************************************************************************
*    www.FindStat.org - The Combinatorial Statistic Finder             *
*                                                                      *
*    Copyright (C) 2013 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.  *
************************************************************************

------------------------------------------------------------------------
Map identifier: Mp00248

------------------------------------------------------------------------
Map name: DEX composition

------------------------------------------------------------------------
Domain: Permutations

------------------------------------------------------------------------
Codomain: Integer compositions

------------------------------------------------------------------------
Description: The DEX composition of a permutation.

Let $\pi$ be a permutation in $\mathfrak S_n$.  Let $\bar\pi$ be the word in the ordered set $\bar 1 < \dots < \bar n < 1 \dots < n$ obtained from $\pi$ by replacing every excedance $\pi(i) > i$ by $\overline{\pi(i)}$.  Then the DEX set of $\pi$ is the set of indices $1 \leq i < n$ such that $\bar\pi(i) > \bar\pi(i+1)$.  Finally, the DEX composition $c_1, \dots, c_k$ of $n$ corresponds to the DEX subset $\{c_1, c_1 + c_2, \dots, c_1 + \dots + c_{k-1}\}$.

The (quasi)symmetric function
$$
\sum_{\pi\in\mathfrak S_{\lambda, j}} F_{DEX(\pi)},
$$
where the sum is over the set of permutations of cycle type $\lambda$ with $j$ excedances, is the Eulerian quasisymmetric function.

------------------------------------------------------------------------
References: [1]   Shareshian, J., Wachs, M. L. Eulerian quasisymmetric functions [[arXiv:0812.0764]]

------------------------------------------------------------------------
Code:

def mapping(pi):
    pi = list(pi)
    n = len(pi)
    for i, e in enumerate(pi):
        if e > i + 1:
            pi[i] = -n-1+e
    return Composition(from_subset=([i for i in range(1, len(pi)) if pi[i-1] > pi[i]], n))


------------------------------------------------------------------------
Map images:

[1]             => [1]
[1,2]           => [2]
[2,1]           => [2]
[1,2,3]         => [3]
[1,3,2]         => [1,2]
[2,1,3]         => [3]
[2,3,1]         => [3]
[3,1,2]         => [3]
[3,2,1]         => [2,1]
[1,2,3,4]       => [4]
[1,2,4,3]       => [2,2]
[1,3,2,4]       => [1,3]
[1,3,4,2]       => [1,3]
[1,4,2,3]       => [1,3]
[1,4,3,2]       => [1,2,1]
[2,1,3,4]       => [4]
[2,1,4,3]       => [2,2]
[2,3,1,4]       => [4]
[2,3,4,1]       => [4]
[2,4,1,3]       => [4]
[2,4,3,1]       => [3,1]
[3,1,2,4]       => [4]
[3,1,4,2]       => [2,2]
[3,2,1,4]       => [2,2]
[3,2,4,1]       => [2,2]
[3,4,1,2]       => [4]
[3,4,2,1]       => [3,1]
[4,1,2,3]       => [4]
[4,1,3,2]       => [3,1]
[4,2,1,3]       => [2,2]
[4,2,3,1]       => [3,1]
[4,3,1,2]       => [1,3]
[4,3,2,1]       => [1,2,1]
[1,2,3,4,5]     => [5]
[1,2,3,5,4]     => [3,2]
[1,2,4,3,5]     => [2,3]
[1,2,4,5,3]     => [2,3]
[1,2,5,3,4]     => [2,3]
[1,2,5,4,3]     => [2,2,1]
[1,3,2,4,5]     => [1,4]
[1,3,2,5,4]     => [1,2,2]
[1,3,4,2,5]     => [1,4]
[1,3,4,5,2]     => [1,4]
[1,3,5,2,4]     => [1,4]
[1,3,5,4,2]     => [1,3,1]
[1,4,2,3,5]     => [1,4]
[1,4,2,5,3]     => [1,2,2]
[1,4,3,2,5]     => [1,2,2]
[1,4,3,5,2]     => [1,2,2]
[1,4,5,2,3]     => [1,4]
[1,4,5,3,2]     => [1,3,1]
[1,5,2,3,4]     => [1,4]
[1,5,2,4,3]     => [1,3,1]
[1,5,3,2,4]     => [1,2,2]
[1,5,3,4,2]     => [1,3,1]
[1,5,4,2,3]     => [1,1,3]
[1,5,4,3,2]     => [1,1,2,1]
[2,1,3,4,5]     => [5]
[2,1,3,5,4]     => [3,2]
[2,1,4,3,5]     => [2,3]
[2,1,4,5,3]     => [2,3]
[2,1,5,3,4]     => [2,3]
[2,1,5,4,3]     => [2,2,1]
[2,3,1,4,5]     => [5]
[2,3,1,5,4]     => [3,2]
[2,3,4,1,5]     => [5]
[2,3,4,5,1]     => [5]
[2,3,5,1,4]     => [5]
[2,3,5,4,1]     => [4,1]
[2,4,1,3,5]     => [5]
[2,4,1,5,3]     => [3,2]
[2,4,3,1,5]     => [3,2]
[2,4,3,5,1]     => [3,2]
[2,4,5,1,3]     => [5]
[2,4,5,3,1]     => [4,1]
[2,5,1,3,4]     => [5]
[2,5,1,4,3]     => [4,1]
[2,5,3,1,4]     => [3,2]
[2,5,3,4,1]     => [4,1]
[2,5,4,1,3]     => [2,3]
[2,5,4,3,1]     => [2,2,1]
[3,1,2,4,5]     => [5]
[3,1,2,5,4]     => [3,2]
[3,1,4,2,5]     => [2,3]
[3,1,4,5,2]     => [2,3]
[3,1,5,2,4]     => [2,3]
