************************************************************************
* 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: Mp00303
------------------------------------------------------------------------
Map name: complement
------------------------------------------------------------------------
Domain: Parking functions
------------------------------------------------------------------------
Codomain: Parking functions
------------------------------------------------------------------------
Description: The complement of a parking function.
Let $p=(p_1,\dots,p_n)$ be a parking function. The complement of $p$ is the unique parking function $(q_1,\dots,q_n)$ such that $q_i + p_i$ is constant modulo $n+1$.
------------------------------------------------------------------------
References:
------------------------------------------------------------------------
Code:
def mapping(p):
n = len(p)
P = ParkingFunctions(n)
pc = [(-e) % (n+1) for e in p]
for i in range(n+1):
if pc in P:
break
pc = [(e + 1) % (n+1) for e in pc]
return ParkingFunction(pc)
------------------------------------------------------------------------
Map images:
[1] => [1]
[1,1] => [1,1]
[1,2] => [2,1]
[2,1] => [1,2]
[1,1,1] => [1,1,1]
[1,1,2] => [2,2,1]
[1,2,1] => [2,1,2]
[2,1,1] => [1,2,2]
[1,1,3] => [1,1,3]
[1,3,1] => [1,3,1]
[3,1,1] => [3,1,1]
[1,2,2] => [2,1,1]
[2,1,2] => [1,2,1]
[2,2,1] => [1,1,2]
[1,2,3] => [3,2,1]
[1,3,2] => [3,1,2]
[2,1,3] => [2,3,1]
[2,3,1] => [2,1,3]
[3,1,2] => [1,3,2]
[3,2,1] => [1,2,3]
[1,1,1,1] => [1,1,1,1]
[1,1,1,2] => [2,2,2,1]
[1,1,2,1] => [2,2,1,2]
[1,2,1,1] => [2,1,2,2]
[2,1,1,1] => [1,2,2,2]
[1,1,1,3] => [1,1,1,4]
[1,1,3,1] => [1,1,4,1]
[1,3,1,1] => [1,4,1,1]
[3,1,1,1] => [4,1,1,1]
[1,1,1,4] => [1,1,1,3]
[1,1,4,1] => [1,1,3,1]
[1,4,1,1] => [1,3,1,1]
[4,1,1,1] => [3,1,1,1]
[1,1,2,2] => [2,2,1,1]
[1,2,1,2] => [2,1,2,1]
[1,2,2,1] => [2,1,1,2]
[2,1,1,2] => [1,2,2,1]
[2,1,2,1] => [1,2,1,2]
[2,2,1,1] => [1,1,2,2]
[1,1,2,3] => [3,3,2,1]
[1,1,3,2] => [3,3,1,2]
[1,2,1,3] => [3,2,3,1]
[1,2,3,1] => [3,2,1,3]
[1,3,1,2] => [3,1,3,2]
[1,3,2,1] => [3,1,2,3]
[2,1,1,3] => [2,3,3,1]
[2,1,3,1] => [2,3,1,3]
[2,3,1,1] => [2,1,3,3]
[3,1,1,2] => [1,3,3,2]
[3,1,2,1] => [1,3,2,3]
[3,2,1,1] => [1,2,3,3]
[1,1,2,4] => [2,2,1,4]
[1,1,4,2] => [2,2,4,1]
[1,2,1,4] => [2,1,2,4]
[1,2,4,1] => [2,1,4,2]
[1,4,1,2] => [2,4,2,1]
[1,4,2,1] => [2,4,1,2]
[2,1,1,4] => [1,2,2,4]
[2,1,4,1] => [1,2,4,2]
[2,4,1,1] => [1,4,2,2]
[4,1,1,2] => [4,2,2,1]
[4,1,2,1] => [4,2,1,2]
[4,2,1,1] => [4,1,2,2]
[1,1,3,3] => [3,3,1,1]
[1,3,1,3] => [3,1,3,1]
[1,3,3,1] => [3,1,1,3]
[3,1,1,3] => [1,3,3,1]
[3,1,3,1] => [1,3,1,3]
[3,3,1,1] => [1,1,3,3]
[1,1,3,4] => [1,1,4,3]
[1,1,4,3] => [1,1,3,4]
[1,3,1,4] => [1,4,1,3]
[1,3,4,1] => [1,4,3,1]
[1,4,1,3] => [1,3,1,4]
[1,4,3,1] => [1,3,4,1]
[3,1,1,4] => [4,1,1,3]
[3,1,4,1] => [4,1,3,1]
[3,4,1,1] => [4,3,1,1]
[4,1,1,3] => [3,1,1,4]
[4,1,3,1] => [3,1,4,1]
[4,3,1,1] => [3,4,1,1]
[1,2,2,2] => [2,1,1,1]
[2,1,2,2] => [1,2,1,1]
[2,2,1,2] => [1,1,2,1]
[2,2,2,1] => [1,1,1,2]
[1,2,2,3] => [3,2,2,1]
[1,2,3,2] => [3,2,1,2]
[1,3,2,2] => [3,1,2,2]
[2,1,2,3] => [2,3,2,1]
[2,1,3,2] => [2,3,1,2]
[2,2,1,3] => [2,2,3,1]
[2,2,3,1] => [2,2,1,3]
[2,3,1,2] => [2,1,3,2]
[2,3,2,1] => [2,1,2,3]
[3,1,2,2] => [1,3,2,2]
[3,2,1,2] => [1,2,3,2]
[3,2,2,1] => [1,2,2,3]
[1,2,2,4] => [2,1,1,4]
[1,2,4,2] => [2,1,4,1]
[1,4,2,2] => [2,4,1,1]
[2,1,2,4] => [1,2,1,4]
[2,1,4,2] => [1,2,4,1]
[2,2,1,4] => [1,1,2,4]
[2,2,4,1] => [1,1,4,2]
[2,4,1,2] => [1,4,2,1]
[2,4,2,1] => [1,4,1,2]
[4,1,2,2] => [4,2,1,1]
[4,2,1,2] => [4,1,2,1]
[4,2,2,1] => [4,1,1,2]
[1,2,3,3] => [3,2,1,1]
[1,3,2,3] => [3,1,2,1]
[1,3,3,2] => [3,1,1,2]
[2,1,3,3] => [2,3,1,1]
[2,3,1,3] => [2,1,3,1]
[2,3,3,1] => [2,1,1,3]
[3,1,2,3] => [1,3,2,1]
[3,1,3,2] => [1,3,1,2]
[3,2,1,3] => [1,2,3,1]
[3,2,3,1] => [1,2,1,3]
[3,3,1,2] => [1,1,3,2]
[3,3,2,1] => [1,1,2,3]
[1,2,3,4] => [4,3,2,1]
[1,2,4,3] => [4,3,1,2]
[1,3,2,4] => [4,2,3,1]
[1,3,4,2] => [4,2,1,3]
[1,4,2,3] => [4,1,3,2]
[1,4,3,2] => [4,1,2,3]
[2,1,3,4] => [3,4,2,1]
[2,1,4,3] => [3,4,1,2]
[2,3,1,4] => [3,2,4,1]
[2,3,4,1] => [3,2,1,4]
[2,4,1,3] => [3,1,4,2]
[2,4,3,1] => [3,1,2,4]
[3,1,2,4] => [2,4,3,1]
