************************************************************************
* 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: Mp00204
------------------------------------------------------------------------
Map name: LLPS
------------------------------------------------------------------------
Domain: Permutations
------------------------------------------------------------------------
Codomain: Integer partitions
------------------------------------------------------------------------
Description: The Lewis-Lyu-Pylyavskyy-Sen shape of a permutation.
An ascent in a sequence $u = (u_1, u_2, \ldots)$ is an index $i$ such that $u_i < u_{i+1}$. Let $\mathrm{asc}(u)$ denote the number of ascents of $u$, and let
$$\mathrm{asc}^{*}(u) := \begin{cases} 0 &\textrm{if u is empty}, \\ 1 + \mathrm{asc}(u) &\textrm{otherwise}.\end{cases}$$
Given a permutation $w$ in the symmetric group $\mathfrak{S}_n$, define
$A'_k := \max_{u_1, \ldots, u_k} (\mathrm{asc}^{*}(u_1) + \cdots + \mathrm{asc}^{*}(u_k))$
where the maximum is taken over disjoint subsequences ${u_i}$ of $w$.
Then $A'_1, A'_2-A'_1, A'_3-A'_2,\dots$ is a partition of $n$. Its conjugate is the Lewis-Lyu-Pylyavskyy-Sen shape of a permutation.
------------------------------------------------------------------------
References: [1] Lewis, J., Lyu, H., Pylyavskyy, P., Sen, A. Scaling limit of soliton lengths in a multicolor box-ball system [[arXiv:1911.04458]]
------------------------------------------------------------------------
Code:
def mapping(pi):
to_standard = sage.combinat.permutation.to_standard
def llis(u):
if len(u) == 1:
return 1
if len(u) == 2:
if u[0] < u[1]:
return 2
return 1
if len(u) == 3:
if u[0] < u[1] < u[2]:
return 3
if u[0] > u[1] > u[2]:
return 1
return 2
return to_standard(u).longest_increasing_subsequence_length()
la = []
n = len(pi)
t = 0
pi = pi.reverse()
for k in range(1, n+1):
a = 0
for p in Compositions(n, length=k):
b = [sum(p[:i]) for i in range(k+1)]
s = sum(llis(pi[b[i]:b[i+1]]) for i in range(k))
a = max(a, s)
d = a - t
if a == t:
return Partition(la)
la.append(d)
t = a
return Partition(la)
------------------------------------------------------------------------
Map images:
[1] => [1]
[1,2] => [1,1]
[2,1] => [2]
[1,2,3] => [1,1,1]
[1,3,2] => [2,1]
[2,1,3] => [2,1]
[2,3,1] => [2,1]
[3,1,2] => [2,1]
[3,2,1] => [3]
[1,2,3,4] => [1,1,1,1]
[1,2,4,3] => [2,1,1]
[1,3,2,4] => [2,1,1]
[1,3,4,2] => [2,1,1]
[1,4,2,3] => [2,1,1]
[1,4,3,2] => [3,1]
[2,1,3,4] => [2,1,1]
[2,1,4,3] => [2,2]
[2,3,1,4] => [2,1,1]
[2,3,4,1] => [2,1,1]
[2,4,1,3] => [2,1,1]
[2,4,3,1] => [3,1]
[3,1,2,4] => [2,1,1]
[3,1,4,2] => [2,2]
[3,2,1,4] => [3,1]
[3,2,4,1] => [3,1]
[3,4,1,2] => [2,1,1]
[3,4,2,1] => [3,1]
[4,1,2,3] => [2,1,1]
[4,1,3,2] => [3,1]
[4,2,1,3] => [3,1]
[4,2,3,1] => [3,1]
[4,3,1,2] => [3,1]
[4,3,2,1] => [4]
[1,2,3,4,5] => [1,1,1,1,1]
[1,2,3,5,4] => [2,1,1,1]
[1,2,4,3,5] => [2,1,1,1]
[1,2,4,5,3] => [2,1,1,1]
[1,2,5,3,4] => [2,1,1,1]
[1,2,5,4,3] => [3,1,1]
[1,3,2,4,5] => [2,1,1,1]
[1,3,2,5,4] => [2,2,1]
[1,3,4,2,5] => [2,1,1,1]
[1,3,4,5,2] => [2,1,1,1]
[1,3,5,2,4] => [2,1,1,1]
[1,3,5,4,2] => [3,1,1]
[1,4,2,3,5] => [2,1,1,1]
[1,4,2,5,3] => [2,2,1]
[1,4,3,2,5] => [3,1,1]
[1,4,3,5,2] => [3,1,1]
[1,4,5,2,3] => [2,1,1,1]
[1,4,5,3,2] => [3,1,1]
[1,5,2,3,4] => [2,1,1,1]
[1,5,2,4,3] => [3,1,1]
[1,5,3,2,4] => [3,1,1]
[1,5,3,4,2] => [3,1,1]
[1,5,4,2,3] => [3,1,1]
[1,5,4,3,2] => [4,1]
[2,1,3,4,5] => [2,1,1,1]
[2,1,3,5,4] => [2,2,1]
[2,1,4,3,5] => [2,2,1]
[2,1,4,5,3] => [2,2,1]
[2,1,5,3,4] => [2,2,1]
[2,1,5,4,3] => [3,2]
[2,3,1,4,5] => [2,1,1,1]
[2,3,1,5,4] => [2,2,1]
[2,3,4,1,5] => [2,1,1,1]
[2,3,4,5,1] => [2,1,1,1]
[2,3,5,1,4] => [2,1,1,1]
[2,3,5,4,1] => [3,1,1]
[2,4,1,3,5] => [2,1,1,1]
[2,4,1,5,3] => [2,2,1]
[2,4,3,1,5] => [3,1,1]
[2,4,3,5,1] => [3,1,1]
[2,4,5,1,3] => [2,1,1,1]
[2,4,5,3,1] => [3,1,1]
[2,5,1,3,4] => [2,1,1,1]
[2,5,1,4,3] => [3,1,1]
[2,5,3,1,4] => [3,1,1]
[2,5,3,4,1] => [3,1,1]
[2,5,4,1,3] => [3,1,1]
[2,5,4,3,1] => [4,1]
[3,1,2,4,5] => [2,1,1,1]
[3,1,2,5,4] => [2,2,1]
[3,1,4,2,5] => [2,2,1]
[3,1,4,5,2] => [2,2,1]
[3,1,5,2,4] => [2,2,1]
[3,1,5,4,2] => [3,2]
[3,2,1,4,5] => [3,1,1]
[3,2,1,5,4] => [3,2]
[3,2,4,1,5] => [3,1,1]
[3,2,4,5,1] => [3,1,1]
[3,2,5,1,4] => [3,1,1]
[3,2,5,4,1] => [3,2]
[3,4,1,2,5] => [2,1,1,1]
[3,4,1,5,2] => [2,2,1]
[3,4,2,1,5] => [3,1,1]
[3,4,2,5,1] => [3,1,1]