[3,1,5,4,2]     => [2,2,1]
[3,2,1,4,5]     => [2,3]
[3,2,1,5,4]     => [2,1,2]
[3,2,4,1,5]     => [2,3]
[3,2,4,5,1]     => [2,3]
[3,2,5,1,4]     => [2,3]
[3,2,5,4,1]     => [2,2,1]
[3,4,1,2,5]     => [5]
[3,4,1,5,2]     => [3,2]
[3,4,2,1,5]     => [3,2]
[3,4,2,5,1]     => [3,2]
[3,4,5,1,2]     => [5]
[3,4,5,2,1]     => [4,1]
[3,5,1,2,4]     => [5]
[3,5,1,4,2]     => [4,1]
[3,5,2,1,4]     => [3,2]
[3,5,2,4,1]     => [4,1]
[3,5,4,1,2]     => [2,3]
[3,5,4,2,1]     => [2,2,1]
[4,1,2,3,5]     => [5]
[4,1,2,5,3]     => [3,2]
[4,1,3,2,5]     => [3,2]
[4,1,3,5,2]     => [3,2]
[4,1,5,2,3]     => [2,3]
[4,1,5,3,2]     => [2,2,1]
[4,2,1,3,5]     => [2,3]
[4,2,1,5,3]     => [2,1,2]
[4,2,3,1,5]     => [3,2]
[4,2,3,5,1]     => [3,2]
[4,2,5,1,3]     => [2,3]
[4,2,5,3,1]     => [2,2,1]
[4,3,1,2,5]     => [1,4]
[4,3,1,5,2]     => [1,2,2]
[4,3,2,1,5]     => [1,2,2]
[4,3,2,5,1]     => [1,2,2]
[4,3,5,1,2]     => [1,4]
[4,3,5,2,1]     => [1,3,1]
[4,5,1,2,3]     => [5]
[4,5,1,3,2]     => [4,1]
[4,5,2,1,3]     => [3,2]
[4,5,2,3,1]     => [4,1]
[4,5,3,1,2]     => [3,2]
[4,5,3,2,1]     => [3,1,1]
[5,1,2,3,4]     => [5]
[5,1,2,4,3]     => [4,1]
[5,1,3,2,4]     => [3,2]
[5,1,3,4,2]     => [4,1]
[5,1,4,2,3]     => [2,3]
[5,1,4,3,2]     => [2,2,1]
[5,2,1,3,4]     => [2,3]
[5,2,1,4,3]     => [2,2,1]
[5,2,3,1,4]     => [3,2]
[5,2,3,4,1]     => [4,1]
[5,2,4,1,3]     => [2,3]
[5,2,4,3,1]     => [2,2,1]
[5,3,1,2,4]     => [1,4]
[5,3,1,4,2]     => [1,3,1]
[5,3,2,1,4]     => [1,2,2]
[5,3,2,4,1]     => [1,3,1]
[5,3,4,1,2]     => [1,4]
[5,3,4,2,1]     => [1,3,1]
[5,4,1,2,3]     => [1,4]
[5,4,1,3,2]     => [1,3,1]
[5,4,2,1,3]     => [1,2,2]
[5,4,2,3,1]     => [1,3,1]
[5,4,3,1,2]     => [1,2,2]
[5,4,3,2,1]     => [1,2,1,1]
[1,2,3,4,5,6]   => [6]
[1,2,3,4,6,5]   => [4,2]
[1,2,3,5,4,6]   => [3,3]
[1,2,3,5,6,4]   => [3,3]
[1,2,3,6,4,5]   => [3,3]
[1,2,3,6,5,4]   => [3,2,1]
[1,2,4,3,5,6]   => [2,4]
[1,2,4,3,6,5]   => [2,2,2]
[1,2,4,5,3,6]   => [2,4]
[1,2,4,5,6,3]   => [2,4]
[1,2,4,6,3,5]   => [2,4]
[1,2,4,6,5,3]   => [2,3,1]
[1,2,5,3,4,6]   => [2,4]
[1,2,5,3,6,4]   => [2,2,2]
[1,2,5,4,3,6]   => [2,2,2]
[1,2,5,4,6,3]   => [2,2,2]
[1,2,5,6,3,4]   => [2,4]
[1,2,5,6,4,3]   => [2,3,1]
[1,2,6,3,4,5]   => [2,4]
[1,2,6,3,5,4]   => [2,3,1]
[1,2,6,4,3,5]   => [2,2,2]
[1,2,6,4,5,3]   => [2,3,1]
[1,2,6,5,3,4]   => [2,1,3]
[1,2,6,5,4,3]   => [2,1,2,1]
[1,3,2,4,5,6]   => [1,5]
[1,3,2,4,6,5]   => [1,3,2]
[1,3,2,5,4,6]   => [1,2,3]
[1,3,2,5,6,4]   => [1,2,3]
[1,3,2,6,4,5]   => [1,2,3]
[1,3,2,6,5,4]   => [1,2,2,1]
[1,3,4,2,5,6]   => [1,5]
[1,3,4,2,6,5]   => [1,3,2]
[1,3,4,5,2,6]   => [1,5]
[1,3,4,5,6,2]   => [1,5]
[1,3,4,6,2,5]   => [1,5]
[1,3,4,6,5,2]   => [1,4,1]
[1,3,5,2,4,6]   => [1,5]
[1,3,5,2,6,4]   => [1,3,2]
[1,3,5,4,2,6]   => [1,3,2]
[1,3,5,4,6,2]   => [1,3,2]
[1,3,5,6,2,4]   => [1,5]
[1,3,5,6,4,2]   => [1,4,1]
[1,3,6,2,4,5]   => [1,5]
[1,3,6,2,5,4]   => [1,4,1]
[1,3,6,4,2,5]   => [1,3,2]
[1,3,6,4,5,2]   => [1,4,1]
[1,3,6,5,2,4]   => [1,2,3]
[1,3,6,5,4,2]   => [1,2,2,1]
[1,4,2,3,5,6]   => [1,5]
[1,4,2,3,6,5]   => [1,3,2]
[1,4,2,5,3,6]   => [1,2,3]
[1,4,2,5,6,3]   => [1,2,3]
[1,4,2,6,3,5]   => [1,2,3]
[1,4,2,6,5,3]   => [1,2,2,1]
[1,4,3,2,5,6]   => [1,2,3]
[1,4,3,2,6,5]   => [1,2,1,2]
[1,4,3,5,2,6]   => [1,2,3]
[1,4,3,5,6,2]   => [1,2,3]
[1,4,3,6,2,5]   => [1,2,3]
[1,4,3,6,5,2]   => [1,2,2,1]
[1,4,5,2,3,6]   => [1,5]
[1,4,5,2,6,3]   => [1,3,2]
[1,4,5,3,2,6]   => [1,3,2]
[1,4,5,3,6,2]   => [1,3,2]
[1,4,5,6,2,3]   => [1,5]
[1,4,5,6,3,2]   => [1,4,1]
[1,4,6,2,3,5]   => [1,5]
[1,4,6,2,5,3]   => [1,4,1]
[1,4,6,3,2,5]   => [1,3,2]
[1,4,6,3,5,2]   => [1,4,1]
[1,4,6,5,2,3]   => [1,2,3]
[1,4,6,5,3,2]   => [1,2,2,1]
[1,5,2,3,4,6]   => [1,5]
[1,5,2,3,6,4]   => [1,3,2]
[1,5,2,4,3,6]   => [1,3,2]
[1,5,2,4,6,3]   => [1,3,2]
[1,5,2,6,3,4]   => [1,2,3]
[1,5,2,6,4,3]   => [1,2,2,1]
[1,5,3,2,4,6]   => [1,2,3]
[1,5,3,2,6,4]   => [1,2,1,2]
[1,5,3,4,2,6]   => [1,3,2]
[1,5,3,4,6,2]   => [1,3,2]
[1,5,3,6,2,4]   => [1,2,3]
[1,5,3,6,4,2]   => [1,2,2,1]
[1,5,4,2,3,6]   => [1,1,4]
[1,5,4,2,6,3]   => [1,1,2,2]
[1,5,4,3,2,6]   => [1,1,2,2]
[1,5,4,3,6,2]   => [1,1,2,2]
[1,5,4,6,2,3]   => [1,1,4]
[1,5,4,6,3,2]   => [1,1,3,1]
[1,5,6,2,3,4]   => [1,5]
[1,5,6,2,4,3]   => [1,4,1]
[1,5,6,3,2,4]   => [1,3,2]
[1,5,6,3,4,2]   => [1,4,1]
[1,5,6,4,2,3]   => [1,3,2]
