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* www.FindStat.org - The Combinatorial Statistic Finder *
* *
* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
* *
* 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. *
*****************************************************************************
-----------------------------------------------------------------------------
Statistic identifier: St000625
-----------------------------------------------------------------------------
Collection: Permutations
-----------------------------------------------------------------------------
Description: The sum of the minimal distances to a greater element.
Set $\pi_0 = \pi_{n+1} = n+1$, then this statistic is
$$
\sum_{i=1}^n \min_d(\pi_{i-d}>\pi_i\text{ or }\pi_{i+d}>\pi_i)
$$
This statistic appears in [1].
The generating function for the sequence of maximal values attained on $\mathfrak S_r$, $r\geq 0$ apparently coincides with [2], which satisfies the functional equation
$$
(x-1)^2 (x+1)^3 f(x^2) - (x-1)^2 (x+1) f(x) + x = 0.
$$
-----------------------------------------------------------------------------
References: [1] newbie How to find a permutation of [n] so that $\sum \{\min (i-l[i],r[i]-i)\}$ is maximized? [[MathOverflow:251968]]
[2] Total number of 1's in binary expansions of 0, ..., n. [[OEIS:A000788]]
-----------------------------------------------------------------------------
Code:
def statistic(pi):
n = len(pi)
def closest_major(i):
ai = pi[i]
distance = 1
while True:
if (i-distance < 0 or pi[i-distance] >= ai or
i+distance >= n or pi[i+distance] >= ai):
return distance
distance += 1
return sum(closest_major(i) for i in range(n))
-----------------------------------------------------------------------------
Statistic values:
[1,2] => 2
[2,1] => 2
[1,2,3] => 3
[1,3,2] => 4
[2,1,3] => 3
[2,3,1] => 4
[3,1,2] => 3
[3,2,1] => 3
[1,2,3,4] => 4
[1,2,4,3] => 5
[1,3,2,4] => 5
[1,3,4,2] => 5
[1,4,2,3] => 5
[1,4,3,2] => 5
[2,1,3,4] => 4
[2,1,4,3] => 5
[2,3,1,4] => 5
[2,3,4,1] => 5
[2,4,1,3] => 5
[2,4,3,1] => 5
[3,1,2,4] => 4
[3,1,4,2] => 5
[3,2,1,4] => 4
[3,2,4,1] => 5
[3,4,1,2] => 5
[3,4,2,1] => 5
[4,1,2,3] => 4
[4,1,3,2] => 5
[4,2,1,3] => 4
[4,2,3,1] => 5
[4,3,1,2] => 4
[4,3,2,1] => 4
[1,2,3,4,5] => 5
[1,2,3,5,4] => 6
[1,2,4,3,5] => 6
[1,2,4,5,3] => 6
[1,2,5,3,4] => 7
[1,2,5,4,3] => 7
[1,3,2,4,5] => 6
[1,3,2,5,4] => 7
[1,3,4,2,5] => 6
[1,3,4,5,2] => 6
[1,3,5,2,4] => 7
[1,3,5,4,2] => 7
[1,4,2,3,5] => 6
[1,4,2,5,3] => 7
[1,4,3,2,5] => 6
[1,4,3,5,2] => 7
[1,4,5,2,3] => 7
[1,4,5,3,2] => 7
[1,5,2,3,4] => 6
[1,5,2,4,3] => 7
[1,5,3,2,4] => 6
[1,5,3,4,2] => 7
[1,5,4,2,3] => 6
[1,5,4,3,2] => 6
[2,1,3,4,5] => 5
[2,1,3,5,4] => 6
[2,1,4,3,5] => 6
[2,1,4,5,3] => 6
[2,1,5,3,4] => 7
[2,1,5,4,3] => 7
[2,3,1,4,5] => 6
[2,3,1,5,4] => 7
[2,3,4,1,5] => 6
[2,3,4,5,1] => 6
[2,3,5,1,4] => 7
[2,3,5,4,1] => 7
[2,4,1,3,5] => 6
[2,4,1,5,3] => 7
[2,4,3,1,5] => 6
[2,4,3,5,1] => 7
[2,4,5,1,3] => 7
[2,4,5,3,1] => 7
[2,5,1,3,4] => 6
[2,5,1,4,3] => 7
[2,5,3,1,4] => 6
[2,5,3,4,1] => 7
[2,5,4,1,3] => 6
[2,5,4,3,1] => 6
[3,1,2,4,5] => 5
[3,1,2,5,4] => 6
[3,1,4,2,5] => 6
[3,1,4,5,2] => 6
[3,1,5,2,4] => 7
[3,1,5,4,2] => 7