[3,4,5,1,2] => [2,1,1,1]
[3,4,5,2,1] => [3,1,1]
[3,5,1,2,4] => [2,1,1,1]
[3,5,1,4,2] => [3,1,1]
[3,5,2,1,4] => [3,1,1]
[3,5,2,4,1] => [3,1,1]
[3,5,4,1,2] => [3,1,1]
[3,5,4,2,1] => [4,1]
[4,1,2,3,5] => [2,1,1,1]
[4,1,2,5,3] => [2,2,1]
[4,1,3,2,5] => [3,1,1]
[4,1,3,5,2] => [3,1,1]
[4,1,5,2,3] => [2,2,1]
[4,1,5,3,2] => [3,2]
[4,2,1,3,5] => [3,1,1]
[4,2,1,5,3] => [3,2]
[4,2,3,1,5] => [3,1,1]
[4,2,3,5,1] => [3,1,1]
[4,2,5,1,3] => [3,1,1]
[4,2,5,3,1] => [3,2]
[4,3,1,2,5] => [3,1,1]
[4,3,1,5,2] => [3,2]
[4,3,2,1,5] => [4,1]
[4,3,2,5,1] => [4,1]
[4,3,5,1,2] => [3,1,1]
[4,3,5,2,1] => [4,1]
[4,5,1,2,3] => [2,1,1,1]
[4,5,1,3,2] => [3,1,1]
[4,5,2,1,3] => [3,1,1]
[4,5,2,3,1] => [3,1,1]
[4,5,3,1,2] => [3,1,1]
[4,5,3,2,1] => [4,1]
[5,1,2,3,4] => [2,1,1,1]
[5,1,2,4,3] => [3,1,1]
[5,1,3,2,4] => [3,1,1]
[5,1,3,4,2] => [3,1,1]
[5,1,4,2,3] => [3,1,1]
[5,1,4,3,2] => [4,1]
[5,2,1,3,4] => [3,1,1]
[5,2,1,4,3] => [3,2]
[5,2,3,1,4] => [3,1,1]
[5,2,3,4,1] => [3,1,1]
[5,2,4,1,3] => [3,1,1]
[5,2,4,3,1] => [4,1]
[5,3,1,2,4] => [3,1,1]
[5,3,1,4,2] => [3,2]
[5,3,2,1,4] => [4,1]
[5,3,2,4,1] => [4,1]
[5,3,4,1,2] => [3,1,1]
[5,3,4,2,1] => [4,1]
[5,4,1,2,3] => [3,1,1]
[5,4,1,3,2] => [4,1]
[5,4,2,1,3] => [4,1]
[5,4,2,3,1] => [4,1]
[5,4,3,1,2] => [4,1]
[5,4,3,2,1] => [5]
[1,2,3,4,5,6] => [1,1,1,1,1,1]
[1,2,3,4,6,5] => [2,1,1,1,1]
[1,2,3,5,4,6] => [2,1,1,1,1]
[1,2,3,5,6,4] => [2,1,1,1,1]
[1,2,3,6,4,5] => [2,1,1,1,1]
[1,2,3,6,5,4] => [3,1,1,1]
[1,2,4,3,5,6] => [2,1,1,1,1]
[1,2,4,3,6,5] => [2,2,1,1]
[1,2,4,5,3,6] => [2,1,1,1,1]
[1,2,4,5,6,3] => [2,1,1,1,1]
[1,2,4,6,3,5] => [2,1,1,1,1]
[1,2,4,6,5,3] => [3,1,1,1]
[1,2,5,3,4,6] => [2,1,1,1,1]
[1,2,5,3,6,4] => [2,2,1,1]
[1,2,5,4,3,6] => [3,1,1,1]
[1,2,5,4,6,3] => [3,1,1,1]
[1,2,5,6,3,4] => [2,1,1,1,1]
[1,2,5,6,4,3] => [3,1,1,1]
[1,2,6,3,4,5] => [2,1,1,1,1]
[1,2,6,3,5,4] => [3,1,1,1]
[1,2,6,4,3,5] => [3,1,1,1]
[1,2,6,4,5,3] => [3,1,1,1]
[1,2,6,5,3,4] => [3,1,1,1]
[1,2,6,5,4,3] => [4,1,1]
[1,3,2,4,5,6] => [2,1,1,1,1]
[1,3,2,4,6,5] => [2,2,1,1]
[1,3,2,5,4,6] => [2,2,1,1]
[1,3,2,5,6,4] => [2,2,1,1]
[1,3,2,6,4,5] => [2,2,1,1]
[1,3,2,6,5,4] => [3,2,1]
[1,3,4,2,5,6] => [2,1,1,1,1]
[1,3,4,2,6,5] => [2,2,1,1]
[1,3,4,5,2,6] => [2,1,1,1,1]
[1,3,4,5,6,2] => [2,1,1,1,1]
[1,3,4,6,2,5] => [2,1,1,1,1]
[1,3,4,6,5,2] => [3,1,1,1]
[1,3,5,2,4,6] => [2,1,1,1,1]
[1,3,5,2,6,4] => [2,2,1,1]
[1,3,5,4,2,6] => [3,1,1,1]
[1,3,5,4,6,2] => [3,1,1,1]
[1,3,5,6,2,4] => [2,1,1,1,1]
[1,3,5,6,4,2] => [3,1,1,1]
[1,3,6,2,4,5] => [2,1,1,1,1]
[1,3,6,2,5,4] => [3,1,1,1]
[1,3,6,4,2,5] => [3,1,1,1]
[1,3,6,4,5,2] => [3,1,1,1]
[1,3,6,5,2,4] => [3,1,1,1]
[1,3,6,5,4,2] => [4,1,1]
[1,4,2,3,5,6] => [2,1,1,1,1]
[1,4,2,3,6,5] => [2,2,1,1]
[1,4,2,5,3,6] => [2,2,1,1]
[1,4,2,5,6,3] => [2,2,1,1]
[1,4,2,6,3,5] => [2,2,1,1]
[1,4,2,6,5,3] => [3,2,1]
[1,4,3,2,5,6] => [3,1,1,1]
[1,4,3,2,6,5] => [3,2,1]
[1,4,3,5,2,6] => [3,1,1,1]
[1,4,3,5,6,2] => [3,1,1,1]
[1,4,3,6,2,5] => [3,1,1,1]
[1,4,3,6,5,2] => [3,2,1]
[1,4,5,2,3,6] => [2,1,1,1,1]
[1,4,5,2,6,3] => [2,2,1,1]
[1,4,5,3,2,6] => [3,1,1,1]
[1,4,5,3,6,2] => [3,1,1,1]
[1,4,5,6,2,3] => [2,1,1,1,1]
[1,4,5,6,3,2] => [3,1,1,1]
[1,4,6,2,3,5] => [2,1,1,1,1]
[1,4,6,2,5,3] => [3,1,1,1]
[1,4,6,3,2,5] => [3,1,1,1]
[1,4,6,3,5,2] => [3,1,1,1]
[1,4,6,5,2,3] => [3,1,1,1]
[1,4,6,5,3,2] => [4,1,1]
[1,5,2,3,4,6] => [2,1,1,1,1]
[1,5,2,3,6,4] => [2,2,1,1]
[1,5,2,4,3,6] => [3,1,1,1]
[1,5,2,4,6,3] => [3,1,1,1]
[1,5,2,6,3,4] => [2,2,1,1]
[1,5,2,6,4,3] => [3,2,1]
[1,5,3,2,4,6] => [3,1,1,1]
[1,5,3,2,6,4] => [3,2,1]
[1,5,3,4,2,6] => [3,1,1,1]
[1,5,3,4,6,2] => [3,1,1,1]
[1,5,3,6,2,4] => [3,1,1,1]
[1,5,3,6,4,2] => [3,2,1]
[1,5,4,2,3,6] => [3,1,1,1]
[1,5,4,2,6,3] => [3,2,1]
[1,5,4,3,2,6] => [4,1,1]
[1,5,4,3,6,2] => [4,1,1]
[1,5,4,6,2,3] => [3,1,1,1]
[1,5,4,6,3,2] => [4,1,1]
[1,5,6,2,3,4] => [2,1,1,1,1]
[1,5,6,2,4,3] => [3,1,1,1]
[1,5,6,3,2,4] => [3,1,1,1]
[1,5,6,3,4,2] => [3,1,1,1]
[1,5,6,4,2,3] => [3,1,1,1]
[1,5,6,4,3,2] => [4,1,1]
[1,6,2,3,4,5] => [2,1,1,1,1]
[1,6,2,3,5,4] => [3,1,1,1]
[1,6,2,4,3,5] => [3,1,1,1]
[1,6,2,4,5,3] => [3,1,1,1]
[1,6,2,5,3,4] => [3,1,1,1]
[1,6,2,5,4,3] => [4,1,1]
[1,6,3,2,4,5] => [3,1,1,1]
[1,6,3,2,5,4] => [3,2,1]
[1,6,3,4,2,5] => [3,1,1,1]
[1,6,3,4,5,2] => [3,1,1,1]
[1,6,3,5,2,4] => [3,1,1,1]
[1,6,3,5,4,2] => [4,1,1]
[1,6,4,2,3,5] => [3,1,1,1]
[1,6,4,2,5,3] => [3,2,1]
[1,6,4,3,2,5] => [4,1,1]
[1,6,4,3,5,2] => [4,1,1]
[1,6,4,5,2,3] => [3,1,1,1]