[1,5,6,4,3,2]   => [1,3,1,1]
[1,6,2,3,4,5]   => [1,5]
[1,6,2,3,5,4]   => [1,4,1]
[1,6,2,4,3,5]   => [1,3,2]
[1,6,2,4,5,3]   => [1,4,1]
[1,6,2,5,3,4]   => [1,2,3]
[1,6,2,5,4,3]   => [1,2,2,1]
[1,6,3,2,4,5]   => [1,2,3]
[1,6,3,2,5,4]   => [1,2,2,1]
[1,6,3,4,2,5]   => [1,3,2]
[1,6,3,4,5,2]   => [1,4,1]
[1,6,3,5,2,4]   => [1,2,3]
[1,6,3,5,4,2]   => [1,2,2,1]
[1,6,4,2,3,5]   => [1,1,4]
[1,6,4,2,5,3]   => [1,1,3,1]
[1,6,4,3,2,5]   => [1,1,2,2]
[1,6,4,3,5,2]   => [1,1,3,1]
[1,6,4,5,2,3]   => [1,1,4]
[1,6,4,5,3,2]   => [1,1,3,1]
[1,6,5,2,3,4]   => [1,1,4]
[1,6,5,2,4,3]   => [1,1,3,1]
[1,6,5,3,2,4]   => [1,1,2,2]
[1,6,5,3,4,2]   => [1,1,3,1]
[1,6,5,4,2,3]   => [1,1,2,2]
[1,6,5,4,3,2]   => [1,1,2,1,1]
[2,1,3,4,5,6]   => [6]
[2,1,3,4,6,5]   => [4,2]
[2,1,3,5,4,6]   => [3,3]
[2,1,3,5,6,4]   => [3,3]
[2,1,3,6,4,5]   => [3,3]
[2,1,3,6,5,4]   => [3,2,1]
[2,1,4,3,5,6]   => [2,4]
[2,1,4,3,6,5]   => [2,2,2]
[2,1,4,5,3,6]   => [2,4]
[2,1,4,5,6,3]   => [2,4]
[2,1,4,6,3,5]   => [2,4]
[2,1,4,6,5,3]   => [2,3,1]
[2,1,5,3,4,6]   => [2,4]
[2,1,5,3,6,4]   => [2,2,2]
[2,1,5,4,3,6]   => [2,2,2]
[2,1,5,4,6,3]   => [2,2,2]
[2,1,5,6,3,4]   => [2,4]
[2,1,5,6,4,3]   => [2,3,1]
[2,1,6,3,4,5]   => [2,4]
[2,1,6,3,5,4]   => [2,3,1]
[2,1,6,4,3,5]   => [2,2,2]
[2,1,6,4,5,3]   => [2,3,1]
[2,1,6,5,3,4]   => [2,1,3]
[2,1,6,5,4,3]   => [2,1,2,1]
[2,3,1,4,5,6]   => [6]
[2,3,1,4,6,5]   => [4,2]
[2,3,1,5,4,6]   => [3,3]
[2,3,1,5,6,4]   => [3,3]
[2,3,1,6,4,5]   => [3,3]
[2,3,1,6,5,4]   => [3,2,1]
[2,3,4,1,5,6]   => [6]
[2,3,4,1,6,5]   => [4,2]
[2,3,4,5,1,6]   => [6]
[2,3,4,5,6,1]   => [6]
[2,3,4,6,1,5]   => [6]
[2,3,4,6,5,1]   => [5,1]
[2,3,5,1,4,6]   => [6]
[2,3,5,1,6,4]   => [4,2]
[2,3,5,4,1,6]   => [4,2]
[2,3,5,4,6,1]   => [4,2]
[2,3,5,6,1,4]   => [6]
[2,3,5,6,4,1]   => [5,1]
[2,3,6,1,4,5]   => [6]
[2,3,6,1,5,4]   => [5,1]
[2,3,6,4,1,5]   => [4,2]
[2,3,6,4,5,1]   => [5,1]
[2,3,6,5,1,4]   => [3,3]
[2,3,6,5,4,1]   => [3,2,1]
[2,4,1,3,5,6]   => [6]
[2,4,1,3,6,5]   => [4,2]
[2,4,1,5,3,6]   => [3,3]
[2,4,1,5,6,3]   => [3,3]
[2,4,1,6,3,5]   => [3,3]
[2,4,1,6,5,3]   => [3,2,1]
[2,4,3,1,5,6]   => [3,3]
[2,4,3,1,6,5]   => [3,1,2]
[2,4,3,5,1,6]   => [3,3]
[2,4,3,5,6,1]   => [3,3]
[2,4,3,6,1,5]   => [3,3]
[2,4,3,6,5,1]   => [3,2,1]
[2,4,5,1,3,6]   => [6]
[2,4,5,1,6,3]   => [4,2]
[2,4,5,3,1,6]   => [4,2]
[2,4,5,3,6,1]   => [4,2]
[2,4,5,6,1,3]   => [6]
[2,4,5,6,3,1]   => [5,1]
[2,4,6,1,3,5]   => [6]
[2,4,6,1,5,3]   => [5,1]
[2,4,6,3,1,5]   => [4,2]
[2,4,6,3,5,1]   => [5,1]
[2,4,6,5,1,3]   => [3,3]
[2,4,6,5,3,1]   => [3,2,1]
[2,5,1,3,4,6]   => [6]
[2,5,1,3,6,4]   => [4,2]
[2,5,1,4,3,6]   => [4,2]
[2,5,1,4,6,3]   => [4,2]
[2,5,1,6,3,4]   => [3,3]
[2,5,1,6,4,3]   => [3,2,1]
[2,5,3,1,4,6]   => [3,3]
[2,5,3,1,6,4]   => [3,1,2]
[2,5,3,4,1,6]   => [4,2]
[2,5,3,4,6,1]   => [4,2]
[2,5,3,6,1,4]   => [3,3]
[2,5,3,6,4,1]   => [3,2,1]
[2,5,4,1,3,6]   => [2,4]
[2,5,4,1,6,3]   => [2,2,2]
[2,5,4,3,1,6]   => [2,2,2]
[2,5,4,3,6,1]   => [2,2,2]
[2,5,4,6,1,3]   => [2,4]
[2,5,4,6,3,1]   => [2,3,1]
[2,5,6,1,3,4]   => [6]
[2,5,6,1,4,3]   => [5,1]
[2,5,6,3,1,4]   => [4,2]
[2,5,6,3,4,1]   => [5,1]
[2,5,6,4,1,3]   => [4,2]
[2,5,6,4,3,1]   => [4,1,1]
[2,6,1,3,4,5]   => [6]
[2,6,1,3,5,4]   => [5,1]
[2,6,1,4,3,5]   => [4,2]
[2,6,1,4,5,3]   => [5,1]
[2,6,1,5,3,4]   => [3,3]
[2,6,1,5,4,3]   => [3,2,1]
[2,6,3,1,4,5]   => [3,3]
[2,6,3,1,5,4]   => [3,2,1]
[2,6,3,4,1,5]   => [4,2]
[2,6,3,4,5,1]   => [5,1]
[2,6,3,5,1,4]   => [3,3]
[2,6,3,5,4,1]   => [3,2,1]
[2,6,4,1,3,5]   => [2,4]
[2,6,4,1,5,3]   => [2,3,1]
[2,6,4,3,1,5]   => [2,2,2]
[2,6,4,3,5,1]   => [2,3,1]
[2,6,4,5,1,3]   => [2,4]
[2,6,4,5,3,1]   => [2,3,1]
[2,6,5,1,3,4]   => [2,4]
[2,6,5,1,4,3]   => [2,3,1]
[2,6,5,3,1,4]   => [2,2,2]
[2,6,5,3,4,1]   => [2,3,1]
[2,6,5,4,1,3]   => [2,2,2]
[2,6,5,4,3,1]   => [2,2,1,1]
[3,1,2,4,5,6]   => [6]
[3,1,2,4,6,5]   => [4,2]
[3,1,2,5,4,6]   => [3,3]
[3,1,2,5,6,4]   => [3,3]
[3,1,2,6,4,5]   => [3,3]
[3,1,2,6,5,4]   => [3,2,1]
[3,1,4,2,5,6]   => [2,4]
[3,1,4,2,6,5]   => [2,2,2]
[3,1,4,5,2,6]   => [2,4]
[3,1,4,5,6,2]   => [2,4]
[3,1,4,6,2,5]   => [2,4]
[3,1,4,6,5,2]   => [2,3,1]
[3,1,5,2,4,6]   => [2,4]
[3,1,5,2,6,4]   => [2,2,2]
[3,1,5,4,2,6]   => [2,2,2]
[3,1,5,4,6,2]   => [2,2,2]
[3,1,5,6,2,4]   => [2,4]
[3,1,5,6,4,2]   => [2,3,1]
[3,1,6,2,4,5]   => [2,4]
[3,1,6,2,5,4]   => [2,3,1]
[3,1,6,4,2,5]   => [2,2,2]
