 2
[1,4,5,2,7,3,6] => 2
[1,4,5,2,7,6,3] => 3
[1,4,5,3,2,6,7] => 4
[1,4,5,3,2,7,6] => 3
[1,4,5,3,6,2,7] => 3
[1,4,5,3,6,7,2] => 2
[1,4,5,3,7,2,6] => 2
[1,4,5,3,7,6,2] => 3
[1,4,5,6,2,3,7] => 3
[1,4,5,6,2,7,3] => 2
[1,4,5,6,3,2,7] => 3
[1,4,5,6,3,7,2] => 2
[1,4,5,6,7,2,3] => 2
[1,4,5,6,7,3,2] => 2
[1,4,5,7,2,3,6] => 2
[1,4,5,7,2,6,3] => 3
[1,4,5,7,3,2,6] => 2
[1,4,5,7,3,6,2] => 3
[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] => 4
[1,4,6,2,5,7,3] => 3
[1,4,6,2,7,3,5] => 2
[1,4,6,2,7,5,3] => 2
[1,4,6,3,2,5,7] => 3
[1,4,6,3,2,7,5] => 2
[1,4,6,3,5,2,7] => 4
[1,4,6,3,5,7,2] => 3
[1,4,6,3,7,2,5] => 2
[1,4,6,3,7,5,2] => 2
[1,4,6,5,2,3,7] => 3
[1,4,6,5,2,7,3] => 2
[1,4,6,5,3,2,7] => 3
-----------------------------------------------------------------------------
Created: Aug 09, 2019 at 21:30 by Martin Rubey
-----------------------------------------------------------------------------
Last Updated: Aug 09, 2019 at 21:30 by Martin Rubey