[3,2,1,4,5] => 5
[3,2,1,5,4] => 6
[3,2,4,1,5] => 6
[3,2,4,5,1] => 6
[3,2,5,1,4] => 7
[3,2,5,4,1] => 7
[3,4,1,2,5] => 6
[3,4,1,5,2] => 7
[3,4,2,1,5] => 6
[3,4,2,5,1] => 7
[3,4,5,1,2] => 7
[3,4,5,2,1] => 7
[3,5,1,2,4] => 6
[3,5,1,4,2] => 7
[3,5,2,1,4] => 6
[3,5,2,4,1] => 7
[3,5,4,1,2] => 6
[3,5,4,2,1] => 6
[4,1,2,3,5] => 5
[4,1,2,5,3] => 6
[4,1,3,2,5] => 6
[4,1,3,5,2] => 6
[4,1,5,2,3] => 7
[4,1,5,3,2] => 7
[4,2,1,3,5] => 5
[4,2,1,5,3] => 6
[4,2,3,1,5] => 6
[4,2,3,5,1] => 6
[4,2,5,1,3] => 7
[4,2,5,3,1] => 7
[4,3,1,2,5] => 5
[4,3,1,5,2] => 6
[4,3,2,1,5] => 5
[4,3,2,5,1] => 6
[4,3,5,1,2] => 7
[4,3,5,2,1] => 7
[4,5,1,2,3] => 6
[4,5,1,3,2] => 7
[4,5,2,1,3] => 6
[4,5,2,3,1] => 7
[4,5,3,1,2] => 6
[4,5,3,2,1] => 6
[5,1,2,3,4] => 5
[5,1,2,4,3] => 6
[5,1,3,2,4] => 6
[5,1,3,4,2] => 6
[5,1,4,2,3] => 6
[5,1,4,3,2] => 6
[5,2,1,3,4] => 5
[5,2,1,4,3] => 6
[5,2,3,1,4] => 6
[5,2,3,4,1] => 6
[5,2,4,1,3] => 6
[5,2,4,3,1] => 6
[5,3,1,2,4] => 5
[5,3,1,4,2] => 6
[5,3,2,1,4] => 5
[5,3,2,4,1] => 6
[5,3,4,1,2] => 6
[5,3,4,2,1] => 6
[5,4,1,2,3] => 5
[5,4,1,3,2] => 6
[5,4,2,1,3] => 5
[5,4,2,3,1] => 6
[5,4,3,1,2] => 5
[5,4,3,2,1] => 5
[1,2,3,4,5,6] => 6
[1,2,3,4,6,5] => 7
[1,2,3,5,4,6] => 7
[1,2,3,5,6,4] => 7
[1,2,3,6,4,5] => 8
[1,2,3,6,5,4] => 8
[1,2,4,3,5,6] => 7
[1,2,4,3,6,5] => 8
[1,2,4,5,3,6] => 7
[1,2,4,5,6,3] => 7
[1,2,4,6,3,5] => 8
[1,2,4,6,5,3] => 8
[1,2,5,3,4,6] => 8
[1,2,5,3,6,4] => 8
[1,2,5,4,3,6] => 8
[1,2,5,4,6,3] => 8
[1,2,5,6,3,4] => 8
[1,2,5,6,4,3] => 8
[1,2,6,3,4,5] => 8
[1,2,6,3,5,4] => 9
[1,2,6,4,3,5] => 8
[1,2,6,4,5,3] => 9
[1,2,6,5,3,4] => 8
[1,2,6,5,4,3] => 8
[1,3,2,4,5,6] => 7
[1,3,2,4,6,5] => 8
[1,3,2,5,4,6] => 8
[1,3,2,5,6,4] => 8
[1,3,2,6,4,5] => 9
[1,3,2,6,5,4] => 9
[1,3,4,2,5,6] => 7
[1,3,4,2,6,5] => 8
[1,3,4,5,2,6] => 7
[1,3,4,5,6,2] => 7
[1,3,4,6,2,5] => 8
[1,3,4,6,5,2] => 8
[1,3,5,2,4,6] => 8
[1,3,5,2,6,4] => 8
[1,3,5,4,2,6] => 8
[1,3,5,4,6,2] => 8
[1,3,5,6,2,4] => 8
[1,3,5,6,4,2] => 8
[1,3,6,2,4,5] => 8
[1,3,6,2,5,4] => 9
[1,3,6,4,2,5] => 8
[1,3,6,4,5,2] => 9
[1,3,6,5,2,4] => 8
[1,3,6,5,4,2] => 8
[1,4,2,3,5,6] => 7
[1,4,2,3,6,5] => 8
[1,4,2,5,3,6] => 8
[1,4,2,5,6,3] => 8
[1,4,2,6,3,5] => 9
[1,4,2,6,5,3] => 9
[1,4,3,2,5,6] => 7
[1,4,3,2,6,5] => 8
[1,4,3,5,2,6] => 8
[1,4,3,5,6,2] => 8
[1,4,3,6,2,5] => 9
[1,4,3,6,5,2] => 9
[1,4,5,2,3,6] => 8
[1,4,5,2,6,3] => 8
[1,4,5,3,2,6] => 8
[1,4,5,3,6,2] => 8
[1,4,5,6,2,3] => 8
[1,4,5,6,3,2] => 8
[1,4,6,2,3,5] => 8
[1,4,6,2,5,3] => 9
[1,4,6,3,2,5] => 8
[1,4,6,3,5,2] => 9
[1,4,6,5,2,3] => 8
[1,4,6,5,3,2] => 8
[1,5,2,3,4,6] => 7
[1,5,2,3,6,4] => 8
[1,5,2,4,3,6] => 8
[1,5,2,4,6,3] => 8
[1,5,2,6,3,4] => 9
[1,5,2,6,4,3] => 9
[1,5,3,2,4,6] => 7
[1,5,3,2,6,4] => 8
[1,5,3,4,2,6] => 8
[1,5,3,4,6,2] => 8
[1,5,3,6,2,4] => 9
[1,5,3,6,4,2] => 9
[1,5,4,2,3,6] => 7
[1,5,4,2,6,3] => 8
[1,5,4,3,2,6] => 7
[1,5,4,3,6,2] => 8
[1,5,4,6,2,3] => 9
[1,5,4,6,3,2] => 9
[1,5,6,2,3,4] => 8
[1,5,6,2,4,3] => 9
[1,5,6,3,2,4] => 8
[1,5,6,3,4,2] => 9
[1,5,6,4,2,3] => 8
[1,5,6,4,3,2] => 8
[1,6,2,3,4,5] => 7
[1,6,2,3,5,4] => 8
[1,6,2,4,3,5] => 8
[1,6,2,4,5,3] => 8
[1,6,2,5,3,4] => 8
[1,6,2,5,4,3] => 8
[1,6,3,2,4,5] => 7
[1,6,3,2,5,4] => 8
[1,6,3,4,2,5] => 8
[1,6,3,4,5,2] => 8