[3,1,6,4,5,2]   => [2,3,1]
[3,1,6,5,2,4]   => [2,1,3]
[3,1,6,5,4,2]   => [2,1,2,1]
[3,2,1,4,5,6]   => [2,4]
[3,2,1,4,6,5]   => [2,2,2]
[3,2,1,5,4,6]   => [2,1,3]
[3,2,1,5,6,4]   => [2,1,3]
[3,2,1,6,4,5]   => [2,1,3]
[3,2,1,6,5,4]   => [2,1,2,1]
[3,2,4,1,5,6]   => [2,4]
[3,2,4,1,6,5]   => [2,2,2]
[3,2,4,5,1,6]   => [2,4]
[3,2,4,5,6,1]   => [2,4]
[3,2,4,6,1,5]   => [2,4]
[3,2,4,6,5,1]   => [2,3,1]
[3,2,5,1,4,6]   => [2,4]
[3,2,5,1,6,4]   => [2,2,2]
[3,2,5,4,1,6]   => [2,2,2]
[3,2,5,4,6,1]   => [2,2,2]
[3,2,5,6,1,4]   => [2,4]
[3,2,5,6,4,1]   => [2,3,1]
[3,2,6,1,4,5]   => [2,4]
[3,2,6,1,5,4]   => [2,3,1]
[3,2,6,4,1,5]   => [2,2,2]
[3,2,6,4,5,1]   => [2,3,1]
[3,2,6,5,1,4]   => [2,1,3]
[3,2,6,5,4,1]   => [2,1,2,1]
[3,4,1,2,5,6]   => [6]
[3,4,1,2,6,5]   => [4,2]
[3,4,1,5,2,6]   => [3,3]
[3,4,1,5,6,2]   => [3,3]
[3,4,1,6,2,5]   => [3,3]
[3,4,1,6,5,2]   => [3,2,1]
[3,4,2,1,5,6]   => [3,3]
[3,4,2,1,6,5]   => [3,1,2]
[3,4,2,5,1,6]   => [3,3]
[3,4,2,5,6,1]   => [3,3]
[3,4,2,6,1,5]   => [3,3]
[3,4,2,6,5,1]   => [3,2,1]
[3,4,5,1,2,6]   => [6]
[3,4,5,1,6,2]   => [4,2]
[3,4,5,2,1,6]   => [4,2]
[3,4,5,2,6,1]   => [4,2]
[3,4,5,6,1,2]   => [6]
[3,4,5,6,2,1]   => [5,1]
[3,4,6,1,2,5]   => [6]
[3,4,6,1,5,2]   => [5,1]
[3,4,6,2,1,5]   => [4,2]
[3,4,6,2,5,1]   => [5,1]
[3,4,6,5,1,2]   => [3,3]
[3,4,6,5,2,1]   => [3,2,1]
[3,5,1,2,4,6]   => [6]
[3,5,1,2,6,4]   => [4,2]
[3,5,1,4,2,6]   => [4,2]
[3,5,1,4,6,2]   => [4,2]
[3,5,1,6,2,4]   => [3,3]
[3,5,1,6,4,2]   => [3,2,1]
[3,5,2,1,4,6]   => [3,3]
[3,5,2,1,6,4]   => [3,1,2]
[3,5,2,4,1,6]   => [4,2]
[3,5,2,4,6,1]   => [4,2]
[3,5,2,6,1,4]   => [3,3]
[3,5,2,6,4,1]   => [3,2,1]
[3,5,4,1,2,6]   => [2,4]
[3,5,4,1,6,2]   => [2,2,2]
[3,5,4,2,1,6]   => [2,2,2]
[3,5,4,2,6,1]   => [2,2,2]
[3,5,4,6,1,2]   => [2,4]
[3,5,4,6,2,1]   => [2,3,1]
[3,5,6,1,2,4]   => [6]
[3,5,6,1,4,2]   => [5,1]
[3,5,6,2,1,4]   => [4,2]
[3,5,6,2,4,1]   => [5,1]
[3,5,6,4,1,2]   => [4,2]
[3,5,6,4,2,1]   => [4,1,1]
[3,6,1,2,4,5]   => [6]
[3,6,1,2,5,4]   => [5,1]
[3,6,1,4,2,5]   => [4,2]
[3,6,1,4,5,2]   => [5,1]
[3,6,1,5,2,4]   => [3,3]
[3,6,1,5,4,2]   => [3,2,1]
[3,6,2,1,4,5]   => [3,3]
[3,6,2,1,5,4]   => [3,2,1]
[3,6,2,4,1,5]   => [4,2]
[3,6,2,4,5,1]   => [5,1]
[3,6,2,5,1,4]   => [3,3]
[3,6,2,5,4,1]   => [3,2,1]
[3,6,4,1,2,5]   => [2,4]
[3,6,4,1,5,2]   => [2,3,1]
[3,6,4,2,1,5]   => [2,2,2]
[3,6,4,2,5,1]   => [2,3,1]
[3,6,4,5,1,2]   => [2,4]
[3,6,4,5,2,1]   => [2,3,1]
[3,6,5,1,2,4]   => [2,4]
[3,6,5,1,4,2]   => [2,3,1]
[3,6,5,2,1,4]   => [2,2,2]
[3,6,5,2,4,1]   => [2,3,1]
[3,6,5,4,1,2]   => [2,2,2]
[3,6,5,4,2,1]   => [2,2,1,1]
[4,1,2,3,5,6]   => [6]
[4,1,2,3,6,5]   => [4,2]
[4,1,2,5,3,6]   => [3,3]
[4,1,2,5,6,3]   => [3,3]
[4,1,2,6,3,5]   => [3,3]
[4,1,2,6,5,3]   => [3,2,1]
[4,1,3,2,5,6]   => [3,3]
[4,1,3,2,6,5]   => [3,1,2]
[4,1,3,5,2,6]   => [3,3]
[4,1,3,5,6,2]   => [3,3]
[4,1,3,6,2,5]   => [3,3]
[4,1,3,6,5,2]   => [3,2,1]
[4,1,5,2,3,6]   => [2,4]
[4,1,5,2,6,3]   => [2,2,2]
[4,1,5,3,2,6]   => [2,2,2]
[4,1,5,3,6,2]   => [2,2,2]
[4,1,5,6,2,3]   => [2,4]
[4,1,5,6,3,2]   => [2,3,1]
[4,1,6,2,3,5]   => [2,4]
[4,1,6,2,5,3]   => [2,3,1]
[4,1,6,3,2,5]   => [2,2,2]
[4,1,6,3,5,2]   => [2,3,1]
[4,1,6,5,2,3]   => [2,1,3]
[4,1,6,5,3,2]   => [2,1,2,1]
[4,2,1,3,5,6]   => [2,4]
[4,2,1,3,6,5]   => [2,2,2]
[4,2,1,5,3,6]   => [2,1,3]
[4,2,1,5,6,3]   => [2,1,3]
[4,2,1,6,3,5]   => [2,1,3]
[4,2,1,6,5,3]   => [2,1,2,1]
[4,2,3,1,5,6]   => [3,3]
[4,2,3,1,6,5]   => [3,1,2]
[4,2,3,5,1,6]   => [3,3]
[4,2,3,5,6,1]   => [3,3]
[4,2,3,6,1,5]   => [3,3]
[4,2,3,6,5,1]   => [3,2,1]
[4,2,5,1,3,6]   => [2,4]
[4,2,5,1,6,3]   => [2,2,2]
[4,2,5,3,1,6]   => [2,2,2]
[4,2,5,3,6,1]   => [2,2,2]
[4,2,5,6,1,3]   => [2,4]
[4,2,5,6,3,1]   => [2,3,1]
[4,2,6,1,3,5]   => [2,4]
[4,2,6,1,5,3]   => [2,3,1]
[4,2,6,3,1,5]   => [2,2,2]
[4,2,6,3,5,1]   => [2,3,1]
[4,2,6,5,1,3]   => [2,1,3]
[4,2,6,5,3,1]   => [2,1,2,1]
[4,3,1,2,5,6]   => [1,5]
[4,3,1,2,6,5]   => [1,3,2]
[4,3,1,5,2,6]   => [1,2,3]
[4,3,1,5,6,2]   => [1,2,3]
[4,3,1,6,2,5]   => [1,2,3]
[4,3,1,6,5,2]   => [1,2,2,1]
[4,3,2,1,5,6]   => [1,2,3]
[4,3,2,1,6,5]   => [1,2,1,2]
[4,3,2,5,1,6]   => [1,2,3]
[4,3,2,5,6,1]   => [1,2,3]
[4,3,2,6,1,5]   => [1,2,3]
[4,3,2,6,5,1]   => [1,2,2,1]
[4,3,5,1,2,6]   => [1,5]
[4,3,5,1,6,2]   => [1,3,2]
[4,3,5,2,1,6]   => [1,3,2]
[4,3,5,2,6,1]   => [1,3,2]
