************************************************************************
*    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: Mp00301

------------------------------------------------------------------------
Map name: leading to repeats

------------------------------------------------------------------------
Domain: Parking functions

------------------------------------------------------------------------
Codomain: Parking functions

------------------------------------------------------------------------
Description: The unique parking function obtained by prepending 0 and shifting the cumulative sums of a Prüfer code, then cyclically shifting.

Pollak's map [1] sends a parking function $(p_1,\dots,p_n)$ to the Prüfer code $(c_1,\dots,c_{n-1})$ with $c_i = p_{i+1} - p_i \pmod{n+1}$.

The inverse is obtained by computing the cumulative sums, and then shifting all elements modulo $n+1$ such that the result is a parking function.

This is the inverse of [[Mp00298]].

This map sends the number of occurrences of the first element to the number of repeated elements [3].

------------------------------------------------------------------------
References: [1]   (service unreachable) [[MathSciNet:0234843]]
[2]   (service unreachable) [[MathSciNet:0335294]]
[3]   Stanley, R. P., Yin, M. Some enumerative properties of parking functions [[arXiv:2306.08681]]

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

def mapping(p):
    return pruefer_to_parking_pollak_riordan(parking_to_pruefer_circular(p))

def pruefer_to_parking_pollak_riordan(c):
    n = len(c) + 1
    pc = [sum(c[:i]) % (n+1) for i in range(n)]
    P = ParkingFunctions(n)
    for i in range(n):
        if pc in P:
            break
        pc = [(e + 1) % (n+1) for e in pc]
    return ParkingFunction(pc)

def parking_to_pruefer_circular(p):
    n = len(p)
    d = p[0]
    return [(p[i] - d) % (n+1) for i in range(1, n)]


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

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

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Created: Jun 16, 2023 at 23:23 by Martin Rubey

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Last Updated: Jun 16, 2023 at 23:23 by Martin Rubey