[1,6,4,5,3,2] => [4,1,1]
[1,6,5,2,3,4] => [3,1,1,1]
[1,6,5,2,4,3] => [4,1,1]
[1,6,5,3,2,4] => [4,1,1]
[1,6,5,3,4,2] => [4,1,1]
[1,6,5,4,2,3] => [4,1,1]
[1,6,5,4,3,2] => [5,1]
[2,1,3,4,5,6] => [2,1,1,1,1]
[2,1,3,4,6,5] => [2,2,1,1]
[2,1,3,5,4,6] => [2,2,1,1]
[2,1,3,5,6,4] => [2,2,1,1]
[2,1,3,6,4,5] => [2,2,1,1]
[2,1,3,6,5,4] => [3,2,1]
[2,1,4,3,5,6] => [2,2,1,1]
[2,1,4,3,6,5] => [2,2,2]
[2,1,4,5,3,6] => [2,2,1,1]
[2,1,4,5,6,3] => [2,2,1,1]
[2,1,4,6,3,5] => [2,2,1,1]
[2,1,4,6,5,3] => [3,2,1]
[2,1,5,3,4,6] => [2,2,1,1]
[2,1,5,3,6,4] => [2,2,2]
[2,1,5,4,3,6] => [3,2,1]
[2,1,5,4,6,3] => [3,2,1]
[2,1,5,6,3,4] => [2,2,1,1]
[2,1,5,6,4,3] => [3,2,1]
[2,1,6,3,4,5] => [2,2,1,1]
[2,1,6,3,5,4] => [3,2,1]
[2,1,6,4,3,5] => [3,2,1]
[2,1,6,4,5,3] => [3,2,1]
[2,1,6,5,3,4] => [3,2,1]
[2,1,6,5,4,3] => [4,2]
[2,3,1,4,5,6] => [2,1,1,1,1]
[2,3,1,4,6,5] => [2,2,1,1]
[2,3,1,5,4,6] => [2,2,1,1]
[2,3,1,5,6,4] => [2,2,1,1]
[2,3,1,6,4,5] => [2,2,1,1]
[2,3,1,6,5,4] => [3,2,1]
[2,3,4,1,5,6] => [2,1,1,1,1]
[2,3,4,1,6,5] => [2,2,1,1]
[2,3,4,5,1,6] => [2,1,1,1,1]
[2,3,4,5,6,1] => [2,1,1,1,1]
[2,3,4,6,1,5] => [2,1,1,1,1]
[2,3,4,6,5,1] => [3,1,1,1]
[2,3,5,1,4,6] => [2,1,1,1,1]
[2,3,5,1,6,4] => [2,2,1,1]
[2,3,5,4,1,6] => [3,1,1,1]
[2,3,5,4,6,1] => [3,1,1,1]
[2,3,5,6,1,4] => [2,1,1,1,1]
[2,3,5,6,4,1] => [3,1,1,1]
[2,3,6,1,4,5] => [2,1,1,1,1]
[2,3,6,1,5,4] => [3,1,1,1]
[2,3,6,4,1,5] => [3,1,1,1]
[2,3,6,4,5,1] => [3,1,1,1]
[2,3,6,5,1,4] => [3,1,1,1]
[2,3,6,5,4,1] => [4,1,1]
[2,4,1,3,5,6] => [2,1,1,1,1]
[2,4,1,3,6,5] => [2,2,1,1]
[2,4,1,5,3,6] => [2,2,1,1]
[2,4,1,5,6,3] => [2,2,1,1]
[2,4,1,6,3,5] => [2,2,1,1]
[2,4,1,6,5,3] => [3,2,1]
[2,4,3,1,5,6] => [3,1,1,1]
[2,4,3,1,6,5] => [3,2,1]
[2,4,3,5,1,6] => [3,1,1,1]
[2,4,3,5,6,1] => [3,1,1,1]
[2,4,3,6,1,5] => [3,1,1,1]
[2,4,3,6,5,1] => [3,2,1]
[2,4,5,1,3,6] => [2,1,1,1,1]
[2,4,5,1,6,3] => [2,2,1,1]
[2,4,5,3,1,6] => [3,1,1,1]
[2,4,5,3,6,1] => [3,1,1,1]
[2,4,5,6,1,3] => [2,1,1,1,1]
[2,4,5,6,3,1] => [3,1,1,1]
[2,4,6,1,3,5] => [2,1,1,1,1]
[2,4,6,1,5,3] => [3,1,1,1]
[2,4,6,3,1,5] => [3,1,1,1]
[2,4,6,3,5,1] => [3,1,1,1]
[2,4,6,5,1,3] => [3,1,1,1]
[2,4,6,5,3,1] => [4,1,1]
[2,5,1,3,4,6] => [2,1,1,1,1]
[2,5,1,3,6,4] => [2,2,1,1]
[2,5,1,4,3,6] => [3,1,1,1]
[2,5,1,4,6,3] => [3,1,1,1]
[2,5,1,6,3,4] => [2,2,1,1]
[2,5,1,6,4,3] => [3,2,1]
[2,5,3,1,4,6] => [3,1,1,1]
[2,5,3,1,6,4] => [3,2,1]
[2,5,3,4,1,6] => [3,1,1,1]
[2,5,3,4,6,1] => [3,1,1,1]
[2,5,3,6,1,4] => [3,1,1,1]
[2,5,3,6,4,1] => [3,2,1]
[2,5,4,1,3,6] => [3,1,1,1]
[2,5,4,1,6,3] => [3,2,1]
[2,5,4,3,1,6] => [4,1,1]
[2,5,4,3,6,1] => [4,1,1]
[2,5,4,6,1,3] => [3,1,1,1]
[2,5,4,6,3,1] => [4,1,1]
[2,5,6,1,3,4] => [2,1,1,1,1]
[2,5,6,1,4,3] => [3,1,1,1]
[2,5,6,3,1,4] => [3,1,1,1]
[2,5,6,3,4,1] => [3,1,1,1]
[2,5,6,4,1,3] => [3,1,1,1]
[2,5,6,4,3,1] => [4,1,1]
[2,6,1,3,4,5] => [2,1,1,1,1]
[2,6,1,3,5,4] => [3,1,1,1]
[2,6,1,4,3,5] => [3,1,1,1]
[2,6,1,4,5,3] => [3,1,1,1]
[2,6,1,5,3,4] => [3,1,1,1]
[2,6,1,5,4,3] => [4,1,1]
[2,6,3,1,4,5] => [3,1,1,1]
[2,6,3,1,5,4] => [3,2,1]
[2,6,3,4,1,5] => [3,1,1,1]
[2,6,3,4,5,1] => [3,1,1,1]
[2,6,3,5,1,4] => [3,1,1,1]
[2,6,3,5,4,1] => [4,1,1]
[2,6,4,1,3,5] => [3,1,1,1]
[2,6,4,1,5,3] => [3,2,1]
[2,6,4,3,1,5] => [4,1,1]
[2,6,4,3,5,1] => [4,1,1]
[2,6,4,5,1,3] => [3,1,1,1]
[2,6,4,5,3,1] => [4,1,1]
[2,6,5,1,3,4] => [3,1,1,1]
[2,6,5,1,4,3] => [4,1,1]
[2,6,5,3,1,4] => [4,1,1]
[2,6,5,3,4,1] => [4,1,1]
[2,6,5,4,1,3] => [4,1,1]
[2,6,5,4,3,1] => [5,1]
[3,1,2,4,5,6] => [2,1,1,1,1]
[3,1,2,4,6,5] => [2,2,1,1]
[3,1,2,5,4,6] => [2,2,1,1]
[3,1,2,5,6,4] => [2,2,1,1]
[3,1,2,6,4,5] => [2,2,1,1]
[3,1,2,6,5,4] => [3,2,1]
[3,1,4,2,5,6] => [2,2,1,1]
[3,1,4,2,6,5] => [2,2,2]
[3,1,4,5,2,6] => [2,2,1,1]
[3,1,4,5,6,2] => [2,2,1,1]
[3,1,4,6,2,5] => [2,2,1,1]
[3,1,4,6,5,2] => [3,2,1]
[3,1,5,2,4,6] => [2,2,1,1]
[3,1,5,2,6,4] => [2,2,2]
[3,1,5,4,2,6] => [3,2,1]
[3,1,5,4,6,2] => [3,2,1]
[3,1,5,6,2,4] => [2,2,1,1]
[3,1,5,6,4,2] => [3,2,1]
[3,1,6,2,4,5] => [2,2,1,1]
[3,1,6,2,5,4] => [3,2,1]
[3,1,6,4,2,5] => [3,2,1]
[3,1,6,4,5,2] => [3,2,1]
[3,1,6,5,2,4] => [3,2,1]
[3,1,6,5,4,2] => [4,2]
[3,2,1,4,5,6] => [3,1,1,1]
[3,2,1,4,6,5] => [3,2,1]
[3,2,1,5,4,6] => [3,2,1]
[3,2,1,5,6,4] => [3,2,1]
[3,2,1,6,4,5] => [3,2,1]
[3,2,1,6,5,4] => [3,3]
[3,2,4,1,5,6] => [3,1,1,1]
[3,2,4,1,6,5] => [3,2,1]
[3,2,4,5,1,6] => [3,1,1,1]
[3,2,4,5,6,1] => [3,1,1,1]
[3,2,4,6,1,5] => [3,1,1,1]
[3,2,4,6,5,1] => [3,2,1]
[3,2,5,1,4,6] => [3,1,1,1]