[3,1,4,2] => [2,4,1,3]
[3,2,1,4] => [2,3,4,1]
[3,2,4,1] => [2,3,1,4]
[3,4,1,2] => [2,1,4,3]
[3,4,2,1] => [2,1,3,4]
[4,1,2,3] => [1,4,3,2]
[4,1,3,2] => [1,4,2,3]
[4,2,1,3] => [1,3,4,2]
[4,2,3,1] => [1,3,2,4]
[4,3,1,2] => [1,2,4,3]
[4,3,2,1] => [1,2,3,4]
[1,1,1,1,1] => [1,1,1,1,1]
[1,1,1,1,2] => [2,2,2,2,1]
[1,1,1,2,1] => [2,2,2,1,2]
[1,1,2,1,1] => [2,2,1,2,2]
[1,2,1,1,1] => [2,1,2,2,2]
[2,1,1,1,1] => [1,2,2,2,2]
[1,1,1,1,3] => [1,1,1,1,5]
[1,1,1,3,1] => [1,1,1,5,1]
[1,1,3,1,1] => [1,1,5,1,1]
[1,3,1,1,1] => [1,5,1,1,1]
[3,1,1,1,1] => [5,1,1,1,1]
[1,1,1,1,4] => [1,1,1,1,4]
[1,1,1,4,1] => [1,1,1,4,1]
[1,1,4,1,1] => [1,1,4,1,1]
[1,4,1,1,1] => [1,4,1,1,1]
[4,1,1,1,1] => [4,1,1,1,1]
[1,1,1,1,5] => [1,1,1,1,3]
[1,1,1,5,1] => [1,1,1,3,1]
[1,1,5,1,1] => [1,1,3,1,1]
[1,5,1,1,1] => [1,3,1,1,1]
[5,1,1,1,1] => [3,1,1,1,1]
[1,1,1,2,2] => [2,2,2,1,1]
[1,1,2,1,2] => [2,2,1,2,1]
[1,1,2,2,1] => [2,2,1,1,2]
[1,2,1,1,2] => [2,1,2,2,1]
[1,2,1,2,1] => [2,1,2,1,2]
[1,2,2,1,1] => [2,1,1,2,2]
[2,1,1,1,2] => [1,2,2,2,1]
[2,1,1,2,1] => [1,2,2,1,2]
[2,1,2,1,1] => [1,2,1,2,2]
[2,2,1,1,1] => [1,1,2,2,2]
[1,1,1,2,3] => [3,3,3,2,1]
[1,1,1,3,2] => [3,3,3,1,2]
[1,1,2,1,3] => [3,3,2,3,1]
[1,1,2,3,1] => [3,3,2,1,3]
[1,1,3,1,2] => [3,3,1,3,2]
[1,1,3,2,1] => [3,3,1,2,3]
[1,2,1,1,3] => [3,2,3,3,1]
[1,2,1,3,1] => [3,2,3,1,3]
[1,2,3,1,1] => [3,2,1,3,3]
[1,3,1,1,2] => [3,1,3,3,2]
[1,3,1,2,1] => [3,1,3,2,3]
[1,3,2,1,1] => [3,1,2,3,3]
[2,1,1,1,3] => [2,3,3,3,1]
[2,1,1,3,1] => [2,3,3,1,3]
[2,1,3,1,1] => [2,3,1,3,3]
[2,3,1,1,1] => [2,1,3,3,3]
[3,1,1,1,2] => [1,3,3,3,2]
[3,1,1,2,1] => [1,3,3,2,3]
[3,1,2,1,1] => [1,3,2,3,3]
[3,2,1,1,1] => [1,2,3,3,3]
[1,1,1,2,4] => [2,2,2,1,5]
[1,1,1,4,2] => [2,2,2,5,1]
[1,1,2,1,4] => [2,2,1,2,5]
[1,1,2,4,1] => [2,2,1,5,2]
[1,1,4,1,2] => [2,2,5,2,1]
[1,1,4,2,1] => [2,2,5,1,2]
[1,2,1,1,4] => [2,1,2,2,5]
[1,2,1,4,1] => [2,1,2,5,2]
[1,2,4,1,1] => [2,1,5,2,2]
[1,4,1,1,2] => [2,5,2,2,1]
[1,4,1,2,1] => [2,5,2,1,2]
[1,4,2,1,1] => [2,5,1,2,2]
[2,1,1,1,4] => [1,2,2,2,5]
[2,1,1,4,1] => [1,2,2,5,2]
[2,1,4,1,1] => [1,2,5,2,2]
[2,4,1,1,1] => [1,5,2,2,2]
[4,1,1,1,2] => [5,2,2,2,1]
[4,1,1,2,1] => [5,2,2,1,2]
[4,1,2,1,1] => [5,2,1,2,2]
[4,2,1,1,1] => [5,1,2,2,2]
[1,1,1,2,5] => [2,2,2,1,4]
[1,1,1,5,2] => [2,2,2,4,1]
[1,1,2,1,5] => [2,2,1,2,4]
[1,1,2,5,1] => [2,2,1,4,2]
[1,1,5,1,2] => [2,2,4,2,1]
[1,1,5,2,1] => [2,2,4,1,2]
[1,2,1,1,5] => [2,1,2,2,4]
[1,2,1,5,1] => [2,1,2,4,2]
[1,2,5,1,1] => [2,1,4,2,2]
[1,5,1,1,2] => [2,4,2,2,1]
[1,5,1,2,1] => [2,4,2,1,2]
[1,5,2,1,1] => [2,4,1,2,2]
[2,1,1,1,5] => [1,2,2,2,4]
[2,1,1,5,1] => [1,2,2,4,2]
[2,1,5,1,1] => [1,2,4,2,2]
[2,5,1,1,1] => [1,4,2,2,2]
[5,1,1,1,2] => [4,2,2,2,1]
[5,1,1,2,1] => [4,2,2,1,2]
[5,1,2,1,1] => [4,2,1,2,2]
[5,2,1,1,1] => [4,1,2,2,2]
[1,1,1,3,3] => [3,3,3,1,1]
[1,1,3,1,3] => [3,3,1,3,1]
[1,1,3,3,1] => [3,3,1,1,3]
[1,3,1,1,3] => [3,1,3,3,1]
[1,3,1,3,1] => [3,1,3,1,3]
[1,3,3,1,1] => [3,1,1,3,3]
[3,1,1,1,3] => [1,3,3,3,1]
[3,1,1,3,1] => [1,3,3,1,3]
[3,1,3,1,1] => [1,3,1,3,3]
[3,3,1,1,1] => [1,1,3,3,3]
[1,1,1,3,4] => [1,1,1,5,4]
[1,1,1,4,3] => [1,1,1,4,5]
[1,1,3,1,4] => [1,1,5,1,4]
[1,1,3,4,1] => [1,1,5,4,1]
[1,1,4,1,3] => [1,1,4,1,5]
[1,1,4,3,1] => [1,1,4,5,1]
[1,3,1,1,4] => [1,5,1,1,4]
[1,3,1,4,1] => [1,5,1,4,1]
[1,3,4,1,1] => [1,5,4,1,1]
[1,4,1,1,3] => [1,4,1,1,5]
[1,4,1,3,1] => [1,4,1,5,1]
[1,4,3,1,1] => [1,4,5,1,1]
[3,1,1,1,4] => [5,1,1,1,4]
[3,1,1,4,1] => [5,1,1,4,1]
[3,1,4,1,1] => [5,1,4,1,1]
[3,4,1,1,1] => [5,4,1,1,1]
[4,1,1,1,3] => [4,1,1,1,5]
[4,1,1,3,1] => [4,1,1,5,1]
[4,1,3,1,1] => [4,1,5,1,1]
[4,3,1,1,1] => [4,5,1,1,1]
[1,1,1,3,5] => [1,1,1,5,3]
[1,1,1,5,3] => [1,1,1,3,5]
[1,1,3,1,5] => [1,1,5,1,3]
[1,1,3,5,1] => [1,1,5,3,1]
[1,1,5,1,3] => [1,1,3,1,5]
[1,1,5,3,1] => [1,1,3,5,1]
[1,3,1,1,5] => [1,5,1,1,3]
[1,3,1,5,1] => [1,5,1,3,1]
[1,3,5,1,1] => [1,5,3,1,1]
[1,5,1,1,3] => [1,3,1,1,5]
[1,5,1,3,1] => [1,3,1,5,1]
[1,5,3,1,1] => [1,3,5,1,1]
[3,1,1,1,5] => [5,1,1,1,3]
[3,1,1,5,1] => [5,1,1,3,1]
[3,1,5,1,1] => [5,1,3,1,1]
[3,5,1,1,1] => [5,3,1,1,1]
[5,1,1,1,3] => [3,1,1,1,5]
[5,1,1,3,1] => [3,1,1,5,1]
[5,1,3,1,1] => [3,1,5,1,1]
[5,3,1,1,1] => [3,5,1,1,1]
[1,1,1,4,4] => [1,1,1,4,4]
[1,1,4,1,4] => [1,1,4,1,4]
[1,1,4,4,1] => [1,1,4,4,1]