[1,6,3,5,2,4] => 8
[1,6,3,5,4,2] => 8
[1,6,4,2,3,5] => 7
[1,6,4,2,5,3] => 8
[1,6,4,3,2,5] => 7
[1,6,4,3,5,2] => 8
[1,6,4,5,2,3] => 8
[1,6,4,5,3,2] => 8
[1,6,5,2,3,4] => 7
[1,6,5,2,4,3] => 8
[1,6,5,3,2,4] => 7
[1,6,5,3,4,2] => 8
[1,6,5,4,2,3] => 7
[1,6,5,4,3,2] => 7
[2,1,3,4,5,6] => 6
[2,1,3,4,6,5] => 7
[2,1,3,5,4,6] => 7
[2,1,3,5,6,4] => 7
[2,1,3,6,4,5] => 8
[2,1,3,6,5,4] => 8
[2,1,4,3,5,6] => 7
[2,1,4,3,6,5] => 8
[2,1,4,5,3,6] => 7
[2,1,4,5,6,3] => 7
[2,1,4,6,3,5] => 8
[2,1,4,6,5,3] => 8
[2,1,5,3,4,6] => 8
[2,1,5,3,6,4] => 8
[2,1,5,4,3,6] => 8
[2,1,5,4,6,3] => 8
[2,1,5,6,3,4] => 8
[2,1,5,6,4,3] => 8
[2,1,6,3,4,5] => 8
[2,1,6,3,5,4] => 9
[2,1,6,4,3,5] => 8
[2,1,6,4,5,3] => 9
[2,1,6,5,3,4] => 8
[2,1,6,5,4,3] => 8
[2,3,1,4,5,6] => 7
[2,3,1,4,6,5] => 8
[2,3,1,5,4,6] => 8
[2,3,1,5,6,4] => 8
[2,3,1,6,4,5] => 9
[2,3,1,6,5,4] => 9
[2,3,4,1,5,6] => 7
[2,3,4,1,6,5] => 8
[2,3,4,5,1,6] => 7
[2,3,4,5,6,1] => 7
[2,3,4,6,1,5] => 8
[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] => 8
[2,3,5,4,6,1] => 8
[2,3,5,6,1,4] => 8
[2,3,5,6,4,1] => 8
[2,3,6,1,4,5] => 8
[2,3,6,1,5,4] => 9
[2,3,6,4,1,5] => 8
[2,3,6,4,5,1] => 9
[2,3,6,5,1,4] => 8
[2,3,6,5,4,1] => 8
[2,4,1,3,5,6] => 7
[2,4,1,3,6,5] => 8
[2,4,1,5,3,6] => 8
[2,4,1,5,6,3] => 8
[2,4,1,6,3,5] => 9
[2,4,1,6,5,3] => 9
[2,4,3,1,5,6] => 7
[2,4,3,1,6,5] => 8
[2,4,3,5,1,6] => 8
[2,4,3,5,6,1] => 8
[2,4,3,6,1,5] => 9
[2,4,3,6,5,1] => 9
[2,4,5,1,3,6] => 8
[2,4,5,1,6,3] => 8
[2,4,5,3,1,6] => 8
[2,4,5,3,6,1] => 8
[2,4,5,6,1,3] => 8
[2,4,5,6,3,1] => 8
[2,4,6,1,3,5] => 8
[2,4,6,1,5,3] => 9
[2,4,6,3,1,5] => 8
[2,4,6,3,5,1] => 9
[2,4,6,5,1,3] => 8
[2,4,6,5,3,1] => 8
[2,5,1,3,4,6] => 7
[2,5,1,3,6,4] => 8
[2,5,1,4,3,6] => 8
[2,5,1,4,6,3] => 8
[2,5,1,6,3,4] => 9
[2,5,1,6,4,3] => 9
[2,5,3,1,4,6] => 7
[2,5,3,1,6,4] => 8
[2,5,3,4,1,6] => 8
[2,5,3,4,6,1] => 8
[2,5,3,6,1,4] => 9
[2,5,3,6,4,1] => 9
[2,5,4,1,3,6] => 7
[2,5,4,1,6,3] => 8
[2,5,4,3,1,6] => 7
[2,5,4,3,6,1] => 8
[2,5,4,6,1,3] => 9
[2,5,4,6,3,1] => 9
[2,5,6,1,3,4] => 8
[2,5,6,1,4,3] => 9
[2,5,6,3,1,4] => 8
[2,5,6,3,4,1] => 9
[2,5,6,4,1,3] => 8
[2,5,6,4,3,1] => 8
[2,6,1,3,4,5] => 7
[2,6,1,3,5,4] => 8
[2,6,1,4,3,5] => 8
[2,6,1,4,5,3] => 8
[2,6,1,5,3,4] => 8
[2,6,1,5,4,3] => 8
[2,6,3,1,4,5] => 7
[2,6,3,1,5,4] => 8
[2,6,3,4,1,5] => 8
[2,6,3,4,5,1] => 8
[2,6,3,5,1,4] => 8
[2,6,3,5,4,1] => 8
[2,6,4,1,3,5] => 7
[2,6,4,1,5,3] => 8
[2,6,4,3,1,5] => 7
[2,6,4,3,5,1] => 8
[2,6,4,5,1,3] => 8
[2,6,4,5,3,1] => 8
[2,6,5,1,3,4] => 7
[2,6,5,1,4,3] => 8
[2,6,5,3,1,4] => 7
[2,6,5,3,4,1] => 8
[2,6,5,4,1,3] => 7
[2,6,5,4,3,1] => 7
[3,1,2,4,5,6] => 6
[3,1,2,4,6,5] => 7
[3,1,2,5,4,6] => 7
[3,1,2,5,6,4] => 7
[3,1,2,6,4,5] => 8
[3,1,2,6,5,4] => 8
[3,1,4,2,5,6] => 7
[3,1,4,2,6,5] => 8
[3,1,4,5,2,6] => 7
[3,1,4,5,6,2] => 7
[3,1,4,6,2,5] => 8
[3,1,4,6,5,2] => 8
[3,1,5,2,4,6] => 8
[3,1,5,2,6,4] => 8
[3,1,5,4,2,6] => 8
[3,1,5,4,6,2] => 8
[3,1,5,6,2,4] => 8
[3,1,5,6,4,2] => 8
[3,1,6,2,4,5] => 8
[3,1,6,2,5,4] => 9
[3,1,6,4,2,5] => 8
[3,1,6,4,5,2] => 9
[3,1,6,5,2,4] => 8
[3,1,6,5,4,2] => 8
[3,2,1,4,5,6] => 6
[3,2,1,4,6,5] => 7
[3,2,1,5,4,6] => 7
[3,2,1,5,6,4] => 7
[3,2,1,6,4,5] => 8
[3,2,1,6,5,4] => 8
[3,2,4,1,5,6] => 7
[3,2,4,1,6,5] => 8
[3,2,4,5,1,6] => 7