[4,3,5,6,1,2]   => [1,5]
[4,3,5,6,2,1]   => [1,4,1]
[4,3,6,1,2,5]   => [1,5]
[4,3,6,1,5,2]   => [1,4,1]
[4,3,6,2,1,5]   => [1,3,2]
[4,3,6,2,5,1]   => [1,4,1]
[4,3,6,5,1,2]   => [1,2,3]
[4,3,6,5,2,1]   => [1,2,2,1]
[4,5,1,2,3,6]   => [6]
[4,5,1,2,6,3]   => [4,2]
[4,5,1,3,2,6]   => [4,2]
[4,5,1,3,6,2]   => [4,2]
[4,5,1,6,2,3]   => [3,3]
[4,5,1,6,3,2]   => [3,2,1]
[4,5,2,1,3,6]   => [3,3]
[4,5,2,1,6,3]   => [3,1,2]
[4,5,2,3,1,6]   => [4,2]
[4,5,2,3,6,1]   => [4,2]
[4,5,2,6,1,3]   => [3,3]
[4,5,2,6,3,1]   => [3,2,1]
[4,5,3,1,2,6]   => [3,3]
[4,5,3,1,6,2]   => [3,1,2]
[4,5,3,2,1,6]   => [3,1,2]
[4,5,3,2,6,1]   => [3,1,2]
[4,5,3,6,1,2]   => [3,3]
[4,5,3,6,2,1]   => [3,2,1]
[4,5,6,1,2,3]   => [6]
[4,5,6,1,3,2]   => [5,1]
[4,5,6,2,1,3]   => [4,2]
[4,5,6,2,3,1]   => [5,1]
[4,5,6,3,1,2]   => [4,2]
[4,5,6,3,2,1]   => [4,1,1]
[4,6,1,2,3,5]   => [6]
[4,6,1,2,5,3]   => [5,1]
[4,6,1,3,2,5]   => [4,2]
[4,6,1,3,5,2]   => [5,1]
[4,6,1,5,2,3]   => [3,3]
[4,6,1,5,3,2]   => [3,2,1]
[4,6,2,1,3,5]   => [3,3]
[4,6,2,1,5,3]   => [3,2,1]
[4,6,2,3,1,5]   => [4,2]
[4,6,2,3,5,1]   => [5,1]
[4,6,2,5,1,3]   => [3,3]
[4,6,2,5,3,1]   => [3,2,1]
[4,6,3,1,2,5]   => [3,3]
[4,6,3,1,5,2]   => [3,2,1]
[4,6,3,2,1,5]   => [3,1,2]
[4,6,3,2,5,1]   => [3,2,1]
[4,6,3,5,1,2]   => [3,3]
[4,6,3,5,2,1]   => [3,2,1]
[4,6,5,1,2,3]   => [2,4]
[4,6,5,1,3,2]   => [2,3,1]
[4,6,5,2,1,3]   => [2,2,2]
[4,6,5,2,3,1]   => [2,3,1]
[4,6,5,3,1,2]   => [2,2,2]
[4,6,5,3,2,1]   => [2,2,1,1]
[5,1,2,3,4,6]   => [6]
[5,1,2,3,6,4]   => [4,2]
[5,1,2,4,3,6]   => [4,2]
[5,1,2,4,6,3]   => [4,2]
[5,1,2,6,3,4]   => [3,3]
[5,1,2,6,4,3]   => [3,2,1]
[5,1,3,2,4,6]   => [3,3]
[5,1,3,2,6,4]   => [3,1,2]
[5,1,3,4,2,6]   => [4,2]
[5,1,3,4,6,2]   => [4,2]
[5,1,3,6,2,4]   => [3,3]
[5,1,3,6,4,2]   => [3,2,1]
[5,1,4,2,3,6]   => [2,4]
[5,1,4,2,6,3]   => [2,2,2]
[5,1,4,3,2,6]   => [2,2,2]
[5,1,4,3,6,2]   => [2,2,2]
[5,1,4,6,2,3]   => [2,4]
[5,1,4,6,3,2]   => [2,3,1]
[5,1,6,2,3,4]   => [2,4]
[5,1,6,2,4,3]   => [2,3,1]
[5,1,6,3,2,4]   => [2,2,2]
[5,1,6,3,4,2]   => [2,3,1]
[5,1,6,4,2,3]   => [2,2,2]
[5,1,6,4,3,2]   => [2,2,1,1]
[5,2,1,3,4,6]   => [2,4]
[5,2,1,3,6,4]   => [2,2,2]
[5,2,1,4,3,6]   => [2,2,2]
[5,2,1,4,6,3]   => [2,2,2]
[5,2,1,6,3,4]   => [2,1,3]
[5,2,1,6,4,3]   => [2,1,2,1]
[5,2,3,1,4,6]   => [3,3]
[5,2,3,1,6,4]   => [3,1,2]
[5,2,3,4,1,6]   => [4,2]
[5,2,3,4,6,1]   => [4,2]
[5,2,3,6,1,4]   => [3,3]
[5,2,3,6,4,1]   => [3,2,1]
[5,2,4,1,3,6]   => [2,4]
[5,2,4,1,6,3]   => [2,2,2]
[5,2,4,3,1,6]   => [2,2,2]
[5,2,4,3,6,1]   => [2,2,2]
[5,2,4,6,1,3]   => [2,4]
[5,2,4,6,3,1]   => [2,3,1]
[5,2,6,1,3,4]   => [2,4]
[5,2,6,1,4,3]   => [2,3,1]
[5,2,6,3,1,4]   => [2,2,2]
[5,2,6,3,4,1]   => [2,3,1]
[5,2,6,4,1,3]   => [2,2,2]
[5,2,6,4,3,1]   => [2,2,1,1]
[5,3,1,2,4,6]   => [1,5]
[5,3,1,2,6,4]   => [1,3,2]
[5,3,1,4,2,6]   => [1,3,2]
[5,3,1,4,6,2]   => [1,3,2]
[5,3,1,6,2,4]   => [1,2,3]
[5,3,1,6,4,2]   => [1,2,2,1]
[5,3,2,1,4,6]   => [1,2,3]
[5,3,2,1,6,4]   => [1,2,1,2]
[5,3,2,4,1,6]   => [1,3,2]
[5,3,2,4,6,1]   => [1,3,2]
[5,3,2,6,1,4]   => [1,2,3]
[5,3,2,6,4,1]   => [1,2,2,1]
[5,3,4,1,2,6]   => [1,5]
[5,3,4,1,6,2]   => [1,3,2]
[5,3,4,2,1,6]   => [1,3,2]
[5,3,4,2,6,1]   => [1,3,2]
[5,3,4,6,1,2]   => [1,5]
[5,3,4,6,2,1]   => [1,4,1]
[5,3,6,1,2,4]   => [1,5]
[5,3,6,1,4,2]   => [1,4,1]
[5,3,6,2,1,4]   => [1,3,2]
[5,3,6,2,4,1]   => [1,4,1]
[5,3,6,4,1,2]   => [1,3,2]
[5,3,6,4,2,1]   => [1,3,1,1]
[5,4,1,2,3,6]   => [1,5]
[5,4,1,2,6,3]   => [1,3,2]
[5,4,1,3,2,6]   => [1,3,2]
[5,4,1,3,6,2]   => [1,3,2]
[5,4,1,6,2,3]   => [1,2,3]
[5,4,1,6,3,2]   => [1,2,2,1]
[5,4,2,1,3,6]   => [1,2,3]
[5,4,2,1,6,3]   => [1,2,1,2]
[5,4,2,3,1,6]   => [1,3,2]
[5,4,2,3,6,1]   => [1,3,2]
[5,4,2,6,1,3]   => [1,2,3]
[5,4,2,6,3,1]   => [1,2,2,1]
[5,4,3,1,2,6]   => [1,2,3]
[5,4,3,1,6,2]   => [1,2,1,2]
[5,4,3,2,1,6]   => [1,2,1,2]
[5,4,3,2,6,1]   => [1,2,1,2]
[5,4,3,6,1,2]   => [1,2,3]
[5,4,3,6,2,1]   => [1,2,2,1]
[5,4,6,1,2,3]   => [1,5]
[5,4,6,1,3,2]   => [1,4,1]
[5,4,6,2,1,3]   => [1,3,2]
[5,4,6,2,3,1]   => [1,4,1]
[5,4,6,3,1,2]   => [1,3,2]
[5,4,6,3,2,1]   => [1,3,1,1]
[5,6,1,2,3,4]   => [6]
[5,6,1,2,4,3]   => [5,1]
[5,6,1,3,2,4]   => [4,2]
[5,6,1,3,4,2]   => [5,1]
[5,6,1,4,2,3]   => [4,2]
[5,6,1,4,3,2]   => [4,1,1]
[5,6,2,1,3,4]   => [3,3]
[5,6,2,1,4,3]   => [3,2,1]
[5,6,2,3,1,4]   => [4,2]
[5,6,2,3,4,1]   => [5,1]