[1,4,1,1,4] => [1,4,1,1,4]
[1,4,1,4,1] => [1,4,1,4,1]
[1,4,4,1,1] => [1,4,4,1,1]
[4,1,1,1,4] => [4,1,1,1,4]
[4,1,1,4,1] => [4,1,1,4,1]
[4,1,4,1,1] => [4,1,4,1,1]
[4,4,1,1,1] => [4,4,1,1,1]
[1,1,1,4,5] => [1,1,1,4,3]
[1,1,1,5,4] => [1,1,1,3,4]
[1,1,4,1,5] => [1,1,4,1,3]
[1,1,4,5,1] => [1,1,4,3,1]
[1,1,5,1,4] => [1,1,3,1,4]
[1,1,5,4,1] => [1,1,3,4,1]
[1,4,1,1,5] => [1,4,1,1,3]
[1,4,1,5,1] => [1,4,1,3,1]
[1,4,5,1,1] => [1,4,3,1,1]
[1,5,1,1,4] => [1,3,1,1,4]
[1,5,1,4,1] => [1,3,1,4,1]
[1,5,4,1,1] => [1,3,4,1,1]
[4,1,1,1,5] => [4,1,1,1,3]
[4,1,1,5,1] => [4,1,1,3,1]
[4,1,5,1,1] => [4,1,3,1,1]
[4,5,1,1,1] => [4,3,1,1,1]
[5,1,1,1,4] => [3,1,1,1,4]
[5,1,1,4,1] => [3,1,1,4,1]
[5,1,4,1,1] => [3,1,4,1,1]
[5,4,1,1,1] => [3,4,1,1,1]
[1,1,2,2,2] => [2,2,1,1,1]
[1,2,1,2,2] => [2,1,2,1,1]
[1,2,2,1,2] => [2,1,1,2,1]
[1,2,2,2,1] => [2,1,1,1,2]
[2,1,1,2,2] => [1,2,2,1,1]
[2,1,2,1,2] => [1,2,1,2,1]
[2,1,2,2,1] => [1,2,1,1,2]
[2,2,1,1,2] => [1,1,2,2,1]
[2,2,1,2,1] => [1,1,2,1,2]
[2,2,2,1,1] => [1,1,1,2,2]
[1,1,2,2,3] => [3,3,2,2,1]
[1,1,2,3,2] => [3,3,2,1,2]
[1,1,3,2,2] => [3,3,1,2,2]
[1,2,1,2,3] => [3,2,3,2,1]
[1,2,1,3,2] => [3,2,3,1,2]
[1,2,2,1,3] => [3,2,2,3,1]
[1,2,2,3,1] => [3,2,2,1,3]
[1,2,3,1,2] => [3,2,1,3,2]
[1,2,3,2,1] => [3,2,1,2,3]
[1,3,1,2,2] => [3,1,3,2,2]
[1,3,2,1,2] => [3,1,2,3,2]
[1,3,2,2,1] => [3,1,2,2,3]
[2,1,1,2,3] => [2,3,3,2,1]
[2,1,1,3,2] => [2,3,3,1,2]
[2,1,2,1,3] => [2,3,2,3,1]
[2,1,2,3,1] => [2,3,2,1,3]
[2,1,3,1,2] => [2,3,1,3,2]
[2,1,3,2,1] => [2,3,1,2,3]
[2,2,1,1,3] => [2,2,3,3,1]
[2,2,1,3,1] => [2,2,3,1,3]
[2,2,3,1,1] => [2,2,1,3,3]
[2,3,1,1,2] => [2,1,3,3,2]
[2,3,1,2,1] => [2,1,3,2,3]
[2,3,2,1,1] => [2,1,2,3,3]
[3,1,1,2,2] => [1,3,3,2,2]
[3,1,2,1,2] => [1,3,2,3,2]
[3,1,2,2,1] => [1,3,2,2,3]
[3,2,1,1,2] => [1,2,3,3,2]
[3,2,1,2,1] => [1,2,3,2,3]
[3,2,2,1,1] => [1,2,2,3,3]
[1,1,2,2,4] => [2,2,1,1,5]
[1,1,2,4,2] => [2,2,1,5,1]
[1,1,4,2,2] => [2,2,5,1,1]
[1,2,1,2,4] => [2,1,2,1,5]
[1,2,1,4,2] => [2,1,2,5,1]
[1,2,2,1,4] => [2,1,1,2,5]
[1,2,2,4,1] => [2,1,1,5,2]
[1,2,4,1,2] => [2,1,5,2,1]
[1,2,4,2,1] => [2,1,5,1,2]
[1,4,1,2,2] => [2,5,2,1,1]
[1,4,2,1,2] => [2,5,1,2,1]
[1,4,2,2,1] => [2,5,1,1,2]
[2,1,1,2,4] => [1,2,2,1,5]
[2,1,1,4,2] => [1,2,2,5,1]
[2,1,2,1,4] => [1,2,1,2,5]
[2,1,2,4,1] => [1,2,1,5,2]
[2,1,4,1,2] => [1,2,5,2,1]
[2,1,4,2,1] => [1,2,5,1,2]
[2,2,1,1,4] => [1,1,2,2,5]
[2,2,1,4,1] => [1,1,2,5,2]
[2,2,4,1,1] => [1,1,5,2,2]
[2,4,1,1,2] => [1,5,2,2,1]
[2,4,1,2,1] => [1,5,2,1,2]
[2,4,2,1,1] => [1,5,1,2,2]
[4,1,1,2,2] => [5,2,2,1,1]
[4,1,2,1,2] => [5,2,1,2,1]
[4,1,2,2,1] => [5,2,1,1,2]
[4,2,1,1,2] => [5,1,2,2,1]
[4,2,1,2,1] => [5,1,2,1,2]
[4,2,2,1,1] => [5,1,1,2,2]
[1,1,2,2,5] => [2,2,1,1,4]
[1,1,2,5,2] => [2,2,1,4,1]
[1,1,5,2,2] => [2,2,4,1,1]
[1,2,1,2,5] => [2,1,2,1,4]
[1,2,1,5,2] => [2,1,2,4,1]
[1,2,2,1,5] => [2,1,1,2,4]
[1,2,2,5,1] => [2,1,1,4,2]
[1,2,5,1,2] => [2,1,4,2,1]
[1,2,5,2,1] => [2,1,4,1,2]
[1,5,1,2,2] => [2,4,2,1,1]
[1,5,2,1,2] => [2,4,1,2,1]
[1,5,2,2,1] => [2,4,1,1,2]
[2,1,1,2,5] => [1,2,2,1,4]
[2,1,1,5,2] => [1,2,2,4,1]
[2,1,2,1,5] => [1,2,1,2,4]
[2,1,2,5,1] => [1,2,1,4,2]
[2,1,5,1,2] => [1,2,4,2,1]
[2,1,5,2,1] => [1,2,4,1,2]
[2,2,1,1,5] => [1,1,2,2,4]
[2,2,1,5,1] => [1,1,2,4,2]
[2,2,5,1,1] => [1,1,4,2,2]
[2,5,1,1,2] => [1,4,2,2,1]
[2,5,1,2,1] => [1,4,2,1,2]
[2,5,2,1,1] => [1,4,1,2,2]
[5,1,1,2,2] => [4,2,2,1,1]
[5,1,2,1,2] => [4,2,1,2,1]
[5,1,2,2,1] => [4,2,1,1,2]
[5,2,1,1,2] => [4,1,2,2,1]
[5,2,1,2,1] => [4,1,2,1,2]
[5,2,2,1,1] => [4,1,1,2,2]
[1,1,2,3,3] => [3,3,2,1,1]
[1,1,3,2,3] => [3,3,1,2,1]
[1,1,3,3,2] => [3,3,1,1,2]
[1,2,1,3,3] => [3,2,3,1,1]
[1,2,3,1,3] => [3,2,1,3,1]
[1,2,3,3,1] => [3,2,1,1,3]
[1,3,1,2,3] => [3,1,3,2,1]
[1,3,1,3,2] => [3,1,3,1,2]
[1,3,2,1,3] => [3,1,2,3,1]
[1,3,2,3,1] => [3,1,2,1,3]
[1,3,3,1,2] => [3,1,1,3,2]
[1,3,3,2,1] => [3,1,1,2,3]
[2,1,1,3,3] => [2,3,3,1,1]
[2,1,3,1,3] => [2,3,1,3,1]
[2,1,3,3,1] => [2,3,1,1,3]
[2,3,1,1,3] => [2,1,3,3,1]
[2,3,1,3,1] => [2,1,3,1,3]
[2,3,3,1,1] => [2,1,1,3,3]
[3,1,1,2,3] => [1,3,3,2,1]
[3,1,1,3,2] => [1,3,3,1,2]
[3,1,2,1,3] => [1,3,2,3,1]
[3,1,2,3,1] => [1,3,2,1,3]
[3,1,3,1,2] => [1,3,1,3,2]
[3,1,3,2,1] => [1,3,1,2,3]
[3,2,1,1,3] => [1,2,3,3,1]
[3,2,1,3,1] => [1,2,3,1,3]
[3,2,3,1,1] => [1,2,1,3,3]