[3,2,5,1,6,4] => [3,2,1]
[3,2,5,4,1,6] => [3,2,1]
[3,2,5,4,6,1] => [3,2,1]
[3,2,5,6,1,4] => [3,1,1,1]
[3,2,5,6,4,1] => [3,2,1]
[3,2,6,1,4,5] => [3,1,1,1]
[3,2,6,1,5,4] => [3,2,1]
[3,2,6,4,1,5] => [3,2,1]
[3,2,6,4,5,1] => [3,2,1]
[3,2,6,5,1,4] => [3,2,1]
[3,2,6,5,4,1] => [4,2]
[3,4,1,2,5,6] => [2,1,1,1,1]
[3,4,1,2,6,5] => [2,2,1,1]
[3,4,1,5,2,6] => [2,2,1,1]
[3,4,1,5,6,2] => [2,2,1,1]
[3,4,1,6,2,5] => [2,2,1,1]
[3,4,1,6,5,2] => [3,2,1]
[3,4,2,1,5,6] => [3,1,1,1]
[3,4,2,1,6,5] => [3,2,1]
[3,4,2,5,1,6] => [3,1,1,1]
[3,4,2,5,6,1] => [3,1,1,1]
[3,4,2,6,1,5] => [3,1,1,1]
[3,4,2,6,5,1] => [3,2,1]
[3,4,5,1,2,6] => [2,1,1,1,1]
[3,4,5,1,6,2] => [2,2,1,1]
[3,4,5,2,1,6] => [3,1,1,1]
[3,4,5,2,6,1] => [3,1,1,1]
[3,4,5,6,1,2] => [2,1,1,1,1]
[3,4,5,6,2,1] => [3,1,1,1]
[3,4,6,1,2,5] => [2,1,1,1,1]
[3,4,6,1,5,2] => [3,1,1,1]
[3,4,6,2,1,5] => [3,1,1,1]
[3,4,6,2,5,1] => [3,1,1,1]
[3,4,6,5,1,2] => [3,1,1,1]
[3,4,6,5,2,1] => [4,1,1]
[3,5,1,2,4,6] => [2,1,1,1,1]
[3,5,1,2,6,4] => [2,2,1,1]
[3,5,1,4,2,6] => [3,1,1,1]
[3,5,1,4,6,2] => [3,1,1,1]
[3,5,1,6,2,4] => [2,2,1,1]
[3,5,1,6,4,2] => [3,2,1]
[3,5,2,1,4,6] => [3,1,1,1]
[3,5,2,1,6,4] => [3,2,1]
[3,5,2,4,1,6] => [3,1,1,1]
[3,5,2,4,6,1] => [3,1,1,1]
[3,5,2,6,1,4] => [3,1,1,1]
[3,5,2,6,4,1] => [3,2,1]
[3,5,4,1,2,6] => [3,1,1,1]
[3,5,4,1,6,2] => [3,2,1]
[3,5,4,2,1,6] => [4,1,1]
[3,5,4,2,6,1] => [4,1,1]
[3,5,4,6,1,2] => [3,1,1,1]
[3,5,4,6,2,1] => [4,1,1]
[3,5,6,1,2,4] => [2,1,1,1,1]
[3,5,6,1,4,2] => [3,1,1,1]
[3,5,6,2,1,4] => [3,1,1,1]
[3,5,6,2,4,1] => [3,1,1,1]
[3,5,6,4,1,2] => [3,1,1,1]
[3,5,6,4,2,1] => [4,1,1]
[3,6,1,2,4,5] => [2,1,1,1,1]
[3,6,1,2,5,4] => [3,1,1,1]
[3,6,1,4,2,5] => [3,1,1,1]
[3,6,1,4,5,2] => [3,1,1,1]
[3,6,1,5,2,4] => [3,1,1,1]
[3,6,1,5,4,2] => [4,1,1]
[3,6,2,1,4,5] => [3,1,1,1]
[3,6,2,1,5,4] => [3,2,1]
[3,6,2,4,1,5] => [3,1,1,1]
[3,6,2,4,5,1] => [3,1,1,1]
[3,6,2,5,1,4] => [3,1,1,1]
[3,6,2,5,4,1] => [4,1,1]
[3,6,4,1,2,5] => [3,1,1,1]
[3,6,4,1,5,2] => [3,2,1]
[3,6,4,2,1,5] => [4,1,1]
[3,6,4,2,5,1] => [4,1,1]
[3,6,4,5,1,2] => [3,1,1,1]
[3,6,4,5,2,1] => [4,1,1]
[3,6,5,1,2,4] => [3,1,1,1]
[3,6,5,1,4,2] => [4,1,1]
[3,6,5,2,1,4] => [4,1,1]
[3,6,5,2,4,1] => [4,1,1]
[3,6,5,4,1,2] => [4,1,1]
[3,6,5,4,2,1] => [5,1]
[4,1,2,3,5,6] => [2,1,1,1,1]
[4,1,2,3,6,5] => [2,2,1,1]
[4,1,2,5,3,6] => [2,2,1,1]
[4,1,2,5,6,3] => [2,2,1,1]
[4,1,2,6,3,5] => [2,2,1,1]
[4,1,2,6,5,3] => [3,2,1]
[4,1,3,2,5,6] => [3,1,1,1]
[4,1,3,2,6,5] => [3,2,1]
[4,1,3,5,2,6] => [3,1,1,1]
[4,1,3,5,6,2] => [3,1,1,1]
[4,1,3,6,2,5] => [3,1,1,1]
[4,1,3,6,5,2] => [3,2,1]
[4,1,5,2,3,6] => [2,2,1,1]
[4,1,5,2,6,3] => [2,2,2]
[4,1,5,3,2,6] => [3,2,1]
[4,1,5,3,6,2] => [3,2,1]
[4,1,5,6,2,3] => [2,2,1,1]
[4,1,5,6,3,2] => [3,2,1]
[4,1,6,2,3,5] => [2,2,1,1]
[4,1,6,2,5,3] => [3,2,1]
[4,1,6,3,2,5] => [3,2,1]
[4,1,6,3,5,2] => [3,2,1]
[4,1,6,5,2,3] => [3,2,1]
[4,1,6,5,3,2] => [4,2]
[4,2,1,3,5,6] => [3,1,1,1]
[4,2,1,3,6,5] => [3,2,1]
[4,2,1,5,3,6] => [3,2,1]
[4,2,1,5,6,3] => [3,2,1]
[4,2,1,6,3,5] => [3,2,1]
[4,2,1,6,5,3] => [3,3]
[4,2,3,1,5,6] => [3,1,1,1]
[4,2,3,1,6,5] => [3,2,1]
[4,2,3,5,1,6] => [3,1,1,1]
[4,2,3,5,6,1] => [3,1,1,1]
[4,2,3,6,1,5] => [3,1,1,1]
[4,2,3,6,5,1] => [3,2,1]
[4,2,5,1,3,6] => [3,1,1,1]
[4,2,5,1,6,3] => [3,2,1]
[4,2,5,3,1,6] => [3,2,1]
[4,2,5,3,6,1] => [3,2,1]
[4,2,5,6,1,3] => [3,1,1,1]
[4,2,5,6,3,1] => [3,2,1]
[4,2,6,1,3,5] => [3,1,1,1]
[4,2,6,1,5,3] => [3,2,1]
[4,2,6,3,1,5] => [3,2,1]
[4,2,6,3,5,1] => [3,2,1]
[4,2,6,5,1,3] => [3,2,1]
[4,2,6,5,3,1] => [4,2]
[4,3,1,2,5,6] => [3,1,1,1]
[4,3,1,2,6,5] => [3,2,1]
[4,3,1,5,2,6] => [3,2,1]
[4,3,1,5,6,2] => [3,2,1]
[4,3,1,6,2,5] => [3,2,1]
[4,3,1,6,5,2] => [3,3]
[4,3,2,1,5,6] => [4,1,1]
[4,3,2,1,6,5] => [4,2]
[4,3,2,5,1,6] => [4,1,1]
[4,3,2,5,6,1] => [4,1,1]
[4,3,2,6,1,5] => [4,1,1]
[4,3,2,6,5,1] => [4,2]
[4,3,5,1,2,6] => [3,1,1,1]
[4,3,5,1,6,2] => [3,2,1]
[4,3,5,2,1,6] => [4,1,1]
[4,3,5,2,6,1] => [4,1,1]
[4,3,5,6,1,2] => [3,1,1,1]
[4,3,5,6,2,1] => [4,1,1]
[4,3,6,1,2,5] => [3,1,1,1]
[4,3,6,1,5,2] => [3,2,1]
[4,3,6,2,1,5] => [4,1,1]
[4,3,6,2,5,1] => [4,1,1]
[4,3,6,5,1,2] => [3,2,1]
[4,3,6,5,2,1] => [4,2]
[4,5,1,2,3,6] => [2,1,1,1,1]
[4,5,1,2,6,3] => [2,2,1,1]
[4,5,1,3,2,6] => [3,1,1,1]
[4,5,1,3,6,2] => [3,1,1,1]
[4,5,1,6,2,3] => [2,2,1,1]
[4,5,1,6,3,2] => [3,2,1]
[4,5,2,1,3,6] => [3,1,1,1]
[4,5,2,1,6,3] => [3,2,1]
[4,5,2,3,1,6] => [3,1,1,1]
[4,5,2,3,6,1] => [3,1,1,1]
[4,5,2,6,1,3] => [3,1,1,1]