[3,2,4,5,6,1] => 7
[3,2,4,6,1,5] => 8
[3,2,4,6,5,1] => 8
[3,2,5,1,4,6] => 8
[3,2,5,1,6,4] => 8
[3,2,5,4,1,6] => 8
[3,2,5,4,6,1] => 8
[3,2,5,6,1,4] => 8
[3,2,5,6,4,1] => 8
[3,2,6,1,4,5] => 8
[3,2,6,1,5,4] => 9
[3,2,6,4,1,5] => 8
[3,2,6,4,5,1] => 9
[3,2,6,5,1,4] => 8
[3,2,6,5,4,1] => 8
[3,4,1,2,5,6] => 7
[3,4,1,2,6,5] => 8
[3,4,1,5,2,6] => 8
[3,4,1,5,6,2] => 8
[3,4,1,6,2,5] => 9
[3,4,1,6,5,2] => 9
[3,4,2,1,5,6] => 7
[3,4,2,1,6,5] => 8
[3,4,2,5,1,6] => 8
[3,4,2,5,6,1] => 8
[3,4,2,6,1,5] => 9
[3,4,2,6,5,1] => 9
[3,4,5,1,2,6] => 8
[3,4,5,1,6,2] => 8
[3,4,5,2,1,6] => 8
[3,4,5,2,6,1] => 8
[3,4,5,6,1,2] => 8
[3,4,5,6,2,1] => 8
[3,4,6,1,2,5] => 8
[3,4,6,1,5,2] => 9
[3,4,6,2,1,5] => 8
[3,4,6,2,5,1] => 9
[3,4,6,5,1,2] => 8
[3,4,6,5,2,1] => 8
[3,5,1,2,4,6] => 7
[3,5,1,2,6,4] => 8
[3,5,1,4,2,6] => 8
[3,5,1,4,6,2] => 8
[3,5,1,6,2,4] => 9
[3,5,1,6,4,2] => 9
[3,5,2,1,4,6] => 7
[3,5,2,1,6,4] => 8
[3,5,2,4,1,6] => 8
[3,5,2,4,6,1] => 8
[3,5,2,6,1,4] => 9
[3,5,2,6,4,1] => 9
[3,5,4,1,2,6] => 7
[3,5,4,1,6,2] => 8
[3,5,4,2,1,6] => 7
[3,5,4,2,6,1] => 8
[3,5,4,6,1,2] => 9
[3,5,4,6,2,1] => 9
[3,5,6,1,2,4] => 8
[3,5,6,1,4,2] => 9
[3,5,6,2,1,4] => 8
[3,5,6,2,4,1] => 9
[3,5,6,4,1,2] => 8
[3,5,6,4,2,1] => 8
[3,6,1,2,4,5] => 7
[3,6,1,2,5,4] => 8
[3,6,1,4,2,5] => 8
[3,6,1,4,5,2] => 8
[3,6,1,5,2,4] => 8
[3,6,1,5,4,2] => 8
[3,6,2,1,4,5] => 7
[3,6,2,1,5,4] => 8
[3,6,2,4,1,5] => 8
[3,6,2,4,5,1] => 8
[3,6,2,5,1,4] => 8
[3,6,2,5,4,1] => 8
[3,6,4,1,2,5] => 7
[3,6,4,1,5,2] => 8
[3,6,4,2,1,5] => 7
[3,6,4,2,5,1] => 8
[3,6,4,5,1,2] => 8
[3,6,4,5,2,1] => 8
[3,6,5,1,2,4] => 7
[3,6,5,1,4,2] => 8
[3,6,5,2,1,4] => 7
[3,6,5,2,4,1] => 8
[3,6,5,4,1,2] => 7
[3,6,5,4,2,1] => 7
[4,1,2,3,5,6] => 6
[4,1,2,3,6,5] => 7
[4,1,2,5,3,6] => 7
[4,1,2,5,6,3] => 7
[4,1,2,6,3,5] => 8
[4,1,2,6,5,3] => 8
[4,1,3,2,5,6] => 7
[4,1,3,2,6,5] => 8
[4,1,3,5,2,6] => 7
[4,1,3,5,6,2] => 7
[4,1,3,6,2,5] => 8
[4,1,3,6,5,2] => 8
[4,1,5,2,3,6] => 8
[4,1,5,2,6,3] => 8
[4,1,5,3,2,6] => 8
[4,1,5,3,6,2] => 8
[4,1,5,6,2,3] => 8
[4,1,5,6,3,2] => 8
[4,1,6,2,3,5] => 8
[4,1,6,2,5,3] => 9
[4,1,6,3,2,5] => 8
[4,1,6,3,5,2] => 9
[4,1,6,5,2,3] => 8
[4,1,6,5,3,2] => 8
[4,2,1,3,5,6] => 6
[4,2,1,3,6,5] => 7
[4,2,1,5,3,6] => 7
[4,2,1,5,6,3] => 7
[4,2,1,6,3,5] => 8
[4,2,1,6,5,3] => 8
[4,2,3,1,5,6] => 7
[4,2,3,1,6,5] => 8
[4,2,3,5,1,6] => 7
[4,2,3,5,6,1] => 7
[4,2,3,6,1,5] => 8
[4,2,3,6,5,1] => 8
[4,2,5,1,3,6] => 8
[4,2,5,1,6,3] => 8
[4,2,5,3,1,6] => 8
[4,2,5,3,6,1] => 8
[4,2,5,6,1,3] => 8
[4,2,5,6,3,1] => 8
[4,2,6,1,3,5] => 8
[4,2,6,1,5,3] => 9
[4,2,6,3,1,5] => 8
[4,2,6,3,5,1] => 9
[4,2,6,5,1,3] => 8
[4,2,6,5,3,1] => 8
[4,3,1,2,5,6] => 6
[4,3,1,2,6,5] => 7
[4,3,1,5,2,6] => 7
[4,3,1,5,6,2] => 7
[4,3,1,6,2,5] => 8
[4,3,1,6,5,2] => 8
[4,3,2,1,5,6] => 6
[4,3,2,1,6,5] => 7
[4,3,2,5,1,6] => 7
[4,3,2,5,6,1] => 7
[4,3,2,6,1,5] => 8
[4,3,2,6,5,1] => 8
[4,3,5,1,2,6] => 8
[4,3,5,1,6,2] => 8
[4,3,5,2,1,6] => 8
[4,3,5,2,6,1] => 8
[4,3,5,6,1,2] => 8
[4,3,5,6,2,1] => 8
[4,3,6,1,2,5] => 8
[4,3,6,1,5,2] => 9
[4,3,6,2,1,5] => 8
[4,3,6,2,5,1] => 9
[4,3,6,5,1,2] => 8
[4,3,6,5,2,1] => 8
[4,5,1,2,3,6] => 7
[4,5,1,2,6,3] => 8
[4,5,1,3,2,6] => 8
[4,5,1,3,6,2] => 8
[4,5,1,6,2,3] => 9
[4,5,1,6,3,2] => 9