[5,6,2,4,1,3]   => [4,2]
[5,6,2,4,3,1]   => [4,1,1]
[5,6,3,1,2,4]   => [3,3]
[5,6,3,1,4,2]   => [3,2,1]
[5,6,3,2,1,4]   => [3,1,2]
[5,6,3,2,4,1]   => [3,2,1]
[5,6,3,4,1,2]   => [4,2]
[5,6,3,4,2,1]   => [4,1,1]
[5,6,4,1,2,3]   => [2,4]
[5,6,4,1,3,2]   => [2,3,1]
[5,6,4,2,1,3]   => [2,2,2]
[5,6,4,2,3,1]   => [2,3,1]
[5,6,4,3,1,2]   => [2,2,2]
[5,6,4,3,2,1]   => [2,2,1,1]
[6,1,2,3,4,5]   => [6]
[6,1,2,3,5,4]   => [5,1]
[6,1,2,4,3,5]   => [4,2]
[6,1,2,4,5,3]   => [5,1]
[6,1,2,5,3,4]   => [3,3]
[6,1,2,5,4,3]   => [3,2,1]
[6,1,3,2,4,5]   => [3,3]
[6,1,3,2,5,4]   => [3,2,1]
[6,1,3,4,2,5]   => [4,2]
[6,1,3,4,5,2]   => [5,1]
[6,1,3,5,2,4]   => [3,3]
[6,1,3,5,4,2]   => [3,2,1]
[6,1,4,2,3,5]   => [2,4]
[6,1,4,2,5,3]   => [2,3,1]
[6,1,4,3,2,5]   => [2,2,2]
[6,1,4,3,5,2]   => [2,3,1]
[6,1,4,5,2,3]   => [2,4]
[6,1,4,5,3,2]   => [2,3,1]
[6,1,5,2,3,4]   => [2,4]
[6,1,5,2,4,3]   => [2,3,1]
[6,1,5,3,2,4]   => [2,2,2]
[6,1,5,3,4,2]   => [2,3,1]
[6,1,5,4,2,3]   => [2,2,2]
[6,1,5,4,3,2]   => [2,2,1,1]
[6,2,1,3,4,5]   => [2,4]
[6,2,1,3,5,4]   => [2,3,1]
[6,2,1,4,3,5]   => [2,2,2]
[6,2,1,4,5,3]   => [2,3,1]
[6,2,1,5,3,4]   => [2,1,3]
[6,2,1,5,4,3]   => [2,1,2,1]
[6,2,3,1,4,5]   => [3,3]
[6,2,3,1,5,4]   => [3,2,1]
[6,2,3,4,1,5]   => [4,2]
[6,2,3,4,5,1]   => [5,1]
[6,2,3,5,1,4]   => [3,3]
[6,2,3,5,4,1]   => [3,2,1]
[6,2,4,1,3,5]   => [2,4]
[6,2,4,1,5,3]   => [2,3,1]
[6,2,4,3,1,5]   => [2,2,2]
[6,2,4,3,5,1]   => [2,3,1]
[6,2,4,5,1,3]   => [2,4]
[6,2,4,5,3,1]   => [2,3,1]
[6,2,5,1,3,4]   => [2,4]
[6,2,5,1,4,3]   => [2,3,1]
[6,2,5,3,1,4]   => [2,2,2]
[6,2,5,3,4,1]   => [2,3,1]
[6,2,5,4,1,3]   => [2,2,2]
[6,2,5,4,3,1]   => [2,2,1,1]
[6,3,1,2,4,5]   => [1,5]
[6,3,1,2,5,4]   => [1,4,1]
[6,3,1,4,2,5]   => [1,3,2]
[6,3,1,4,5,2]   => [1,4,1]
[6,3,1,5,2,4]   => [1,2,3]
[6,3,1,5,4,2]   => [1,2,2,1]
[6,3,2,1,4,5]   => [1,2,3]
[6,3,2,1,5,4]   => [1,2,2,1]
[6,3,2,4,1,5]   => [1,3,2]
[6,3,2,4,5,1]   => [1,4,1]
[6,3,2,5,1,4]   => [1,2,3]
[6,3,2,5,4,1]   => [1,2,2,1]
[6,3,4,1,2,5]   => [1,5]
[6,3,4,1,5,2]   => [1,4,1]
[6,3,4,2,1,5]   => [1,3,2]
[6,3,4,2,5,1]   => [1,4,1]
[6,3,4,5,1,2]   => [1,5]
[6,3,4,5,2,1]   => [1,4,1]
[6,3,5,1,2,4]   => [1,5]
[6,3,5,1,4,2]   => [1,4,1]
[6,3,5,2,1,4]   => [1,3,2]
[6,3,5,2,4,1]   => [1,4,1]
[6,3,5,4,1,2]   => [1,3,2]
[6,3,5,4,2,1]   => [1,3,1,1]
[6,4,1,2,3,5]   => [1,5]
[6,4,1,2,5,3]   => [1,4,1]
[6,4,1,3,2,5]   => [1,3,2]
[6,4,1,3,5,2]   => [1,4,1]
[6,4,1,5,2,3]   => [1,2,3]
[6,4,1,5,3,2]   => [1,2,2,1]
[6,4,2,1,3,5]   => [1,2,3]
[6,4,2,1,5,3]   => [1,2,2,1]
[6,4,2,3,1,5]   => [1,3,2]
[6,4,2,3,5,1]   => [1,4,1]
[6,4,2,5,1,3]   => [1,2,3]
[6,4,2,5,3,1]   => [1,2,2,1]
[6,4,3,1,2,5]   => [1,2,3]
[6,4,3,1,5,2]   => [1,2,2,1]
[6,4,3,2,1,5]   => [1,2,1,2]
[6,4,3,2,5,1]   => [1,2,2,1]
[6,4,3,5,1,2]   => [1,2,3]
[6,4,3,5,2,1]   => [1,2,2,1]
[6,4,5,1,2,3]   => [1,5]
[6,4,5,1,3,2]   => [1,4,1]
[6,4,5,2,1,3]   => [1,3,2]
[6,4,5,2,3,1]   => [1,4,1]
[6,4,5,3,1,2]   => [1,3,2]
[6,4,5,3,2,1]   => [1,3,1,1]
[6,5,1,2,3,4]   => [1,5]
[6,5,1,2,4,3]   => [1,4,1]
[6,5,1,3,2,4]   => [1,3,2]
[6,5,1,3,4,2]   => [1,4,1]
[6,5,1,4,2,3]   => [1,3,2]
[6,5,1,4,3,2]   => [1,3,1,1]
[6,5,2,1,3,4]   => [1,2,3]
[6,5,2,1,4,3]   => [1,2,2,1]
[6,5,2,3,1,4]   => [1,3,2]
[6,5,2,3,4,1]   => [1,4,1]
[6,5,2,4,1,3]   => [1,3,2]
[6,5,2,4,3,1]   => [1,3,1,1]
[6,5,3,1,2,4]   => [1,2,3]
[6,5,3,1,4,2]   => [1,2,2,1]
[6,5,3,2,1,4]   => [1,2,1,2]
[6,5,3,2,4,1]   => [1,2,2,1]
[6,5,3,4,1,2]   => [1,3,2]
[6,5,3,4,2,1]   => [1,3,1,1]
[6,5,4,1,2,3]   => [1,1,4]
[6,5,4,1,3,2]   => [1,1,3,1]
[6,5,4,2,1,3]   => [1,1,2,2]
[6,5,4,2,3,1]   => [1,1,3,1]
[6,5,4,3,1,2]   => [1,1,2,2]
[6,5,4,3,2,1]   => [1,1,2,1,1]
[1,2,3,4,5,6,7] => [7]
[1,2,3,4,5,7,6] => [5,2]
[1,2,3,4,6,5,7] => [4,3]
[1,2,3,4,6,7,5] => [4,3]
[1,2,3,4,7,5,6] => [4,3]
[1,2,3,4,7,6,5] => [4,2,1]
[1,2,3,5,4,6,7] => [3,4]
[1,2,3,5,4,7,6] => [3,2,2]
[1,2,3,5,6,4,7] => [3,4]
[1,2,3,5,6,7,4] => [3,4]
[1,2,3,5,7,4,6] => [3,4]
[1,2,3,5,7,6,4] => [3,3,1]
[1,2,3,6,4,5,7] => [3,4]
[1,2,3,6,4,7,5] => [3,2,2]
[1,2,3,6,5,4,7] => [3,2,2]
[1,2,3,6,5,7,4] => [3,2,2]
[1,2,3,6,7,4,5] => [3,4]
[1,2,3,6,7,5,4] => [3,3,1]
[1,2,3,7,4,5,6] => [3,4]
[1,2,3,7,4,6,5] => [3,3,1]
[1,2,3,7,5,4,6] => [3,2,2]
[1,2,3,7,5,6,4] => [3,3,1]
[1,2,3,7,6,4,5] => [3,1,3]
[1,2,3,7,6,5,4] => [3,1,2,1]
[1,2,4,3,5,6,7] => [2,5]
[1,2,4,3,5,7,6] => [2,3,2]