[4,5,2,6,3,1] => [3,2,1]
[4,5,3,1,2,6] => [3,1,1,1]
[4,5,3,1,6,2] => [3,2,1]
[4,5,3,2,1,6] => [4,1,1]
[4,5,3,2,6,1] => [4,1,1]
[4,5,3,6,1,2] => [3,1,1,1]
[4,5,3,6,2,1] => [4,1,1]
[4,5,6,1,2,3] => [2,1,1,1,1]
[4,5,6,1,3,2] => [3,1,1,1]
[4,5,6,2,1,3] => [3,1,1,1]
[4,5,6,2,3,1] => [3,1,1,1]
[4,5,6,3,1,2] => [3,1,1,1]
[4,5,6,3,2,1] => [4,1,1]
[4,6,1,2,3,5] => [2,1,1,1,1]
[4,6,1,2,5,3] => [3,1,1,1]
[4,6,1,3,2,5] => [3,1,1,1]
[4,6,1,3,5,2] => [3,1,1,1]
[4,6,1,5,2,3] => [3,1,1,1]
[4,6,1,5,3,2] => [4,1,1]
[4,6,2,1,3,5] => [3,1,1,1]
[4,6,2,1,5,3] => [3,2,1]
[4,6,2,3,1,5] => [3,1,1,1]
[4,6,2,3,5,1] => [3,1,1,1]
[4,6,2,5,1,3] => [3,1,1,1]
[4,6,2,5,3,1] => [4,1,1]
[4,6,3,1,2,5] => [3,1,1,1]
[4,6,3,1,5,2] => [3,2,1]
[4,6,3,2,1,5] => [4,1,1]
[4,6,3,2,5,1] => [4,1,1]
[4,6,3,5,1,2] => [3,1,1,1]
[4,6,3,5,2,1] => [4,1,1]
[4,6,5,1,2,3] => [3,1,1,1]
[4,6,5,1,3,2] => [4,1,1]
[4,6,5,2,1,3] => [4,1,1]
[4,6,5,2,3,1] => [4,1,1]
[4,6,5,3,1,2] => [4,1,1]
[4,6,5,3,2,1] => [5,1]
[5,1,2,3,4,6] => [2,1,1,1,1]
[5,1,2,3,6,4] => [2,2,1,1]
[5,1,2,4,3,6] => [3,1,1,1]
[5,1,2,4,6,3] => [3,1,1,1]
[5,1,2,6,3,4] => [2,2,1,1]
[5,1,2,6,4,3] => [3,2,1]
[5,1,3,2,4,6] => [3,1,1,1]
[5,1,3,2,6,4] => [3,2,1]
[5,1,3,4,2,6] => [3,1,1,1]
[5,1,3,4,6,2] => [3,1,1,1]
[5,1,3,6,2,4] => [3,1,1,1]
[5,1,3,6,4,2] => [3,2,1]
[5,1,4,2,3,6] => [3,1,1,1]
[5,1,4,2,6,3] => [3,2,1]
[5,1,4,3,2,6] => [4,1,1]
[5,1,4,3,6,2] => [4,1,1]
[5,1,4,6,2,3] => [3,1,1,1]
[5,1,4,6,3,2] => [4,1,1]
[5,1,6,2,3,4] => [2,2,1,1]
[5,1,6,2,4,3] => [3,2,1]
[5,1,6,3,2,4] => [3,2,1]
[5,1,6,3,4,2] => [3,2,1]
[5,1,6,4,2,3] => [3,2,1]
[5,1,6,4,3,2] => [4,2]
[5,2,1,3,4,6] => [3,1,1,1]
[5,2,1,3,6,4] => [3,2,1]
[5,2,1,4,3,6] => [3,2,1]
[5,2,1,4,6,3] => [3,2,1]
[5,2,1,6,3,4] => [3,2,1]
[5,2,1,6,4,3] => [3,3]
[5,2,3,1,4,6] => [3,1,1,1]
[5,2,3,1,6,4] => [3,2,1]
[5,2,3,4,1,6] => [3,1,1,1]
[5,2,3,4,6,1] => [3,1,1,1]
[5,2,3,6,1,4] => [3,1,1,1]
[5,2,3,6,4,1] => [3,2,1]
[5,2,4,1,3,6] => [3,1,1,1]
[5,2,4,1,6,3] => [3,2,1]
[5,2,4,3,1,6] => [4,1,1]
[5,2,4,3,6,1] => [4,1,1]
[5,2,4,6,1,3] => [3,1,1,1]
[5,2,4,6,3,1] => [4,1,1]
[5,2,6,1,3,4] => [3,1,1,1]
[5,2,6,1,4,3] => [3,2,1]
[5,2,6,3,1,4] => [3,2,1]
[5,2,6,3,4,1] => [3,2,1]
[5,2,6,4,1,3] => [3,2,1]
[5,2,6,4,3,1] => [4,2]
[5,3,1,2,4,6] => [3,1,1,1]
[5,3,1,2,6,4] => [3,2,1]
[5,3,1,4,2,6] => [3,2,1]
[5,3,1,4,6,2] => [3,2,1]
[5,3,1,6,2,4] => [3,2,1]
[5,3,1,6,4,2] => [3,3]
[5,3,2,1,4,6] => [4,1,1]
[5,3,2,1,6,4] => [4,2]
[5,3,2,4,1,6] => [4,1,1]
[5,3,2,4,6,1] => [4,1,1]
[5,3,2,6,1,4] => [4,1,1]
[5,3,2,6,4,1] => [4,2]
[5,3,4,1,2,6] => [3,1,1,1]
[5,3,4,1,6,2] => [3,2,1]
[5,3,4,2,1,6] => [4,1,1]
[5,3,4,2,6,1] => [4,1,1]
[5,3,4,6,1,2] => [3,1,1,1]
[5,3,4,6,2,1] => [4,1,1]
[5,3,6,1,2,4] => [3,1,1,1]
[5,3,6,1,4,2] => [3,2,1]
[5,3,6,2,1,4] => [4,1,1]
[5,3,6,2,4,1] => [4,1,1]
[5,3,6,4,1,2] => [3,2,1]
[5,3,6,4,2,1] => [4,2]
[5,4,1,2,3,6] => [3,1,1,1]
[5,4,1,2,6,3] => [3,2,1]
[5,4,1,3,2,6] => [4,1,1]
[5,4,1,3,6,2] => [4,1,1]
[5,4,1,6,2,3] => [3,2,1]
[5,4,1,6,3,2] => [4,2]
[5,4,2,1,3,6] => [4,1,1]
[5,4,2,1,6,3] => [4,2]
[5,4,2,3,1,6] => [4,1,1]
[5,4,2,3,6,1] => [4,1,1]
[5,4,2,6,1,3] => [4,1,1]
[5,4,2,6,3,1] => [4,2]
[5,4,3,1,2,6] => [4,1,1]
[5,4,3,1,6,2] => [4,2]
[5,4,3,2,1,6] => [5,1]
[5,4,3,2,6,1] => [5,1]
[5,4,3,6,1,2] => [4,1,1]
[5,4,3,6,2,1] => [5,1]
[5,4,6,1,2,3] => [3,1,1,1]
[5,4,6,1,3,2] => [4,1,1]
[5,4,6,2,1,3] => [4,1,1]
[5,4,6,2,3,1] => [4,1,1]
[5,4,6,3,1,2] => [4,1,1]
[5,4,6,3,2,1] => [5,1]
[5,6,1,2,3,4] => [2,1,1,1,1]
[5,6,1,2,4,3] => [3,1,1,1]
[5,6,1,3,2,4] => [3,1,1,1]
[5,6,1,3,4,2] => [3,1,1,1]
[5,6,1,4,2,3] => [3,1,1,1]
[5,6,1,4,3,2] => [4,1,1]
[5,6,2,1,3,4] => [3,1,1,1]
[5,6,2,1,4,3] => [3,2,1]
[5,6,2,3,1,4] => [3,1,1,1]
[5,6,2,3,4,1] => [3,1,1,1]
[5,6,2,4,1,3] => [3,1,1,1]
[5,6,2,4,3,1] => [4,1,1]
[5,6,3,1,2,4] => [3,1,1,1]
[5,6,3,1,4,2] => [3,2,1]
[5,6,3,2,1,4] => [4,1,1]
[5,6,3,2,4,1] => [4,1,1]
[5,6,3,4,1,2] => [3,1,1,1]
[5,6,3,4,2,1] => [4,1,1]
[5,6,4,1,2,3] => [3,1,1,1]
[5,6,4,1,3,2] => [4,1,1]
[5,6,4,2,1,3] => [4,1,1]
[5,6,4,2,3,1] => [4,1,1]
[5,6,4,3,1,2] => [4,1,1]
[5,6,4,3,2,1] => [5,1]
[6,1,2,3,4,5] => [2,1,1,1,1]
[6,1,2,3,5,4] => [3,1,1,1]
[6,1,2,4,3,5] => [3,1,1,1]
[6,1,2,4,5,3] => [3,1,1,1]
[6,1,2,5,3,4] => [3,1,1,1]
[6,1,2,5,4,3] => [4,1,1]
[6,1,3,2,4,5] => [3,1,1,1]
[6,1,3,2,5,4] => [3,2,1]
[6,1,3,4,2,5] => [3,1,1,1]
[6,1,3,4,5,2] => [3,1,1,1]
[6,1,3,5,2,4] => [3,1,1,1]
[6,1,3,5,4,2] => [4,1,1]