[4,5,2,1,3,6] => 7
[4,5,2,1,6,3] => 8
[4,5,2,3,1,6] => 8
[4,5,2,3,6,1] => 8
[4,5,2,6,1,3] => 9
[4,5,2,6,3,1] => 9
[4,5,3,1,2,6] => 7
[4,5,3,1,6,2] => 8
[4,5,3,2,1,6] => 7
[4,5,3,2,6,1] => 8
[4,5,3,6,1,2] => 9
[4,5,3,6,2,1] => 9
[4,5,6,1,2,3] => 8
[4,5,6,1,3,2] => 9
[4,5,6,2,1,3] => 8
[4,5,6,2,3,1] => 9
[4,5,6,3,1,2] => 8
[4,5,6,3,2,1] => 8
[4,6,1,2,3,5] => 7
[4,6,1,2,5,3] => 8
[4,6,1,3,2,5] => 8
[4,6,1,3,5,2] => 8
[4,6,1,5,2,3] => 8
[4,6,1,5,3,2] => 8
[4,6,2,1,3,5] => 7
[4,6,2,1,5,3] => 8
[4,6,2,3,1,5] => 8
[4,6,2,3,5,1] => 8
[4,6,2,5,1,3] => 8
[4,6,2,5,3,1] => 8
[4,6,3,1,2,5] => 7
[4,6,3,1,5,2] => 8
[4,6,3,2,1,5] => 7
[4,6,3,2,5,1] => 8
[4,6,3,5,1,2] => 8
[4,6,3,5,2,1] => 8
[4,6,5,1,2,3] => 7
[4,6,5,1,3,2] => 8
[4,6,5,2,1,3] => 7
[4,6,5,2,3,1] => 8
[4,6,5,3,1,2] => 7
[4,6,5,3,2,1] => 7
[5,1,2,3,4,6] => 6
[5,1,2,3,6,4] => 7
[5,1,2,4,3,6] => 7
[5,1,2,4,6,3] => 7
[5,1,2,6,3,4] => 8
[5,1,2,6,4,3] => 8
[5,1,3,2,4,6] => 7
[5,1,3,2,6,4] => 8
[5,1,3,4,2,6] => 7
[5,1,3,4,6,2] => 7
[5,1,3,6,2,4] => 8
[5,1,3,6,4,2] => 8
[5,1,4,2,3,6] => 7
[5,1,4,2,6,3] => 8
[5,1,4,3,2,6] => 7
[5,1,4,3,6,2] => 8
[5,1,4,6,2,3] => 8
[5,1,4,6,3,2] => 8
[5,1,6,2,3,4] => 8
[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] => 8
[5,1,6,4,3,2] => 8
[5,2,1,3,4,6] => 6
[5,2,1,3,6,4] => 7
[5,2,1,4,3,6] => 7
[5,2,1,4,6,3] => 7
[5,2,1,6,3,4] => 8
[5,2,1,6,4,3] => 8
[5,2,3,1,4,6] => 7
[5,2,3,1,6,4] => 8
[5,2,3,4,1,6] => 7
[5,2,3,4,6,1] => 7
[5,2,3,6,1,4] => 8
[5,2,3,6,4,1] => 8
[5,2,4,1,3,6] => 7
[5,2,4,1,6,3] => 8
[5,2,4,3,1,6] => 7
[5,2,4,3,6,1] => 8
[5,2,4,6,1,3] => 8
[5,2,4,6,3,1] => 8
[5,2,6,1,3,4] => 8
[5,2,6,1,4,3] => 9
[5,2,6,3,1,4] => 8
[5,2,6,3,4,1] => 9
[5,2,6,4,1,3] => 8
[5,2,6,4,3,1] => 8
[5,3,1,2,4,6] => 6
[5,3,1,2,6,4] => 7
[5,3,1,4,2,6] => 7
[5,3,1,4,6,2] => 7
[5,3,1,6,2,4] => 8
[5,3,1,6,4,2] => 8
[5,3,2,1,4,6] => 6
[5,3,2,1,6,4] => 7
[5,3,2,4,1,6] => 7
[5,3,2,4,6,1] => 7
[5,3,2,6,1,4] => 8
[5,3,2,6,4,1] => 8
[5,3,4,1,2,6] => 7
[5,3,4,1,6,2] => 8
[5,3,4,2,1,6] => 7
[5,3,4,2,6,1] => 8
[5,3,4,6,1,2] => 8
[5,3,4,6,2,1] => 8
[5,3,6,1,2,4] => 8
[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] => 8
[5,3,6,4,2,1] => 8
[5,4,1,2,3,6] => 6
[5,4,1,2,6,3] => 7
[5,4,1,3,2,6] => 7
[5,4,1,3,6,2] => 7
[5,4,1,6,2,3] => 8
[5,4,1,6,3,2] => 8
[5,4,2,1,3,6] => 6
[5,4,2,1,6,3] => 7
[5,4,2,3,1,6] => 7
[5,4,2,3,6,1] => 7
[5,4,2,6,1,3] => 8
[5,4,2,6,3,1] => 8
[5,4,3,1,2,6] => 6
[5,4,3,1,6,2] => 7
[5,4,3,2,1,6] => 6
[5,4,3,2,6,1] => 7
[5,4,3,6,1,2] => 8
[5,4,3,6,2,1] => 8
[5,4,6,1,2,3] => 8
[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] => 8
[5,6,1,2,3,4] => 7
[5,6,1,2,4,3] => 8
[5,6,1,3,2,4] => 8
[5,6,1,3,4,2] => 8
[5,6,1,4,2,3] => 8
[5,6,1,4,3,2] => 8
[5,6,2,1,3,4] => 7
[5,6,2,1,4,3] => 8
[5,6,2,3,1,4] => 8
[5,6,2,3,4,1] => 8
[5,6,2,4,1,3] => 8
[5,6,2,4,3,1] => 8
[5,6,3,1,2,4] => 7
[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] => 8
[5,6,3,4,2,1] => 8
[5,6,4,1,2,3] => 7
[5,6,4,1,3,2] => 8
[5,6,4,2,1,3] => 7
[5,6,4,2,3,1] => 8
[5,6,4,3,1,2] => 7
[5,6,4,3,2,1] => 7
[6,1,2,3,4,5] => 6
[6,1,2,3,5,4] => 7
[6,1,2,4,3,5] => 7
[6,1,2,4,5,3] => 7
[6,1,2,5,3,4] => 8
[6,1,2,5,4,3] => 8
[6,1,3,2,4,5] => 7
[6,1,3,2,5,4] => 8