[3,3,1,1,2] => [1,1,3,3,2]
[3,3,1,2,1] => [1,1,3,2,3]
[3,3,2,1,1] => [1,1,2,3,3]
[1,1,2,3,4] => [4,4,3,2,1]
[1,1,2,4,3] => [4,4,3,1,2]
[1,1,3,2,4] => [4,4,2,3,1]
[1,1,3,4,2] => [4,4,2,1,3]
[1,1,4,2,3] => [4,4,1,3,2]
[1,1,4,3,2] => [4,4,1,2,3]
[1,2,1,3,4] => [4,3,4,2,1]
[1,2,1,4,3] => [4,3,4,1,2]
[1,2,3,1,4] => [4,3,2,4,1]
[1,2,3,4,1] => [4,3,2,1,4]
[1,2,4,1,3] => [4,3,1,4,2]
[1,2,4,3,1] => [4,3,1,2,4]
[1,3,1,2,4] => [4,2,4,3,1]
[1,3,1,4,2] => [4,2,4,1,3]
[1,3,2,1,4] => [4,2,3,4,1]
[1,3,2,4,1] => [4,2,3,1,4]
[1,3,4,1,2] => [4,2,1,4,3]
[1,3,4,2,1] => [4,2,1,3,4]
[1,4,1,2,3] => [4,1,4,3,2]
[1,4,1,3,2] => [4,1,4,2,3]
[1,4,2,1,3] => [4,1,3,4,2]
[1,4,2,3,1] => [4,1,3,2,4]
[1,4,3,1,2] => [4,1,2,4,3]
[1,4,3,2,1] => [4,1,2,3,4]
[2,1,1,3,4] => [3,4,4,2,1]
[2,1,1,4,3] => [3,4,4,1,2]
[2,1,3,1,4] => [3,4,2,4,1]
[2,1,3,4,1] => [3,4,2,1,4]
[2,1,4,1,3] => [3,4,1,4,2]
[2,1,4,3,1] => [3,4,1,2,4]
[2,3,1,1,4] => [3,2,4,4,1]
[2,3,1,4,1] => [3,2,4,1,4]
[2,3,4,1,1] => [3,2,1,4,4]
[2,4,1,1,3] => [3,1,4,4,2]
[2,4,1,3,1] => [3,1,4,2,4]
[2,4,3,1,1] => [3,1,2,4,4]
[3,1,1,2,4] => [2,4,4,3,1]
[3,1,1,4,2] => [2,4,4,1,3]
[3,1,2,1,4] => [2,4,3,4,1]
[3,1,2,4,1] => [2,4,3,1,4]
[3,1,4,1,2] => [2,4,1,4,3]
[3,1,4,2,1] => [2,4,1,3,4]
[3,2,1,1,4] => [2,3,4,4,1]
[3,2,1,4,1] => [2,3,4,1,4]
[3,2,4,1,1] => [2,3,1,4,4]
[3,4,1,1,2] => [2,1,4,4,3]
[3,4,1,2,1] => [2,1,4,3,4]
[3,4,2,1,1] => [2,1,3,4,4]
[4,1,1,2,3] => [1,4,4,3,2]
[4,1,1,3,2] => [1,4,4,2,3]
[4,1,2,1,3] => [1,4,3,4,2]
[4,1,2,3,1] => [1,4,3,2,4]
[4,1,3,1,2] => [1,4,2,4,3]
[4,1,3,2,1] => [1,4,2,3,4]
[4,2,1,1,3] => [1,3,4,4,2]
[4,2,1,3,1] => [1,3,4,2,4]
[4,2,3,1,1] => [1,3,2,4,4]
[4,3,1,1,2] => [1,2,4,4,3]
[4,3,1,2,1] => [1,2,4,3,4]
[4,3,2,1,1] => [1,2,3,4,4]
[1,1,2,3,5] => [3,3,2,1,5]
[1,1,2,5,3] => [3,3,2,5,1]
[1,1,3,2,5] => [3,3,1,2,5]
[1,1,3,5,2] => [3,3,1,5,2]
[1,1,5,2,3] => [3,3,5,2,1]
[1,1,5,3,2] => [3,3,5,1,2]
[1,2,1,3,5] => [3,2,3,1,5]
[1,2,1,5,3] => [3,2,3,5,1]
[1,2,3,1,5] => [3,2,1,3,5]
[1,2,3,5,1] => [3,2,1,5,3]
[1,2,5,1,3] => [3,2,5,3,1]
[1,2,5,3,1] => [3,2,5,1,3]
[1,3,1,2,5] => [3,1,3,2,5]
[1,3,1,5,2] => [3,1,3,5,2]
[1,3,2,1,5] => [3,1,2,3,5]
[1,3,2,5,1] => [3,1,2,5,3]
[1,3,5,1,2] => [3,1,5,3,2]
[1,3,5,2,1] => [3,1,5,2,3]
[1,5,1,2,3] => [3,5,3,2,1]
[1,5,1,3,2] => [3,5,3,1,2]
[1,5,2,1,3] => [3,5,2,3,1]
[1,5,2,3,1] => [3,5,2,1,3]
[1,5,3,1,2] => [3,5,1,3,2]
[1,5,3,2,1] => [3,5,1,2,3]
[2,1,1,3,5] => [2,3,3,1,5]
[2,1,1,5,3] => [2,3,3,5,1]
[2,1,3,1,5] => [2,3,1,3,5]
[2,1,3,5,1] => [2,3,1,5,3]
[2,1,5,1,3] => [2,3,5,3,1]
[2,1,5,3,1] => [2,3,5,1,3]
[2,3,1,1,5] => [2,1,3,3,5]
[2,3,1,5,1] => [2,1,3,5,3]
[2,3,5,1,1] => [2,1,5,3,3]
[2,5,1,1,3] => [2,5,3,3,1]
[2,5,1,3,1] => [2,5,3,1,3]
[2,5,3,1,1] => [2,5,1,3,3]
[3,1,1,2,5] => [1,3,3,2,5]
[3,1,1,5,2] => [1,3,3,5,2]
[3,1,2,1,5] => [1,3,2,3,5]
[3,1,2,5,1] => [1,3,2,5,3]
[3,1,5,1,2] => [1,3,5,3,2]
[3,1,5,2,1] => [1,3,5,2,3]
[3,2,1,1,5] => [1,2,3,3,5]
[3,2,1,5,1] => [1,2,3,5,3]
[3,2,5,1,1] => [1,2,5,3,3]
[3,5,1,1,2] => [1,5,3,3,2]
[3,5,1,2,1] => [1,5,3,2,3]
[3,5,2,1,1] => [1,5,2,3,3]
[5,1,1,2,3] => [5,3,3,2,1]
[5,1,1,3,2] => [5,3,3,1,2]
[5,1,2,1,3] => [5,3,2,3,1]
[5,1,2,3,1] => [5,3,2,1,3]
[5,1,3,1,2] => [5,3,1,3,2]
[5,1,3,2,1] => [5,3,1,2,3]
[5,2,1,1,3] => [5,2,3,3,1]
[5,2,1,3,1] => [5,2,3,1,3]
[5,2,3,1,1] => [5,2,1,3,3]
[5,3,1,1,2] => [5,1,3,3,2]
[5,3,1,2,1] => [5,1,3,2,3]
[5,3,2,1,1] => [5,1,2,3,3]
[1,1,2,4,4] => [4,4,3,1,1]
[1,1,4,2,4] => [4,4,1,3,1]
[1,1,4,4,2] => [4,4,1,1,3]
[1,2,1,4,4] => [4,3,4,1,1]
[1,2,4,1,4] => [4,3,1,4,1]
[1,2,4,4,1] => [4,3,1,1,4]
[1,4,1,2,4] => [4,1,4,3,1]
[1,4,1,4,2] => [4,1,4,1,3]
[1,4,2,1,4] => [4,1,3,4,1]
[1,4,2,4,1] => [4,1,3,1,4]
[1,4,4,1,2] => [4,1,1,4,3]
[1,4,4,2,1] => [4,1,1,3,4]
[2,1,1,4,4] => [3,4,4,1,1]
[2,1,4,1,4] => [3,4,1,4,1]
[2,1,4,4,1] => [3,4,1,1,4]
[2,4,1,1,4] => [3,1,4,4,1]
[2,4,1,4,1] => [3,1,4,1,4]
[2,4,4,1,1] => [3,1,1,4,4]
[4,1,1,2,4] => [1,4,4,3,1]
[4,1,1,4,2] => [1,4,4,1,3]
[4,1,2,1,4] => [1,4,3,4,1]
[4,1,2,4,1] => [1,4,3,1,4]
[4,1,4,1,2] => [1,4,1,4,3]
[4,1,4,2,1] => [1,4,1,3,4]
[4,2,1,1,4] => [1,3,4,4,1]
[4,2,1,4,1] => [1,3,4,1,4]
[4,2,4,1,1] => [1,3,1,4,4]
[4,4,1,1,2] => [1,1,4,4,3]
[4,4,1,2,1] => [1,1,4,3,4]
[4,4,2,1,1] => [1,1,3,4,4]