[6,1,4,2,3,5] => [3,1,1,1]
[6,1,4,2,5,3] => [3,2,1]
[6,1,4,3,2,5] => [4,1,1]
[6,1,4,3,5,2] => [4,1,1]
[6,1,4,5,2,3] => [3,1,1,1]
[6,1,4,5,3,2] => [4,1,1]
[6,1,5,2,3,4] => [3,1,1,1]
[6,1,5,2,4,3] => [4,1,1]
[6,1,5,3,2,4] => [4,1,1]
[6,1,5,3,4,2] => [4,1,1]
[6,1,5,4,2,3] => [4,1,1]
[6,1,5,4,3,2] => [5,1]
[6,2,1,3,4,5] => [3,1,1,1]
[6,2,1,3,5,4] => [3,2,1]
[6,2,1,4,3,5] => [3,2,1]
[6,2,1,4,5,3] => [3,2,1]
[6,2,1,5,3,4] => [3,2,1]
[6,2,1,5,4,3] => [4,2]
[6,2,3,1,4,5] => [3,1,1,1]
[6,2,3,1,5,4] => [3,2,1]
[6,2,3,4,1,5] => [3,1,1,1]
[6,2,3,4,5,1] => [3,1,1,1]
[6,2,3,5,1,4] => [3,1,1,1]
[6,2,3,5,4,1] => [4,1,1]
[6,2,4,1,3,5] => [3,1,1,1]
[6,2,4,1,5,3] => [3,2,1]
[6,2,4,3,1,5] => [4,1,1]
[6,2,4,3,5,1] => [4,1,1]
[6,2,4,5,1,3] => [3,1,1,1]
[6,2,4,5,3,1] => [4,1,1]
[6,2,5,1,3,4] => [3,1,1,1]
[6,2,5,1,4,3] => [4,1,1]
[6,2,5,3,1,4] => [4,1,1]
[6,2,5,3,4,1] => [4,1,1]
[6,2,5,4,1,3] => [4,1,1]
[6,2,5,4,3,1] => [5,1]
[6,3,1,2,4,5] => [3,1,1,1]
[6,3,1,2,5,4] => [3,2,1]
[6,3,1,4,2,5] => [3,2,1]
[6,3,1,4,5,2] => [3,2,1]
[6,3,1,5,2,4] => [3,2,1]
[6,3,1,5,4,2] => [4,2]
[6,3,2,1,4,5] => [4,1,1]
[6,3,2,1,5,4] => [4,2]
[6,3,2,4,1,5] => [4,1,1]
[6,3,2,4,5,1] => [4,1,1]
[6,3,2,5,1,4] => [4,1,1]
[6,3,2,5,4,1] => [4,2]
[6,3,4,1,2,5] => [3,1,1,1]
[6,3,4,1,5,2] => [3,2,1]
[6,3,4,2,1,5] => [4,1,1]
[6,3,4,2,5,1] => [4,1,1]
[6,3,4,5,1,2] => [3,1,1,1]
[6,3,4,5,2,1] => [4,1,1]
[6,3,5,1,2,4] => [3,1,1,1]
[6,3,5,1,4,2] => [4,1,1]
[6,3,5,2,1,4] => [4,1,1]
[6,3,5,2,4,1] => [4,1,1]
[6,3,5,4,1,2] => [4,1,1]
[6,3,5,4,2,1] => [5,1]
[6,4,1,2,3,5] => [3,1,1,1]
[6,4,1,2,5,3] => [3,2,1]
[6,4,1,3,2,5] => [4,1,1]
[6,4,1,3,5,2] => [4,1,1]
[6,4,1,5,2,3] => [3,2,1]
[6,4,1,5,3,2] => [4,2]
[6,4,2,1,3,5] => [4,1,1]
[6,4,2,1,5,3] => [4,2]
[6,4,2,3,1,5] => [4,1,1]
[6,4,2,3,5,1] => [4,1,1]
[6,4,2,5,1,3] => [4,1,1]
[6,4,2,5,3,1] => [4,2]
[6,4,3,1,2,5] => [4,1,1]
[6,4,3,1,5,2] => [4,2]
[6,4,3,2,1,5] => [5,1]
[6,4,3,2,5,1] => [5,1]
[6,4,3,5,1,2] => [4,1,1]
[6,4,3,5,2,1] => [5,1]
[6,4,5,1,2,3] => [3,1,1,1]
[6,4,5,1,3,2] => [4,1,1]
[6,4,5,2,1,3] => [4,1,1]
[6,4,5,2,3,1] => [4,1,1]
[6,4,5,3,1,2] => [4,1,1]
[6,4,5,3,2,1] => [5,1]
[6,5,1,2,3,4] => [3,1,1,1]
[6,5,1,2,4,3] => [4,1,1]
[6,5,1,3,2,4] => [4,1,1]
[6,5,1,3,4,2] => [4,1,1]
[6,5,1,4,2,3] => [4,1,1]
[6,5,1,4,3,2] => [5,1]
[6,5,2,1,3,4] => [4,1,1]
[6,5,2,1,4,3] => [4,2]
[6,5,2,3,1,4] => [4,1,1]
[6,5,2,3,4,1] => [4,1,1]
[6,5,2,4,1,3] => [4,1,1]
[6,5,2,4,3,1] => [5,1]
[6,5,3,1,2,4] => [4,1,1]
[6,5,3,1,4,2] => [4,2]
[6,5,3,2,1,4] => [5,1]
[6,5,3,2,4,1] => [5,1]
[6,5,3,4,1,2] => [4,1,1]
[6,5,3,4,2,1] => [5,1]
[6,5,4,1,2,3] => [4,1,1]
[6,5,4,1,3,2] => [5,1]
[6,5,4,2,1,3] => [5,1]
[6,5,4,2,3,1] => [5,1]
[6,5,4,3,1,2] => [5,1]
[6,5,4,3,2,1] => [6]
[1,2,3,4,5,6,7] => [1,1,1,1,1,1,1]
[1,2,3,4,5,7,6] => [2,1,1,1,1,1]
[1,2,3,4,6,5,7] => [2,1,1,1,1,1]
[1,2,3,4,6,7,5] => [2,1,1,1,1,1]
[1,2,3,4,7,5,6] => [2,1,1,1,1,1]
[1,2,3,4,7,6,5] => [3,1,1,1,1]
[1,2,3,5,4,6,7] => [2,1,1,1,1,1]
[1,2,3,5,4,7,6] => [2,2,1,1,1]
[1,2,3,5,6,4,7] => [2,1,1,1,1,1]
[1,2,3,5,6,7,4] => [2,1,1,1,1,1]
[1,2,3,5,7,4,6] => [2,1,1,1,1,1]
[1,2,3,5,7,6,4] => [3,1,1,1,1]
[1,2,3,6,4,5,7] => [2,1,1,1,1,1]
[1,2,3,6,4,7,5] => [2,2,1,1,1]
[1,2,3,6,5,4,7] => [3,1,1,1,1]
[1,2,3,6,5,7,4] => [3,1,1,1,1]
[1,2,3,6,7,4,5] => [2,1,1,1,1,1]
[1,2,3,6,7,5,4] => [3,1,1,1,1]
[1,2,3,7,4,5,6] => [2,1,1,1,1,1]
[1,2,3,7,4,6,5] => [3,1,1,1,1]
[1,2,3,7,5,4,6] => [3,1,1,1,1]
[1,2,3,7,5,6,4] => [3,1,1,1,1]
[1,2,3,7,6,4,5] => [3,1,1,1,1]
[1,2,3,7,6,5,4] => [4,1,1,1]
[1,2,4,3,5,6,7] => [2,1,1,1,1,1]
[1,2,4,3,5,7,6] => [2,2,1,1,1]
[1,2,4,3,6,5,7] => [2,2,1,1,1]
[1,2,4,3,6,7,5] => [2,2,1,1,1]
[1,2,4,3,7,5,6] => [2,2,1,1,1]
[1,2,4,3,7,6,5] => [3,2,1,1]
[1,2,4,5,3,6,7] => [2,1,1,1,1,1]
[1,2,4,5,3,7,6] => [2,2,1,1,1]
[1,2,4,5,6,3,7] => [2,1,1,1,1,1]
[1,2,4,5,6,7,3] => [2,1,1,1,1,1]
[1,2,4,5,7,3,6] => [2,1,1,1,1,1]
[1,2,4,5,7,6,3] => [3,1,1,1,1]
[1,2,4,6,3,5,7] => [2,1,1,1,1,1]
[1,2,4,6,3,7,5] => [2,2,1,1,1]
[1,2,4,6,5,3,7] => [3,1,1,1,1]
[1,2,4,6,5,7,3] => [3,1,1,1,1]
[1,2,4,6,7,3,5] => [2,1,1,1,1,1]
[1,2,4,6,7,5,3] => [3,1,1,1,1]
[1,2,4,7,3,5,6] => [2,1,1,1,1,1]
[1,2,4,7,3,6,5] => [3,1,1,1,1]
[1,2,4,7,5,3,6] => [3,1,1,1,1]
[1,2,4,7,5,6,3] => [3,1,1,1,1]
[1,2,4,7,6,3,5] => [3,1,1,1,1]
[1,2,4,7,6,5,3] => [4,1,1,1]
[1,2,5,3,4,6,7] => [2,1,1,1,1,1]
[1,2,5,3,4,7,6] => [2,2,1,1,1]
[1,2,5,3,6,4,7] => [2,2,1,1,1]