[1,2,4,3,6,5,7] => [2,2,3]
[1,2,4,3,6,7,5] => [2,2,3]
[1,2,4,3,7,5,6] => [2,2,3]
[1,2,4,3,7,6,5] => [2,2,2,1]
[1,2,4,5,3,6,7] => [2,5]
[1,2,4,5,3,7,6] => [2,3,2]
[1,2,4,5,6,3,7] => [2,5]
[1,2,4,5,6,7,3] => [2,5]
[1,2,4,5,7,3,6] => [2,5]
[1,2,4,5,7,6,3] => [2,4,1]
[1,2,4,6,3,5,7] => [2,5]
[1,2,4,6,3,7,5] => [2,3,2]
[1,2,4,6,5,3,7] => [2,3,2]
[1,2,4,6,5,7,3] => [2,3,2]
[1,2,4,6,7,3,5] => [2,5]
[1,2,4,6,7,5,3] => [2,4,1]
[1,2,4,7,3,5,6] => [2,5]
[1,2,4,7,3,6,5] => [2,4,1]
[1,2,4,7,5,3,6] => [2,3,2]
[1,2,4,7,5,6,3] => [2,4,1]
[1,2,4,7,6,3,5] => [2,2,3]
[1,2,4,7,6,5,3] => [2,2,2,1]
[1,2,5,3,4,6,7] => [2,5]
[1,2,5,3,4,7,6] => [2,3,2]
[1,2,5,3,6,4,7] => [2,2,3]
[1,2,5,3,6,7,4] => [2,2,3]
[1,2,5,3,7,4,6] => [2,2,3]
[1,2,5,3,7,6,4] => [2,2,2,1]
[1,2,5,4,3,6,7] => [2,2,3]
[1,2,5,4,3,7,6] => [2,2,1,2]
[1,2,5,4,6,3,7] => [2,2,3]
[1,2,5,4,6,7,3] => [2,2,3]
[1,2,5,4,7,3,6] => [2,2,3]
[1,2,5,4,7,6,3] => [2,2,2,1]
[1,2,5,6,3,4,7] => [2,5]
[1,2,5,6,3,7,4] => [2,3,2]
[1,2,5,6,4,3,7] => [2,3,2]
[1,2,5,6,4,7,3] => [2,3,2]
[1,2,5,6,7,3,4] => [2,5]
[1,2,5,6,7,4,3] => [2,4,1]
[1,2,5,7,3,4,6] => [2,5]
[1,2,5,7,3,6,4] => [2,4,1]
[1,2,5,7,4,3,6] => [2,3,2]
[1,2,5,7,4,6,3] => [2,4,1]
[1,2,5,7,6,3,4] => [2,2,3]
[1,2,5,7,6,4,3] => [2,2,2,1]
[1,2,6,3,4,5,7] => [2,5]
[1,2,6,3,4,7,5] => [2,3,2]
[1,2,6,3,5,4,7] => [2,3,2]
[1,2,6,3,5,7,4] => [2,3,2]
[1,2,6,3,7,4,5] => [2,2,3]
[1,2,6,3,7,5,4] => [2,2,2,1]
[1,2,6,4,3,5,7] => [2,2,3]
[1,2,6,4,3,7,5] => [2,2,1,2]
[1,2,6,4,5,3,7] => [2,3,2]
[1,2,6,4,5,7,3] => [2,3,2]
[1,2,6,4,7,3,5] => [2,2,3]
[1,2,6,4,7,5,3] => [2,2,2,1]
[1,2,6,5,3,4,7] => [2,1,4]
[1,2,6,5,3,7,4] => [2,1,2,2]
[1,2,6,5,4,3,7] => [2,1,2,2]
[1,2,6,5,4,7,3] => [2,1,2,2]
[1,2,6,5,7,3,4] => [2,1,4]
[1,2,6,5,7,4,3] => [2,1,3,1]
[1,2,6,7,3,4,5] => [2,5]
[1,2,6,7,3,5,4] => [2,4,1]
[1,2,6,7,4,3,5] => [2,3,2]
[1,2,6,7,4,5,3] => [2,4,1]
[1,2,6,7,5,3,4] => [2,3,2]
[1,2,6,7,5,4,3] => [2,3,1,1]
[1,2,7,3,4,5,6] => [2,5]
[1,2,7,3,4,6,5] => [2,4,1]
[1,2,7,3,5,4,6] => [2,3,2]
[1,2,7,3,5,6,4] => [2,4,1]
[1,2,7,3,6,4,5] => [2,2,3]
[1,2,7,3,6,5,4] => [2,2,2,1]
[1,2,7,4,3,5,6] => [2,2,3]
[1,2,7,4,3,6,5] => [2,2,2,1]
[1,2,7,4,5,3,6] => [2,3,2]
[1,2,7,4,5,6,3] => [2,4,1]
[1,2,7,4,6,3,5] => [2,2,3]
[1,2,7,4,6,5,3] => [2,2,2,1]
[1,2,7,5,3,4,6] => [2,1,4]
[1,2,7,5,3,6,4] => [2,1,3,1]
[1,2,7,5,4,3,6] => [2,1,2,2]
[1,2,7,5,4,6,3] => [2,1,3,1]
[1,2,7,5,6,3,4] => [2,1,4]
[1,2,7,5,6,4,3] => [2,1,3,1]
[1,2,7,6,3,4,5] => [2,1,4]
[1,2,7,6,3,5,4] => [2,1,3,1]
[1,2,7,6,4,3,5] => [2,1,2,2]
[1,2,7,6,4,5,3] => [2,1,3,1]
[1,2,7,6,5,3,4] => [2,1,2,2]
[1,2,7,6,5,4,3] => [2,1,2,1,1]
[1,3,2,4,5,6,7] => [1,6]
[1,3,2,4,5,7,6] => [1,4,2]
[1,3,2,4,6,5,7] => [1,3,3]
[1,3,2,4,6,7,5] => [1,3,3]
[1,3,2,4,7,5,6] => [1,3,3]
[1,3,2,4,7,6,5] => [1,3,2,1]
[1,3,2,5,4,6,7] => [1,2,4]
[1,3,2,5,4,7,6] => [1,2,2,2]
[1,3,2,5,6,4,7] => [1,2,4]
[1,3,2,5,6,7,4] => [1,2,4]
[1,3,2,5,7,4,6] => [1,2,4]
[1,3,2,5,7,6,4] => [1,2,3,1]
[1,3,2,6,4,5,7] => [1,2,4]
[1,3,2,6,4,7,5] => [1,2,2,2]
[1,3,2,6,5,4,7] => [1,2,2,2]
[1,3,2,6,5,7,4] => [1,2,2,2]
[1,3,2,6,7,4,5] => [1,2,4]
[1,3,2,6,7,5,4] => [1,2,3,1]
[1,3,2,7,4,5,6] => [1,2,4]
[1,3,2,7,4,6,5] => [1,2,3,1]
[1,3,2,7,5,4,6] => [1,2,2,2]
[1,3,2,7,5,6,4] => [1,2,3,1]
[1,3,2,7,6,4,5] => [1,2,1,3]
[1,3,2,7,6,5,4] => [1,2,1,2,1]
[1,3,4,2,5,6,7] => [1,6]
[1,3,4,2,5,7,6] => [1,4,2]
[1,3,4,2,6,5,7] => [1,3,3]
[1,3,4,2,6,7,5] => [1,3,3]
[1,3,4,2,7,5,6] => [1,3,3]
[1,3,4,2,7,6,5] => [1,3,2,1]
[1,3,4,5,2,6,7] => [1,6]
[1,3,4,5,2,7,6] => [1,4,2]
[1,3,4,5,6,2,7] => [1,6]
[1,3,4,5,6,7,2] => [1,6]
[1,3,4,5,7,2,6] => [1,6]
[1,3,4,5,7,6,2] => [1,5,1]
[1,3,4,6,2,5,7] => [1,6]
[1,3,4,6,2,7,5] => [1,4,2]
[1,3,4,6,5,2,7] => [1,4,2]
[1,3,4,6,5,7,2] => [1,4,2]
[1,3,4,6,7,2,5] => [1,6]
[1,3,4,6,7,5,2] => [1,5,1]
[1,3,4,7,2,5,6] => [1,6]
[1,3,4,7,2,6,5] => [1,5,1]
[1,3,4,7,5,2,6] => [1,4,2]
[1,3,4,7,5,6,2] => [1,5,1]
[1,3,4,7,6,2,5] => [1,3,3]
[1,3,4,7,6,5,2] => [1,3,2,1]
[1,3,5,2,4,6,7] => [1,6]
[1,3,5,2,4,7,6] => [1,4,2]
[1,3,5,2,6,4,7] => [1,3,3]
[1,3,5,2,6,7,4] => [1,3,3]
[1,3,5,2,7,4,6] => [1,3,3]
[1,3,5,2,7,6,4] => [1,3,2,1]
[1,3,5,4,2,6,7] => [1,3,3]
[1,3,5,4,2,7,6] => [1,3,1,2]
[1,3,5,4,6,2,7] => [1,3,3]
[1,3,5,4,6,7,2] => [1,3,3]
[1,3,5,4,7,2,6] => [1,3,3]
[1,3,5,4,7,6,2] => [1,3,2,1]
[1,3,5,6,2,4,7] => [1,6]
[1,3,5,6,2,7,4] => [1,4,2]