[1,1,2,4,5] => [2,2,1,5,4]
[1,1,2,5,4] => [2,2,1,4,5]
[1,1,4,2,5] => [2,2,5,1,4]
[1,1,4,5,2] => [2,2,5,4,1]
[1,1,5,2,4] => [2,2,4,1,5]
[1,1,5,4,2] => [2,2,4,5,1]
[1,2,1,4,5] => [2,1,2,5,4]
[1,2,1,5,4] => [2,1,2,4,5]
[1,2,4,1,5] => [2,1,5,2,4]
[1,2,4,5,1] => [2,1,5,4,2]
[1,2,5,1,4] => [2,1,4,2,5]
[1,2,5,4,1] => [2,1,4,5,2]
[1,4,1,2,5] => [2,5,2,1,4]
[1,4,1,5,2] => [2,5,2,4,1]
[1,4,2,1,5] => [2,5,1,2,4]
[1,4,2,5,1] => [2,5,1,4,2]
[1,4,5,1,2] => [2,5,4,2,1]
[1,4,5,2,1] => [2,5,4,1,2]
[1,5,1,2,4] => [2,4,2,1,5]
[1,5,1,4,2] => [2,4,2,5,1]
[1,5,2,1,4] => [2,4,1,2,5]
[1,5,2,4,1] => [2,4,1,5,2]
[1,5,4,1,2] => [2,4,5,2,1]
[1,5,4,2,1] => [2,4,5,1,2]
[2,1,1,4,5] => [1,2,2,5,4]
[2,1,1,5,4] => [1,2,2,4,5]
[2,1,4,1,5] => [1,2,5,2,4]
[2,1,4,5,1] => [1,2,5,4,2]
[2,1,5,1,4] => [1,2,4,2,5]
[2,1,5,4,1] => [1,2,4,5,2]
[2,4,1,1,5] => [1,5,2,2,4]
[2,4,1,5,1] => [1,5,2,4,2]
[2,4,5,1,1] => [1,5,4,2,2]
[2,5,1,1,4] => [1,4,2,2,5]
[2,5,1,4,1] => [1,4,2,5,2]
[2,5,4,1,1] => [1,4,5,2,2]
[4,1,1,2,5] => [5,2,2,1,4]
[4,1,1,5,2] => [5,2,2,4,1]
[4,1,2,1,5] => [5,2,1,2,4]
[4,1,2,5,1] => [5,2,1,4,2]
[4,1,5,1,2] => [5,2,4,2,1]
[4,1,5,2,1] => [5,2,4,1,2]
[4,2,1,1,5] => [5,1,2,2,4]
[4,2,1,5,1] => [5,1,2,4,2]
[4,2,5,1,1] => [5,1,4,2,2]
[4,5,1,1,2] => [5,4,2,2,1]
[4,5,1,2,1] => [5,4,2,1,2]
[4,5,2,1,1] => [5,4,1,2,2]
[5,1,1,2,4] => [4,2,2,1,5]
[5,1,1,4,2] => [4,2,2,5,1]
[5,1,2,1,4] => [4,2,1,2,5]
[5,1,2,4,1] => [4,2,1,5,2]
[5,1,4,1,2] => [4,2,5,2,1]
[5,1,4,2,1] => [4,2,5,1,2]
[5,2,1,1,4] => [4,1,2,2,5]
[5,2,1,4,1] => [4,1,2,5,2]
[5,2,4,1,1] => [4,1,5,2,2]
[5,4,1,1,2] => [4,5,2,2,1]
[5,4,1,2,1] => [4,5,2,1,2]
[5,4,2,1,1] => [4,5,1,2,2]
[1,1,3,3,3] => [3,3,1,1,1]
[1,3,1,3,3] => [3,1,3,1,1]
[1,3,3,1,3] => [3,1,1,3,1]
[1,3,3,3,1] => [3,1,1,1,3]
[3,1,1,3,3] => [1,3,3,1,1]
[3,1,3,1,3] => [1,3,1,3,1]
[3,1,3,3,1] => [1,3,1,1,3]
[3,3,1,1,3] => [1,1,3,3,1]
[3,3,1,3,1] => [1,1,3,1,3]
[3,3,3,1,1] => [1,1,1,3,3]
[1,1,3,3,4] => [4,4,2,2,1]
[1,1,3,4,3] => [4,4,2,1,2]
[1,1,4,3,3] => [4,4,1,2,2]
[1,3,1,3,4] => [4,2,4,2,1]
[1,3,1,4,3] => [4,2,4,1,2]
[1,3,3,1,4] => [4,2,2,4,1]
[1,3,3,4,1] => [4,2,2,1,4]
[1,3,4,1,3] => [4,2,1,4,2]
[1,3,4,3,1] => [4,2,1,2,4]
[1,4,1,3,3] => [4,1,4,2,2]
[1,4,3,1,3] => [4,1,2,4,2]
[1,4,3,3,1] => [4,1,2,2,4]
[3,1,1,3,4] => [2,4,4,2,1]
[3,1,1,4,3] => [2,4,4,1,2]
[3,1,3,1,4] => [2,4,2,4,1]
[3,1,3,4,1] => [2,4,2,1,4]
[3,1,4,1,3] => [2,4,1,4,2]
[3,1,4,3,1] => [2,4,1,2,4]
[3,3,1,1,4] => [2,2,4,4,1]
[3,3,1,4,1] => [2,2,4,1,4]
[3,3,4,1,1] => [2,2,1,4,4]
[3,4,1,1,3] => [2,1,4,4,2]
[3,4,1,3,1] => [2,1,4,2,4]
[3,4,3,1,1] => [2,1,2,4,4]
[4,1,1,3,3] => [1,4,4,2,2]
[4,1,3,1,3] => [1,4,2,4,2]
[4,1,3,3,1] => [1,4,2,2,4]
[4,3,1,1,3] => [1,2,4,4,2]
[4,3,1,3,1] => [1,2,4,2,4]
[4,3,3,1,1] => [1,2,2,4,4]
[1,1,3,3,5] => [3,3,1,1,5]
[1,1,3,5,3] => [3,3,1,5,1]
[1,1,5,3,3] => [3,3,5,1,1]
[1,3,1,3,5] => [3,1,3,1,5]
[1,3,1,5,3] => [3,1,3,5,1]
[1,3,3,1,5] => [3,1,1,3,5]
[1,3,3,5,1] => [3,1,1,5,3]
[1,3,5,1,3] => [3,1,5,3,1]
[1,3,5,3,1] => [3,1,5,1,3]
[1,5,1,3,3] => [3,5,3,1,1]
[1,5,3,1,3] => [3,5,1,3,1]
[1,5,3,3,1] => [3,5,1,1,3]
[3,1,1,3,5] => [1,3,3,1,5]
[3,1,1,5,3] => [1,3,3,5,1]
[3,1,3,1,5] => [1,3,1,3,5]
[3,1,3,5,1] => [1,3,1,5,3]
[3,1,5,1,3] => [1,3,5,3,1]
[3,1,5,3,1] => [1,3,5,1,3]
[3,3,1,1,5] => [1,1,3,3,5]
[3,3,1,5,1] => [1,1,3,5,3]
[3,3,5,1,1] => [1,1,5,3,3]
[3,5,1,1,3] => [1,5,3,3,1]
[3,5,1,3,1] => [1,5,3,1,3]
[3,5,3,1,1] => [1,5,1,3,3]
[5,1,1,3,3] => [5,3,3,1,1]
[5,1,3,1,3] => [5,3,1,3,1]
[5,1,3,3,1] => [5,3,1,1,3]
[5,3,1,1,3] => [5,1,3,3,1]
[5,3,1,3,1] => [5,1,3,1,3]
[5,3,3,1,1] => [5,1,1,3,3]
[1,1,3,4,4] => [4,4,2,1,1]
[1,1,4,3,4] => [4,4,1,2,1]
[1,1,4,4,3] => [4,4,1,1,2]
[1,3,1,4,4] => [4,2,4,1,1]
[1,3,4,1,4] => [4,2,1,4,1]
[1,3,4,4,1] => [4,2,1,1,4]
[1,4,1,3,4] => [4,1,4,2,1]
[1,4,1,4,3] => [4,1,4,1,2]
[1,4,3,1,4] => [4,1,2,4,1]
[1,4,3,4,1] => [4,1,2,1,4]
[1,4,4,1,3] => [4,1,1,4,2]
[1,4,4,3,1] => [4,1,1,2,4]
[3,1,1,4,4] => [2,4,4,1,1]
[3,1,4,1,4] => [2,4,1,4,1]
[3,1,4,4,1] => [2,4,1,1,4]
[3,4,1,1,4] => [2,1,4,4,1]
[3,4,1,4,1] => [2,1,4,1,4]
[3,4,4,1,1] => [2,1,1,4,4]
[4,1,1,3,4] => [1,4,4,2,1]
[4,1,1,4,3] => [1,4,4,1,2]
[4,1,3,1,4] => [1,4,2,4,1]
[4,1,3,4,1] => [1,4,2,1,4]
[4,1,4,1,3] => [1,4,1,4,2]