[1,2,5,3,6,7,4] => [2,2,1,1,1]
[1,2,5,3,7,4,6] => [2,2,1,1,1]
[1,2,5,3,7,6,4] => [3,2,1,1]
[1,2,5,4,3,6,7] => [3,1,1,1,1]
[1,2,5,4,3,7,6] => [3,2,1,1]
[1,2,5,4,6,3,7] => [3,1,1,1,1]
[1,2,5,4,6,7,3] => [3,1,1,1,1]
[1,2,5,4,7,3,6] => [3,1,1,1,1]
[1,2,5,4,7,6,3] => [3,2,1,1]
[1,2,5,6,3,4,7] => [2,1,1,1,1,1]
[1,2,5,6,3,7,4] => [2,2,1,1,1]
[1,2,5,6,4,3,7] => [3,1,1,1,1]
[1,2,5,6,4,7,3] => [3,1,1,1,1]
[1,2,5,6,7,3,4] => [2,1,1,1,1,1]
[1,2,5,6,7,4,3] => [3,1,1,1,1]
[1,2,5,7,3,4,6] => [2,1,1,1,1,1]
[1,2,5,7,3,6,4] => [3,1,1,1,1]
[1,2,5,7,4,3,6] => [3,1,1,1,1]
[1,2,5,7,4,6,3] => [3,1,1,1,1]
[1,2,5,7,6,3,4] => [3,1,1,1,1]
[1,2,5,7,6,4,3] => [4,1,1,1]
[1,2,6,3,4,5,7] => [2,1,1,1,1,1]
[1,2,6,3,4,7,5] => [2,2,1,1,1]
[1,2,6,3,5,4,7] => [3,1,1,1,1]
[1,2,6,3,5,7,4] => [3,1,1,1,1]
[1,2,6,3,7,4,5] => [2,2,1,1,1]
[1,2,6,3,7,5,4] => [3,2,1,1]
[1,2,6,4,3,5,7] => [3,1,1,1,1]
[1,2,6,4,3,7,5] => [3,2,1,1]
[1,2,6,4,5,3,7] => [3,1,1,1,1]
[1,2,6,4,5,7,3] => [3,1,1,1,1]
[1,2,6,4,7,3,5] => [3,1,1,1,1]
[1,2,6,4,7,5,3] => [3,2,1,1]
[1,2,6,5,3,4,7] => [3,1,1,1,1]
[1,2,6,5,3,7,4] => [3,2,1,1]
[1,2,6,5,4,3,7] => [4,1,1,1]
[1,2,6,5,4,7,3] => [4,1,1,1]
[1,2,6,5,7,3,4] => [3,1,1,1,1]
[1,2,6,5,7,4,3] => [4,1,1,1]
[1,2,6,7,3,4,5] => [2,1,1,1,1,1]
[1,2,6,7,3,5,4] => [3,1,1,1,1]
[1,2,6,7,4,3,5] => [3,1,1,1,1]
[1,2,6,7,4,5,3] => [3,1,1,1,1]
[1,2,6,7,5,3,4] => [3,1,1,1,1]
[1,2,6,7,5,4,3] => [4,1,1,1]
[1,2,7,3,4,5,6] => [2,1,1,1,1,1]
[1,2,7,3,4,6,5] => [3,1,1,1,1]
[1,2,7,3,5,4,6] => [3,1,1,1,1]
[1,2,7,3,5,6,4] => [3,1,1,1,1]
[1,2,7,3,6,4,5] => [3,1,1,1,1]
[1,2,7,3,6,5,4] => [4,1,1,1]
[1,2,7,4,3,5,6] => [3,1,1,1,1]
[1,2,7,4,3,6,5] => [3,2,1,1]
[1,2,7,4,5,3,6] => [3,1,1,1,1]
[1,2,7,4,5,6,3] => [3,1,1,1,1]
[1,2,7,4,6,3,5] => [3,1,1,1,1]
[1,2,7,4,6,5,3] => [4,1,1,1]
[1,2,7,5,3,4,6] => [3,1,1,1,1]
[1,2,7,5,3,6,4] => [3,2,1,1]
[1,2,7,5,4,3,6] => [4,1,1,1]
[1,2,7,5,4,6,3] => [4,1,1,1]
[1,2,7,5,6,3,4] => [3,1,1,1,1]
[1,2,7,5,6,4,3] => [4,1,1,1]
[1,2,7,6,3,4,5] => [3,1,1,1,1]
[1,2,7,6,3,5,4] => [4,1,1,1]
[1,2,7,6,4,3,5] => [4,1,1,1]
[1,2,7,6,4,5,3] => [4,1,1,1]
[1,2,7,6,5,3,4] => [4,1,1,1]
[1,2,7,6,5,4,3] => [5,1,1]
[1,3,2,4,5,6,7] => [2,1,1,1,1,1]
[1,3,2,4,5,7,6] => [2,2,1,1,1]
[1,3,2,4,6,5,7] => [2,2,1,1,1]
[1,3,2,4,6,7,5] => [2,2,1,1,1]
[1,3,2,4,7,5,6] => [2,2,1,1,1]
[1,3,2,4,7,6,5] => [3,2,1,1]
[1,3,2,5,4,6,7] => [2,2,1,1,1]
[1,3,2,5,4,7,6] => [2,2,2,1]
[1,3,2,5,6,4,7] => [2,2,1,1,1]
[1,3,2,5,6,7,4] => [2,2,1,1,1]
[1,3,2,5,7,4,6] => [2,2,1,1,1]
[1,3,2,5,7,6,4] => [3,2,1,1]
[1,3,2,6,4,5,7] => [2,2,1,1,1]
[1,3,2,6,4,7,5] => [2,2,2,1]
[1,3,2,6,5,4,7] => [3,2,1,1]
[1,3,2,6,5,7,4] => [3,2,1,1]
[1,3,2,6,7,4,5] => [2,2,1,1,1]
[1,3,2,6,7,5,4] => [3,2,1,1]
[1,3,2,7,4,5,6] => [2,2,1,1,1]
[1,3,2,7,4,6,5] => [3,2,1,1]
[1,3,2,7,5,4,6] => [3,2,1,1]
[1,3,2,7,5,6,4] => [3,2,1,1]
[1,3,2,7,6,4,5] => [3,2,1,1]
[1,3,2,7,6,5,4] => [4,2,1]
[1,3,4,2,5,6,7] => [2,1,1,1,1,1]
[1,3,4,2,5,7,6] => [2,2,1,1,1]
[1,3,4,2,6,5,7] => [2,2,1,1,1]
[1,3,4,2,6,7,5] => [2,2,1,1,1]
[1,3,4,2,7,5,6] => [2,2,1,1,1]
[1,3,4,2,7,6,5] => [3,2,1,1]
[1,3,4,5,2,6,7] => [2,1,1,1,1,1]
[1,3,4,5,2,7,6] => [2,2,1,1,1]
[1,3,4,5,6,2,7] => [2,1,1,1,1,1]
[1,3,4,5,6,7,2] => [2,1,1,1,1,1]
[1,3,4,5,7,2,6] => [2,1,1,1,1,1]
[1,3,4,5,7,6,2] => [3,1,1,1,1]
[1,3,4,6,2,5,7] => [2,1,1,1,1,1]
[1,3,4,6,2,7,5] => [2,2,1,1,1]
[1,3,4,6,5,2,7] => [3,1,1,1,1]
[1,3,4,6,5,7,2] => [3,1,1,1,1]
[1,3,4,6,7,2,5] => [2,1,1,1,1,1]
[1,3,4,6,7,5,2] => [3,1,1,1,1]
[1,3,4,7,2,5,6] => [2,1,1,1,1,1]
[1,3,4,7,2,6,5] => [3,1,1,1,1]
[1,3,4,7,5,2,6] => [3,1,1,1,1]
[1,3,4,7,5,6,2] => [3,1,1,1,1]
[1,3,4,7,6,2,5] => [3,1,1,1,1]
[1,3,4,7,6,5,2] => [4,1,1,1]
[1,3,5,2,4,6,7] => [2,1,1,1,1,1]
[1,3,5,2,4,7,6] => [2,2,1,1,1]
[1,3,5,2,6,4,7] => [2,2,1,1,1]
[1,3,5,2,6,7,4] => [2,2,1,1,1]
[1,3,5,2,7,4,6] => [2,2,1,1,1]
[1,3,5,2,7,6,4] => [3,2,1,1]
[1,3,5,4,2,6,7] => [3,1,1,1,1]
[1,3,5,4,2,7,6] => [3,2,1,1]
[1,3,5,4,6,2,7] => [3,1,1,1,1]
[1,3,5,4,6,7,2] => [3,1,1,1,1]
[1,3,5,4,7,2,6] => [3,1,1,1,1]
[1,3,5,4,7,6,2] => [3,2,1,1]
[1,3,5,6,2,4,7] => [2,1,1,1,1,1]
[1,3,5,6,2,7,4] => [2,2,1,1,1]
[1,3,5,6,4,2,7] => [3,1,1,1,1]
[1,3,5,6,4,7,2] => [3,1,1,1,1]
[1,3,5,6,7,2,4] => [2,1,1,1,1,1]
[1,3,5,6,7,4,2] => [3,1,1,1,1]
[1,3,5,7,2,4,6] => [2,1,1,1,1,1]
[1,3,5,7,2,6,4] => [3,1,1,1,1]
[1,3,5,7,4,2,6] => [3,1,1,1,1]
[1,3,5,7,4,6,2] => [3,1,1,1,1]
[1,3,5,7,6,2,4] => [3,1,1,1,1]
[1,3,5,7,6,4,2] => [4,1,1,1]