[6,1,3,4,2,5] => 7
[6,1,3,4,5,2] => 7
[6,1,3,5,2,4] => 8
[6,1,3,5,4,2] => 8
[6,1,4,2,3,5] => 7
[6,1,4,2,5,3] => 8
[6,1,4,3,2,5] => 7
[6,1,4,3,5,2] => 8
[6,1,4,5,2,3] => 8
[6,1,4,5,3,2] => 8
[6,1,5,2,3,4] => 7
[6,1,5,2,4,3] => 8
[6,1,5,3,2,4] => 7
[6,1,5,3,4,2] => 8
[6,1,5,4,2,3] => 7
[6,1,5,4,3,2] => 7
[6,2,1,3,4,5] => 6
[6,2,1,3,5,4] => 7
[6,2,1,4,3,5] => 7
[6,2,1,4,5,3] => 7
[6,2,1,5,3,4] => 8
[6,2,1,5,4,3] => 8
[6,2,3,1,4,5] => 7
[6,2,3,1,5,4] => 8
[6,2,3,4,1,5] => 7
[6,2,3,4,5,1] => 7
[6,2,3,5,1,4] => 8
[6,2,3,5,4,1] => 8
[6,2,4,1,3,5] => 7
[6,2,4,1,5,3] => 8
[6,2,4,3,1,5] => 7
[6,2,4,3,5,1] => 8
[6,2,4,5,1,3] => 8
[6,2,4,5,3,1] => 8
[6,2,5,1,3,4] => 7
[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] => 7
[6,2,5,4,3,1] => 7
[6,3,1,2,4,5] => 6
[6,3,1,2,5,4] => 7
[6,3,1,4,2,5] => 7
[6,3,1,4,5,2] => 7
[6,3,1,5,2,4] => 8
[6,3,1,5,4,2] => 8
[6,3,2,1,4,5] => 6
[6,3,2,1,5,4] => 7
[6,3,2,4,1,5] => 7
[6,3,2,4,5,1] => 7
[6,3,2,5,1,4] => 8
[6,3,2,5,4,1] => 8
[6,3,4,1,2,5] => 7
[6,3,4,1,5,2] => 8
[6,3,4,2,1,5] => 7
[6,3,4,2,5,1] => 8
[6,3,4,5,1,2] => 8
[6,3,4,5,2,1] => 8
[6,3,5,1,2,4] => 7
[6,3,5,1,4,2] => 8
[6,3,5,2,1,4] => 7
[6,3,5,2,4,1] => 8
[6,3,5,4,1,2] => 7
[6,3,5,4,2,1] => 7
[6,4,1,2,3,5] => 6
[6,4,1,2,5,3] => 7
[6,4,1,3,2,5] => 7
[6,4,1,3,5,2] => 7
[6,4,1,5,2,3] => 8
[6,4,1,5,3,2] => 8
[6,4,2,1,3,5] => 6
[6,4,2,1,5,3] => 7
[6,4,2,3,1,5] => 7
[6,4,2,3,5,1] => 7
[6,4,2,5,1,3] => 8
[6,4,2,5,3,1] => 8
[6,4,3,1,2,5] => 6
[6,4,3,1,5,2] => 7
[6,4,3,2,1,5] => 6
[6,4,3,2,5,1] => 7
[6,4,3,5,1,2] => 8
[6,4,3,5,2,1] => 8
[6,4,5,1,2,3] => 7
[6,4,5,1,3,2] => 8
[6,4,5,2,1,3] => 7
[6,4,5,2,3,1] => 8
[6,4,5,3,1,2] => 7
[6,4,5,3,2,1] => 7
[6,5,1,2,3,4] => 6
[6,5,1,2,4,3] => 7
[6,5,1,3,2,4] => 7
[6,5,1,3,4,2] => 7
[6,5,1,4,2,3] => 7
[6,5,1,4,3,2] => 7
[6,5,2,1,3,4] => 6
[6,5,2,1,4,3] => 7
[6,5,2,3,1,4] => 7
[6,5,2,3,4,1] => 7
[6,5,2,4,1,3] => 7
[6,5,2,4,3,1] => 7
[6,5,3,1,2,4] => 6
[6,5,3,1,4,2] => 7
[6,5,3,2,1,4] => 6
[6,5,3,2,4,1] => 7
[6,5,3,4,1,2] => 7
[6,5,3,4,2,1] => 7
[6,5,4,1,2,3] => 6
[6,5,4,1,3,2] => 7
[6,5,4,2,1,3] => 6
[6,5,4,2,3,1] => 7
[6,5,4,3,1,2] => 6
[6,5,4,3,2,1] => 6
[1,2,3,4,5,6,7] => 7
[1,2,3,4,5,7,6] => 8
[1,2,3,4,6,5,7] => 8
[1,2,3,4,6,7,5] => 8
[1,2,3,4,7,5,6] => 9
[1,2,3,4,7,6,5] => 9
[1,2,3,5,4,6,7] => 8
[1,2,3,5,4,7,6] => 9
[1,2,3,5,6,4,7] => 8
[1,2,3,5,6,7,4] => 8
[1,2,3,5,7,4,6] => 9
[1,2,3,5,7,6,4] => 9
[1,2,3,6,4,5,7] => 9
[1,2,3,6,4,7,5] => 9
[1,2,3,6,5,4,7] => 9
[1,2,3,6,5,7,4] => 9
[1,2,3,6,7,4,5] => 9
[1,2,3,6,7,5,4] => 9
[1,2,3,7,4,5,6] => 10
[1,2,3,7,4,6,5] => 11
[1,2,3,7,5,4,6] => 10
[1,2,3,7,5,6,4] => 11
[1,2,3,7,6,4,5] => 10
[1,2,3,7,6,5,4] => 10
[1,2,4,3,5,6,7] => 8
[1,2,4,3,5,7,6] => 9
[1,2,4,3,6,5,7] => 9
[1,2,4,3,6,7,5] => 9
[1,2,4,3,7,5,6] => 10
[1,2,4,3,7,6,5] => 10
[1,2,4,5,3,6,7] => 8
[1,2,4,5,3,7,6] => 9
[1,2,4,5,6,3,7] => 8
[1,2,4,5,6,7,3] => 8
[1,2,4,5,7,3,6] => 9
[1,2,4,5,7,6,3] => 9
[1,2,4,6,3,5,7] => 9
[1,2,4,6,3,7,5] => 9
[1,2,4,6,5,3,7] => 9
[1,2,4,6,5,7,3] => 9
[1,2,4,6,7,3,5] => 9
[1,2,4,6,7,5,3] => 9
[1,2,4,7,3,5,6] => 10
[1,2,4,7,3,6,5] => 11
[1,2,4,7,5,3,6] => 10
[1,2,4,7,5,6,3] => 11
[1,2,4,7,6,3,5] => 10
[1,2,4,7,6,5,3] => 10
[1,2,5,3,4,6,7] => 9