[4,1,4,3,1] => [1,4,1,2,4]
[4,3,1,1,4] => [1,2,4,4,1]
[4,3,1,4,1] => [1,2,4,1,4]
[4,3,4,1,1] => [1,2,1,4,4]
[4,4,1,1,3] => [1,1,4,4,2]
[4,4,1,3,1] => [1,1,4,2,4]
[4,4,3,1,1] => [1,1,2,4,4]
[1,1,3,4,5] => [1,1,5,4,3]
[1,1,3,5,4] => [1,1,5,3,4]
[1,1,4,3,5] => [1,1,4,5,3]
[1,1,4,5,3] => [1,1,4,3,5]
[1,1,5,3,4] => [1,1,3,5,4]
[1,1,5,4,3] => [1,1,3,4,5]
[1,3,1,4,5] => [1,5,1,4,3]
[1,3,1,5,4] => [1,5,1,3,4]
[1,3,4,1,5] => [1,5,4,1,3]
[1,3,4,5,1] => [1,5,4,3,1]
[1,3,5,1,4] => [1,5,3,1,4]
[1,3,5,4,1] => [1,5,3,4,1]
[1,4,1,3,5] => [1,4,1,5,3]
[1,4,1,5,3] => [1,4,1,3,5]
[1,4,3,1,5] => [1,4,5,1,3]
[1,4,3,5,1] => [1,4,5,3,1]
[1,4,5,1,3] => [1,4,3,1,5]
[1,4,5,3,1] => [1,4,3,5,1]
[1,5,1,3,4] => [1,3,1,5,4]
[1,5,1,4,3] => [1,3,1,4,5]
[1,5,3,1,4] => [1,3,5,1,4]
[1,5,3,4,1] => [1,3,5,4,1]
[1,5,4,1,3] => [1,3,4,1,5]
[1,5,4,3,1] => [1,3,4,5,1]
[3,1,1,4,5] => [5,1,1,4,3]
[3,1,1,5,4] => [5,1,1,3,4]
[3,1,4,1,5] => [5,1,4,1,3]
[3,1,4,5,1] => [5,1,4,3,1]
[3,1,5,1,4] => [5,1,3,1,4]
[3,1,5,4,1] => [5,1,3,4,1]
[3,4,1,1,5] => [5,4,1,1,3]
[3,4,1,5,1] => [5,4,1,3,1]
[3,4,5,1,1] => [5,4,3,1,1]
[3,5,1,1,4] => [5,3,1,1,4]
[3,5,1,4,1] => [5,3,1,4,1]
[3,5,4,1,1] => [5,3,4,1,1]
[4,1,1,3,5] => [4,1,1,5,3]
[4,1,1,5,3] => [4,1,1,3,5]
[4,1,3,1,5] => [4,1,5,1,3]
[4,1,3,5,1] => [4,1,5,3,1]
[4,1,5,1,3] => [4,1,3,1,5]
[4,1,5,3,1] => [4,1,3,5,1]
[4,3,1,1,5] => [4,5,1,1,3]
[4,3,1,5,1] => [4,5,1,3,1]
[4,3,5,1,1] => [4,5,3,1,1]
[4,5,1,1,3] => [4,3,1,1,5]
[4,5,1,3,1] => [4,3,1,5,1]
[4,5,3,1,1] => [4,3,5,1,1]
[5,1,1,3,4] => [3,1,1,5,4]
[5,1,1,4,3] => [3,1,1,4,5]
[5,1,3,1,4] => [3,1,5,1,4]
[5,1,3,4,1] => [3,1,5,4,1]
[5,1,4,1,3] => [3,1,4,1,5]
[5,1,4,3,1] => [3,1,4,5,1]
[5,3,1,1,4] => [3,5,1,1,4]
[5,3,1,4,1] => [3,5,1,4,1]
[5,3,4,1,1] => [3,5,4,1,1]
[5,4,1,1,3] => [3,4,1,1,5]
[5,4,1,3,1] => [3,4,1,5,1]
[5,4,3,1,1] => [3,4,5,1,1]
[1,2,2,2,2] => [2,1,1,1,1]
[2,1,2,2,2] => [1,2,1,1,1]
[2,2,1,2,2] => [1,1,2,1,1]
[2,2,2,1,2] => [1,1,1,2,1]
[2,2,2,2,1] => [1,1,1,1,2]
[1,2,2,2,3] => [3,2,2,2,1]
[1,2,2,3,2] => [3,2,2,1,2]
[1,2,3,2,2] => [3,2,1,2,2]
[1,3,2,2,2] => [3,1,2,2,2]
[2,1,2,2,3] => [2,3,2,2,1]
[2,1,2,3,2] => [2,3,2,1,2]
[2,1,3,2,2] => [2,3,1,2,2]
[2,2,1,2,3] => [2,2,3,2,1]
[2,2,1,3,2] => [2,2,3,1,2]
[2,2,2,1,3] => [2,2,2,3,1]
[2,2,2,3,1] => [2,2,2,1,3]
[2,2,3,1,2] => [2,2,1,3,2]
[2,2,3,2,1] => [2,2,1,2,3]
[2,3,1,2,2] => [2,1,3,2,2]
[2,3,2,1,2] => [2,1,2,3,2]
[2,3,2,2,1] => [2,1,2,2,3]
[3,1,2,2,2] => [1,3,2,2,2]
[3,2,1,2,2] => [1,2,3,2,2]
[3,2,2,1,2] => [1,2,2,3,2]
[3,2,2,2,1] => [1,2,2,2,3]
[1,2,2,2,4] => [2,1,1,1,5]
[1,2,2,4,2] => [2,1,1,5,1]
[1,2,4,2,2] => [2,1,5,1,1]
[1,4,2,2,2] => [2,5,1,1,1]
[2,1,2,2,4] => [1,2,1,1,5]
[2,1,2,4,2] => [1,2,1,5,1]
[2,1,4,2,2] => [1,2,5,1,1]
[2,2,1,2,4] => [1,1,2,1,5]
[2,2,1,4,2] => [1,1,2,5,1]
[2,2,2,1,4] => [1,1,1,2,5]
[2,2,2,4,1] => [1,1,1,5,2]
[2,2,4,1,2] => [1,1,5,2,1]
[2,2,4,2,1] => [1,1,5,1,2]
[2,4,1,2,2] => [1,5,2,1,1]
[2,4,2,1,2] => [1,5,1,2,1]
[2,4,2,2,1] => [1,5,1,1,2]
[4,1,2,2,2] => [5,2,1,1,1]
[4,2,1,2,2] => [5,1,2,1,1]
[4,2,2,1,2] => [5,1,1,2,1]
[4,2,2,2,1] => [5,1,1,1,2]
[1,2,2,2,5] => [2,1,1,1,4]
[1,2,2,5,2] => [2,1,1,4,1]
[1,2,5,2,2] => [2,1,4,1,1]
[1,5,2,2,2] => [2,4,1,1,1]
[2,1,2,2,5] => [1,2,1,1,4]
[2,1,2,5,2] => [1,2,1,4,1]
[2,1,5,2,2] => [1,2,4,1,1]
[2,2,1,2,5] => [1,1,2,1,4]
[2,2,1,5,2] => [1,1,2,4,1]
[2,2,2,1,5] => [1,1,1,2,4]
[2,2,2,5,1] => [1,1,1,4,2]
[2,2,5,1,2] => [1,1,4,2,1]
[2,2,5,2,1] => [1,1,4,1,2]
[2,5,1,2,2] => [1,4,2,1,1]
[2,5,2,1,2] => [1,4,1,2,1]
[2,5,2,2,1] => [1,4,1,1,2]
[5,1,2,2,2] => [4,2,1,1,1]
[5,2,1,2,2] => [4,1,2,1,1]
[5,2,2,1,2] => [4,1,1,2,1]
[5,2,2,2,1] => [4,1,1,1,2]
[1,2,2,3,3] => [3,2,2,1,1]
[1,2,3,2,3] => [3,2,1,2,1]
[1,2,3,3,2] => [3,2,1,1,2]
[1,3,2,2,3] => [3,1,2,2,1]
[1,3,2,3,2] => [3,1,2,1,2]
[1,3,3,2,2] => [3,1,1,2,2]
[2,1,2,3,3] => [2,3,2,1,1]
[2,1,3,2,3] => [2,3,1,2,1]
[2,1,3,3,2] => [2,3,1,1,2]
[2,2,1,3,3] => [2,2,3,1,1]
[2,2,3,1,3] => [2,2,1,3,1]
[2,2,3,3,1] => [2,2,1,1,3]
[2,3,1,2,3] => [2,1,3,2,1]
[2,3,1,3,2] => [2,1,3,1,2]
[2,3,2,1,3] => [2,1,2,3,1]
[2,3,2,3,1] => [2,1,2,1,3]
[2,3,3,1,2] => [2,1,1,3,2]
[2,3,3,2,1] => [2,1,1,2,3]
[3,1,2,2,3] => [1,3,2,2,1]
[3,1,2,3,2] => [1,3,2,1,2]
[3,1,3,2,2] => [1,3,1,2,2]
[3,2,1,2,3] => [1,2,3,2,1]