[1,3,6,2,4,5,7] => [2,1,1,1,1,1]
[1,3,6,2,4,7,5] => [2,2,1,1,1]
[1,3,6,2,5,4,7] => [3,1,1,1,1]
[1,3,6,2,5,7,4] => [3,1,1,1,1]
[1,3,6,2,7,4,5] => [2,2,1,1,1]
[1,3,6,2,7,5,4] => [3,2,1,1]
[1,3,6,4,2,5,7] => [3,1,1,1,1]
[1,3,6,4,2,7,5] => [3,2,1,1]
[1,3,6,4,5,2,7] => [3,1,1,1,1]
[1,3,6,4,5,7,2] => [3,1,1,1,1]
[1,3,6,4,7,2,5] => [3,1,1,1,1]
[1,3,6,4,7,5,2] => [3,2,1,1]
[1,3,6,5,2,4,7] => [3,1,1,1,1]
[1,3,6,5,2,7,4] => [3,2,1,1]
[1,3,6,5,4,2,7] => [4,1,1,1]
[1,3,6,5,4,7,2] => [4,1,1,1]
[1,3,6,5,7,2,4] => [3,1,1,1,1]
[1,3,6,5,7,4,2] => [4,1,1,1]
[1,3,6,7,2,4,5] => [2,1,1,1,1,1]
[1,3,6,7,2,5,4] => [3,1,1,1,1]
[1,3,6,7,4,2,5] => [3,1,1,1,1]
[1,3,6,7,4,5,2] => [3,1,1,1,1]
[1,3,6,7,5,2,4] => [3,1,1,1,1]
[1,3,6,7,5,4,2] => [4,1,1,1]
[1,3,7,2,4,5,6] => [2,1,1,1,1,1]
[1,3,7,2,4,6,5] => [3,1,1,1,1]
[1,3,7,2,5,4,6] => [3,1,1,1,1]
[1,3,7,2,5,6,4] => [3,1,1,1,1]
[1,3,7,2,6,4,5] => [3,1,1,1,1]
[1,3,7,2,6,5,4] => [4,1,1,1]
[1,3,7,4,2,5,6] => [3,1,1,1,1]
[1,3,7,4,2,6,5] => [3,2,1,1]
[1,3,7,4,5,2,6] => [3,1,1,1,1]
[1,3,7,4,5,6,2] => [3,1,1,1,1]
[1,3,7,4,6,2,5] => [3,1,1,1,1]
[1,3,7,4,6,5,2] => [4,1,1,1]
[1,3,7,5,2,4,6] => [3,1,1,1,1]
[1,3,7,5,2,6,4] => [3,2,1,1]
[1,3,7,5,4,2,6] => [4,1,1,1]
[1,3,7,5,4,6,2] => [4,1,1,1]
[1,3,7,5,6,2,4] => [3,1,1,1,1]
[1,3,7,5,6,4,2] => [4,1,1,1]
[1,3,7,6,2,4,5] => [3,1,1,1,1]
[1,3,7,6,2,5,4] => [4,1,1,1]
[1,3,7,6,4,2,5] => [4,1,1,1]
[1,3,7,6,4,5,2] => [4,1,1,1]
[1,3,7,6,5,2,4] => [4,1,1,1]
[1,3,7,6,5,4,2] => [5,1,1]
[1,4,2,3,5,6,7] => [2,1,1,1,1,1]
[1,4,2,3,5,7,6] => [2,2,1,1,1]
[1,4,2,3,6,5,7] => [2,2,1,1,1]
[1,4,2,3,6,7,5] => [2,2,1,1,1]
[1,4,2,3,7,5,6] => [2,2,1,1,1]
[1,4,2,3,7,6,5] => [3,2,1,1]
[1,4,2,5,3,6,7] => [2,2,1,1,1]
[1,4,2,5,3,7,6] => [2,2,2,1]
[1,4,2,5,6,3,7] => [2,2,1,1,1]
[1,4,2,5,6,7,3] => [2,2,1,1,1]
[1,4,2,5,7,3,6] => [2,2,1,1,1]
[1,4,2,5,7,6,3] => [3,2,1,1]
[1,4,2,6,3,5,7] => [2,2,1,1,1]
[1,4,2,6,3,7,5] => [2,2,2,1]
[1,4,2,6,5,3,7] => [3,2,1,1]
[1,4,2,6,5,7,3] => [3,2,1,1]
[1,4,2,6,7,3,5] => [2,2,1,1,1]
[1,4,2,6,7,5,3] => [3,2,1,1]
[1,4,2,7,3,5,6] => [2,2,1,1,1]
[1,4,2,7,3,6,5] => [3,2,1,1]
[1,4,2,7,5,3,6] => [3,2,1,1]
[1,4,2,7,5,6,3] => [3,2,1,1]
[1,4,2,7,6,3,5] => [3,2,1,1]
[1,4,2,7,6,5,3] => [4,2,1]
[1,4,3,2,5,6,7] => [3,1,1,1,1]
[1,4,3,2,5,7,6] => [3,2,1,1]
[1,4,3,2,6,5,7] => [3,2,1,1]
[1,4,3,2,6,7,5] => [3,2,1,1]
[1,4,3,2,7,5,6] => [3,2,1,1]
[1,4,3,2,7,6,5] => [3,3,1]
[1,4,3,5,2,6,7] => [3,1,1,1,1]
[1,4,3,5,2,7,6] => [3,2,1,1]
[1,4,3,5,6,2,7] => [3,1,1,1,1]
[1,4,3,5,6,7,2] => [3,1,1,1,1]
[1,4,3,5,7,2,6] => [3,1,1,1,1]
[1,4,3,5,7,6,2] => [3,2,1,1]
[1,4,3,6,2,5,7] => [3,1,1,1,1]
[1,4,3,6,2,7,5] => [3,2,1,1]
[1,4,3,6,5,2,7] => [3,2,1,1]
[1,4,3,6,5,7,2] => [3,2,1,1]
[1,4,3,6,7,2,5] => [3,1,1,1,1]
[1,4,3,6,7,5,2] => [3,2,1,1]
[1,4,3,7,2,5,6] => [3,1,1,1,1]
[1,4,3,7,2,6,5] => [3,2,1,1]
[1,4,3,7,5,2,6] => [3,2,1,1]
[1,4,3,7,5,6,2] => [3,2,1,1]
[1,4,3,7,6,2,5] => [3,2,1,1]
[1,4,3,7,6,5,2] => [4,2,1]
[1,4,5,2,3,6,7] => [2,1,1,1,1,1]
[1,4,5,2,3,7,6] => [2,2,1,1,1]
[1,4,5,2,6,3,7] => [2,2,1,1,1]
[1,4,5,2,6,7,3] => [2,2,1,1,1]
[1,4,5,2,7,3,6] => [2,2,1,1,1]
[1,4,5,2,7,6,3] => [3,2,1,1]
[1,4,5,3,2,6,7] => [3,1,1,1,1]
[1,4,5,3,2,7,6] => [3,2,1,1]
[1,4,5,3,6,2,7] => [3,1,1,1,1]
[1,4,5,3,6,7,2] => [3,1,1,1,1]
[1,4,5,3,7,2,6] => [3,1,1,1,1]
[1,4,5,3,7,6,2] => [3,2,1,1]
[1,4,5,6,2,3,7] => [2,1,1,1,1,1]
[1,4,5,6,2,7,3] => [2,2,1,1,1]
[1,4,5,6,3,2,7] => [3,1,1,1,1]
[1,4,5,6,3,7,2] => [3,1,1,1,1]
[1,4,5,6,7,2,3] => [2,1,1,1,1,1]
[1,4,5,6,7,3,2] => [3,1,1,1,1]
[1,4,5,7,2,3,6] => [2,1,1,1,1,1]
[1,4,5,7,2,6,3] => [3,1,1,1,1]
[1,4,5,7,3,2,6] => [3,1,1,1,1]
[1,4,5,7,3,6,2] => [3,1,1,1,1]
[1,4,5,7,6,2,3] => [3,1,1,1,1]
[1,4,5,7,6,3,2] => [4,1,1,1]
[1,4,6,2,3,5,7] => [2,1,1,1,1,1]
[1,4,6,2,3,7,5] => [2,2,1,1,1]
[1,4,6,2,5,3,7] => [3,1,1,1,1]
[1,4,6,2,5,7,3] => [3,1,1,1,1]
[1,4,6,2,7,3,5] => [2,2,1,1,1]
[1,4,6,2,7,5,3] => [3,2,1,1]
[1,4,6,3,2,5,7] => [3,1,1,1,1]
[1,4,6,3,2,7,5] => [3,2,1,1]
[1,4,6,3,5,2,7] => [3,1,1,1,1]
[1,4,6,3,5,7,2] => [3,1,1,1,1]
[1,4,6,3,7,2,5] => [3,1,1,1,1]
[1,4,6,3,7,5,2] => [3,2,1,1]
[1,4,6,5,2,3,7] => [3,1,1,1,1]
[1,4,6,5,2,7,3] => [3,2,1,1]
[1,4,6,5,3,2,7] => [4,1,1,1]
-----------------------------------------------------------------------------
Created: Jan 28, 2021 at 12:18 by Martin Rubey
-----------------------------------------------------------------------------
Last Updated: Feb 01, 2021 at 12:27 by Martin Rubey