[1,2,5,3,4,7,6] => 10
[1,2,5,3,6,4,7] => 9
[1,2,5,3,6,7,4] => 9
[1,2,5,3,7,4,6] => 10
[1,2,5,3,7,6,4] => 10
[1,2,5,4,3,6,7] => 9
[1,2,5,4,3,7,6] => 10
[1,2,5,4,6,3,7] => 9
[1,2,5,4,6,7,3] => 9
[1,2,5,4,7,3,6] => 10
[1,2,5,4,7,6,3] => 10
[1,2,5,6,3,4,7] => 9
[1,2,5,6,3,7,4] => 9
[1,2,5,6,4,3,7] => 9
[1,2,5,6,4,7,3] => 9
[1,2,5,6,7,3,4] => 9
[1,2,5,6,7,4,3] => 9
[1,2,5,7,3,4,6] => 10
[1,2,5,7,3,6,4] => 11
[1,2,5,7,4,3,6] => 10
[1,2,5,7,4,6,3] => 11
[1,2,5,7,6,3,4] => 10
[1,2,5,7,6,4,3] => 10
[1,2,6,3,4,5,7] => 9
[1,2,6,3,4,7,5] => 10
[1,2,6,3,5,4,7] => 10
[1,2,6,3,5,7,4] => 10
[1,2,6,3,7,4,5] => 10
[1,2,6,3,7,5,4] => 10
[1,2,6,4,3,5,7] => 9
[1,2,6,4,3,7,5] => 10
[1,2,6,4,5,3,7] => 10
[1,2,6,4,5,7,3] => 10
[1,2,6,4,7,3,5] => 10
[1,2,6,4,7,5,3] => 10
[1,2,6,5,3,4,7] => 9
[1,2,6,5,3,7,4] => 10
[1,2,6,5,4,3,7] => 9
[1,2,6,5,4,7,3] => 10
[1,2,6,5,7,3,4] => 10
[1,2,6,5,7,4,3] => 10
[1,2,6,7,3,4,5] => 10
[1,2,6,7,3,5,4] => 11
[1,2,6,7,4,3,5] => 10
[1,2,6,7,4,5,3] => 11
[1,2,6,7,5,3,4] => 10
[1,2,6,7,5,4,3] => 10
[1,2,7,3,4,5,6] => 9
[1,2,7,3,4,6,5] => 10
[1,2,7,3,5,4,6] => 10
[1,2,7,3,5,6,4] => 10
[1,2,7,3,6,4,5] => 10
[1,2,7,3,6,5,4] => 10
[1,2,7,4,3,5,6] => 9
[1,2,7,4,3,6,5] => 10
[1,2,7,4,5,3,6] => 10
[1,2,7,4,5,6,3] => 10
[1,2,7,4,6,3,5] => 10
[1,2,7,4,6,5,3] => 10
[1,2,7,5,3,4,6] => 9
[1,2,7,5,3,6,4] => 10
[1,2,7,5,4,3,6] => 9
[1,2,7,5,4,6,3] => 10
[1,2,7,5,6,3,4] => 10
[1,2,7,5,6,4,3] => 10
[1,2,7,6,3,4,5] => 9
[1,2,7,6,3,5,4] => 10
[1,2,7,6,4,3,5] => 9
[1,2,7,6,4,5,3] => 10
[1,2,7,6,5,3,4] => 9
[1,2,7,6,5,4,3] => 9
[1,3,2,4,5,6,7] => 8
[1,3,2,4,5,7,6] => 9
[1,3,2,4,6,5,7] => 9
[1,3,2,4,6,7,5] => 9
[1,3,2,4,7,5,6] => 10
[1,3,2,4,7,6,5] => 10
[1,3,2,5,4,6,7] => 9
[1,3,2,5,4,7,6] => 10
[1,3,2,5,6,4,7] => 9
[1,3,2,5,6,7,4] => 9
[1,3,2,5,7,4,6] => 10
[1,3,2,5,7,6,4] => 10
[1,3,2,6,4,5,7] => 10
[1,3,2,6,4,7,5] => 10
[1,3,2,6,5,4,7] => 10
[1,3,2,6,5,7,4] => 10
[1,3,2,6,7,4,5] => 10
[1,3,2,6,7,5,4] => 10
[1,3,2,7,4,5,6] => 11
[1,3,2,7,4,6,5] => 12
[1,3,2,7,5,4,6] => 11
[1,3,2,7,5,6,4] => 12
[1,3,2,7,6,4,5] => 11
[1,3,2,7,6,5,4] => 11
[1,3,4,2,5,6,7] => 8
[1,3,4,2,5,7,6] => 9
[1,3,4,2,6,5,7] => 9
[1,3,4,2,6,7,5] => 9
[1,3,4,2,7,5,6] => 10
[1,3,4,2,7,6,5] => 10
[1,3,4,5,2,6,7] => 8
[1,3,4,5,2,7,6] => 9
[1,3,4,5,6,2,7] => 8
[1,3,4,5,6,7,2] => 8
[1,3,4,5,7,2,6] => 9
[1,3,4,5,7,6,2] => 9
[1,3,4,6,2,5,7] => 9
[1,3,4,6,2,7,5] => 9
[1,3,4,6,5,2,7] => 9
[1,3,4,6,5,7,2] => 9
[1,3,4,6,7,2,5] => 9
[1,3,4,6,7,5,2] => 9
[1,3,4,7,2,5,6] => 10
[1,3,4,7,2,6,5] => 11
[1,3,4,7,5,2,6] => 10
[1,3,4,7,5,6,2] => 11
[1,3,4,7,6,2,5] => 10
[1,3,4,7,6,5,2] => 10
[1,3,5,2,4,6,7] => 9
[1,3,5,2,4,7,6] => 10
[1,3,5,2,6,4,7] => 9
[1,3,5,2,6,7,4] => 9
[1,3,5,2,7,4,6] => 10
[1,3,5,2,7,6,4] => 10
[1,3,5,4,2,6,7] => 9
[1,3,5,4,2,7,6] => 10
[1,3,5,4,6,2,7] => 9
[1,3,5,4,6,7,2] => 9
[1,3,5,4,7,2,6] => 10
[1,3,5,4,7,6,2] => 10
[1,3,5,6,2,4,7] => 9
[1,3,5,6,2,7,4] => 9
[1,3,5,6,4,2,7] => 9
[1,3,5,6,4,7,2] => 9
[1,3,5,6,7,2,4] => 9
[1,3,5,6,7,4,2] => 9
[1,3,5,7,2,4,6] => 10
[1,3,5,7,2,6,4] => 11
[1,3,5,7,4,2,6] => 10
[1,3,5,7,4,6,2] => 11
[1,3,5,7,6,2,4] => 10
[1,3,5,7,6,4,2] => 10
[1,3,6,2,4,5,7] => 9
[1,3,6,2,4,7,5] => 10
[1,3,6,2,5,4,7] => 10