[3,2,1,3,2] => [1,2,3,1,2]
[3,2,2,1,3] => [1,2,2,3,1]
[3,2,2,3,1] => [1,2,2,1,3]
[3,2,3,1,2] => [1,2,1,3,2]
[3,2,3,2,1] => [1,2,1,2,3]
[3,3,1,2,2] => [1,1,3,2,2]
[3,3,2,1,2] => [1,1,2,3,2]
[3,3,2,2,1] => [1,1,2,2,3]
[1,2,2,3,4] => [4,3,3,2,1]
[1,2,2,4,3] => [4,3,3,1,2]
[1,2,3,2,4] => [4,3,2,3,1]
[1,2,3,4,2] => [4,3,2,1,3]
[1,2,4,2,3] => [4,3,1,3,2]
[1,2,4,3,2] => [4,3,1,2,3]
[1,3,2,2,4] => [4,2,3,3,1]
[1,3,2,4,2] => [4,2,3,1,3]
[1,3,4,2,2] => [4,2,1,3,3]
[1,4,2,2,3] => [4,1,3,3,2]
[1,4,2,3,2] => [4,1,3,2,3]
[1,4,3,2,2] => [4,1,2,3,3]
[2,1,2,3,4] => [3,4,3,2,1]
[2,1,2,4,3] => [3,4,3,1,2]
[2,1,3,2,4] => [3,4,2,3,1]
[2,1,3,4,2] => [3,4,2,1,3]
[2,1,4,2,3] => [3,4,1,3,2]
[2,1,4,3,2] => [3,4,1,2,3]
[2,2,1,3,4] => [3,3,4,2,1]
[2,2,1,4,3] => [3,3,4,1,2]
[2,2,3,1,4] => [3,3,2,4,1]
[2,2,3,4,1] => [3,3,2,1,4]
[2,2,4,1,3] => [3,3,1,4,2]
[2,2,4,3,1] => [3,3,1,2,4]
[2,3,1,2,4] => [3,2,4,3,1]
[2,3,1,4,2] => [3,2,4,1,3]
[2,3,2,1,4] => [3,2,3,4,1]
[2,3,2,4,1] => [3,2,3,1,4]
[2,3,4,1,2] => [3,2,1,4,3]
[2,3,4,2,1] => [3,2,1,3,4]
[2,4,1,2,3] => [3,1,4,3,2]
[2,4,1,3,2] => [3,1,4,2,3]
[2,4,2,1,3] => [3,1,3,4,2]
[2,4,2,3,1] => [3,1,3,2,4]
[2,4,3,1,2] => [3,1,2,4,3]
[2,4,3,2,1] => [3,1,2,3,4]
[3,1,2,2,4] => [2,4,3,3,1]
[3,1,2,4,2] => [2,4,3,1,3]
[3,1,4,2,2] => [2,4,1,3,3]
[3,2,1,2,4] => [2,3,4,3,1]
[3,2,1,4,2] => [2,3,4,1,3]
[3,2,2,1,4] => [2,3,3,4,1]
[3,2,2,4,1] => [2,3,3,1,4]
[3,2,4,1,2] => [2,3,1,4,3]
[3,2,4,2,1] => [2,3,1,3,4]
[3,4,1,2,2] => [2,1,4,3,3]
[3,4,2,1,2] => [2,1,3,4,3]
[3,4,2,2,1] => [2,1,3,3,4]
[4,1,2,2,3] => [1,4,3,3,2]
[4,1,2,3,2] => [1,4,3,2,3]
[4,1,3,2,2] => [1,4,2,3,3]
[4,2,1,2,3] => [1,3,4,3,2]
[4,2,1,3,2] => [1,3,4,2,3]
[4,2,2,1,3] => [1,3,3,4,2]
[4,2,2,3,1] => [1,3,3,2,4]
[4,2,3,1,2] => [1,3,2,4,3]
[4,2,3,2,1] => [1,3,2,3,4]
[4,3,1,2,2] => [1,2,4,3,3]
[4,3,2,1,2] => [1,2,3,4,3]
[4,3,2,2,1] => [1,2,3,3,4]
[1,2,2,3,5] => [3,2,2,1,5]
[1,2,2,5,3] => [3,2,2,5,1]
[1,2,3,2,5] => [3,2,1,2,5]
[1,2,3,5,2] => [3,2,1,5,2]
[1,2,5,2,3] => [3,2,5,2,1]
[1,2,5,3,2] => [3,2,5,1,2]
[1,3,2,2,5] => [3,1,2,2,5]
[1,3,2,5,2] => [3,1,2,5,2]
[1,3,5,2,2] => [3,1,5,2,2]
[1,5,2,2,3] => [3,5,2,2,1]
[1,5,2,3,2] => [3,5,2,1,2]
[1,5,3,2,2] => [3,5,1,2,2]
[2,1,2,3,5] => [2,3,2,1,5]
[2,1,2,5,3] => [2,3,2,5,1]
[2,1,3,2,5] => [2,3,1,2,5]
[2,1,3,5,2] => [2,3,1,5,2]
[2,1,5,2,3] => [2,3,5,2,1]
[2,1,5,3,2] => [2,3,5,1,2]
[2,2,1,3,5] => [2,2,3,1,5]
[2,2,1,5,3] => [2,2,3,5,1]
[2,2,3,1,5] => [2,2,1,3,5]
[2,2,3,5,1] => [2,2,1,5,3]
[2,2,5,1,3] => [2,2,5,3,1]
[2,2,5,3,1] => [2,2,5,1,3]
[2,3,1,2,5] => [2,1,3,2,5]
[2,3,1,5,2] => [2,1,3,5,2]
[2,3,2,1,5] => [2,1,2,3,5]
[2,3,2,5,1] => [2,1,2,5,3]
[2,3,5,1,2] => [2,1,5,3,2]
[2,3,5,2,1] => [2,1,5,2,3]
[2,5,1,2,3] => [2,5,3,2,1]
[2,5,1,3,2] => [2,5,3,1,2]
[2,5,2,1,3] => [2,5,2,3,1]
[2,5,2,3,1] => [2,5,2,1,3]
[2,5,3,1,2] => [2,5,1,3,2]
[2,5,3,2,1] => [2,5,1,2,3]
[3,1,2,2,5] => [1,3,2,2,5]
[3,1,2,5,2] => [1,3,2,5,2]
[3,1,5,2,2] => [1,3,5,2,2]
[3,2,1,2,5] => [1,2,3,2,5]
[3,2,1,5,2] => [1,2,3,5,2]
[3,2,2,1,5] => [1,2,2,3,5]
[3,2,2,5,1] => [1,2,2,5,3]
[3,2,5,1,2] => [1,2,5,3,2]
[3,2,5,2,1] => [1,2,5,2,3]
[3,5,1,2,2] => [1,5,3,2,2]
[3,5,2,1,2] => [1,5,2,3,2]
[3,5,2,2,1] => [1,5,2,2,3]
[5,1,2,2,3] => [5,3,2,2,1]
[5,1,2,3,2] => [5,3,2,1,2]
[5,1,3,2,2] => [5,3,1,2,2]
[5,2,1,2,3] => [5,2,3,2,1]
[5,2,1,3,2] => [5,2,3,1,2]
[5,2,2,1,3] => [5,2,2,3,1]
[5,2,2,3,1] => [5,2,2,1,3]
[5,2,3,1,2] => [5,2,1,3,2]
[5,2,3,2,1] => [5,2,1,2,3]
[5,3,1,2,2] => [5,1,3,2,2]
[5,3,2,1,2] => [5,1,2,3,2]
[5,3,2,2,1] => [5,1,2,2,3]
[1,2,2,4,4] => [4,3,3,1,1]
[1,2,4,2,4] => [4,3,1,3,1]
[1,2,4,4,2] => [4,3,1,1,3]
[1,4,2,2,4] => [4,1,3,3,1]
[1,4,2,4,2] => [4,1,3,1,3]
[1,4,4,2,2] => [4,1,1,3,3]
[2,1,2,4,4] => [3,4,3,1,1]
[2,1,4,2,4] => [3,4,1,3,1]
[2,1,4,4,2] => [3,4,1,1,3]
[2,2,1,4,4] => [3,3,4,1,1]
[2,2,4,1,4] => [3,3,1,4,1]
[2,2,4,4,1] => [3,3,1,1,4]
[2,4,1,2,4] => [3,1,4,3,1]
[2,4,1,4,2] => [3,1,4,1,3]
[2,4,2,1,4] => [3,1,3,4,1]
[2,4,2,4,1] => [3,1,3,1,4]
[2,4,4,1,2] => [3,1,1,4,3]
[2,4,4,2,1] => [3,1,1,3,4]
[4,1,2,2,4] => [1,4,3,3,1]
[4,1,2,4,2] => [1,4,3,1,3]
[4,1,4,2,2] => [1,4,1,3,3]
[4,2,1,2,4] => [1,3,4,3,1]
[4,2,1,4,2] => [1,3,4,1,3]
[4,2,2,1,4] => [1,3,3,4,1]
[4,2,2,4,1] => [1,3,3,1,4]