[1,3,5,6,4,2,7] => [1,4,2]
[1,3,5,6,4,7,2] => [1,4,2]
[1,3,5,6,7,2,4] => [1,6]
[1,3,5,6,7,4,2] => [1,5,1]
[1,3,5,7,2,4,6] => [1,6]
[1,3,5,7,2,6,4] => [1,5,1]
[1,3,5,7,4,2,6] => [1,4,2]
[1,3,5,7,4,6,2] => [1,5,1]
[1,3,5,7,6,2,4] => [1,3,3]
[1,3,5,7,6,4,2] => [1,3,2,1]
[1,3,6,2,4,5,7] => [1,6]
[1,3,6,2,4,7,5] => [1,4,2]
[1,3,6,2,5,4,7] => [1,4,2]
[1,3,6,2,5,7,4] => [1,4,2]
[1,3,6,2,7,4,5] => [1,3,3]
[1,3,6,2,7,5,4] => [1,3,2,1]
[1,3,6,4,2,5,7] => [1,3,3]
[1,3,6,4,2,7,5] => [1,3,1,2]
[1,3,6,4,5,2,7] => [1,4,2]
[1,3,6,4,5,7,2] => [1,4,2]
[1,3,6,4,7,2,5] => [1,3,3]
[1,3,6,4,7,5,2] => [1,3,2,1]
[1,3,6,5,2,4,7] => [1,2,4]
[1,3,6,5,2,7,4] => [1,2,2,2]
[1,3,6,5,4,2,7] => [1,2,2,2]
[1,3,6,5,4,7,2] => [1,2,2,2]
[1,3,6,5,7,2,4] => [1,2,4]
[1,3,6,5,7,4,2] => [1,2,3,1]
[1,3,6,7,2,4,5] => [1,6]
[1,3,6,7,2,5,4] => [1,5,1]
[1,3,6,7,4,2,5] => [1,4,2]
[1,3,6,7,4,5,2] => [1,5,1]
[1,3,6,7,5,2,4] => [1,4,2]
[1,3,6,7,5,4,2] => [1,4,1,1]
[1,3,7,2,4,5,6] => [1,6]
[1,3,7,2,4,6,5] => [1,5,1]
[1,3,7,2,5,4,6] => [1,4,2]
[1,3,7,2,5,6,4] => [1,5,1]
[1,3,7,2,6,4,5] => [1,3,3]
[1,3,7,2,6,5,4] => [1,3,2,1]
[1,3,7,4,2,5,6] => [1,3,3]
[1,3,7,4,2,6,5] => [1,3,2,1]
[1,3,7,4,5,2,6] => [1,4,2]
[1,3,7,4,5,6,2] => [1,5,1]
[1,3,7,4,6,2,5] => [1,3,3]
[1,3,7,4,6,5,2] => [1,3,2,1]
[1,3,7,5,2,4,6] => [1,2,4]
[1,3,7,5,2,6,4] => [1,2,3,1]
[1,3,7,5,4,2,6] => [1,2,2,2]
[1,3,7,5,4,6,2] => [1,2,3,1]
[1,3,7,5,6,2,4] => [1,2,4]
[1,3,7,5,6,4,2] => [1,2,3,1]
[1,3,7,6,2,4,5] => [1,2,4]
[1,3,7,6,2,5,4] => [1,2,3,1]
[1,3,7,6,4,2,5] => [1,2,2,2]
[1,3,7,6,4,5,2] => [1,2,3,1]
[1,3,7,6,5,2,4] => [1,2,2,2]
[1,3,7,6,5,4,2] => [1,2,2,1,1]
[1,4,2,3,5,6,7] => [1,6]
[1,4,2,3,5,7,6] => [1,4,2]
[1,4,2,3,6,5,7] => [1,3,3]
[1,4,2,3,6,7,5] => [1,3,3]
[1,4,2,3,7,5,6] => [1,3,3]
[1,4,2,3,7,6,5] => [1,3,2,1]
[1,4,2,5,3,6,7] => [1,2,4]
[1,4,2,5,3,7,6] => [1,2,2,2]
[1,4,2,5,6,3,7] => [1,2,4]
[1,4,2,5,6,7,3] => [1,2,4]
[1,4,2,5,7,3,6] => [1,2,4]
[1,4,2,5,7,6,3] => [1,2,3,1]
[1,4,2,6,3,5,7] => [1,2,4]
[1,4,2,6,3,7,5] => [1,2,2,2]
[1,4,2,6,5,3,7] => [1,2,2,2]
[1,4,2,6,5,7,3] => [1,2,2,2]
[1,4,2,6,7,3,5] => [1,2,4]
[1,4,2,6,7,5,3] => [1,2,3,1]
[1,4,2,7,3,5,6] => [1,2,4]
[1,4,2,7,3,6,5] => [1,2,3,1]
[1,4,2,7,5,3,6] => [1,2,2,2]
[1,4,2,7,5,6,3] => [1,2,3,1]
[1,4,2,7,6,3,5] => [1,2,1,3]
[1,4,2,7,6,5,3] => [1,2,1,2,1]
[1,4,3,2,5,6,7] => [1,2,4]
[1,4,3,2,5,7,6] => [1,2,2,2]
[1,4,3,2,6,5,7] => [1,2,1,3]
[1,4,3,2,6,7,5] => [1,2,1,3]
[1,4,3,2,7,5,6] => [1,2,1,3]
[1,4,3,2,7,6,5] => [1,2,1,2,1]
[1,4,3,5,2,6,7] => [1,2,4]
[1,4,3,5,2,7,6] => [1,2,2,2]
[1,4,3,5,6,2,7] => [1,2,4]
[1,4,3,5,6,7,2] => [1,2,4]
[1,4,3,5,7,2,6] => [1,2,4]
[1,4,3,5,7,6,2] => [1,2,3,1]
[1,4,3,6,2,5,7] => [1,2,4]
[1,4,3,6,2,7,5] => [1,2,2,2]
[1,4,3,6,5,2,7] => [1,2,2,2]
[1,4,3,6,5,7,2] => [1,2,2,2]
[1,4,3,6,7,2,5] => [1,2,4]
[1,4,3,6,7,5,2] => [1,2,3,1]
[1,4,3,7,2,5,6] => [1,2,4]
[1,4,3,7,2,6,5] => [1,2,3,1]
[1,4,3,7,5,2,6] => [1,2,2,2]
[1,4,3,7,5,6,2] => [1,2,3,1]
[1,4,3,7,6,2,5] => [1,2,1,3]
[1,4,3,7,6,5,2] => [1,2,1,2,1]
[1,4,5,2,3,6,7] => [1,6]
[1,4,5,2,3,7,6] => [1,4,2]
[1,4,5,2,6,3,7] => [1,3,3]
[1,4,5,2,6,7,3] => [1,3,3]
[1,4,5,2,7,3,6] => [1,3,3]
[1,4,5,2,7,6,3] => [1,3,2,1]
[1,4,5,3,2,6,7] => [1,3,3]
[1,4,5,3,2,7,6] => [1,3,1,2]
[1,4,5,3,6,2,7] => [1,3,3]
[1,4,5,3,6,7,2] => [1,3,3]
[1,4,5,3,7,2,6] => [1,3,3]
[1,4,5,3,7,6,2] => [1,3,2,1]
[1,4,5,6,2,3,7] => [1,6]
[1,4,5,6,2,7,3] => [1,4,2]
[1,4,5,6,3,2,7] => [1,4,2]
[1,4,5,6,3,7,2] => [1,4,2]
[1,4,5,6,7,2,3] => [1,6]
[1,4,5,6,7,3,2] => [1,5,1]
[1,4,5,7,2,3,6] => [1,6]
[1,4,5,7,2,6,3] => [1,5,1]
[1,4,5,7,3,2,6] => [1,4,2]
[1,4,5,7,3,6,2] => [1,5,1]
[1,4,5,7,6,2,3] => [1,3,3]
[1,4,5,7,6,3,2] => [1,3,2,1]
[1,4,6,2,3,5,7] => [1,6]
[1,4,6,2,3,7,5] => [1,4,2]
[1,4,6,2,5,3,7] => [1,4,2]
[1,4,6,2,5,7,3] => [1,4,2]
[1,4,6,2,7,3,5] => [1,3,3]
[1,4,6,2,7,5,3] => [1,3,2,1]
[1,4,6,3,2,5,7] => [1,3,3]
[1,4,6,3,2,7,5] => [1,3,1,2]
[1,4,6,3,5,2,7] => [1,4,2]
[1,4,6,3,5,7,2] => [1,4,2]
[1,4,6,3,7,2,5] => [1,3,3]
[1,4,6,3,7,5,2] => [1,3,2,1]
[1,4,6,5,2,3,7] => [1,2,4]
[1,4,6,5,2,7,3] => [1,2,2,2]
[1,4,6,5,3,2,7] => [1,2,2,2]

-----------------------------------------------------------------------------
Created: Feb 20, 2022 at 19:42 by Martin Rubey

-----------------------------------------------------------------------------
Last Updated: Feb 20, 2022 at 19:42 by Martin Rubey