[1,3,6,2,5,7,4] => 10
[1,3,6,2,7,4,5] => 10
[1,3,6,2,7,5,4] => 10
[1,3,6,4,2,5,7] => 9
[1,3,6,4,2,7,5] => 10
[1,3,6,4,5,2,7] => 10
[1,3,6,4,5,7,2] => 10
[1,3,6,4,7,2,5] => 10
[1,3,6,4,7,5,2] => 10
[1,3,6,5,2,4,7] => 9
[1,3,6,5,2,7,4] => 10
[1,3,6,5,4,2,7] => 9
[1,3,6,5,4,7,2] => 10
[1,3,6,5,7,2,4] => 10
[1,3,6,5,7,4,2] => 10
[1,3,6,7,2,4,5] => 10
[1,3,6,7,2,5,4] => 11
[1,3,6,7,4,2,5] => 10
[1,3,6,7,4,5,2] => 11
[1,3,6,7,5,2,4] => 10
[1,3,6,7,5,4,2] => 10
[1,3,7,2,4,5,6] => 9
[1,3,7,2,4,6,5] => 10
[1,3,7,2,5,4,6] => 10
[1,3,7,2,5,6,4] => 10
[1,3,7,2,6,4,5] => 10
[1,3,7,2,6,5,4] => 10
[1,3,7,4,2,5,6] => 9
[1,3,7,4,2,6,5] => 10
[1,3,7,4,5,2,6] => 10
[1,3,7,4,5,6,2] => 10
[1,3,7,4,6,2,5] => 10
[1,3,7,4,6,5,2] => 10
[1,3,7,5,2,4,6] => 9
[1,3,7,5,2,6,4] => 10
[1,3,7,5,4,2,6] => 9
[1,3,7,5,4,6,2] => 10
[1,3,7,5,6,2,4] => 10
[1,3,7,5,6,4,2] => 10
[1,3,7,6,2,4,5] => 9
[1,3,7,6,2,5,4] => 10
[1,3,7,6,4,2,5] => 9
[1,3,7,6,4,5,2] => 10
[1,3,7,6,5,2,4] => 9
[1,3,7,6,5,4,2] => 9
[1,4,2,3,5,6,7] => 8
[1,4,2,3,5,7,6] => 9
[1,4,2,3,6,5,7] => 9
[1,4,2,3,6,7,5] => 9
[1,4,2,3,7,5,6] => 10
[1,4,2,3,7,6,5] => 10
[1,4,2,5,3,6,7] => 9
[1,4,2,5,3,7,6] => 10
[1,4,2,5,6,3,7] => 9
[1,4,2,5,6,7,3] => 9
[1,4,2,5,7,3,6] => 10
[1,4,2,5,7,6,3] => 10
[1,4,2,6,3,5,7] => 10
[1,4,2,6,3,7,5] => 10
[1,4,2,6,5,3,7] => 10
[1,4,2,6,5,7,3] => 10
[1,4,2,6,7,3,5] => 10
[1,4,2,6,7,5,3] => 10
[1,4,2,7,3,5,6] => 11
[1,4,2,7,3,6,5] => 12
[1,4,2,7,5,3,6] => 11
[1,4,2,7,5,6,3] => 12
[1,4,2,7,6,3,5] => 11
[1,4,2,7,6,5,3] => 11
[1,4,3,2,5,6,7] => 8
[1,4,3,2,5,7,6] => 9
[1,4,3,2,6,5,7] => 9
[1,4,3,2,6,7,5] => 9
[1,4,3,2,7,5,6] => 10
[1,4,3,2,7,6,5] => 10
[1,4,3,5,2,6,7] => 9
[1,4,3,5,2,7,6] => 10
[1,4,3,5,6,2,7] => 9
[1,4,3,5,6,7,2] => 9
[1,4,3,5,7,2,6] => 10
[1,4,3,5,7,6,2] => 10
[1,4,3,6,2,5,7] => 10
[1,4,3,6,2,7,5] => 10
[1,4,3,6,5,2,7] => 10
[1,4,3,6,5,7,2] => 10
[1,4,3,6,7,2,5] => 10
[1,4,3,6,7,5,2] => 10
[1,4,3,7,2,5,6] => 11
[1,4,3,7,2,6,5] => 12
[1,4,3,7,5,2,6] => 11
[1,4,3,7,5,6,2] => 12
[1,4,3,7,6,2,5] => 11
[1,4,3,7,6,5,2] => 11
[1,4,5,2,3,6,7] => 9
[1,4,5,2,3,7,6] => 10
[1,4,5,2,6,3,7] => 9
[1,4,5,2,6,7,3] => 9
[1,4,5,2,7,3,6] => 10
[1,4,5,2,7,6,3] => 10
[1,4,5,3,2,6,7] => 9
[1,4,5,3,2,7,6] => 10
[1,4,5,3,6,2,7] => 9
[1,4,5,3,6,7,2] => 9
[1,4,5,3,7,2,6] => 10
[1,4,5,3,7,6,2] => 10
[1,4,5,6,2,3,7] => 9
[1,4,5,6,2,7,3] => 9
[1,4,5,6,3,2,7] => 9
[1,4,5,6,3,7,2] => 9
[1,4,5,6,7,2,3] => 9
[1,4,5,6,7,3,2] => 9
[1,4,5,7,2,3,6] => 10
[1,4,5,7,2,6,3] => 11
[1,4,5,7,3,2,6] => 10
[1,4,5,7,3,6,2] => 11
[1,4,5,7,6,2,3] => 10
[1,4,5,7,6,3,2] => 10
[1,4,6,2,3,5,7] => 9
[1,4,6,2,3,7,5] => 10
[1,4,6,2,5,3,7] => 10
[1,4,6,2,5,7,3] => 10
[1,4,6,2,7,3,5] => 10
[1,4,6,2,7,5,3] => 10
[1,4,6,3,2,5,7] => 9
[1,4,6,3,2,7,5] => 10
[1,4,6,3,5,2,7] => 10
[1,4,6,3,5,7,2] => 10
[1,4,6,3,7,2,5] => 10
[1,4,6,3,7,5,2] => 10
[1,4,6,5,2,3,7] => 9
[1,4,6,5,2,7,3] => 10
[1,4,6,5,3,2,7] => 9
[1,4,6,5,3,7,2] => 10
-----------------------------------------------------------------------------
Created: Oct 15, 2016 at 21:57 by Martin Rubey
-----------------------------------------------------------------------------
Last Updated: Oct 15, 2016 at 21:57 by Martin Rubey