[4,2,4,1,2] => [1,3,1,4,3]
[4,2,4,2,1] => [1,3,1,3,4]
[4,4,1,2,2] => [1,1,4,3,3]
[4,4,2,1,2] => [1,1,3,4,3]
[4,4,2,2,1] => [1,1,3,3,4]
[1,2,2,4,5] => [2,1,1,5,4]
[1,2,2,5,4] => [2,1,1,4,5]
[1,2,4,2,5] => [2,1,5,1,4]
[1,2,4,5,2] => [2,1,5,4,1]
[1,2,5,2,4] => [2,1,4,1,5]
[1,2,5,4,2] => [2,1,4,5,1]
[1,4,2,2,5] => [2,5,1,1,4]
[1,4,2,5,2] => [2,5,1,4,1]
[1,4,5,2,2] => [2,5,4,1,1]
[1,5,2,2,4] => [2,4,1,1,5]
[1,5,2,4,2] => [2,4,1,5,1]
[1,5,4,2,2] => [2,4,5,1,1]
[2,1,2,4,5] => [1,2,1,5,4]
[2,1,2,5,4] => [1,2,1,4,5]
[2,1,4,2,5] => [1,2,5,1,4]
[2,1,4,5,2] => [1,2,5,4,1]
[2,1,5,2,4] => [1,2,4,1,5]
[2,1,5,4,2] => [1,2,4,5,1]
[2,2,1,4,5] => [1,1,2,5,4]
[2,2,1,5,4] => [1,1,2,4,5]
[2,2,4,1,5] => [1,1,5,2,4]
[2,2,4,5,1] => [1,1,5,4,2]
[2,2,5,1,4] => [1,1,4,2,5]
[2,2,5,4,1] => [1,1,4,5,2]
[2,4,1,2,5] => [1,5,2,1,4]
[2,4,1,5,2] => [1,5,2,4,1]
[2,4,2,1,5] => [1,5,1,2,4]
[2,4,2,5,1] => [1,5,1,4,2]
[2,4,5,1,2] => [1,5,4,2,1]
[2,4,5,2,1] => [1,5,4,1,2]
[2,5,1,2,4] => [1,4,2,1,5]
[2,5,1,4,2] => [1,4,2,5,1]
[2,5,2,1,4] => [1,4,1,2,5]
[2,5,2,4,1] => [1,4,1,5,2]
[2,5,4,1,2] => [1,4,5,2,1]
[2,5,4,2,1] => [1,4,5,1,2]
[4,1,2,2,5] => [5,2,1,1,4]
[4,1,2,5,2] => [5,2,1,4,1]
[4,1,5,2,2] => [5,2,4,1,1]
[4,2,1,2,5] => [5,1,2,1,4]
[4,2,1,5,2] => [5,1,2,4,1]
[4,2,2,1,5] => [5,1,1,2,4]
[4,2,2,5,1] => [5,1,1,4,2]
[4,2,5,1,2] => [5,1,4,2,1]
[4,2,5,2,1] => [5,1,4,1,2]
[4,5,1,2,2] => [5,4,2,1,1]
[4,5,2,1,2] => [5,4,1,2,1]
[4,5,2,2,1] => [5,4,1,1,2]
[5,1,2,2,4] => [4,2,1,1,5]
[5,1,2,4,2] => [4,2,1,5,1]
[5,1,4,2,2] => [4,2,5,1,1]
[5,2,1,2,4] => [4,1,2,1,5]
[5,2,1,4,2] => [4,1,2,5,1]
[5,2,2,1,4] => [4,1,1,2,5]
[5,2,2,4,1] => [4,1,1,5,2]
[5,2,4,1,2] => [4,1,5,2,1]
[5,2,4,2,1] => [4,1,5,1,2]
[5,4,1,2,2] => [4,5,2,1,1]
[5,4,2,1,2] => [4,5,1,2,1]
[5,4,2,2,1] => [4,5,1,1,2]
[1,2,3,3,3] => [3,2,1,1,1]
[1,3,2,3,3] => [3,1,2,1,1]
[1,3,3,2,3] => [3,1,1,2,1]
[1,3,3,3,2] => [3,1,1,1,2]
[2,1,3,3,3] => [2,3,1,1,1]
[2,3,1,3,3] => [2,1,3,1,1]
[2,3,3,1,3] => [2,1,1,3,1]
[2,3,3,3,1] => [2,1,1,1,3]
[3,1,2,3,3] => [1,3,2,1,1]
[3,1,3,2,3] => [1,3,1,2,1]
[3,1,3,3,2] => [1,3,1,1,2]
[3,2,1,3,3] => [1,2,3,1,1]
[3,2,3,1,3] => [1,2,1,3,1]
[3,2,3,3,1] => [1,2,1,1,3]
[3,3,1,2,3] => [1,1,3,2,1]
[3,3,1,3,2] => [1,1,3,1,2]
[3,3,2,1,3] => [1,1,2,3,1]
[3,3,2,3,1] => [1,1,2,1,3]
[3,3,3,1,2] => [1,1,1,3,2]
[3,3,3,2,1] => [1,1,1,2,3]
[1,2,3,3,4] => [4,3,2,2,1]
[1,2,3,4,3] => [4,3,2,1,2]
[1,2,4,3,3] => [4,3,1,2,2]
[1,3,2,3,4] => [4,2,3,2,1]
[1,3,2,4,3] => [4,2,3,1,2]
[1,3,3,2,4] => [4,2,2,3,1]
[1,3,3,4,2] => [4,2,2,1,3]
[1,3,4,2,3] => [4,2,1,3,2]
[1,3,4,3,2] => [4,2,1,2,3]
[1,4,2,3,3] => [4,1,3,2,2]
[1,4,3,2,3] => [4,1,2,3,2]
[1,4,3,3,2] => [4,1,2,2,3]
[2,1,3,3,4] => [3,4,2,2,1]
[2,1,3,4,3] => [3,4,2,1,2]
[2,1,4,3,3] => [3,4,1,2,2]
[2,3,1,3,4] => [3,2,4,2,1]
[2,3,1,4,3] => [3,2,4,1,2]
[2,3,3,1,4] => [3,2,2,4,1]
[2,3,3,4,1] => [3,2,2,1,4]
[2,3,4,1,3] => [3,2,1,4,2]
[2,3,4,3,1] => [3,2,1,2,4]
[2,4,1,3,3] => [3,1,4,2,2]
[2,4,3,1,3] => [3,1,2,4,2]
[2,4,3,3,1] => [3,1,2,2,4]
[3,1,2,3,4] => [2,4,3,2,1]
[3,1,2,4,3] => [2,4,3,1,2]
[3,1,3,2,4] => [2,4,2,3,1]
[3,1,3,4,2] => [2,4,2,1,3]
[3,1,4,2,3] => [2,4,1,3,2]
[3,1,4,3,2] => [2,4,1,2,3]
[3,2,1,3,4] => [2,3,4,2,1]
[3,2,1,4,3] => [2,3,4,1,2]
[3,2,3,1,4] => [2,3,2,4,1]
[3,2,3,4,1] => [2,3,2,1,4]
[3,2,4,1,3] => [2,3,1,4,2]
[3,2,4,3,1] => [2,3,1,2,4]
[3,3,1,2,4] => [2,2,4,3,1]
[3,3,1,4,2] => [2,2,4,1,3]
[3,3,2,1,4] => [2,2,3,4,1]
[3,3,2,4,1] => [2,2,3,1,4]
[3,3,4,1,2] => [2,2,1,4,3]
[3,3,4,2,1] => [2,2,1,3,4]
[3,4,1,2,3] => [2,1,4,3,2]
[3,4,1,3,2] => [2,1,4,2,3]
[3,4,2,1,3] => [2,1,3,4,2]
[3,4,2,3,1] => [2,1,3,2,4]
[3,4,3,1,2] => [2,1,2,4,3]
[3,4,3,2,1] => [2,1,2,3,4]
[4,1,2,3,3] => [1,4,3,2,2]
[4,1,3,2,3] => [1,4,2,3,2]
[4,1,3,3,2] => [1,4,2,2,3]
[4,2,1,3,3] => [1,3,4,2,2]
[4,2,3,1,3] => [1,3,2,4,2]
[4,2,3,3,1] => [1,3,2,2,4]
[4,3,1,2,3] => [1,2,4,3,2]
[4,3,1,3,2] => [1,2,4,2,3]
[4,3,2,1,3] => [1,2,3,4,2]
[4,3,2,3,1] => [1,2,3,2,4]
[4,3,3,1,2] => [1,2,2,4,3]
-----------------------------------------------------------------------------
Created: Jun 17, 2023 at 16:17 by Martin Rubey
-----------------------------------------------------------------------------
Last Updated: Oct 15, 2024 at 00:13 by Nadia Lafreniere