*****************************************************************************
* www.FindStat.org - The Combinatorial Statistic Finder *
* *
* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
* *
* This information is distributed in the hope that it will be useful, *
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. *
*****************************************************************************
-----------------------------------------------------------------------------
Statistic identifier: St001209
-----------------------------------------------------------------------------
Collection: Parking functions
-----------------------------------------------------------------------------
Description: The pmaj statistic of a parking function.
This is the parking function analogue of the bounce statistic, see [1, Section 1.3].
The definition given there is equivalent to the following: One again and again scans the parking function from right to left, keeping track of how often one has started over again. At step $i$, one marks the next position whose value is at most $i$ with the number of restarts from the end of the parking function. The pmaj statistic is then the sum of the markings.
For example, consider the parking function $[6,2,4,1,4,1,7,3]$.
In the first round, we mark positions $6,4,2$ with $0$'s.
In the second round, we mark positions $8,5,3,1$ with $1$'s.
In the third round, we mark position $7$ with a $2$.
In total, we obtain that
$$\operatorname{pmaj}([6,2,4,1,4,1,7,3]) = 6.$$
This statistic is equidistributed with the area statistic [[St000188]] and the dinv statistic [[St000136]].
-----------------------------------------------------------------------------
References: [1] Loehr, N. A. Combinatorics of $q$, $t$-parking functions [[MathSciNet:2110560]]
-----------------------------------------------------------------------------
Code:
def statistic(PF):
PF = list(PF)
PF.reverse()
n = len(PF)
count = 1
run = 0
pm = 0
while any( not x is Infinity for x in PF ):
for i in range(n):
if PF[i] <= count:
count += 1
PF[i] = Infinity
pm += run
run += 1
return pm
-----------------------------------------------------------------------------
Statistic values:
[1] => 0
[1,1] => 0
[1,2] => 1
[2,1] => 0
[1,1,1] => 0
[1,1,2] => 1
[1,2,1] => 0
[2,1,1] => 0
[1,1,3] => 1
[1,3,1] => 1
[3,1,1] => 0
[1,2,2] => 2
[2,1,2] => 1
[2,2,1] => 0
[1,2,3] => 3
[1,3,2] => 2
[2,1,3] => 1
[2,3,1] => 1
[3,1,2] => 2
[3,2,1] => 0
[1,1,1,1] => 0
[1,1,1,2] => 1
[1,1,2,1] => 0
[1,2,1,1] => 0
[2,1,1,1] => 0
[1,1,1,3] => 1
[1,1,3,1] => 1
[1,3,1,1] => 0
[3,1,1,1] => 0
[1,1,1,4] => 1
[1,1,4,1] => 1
[1,4,1,1] => 1
[4,1,1,1] => 0
[1,1,2,2] => 2
[1,2,1,2] => 1
[1,2,2,1] => 0
[2,1,1,2] => 1
[2,1,2,1] => 0
[2,2,1,1] => 0
[1,1,2,3] => 2
[1,1,3,2] => 2
[1,2,1,3] => 1
[1,2,3,1] => 1
[1,3,1,2] => 2
[1,3,2,1] => 0
[2,1,1,3] => 1
[2,1,3,1] => 1
[2,3,1,1] => 0
[3,1,1,2] => 1
[3,1,2,1] => 0
[3,2,1,1] => 0
[1,1,2,4] => 3
[1,1,4,2] => 2
[1,2,1,4] => 1
[1,2,4,1] => 1
[1,4,1,2] => 2
[1,4,2,1] => 1
[2,1,1,4] => 1
[2,1,4,1] => 1
[2,4,1,1] => 1
[4,1,1,2] => 2
[4,1,2,1] => 0
[4,2,1,1] => 0
[1,1,3,3] => 2
[1,3,1,3] => 2
[1,3,3,1] => 2
[3,1,1,3] => 1
[3,1,3,1] => 1
[3,3,1,1] => 0
[1,1,3,4] => 3
[1,1,4,3] => 2
[1,3,1,4] => 3
[1,3,4,1] => 3
[1,4,1,3] => 2
[1,4,3,1] => 2
[3,1,1,4] => 1
[3,1,4,1] => 1
[3,4,1,1] => 1
[4,1,1,3] => 2
[4,1,3,1] => 2
[4,3,1,1] => 0
[1,2,2,2] => 3
[2,1,2,2] => 2
[2,2,1,2] => 1
[2,2,2,1] => 0
[1,2,2,3] => 4
[1,2,3,2] => 3
[1,3,2,2] => 3
[2,1,2,3] => 2
[2,1,3,2] => 2
[2,2,1,3] => 1
[2,2,3,1] => 1
[2,3,1,2] => 2
[2,3,2,1] => 0
[3,1,2,2] => 3
[3,2,1,2] => 1
[3,2,2,1] => 0
[1,2,2,4] => 4
[1,2,4,2] => 4
[1,4,2,2] => 3
[2,1,2,4] => 3
[2,1,4,2] => 2
[2,2,1,4] => 1
[2,2,4,1] => 1
[2,4,1,2] => 2
[2,4,2,1] => 1
[4,1,2,2] => 3
[4,2,1,2] => 2
[4,2,2,1] => 0
[1,2,3,3] => 5
[1,3,2,3] => 4
[1,3,3,2] => 3
[2,1,3,3] => 2
[2,3,1,3] => 2
[2,3,3,1] => 2
[3,1,2,3] => 4
[3,1,3,2] => 3
[3,2,1,3] => 1
[3,2,3,1] => 1
[3,3,1,2] => 3
[3,3,2,1] => 0
[1,2,3,4] => 6
[1,2,4,3] => 5
[1,3,2,4] => 4
[1,3,4,2] => 4
[1,4,2,3] => 5
[1,4,3,2] => 3
[2,1,3,4] => 3
[2,1,4,3] => 2
[2,3,1,4] => 3
[2,3,4,1] => 3
[2,4,1,3] => 2
[2,4,3,1] => 2
[3,1,2,4] => 4
[3,1,4,2] => 4
[3,2,1,4] => 1
[3,2,4,1] => 1
[3,4,1,2] => 4
[3,4,2,1] => 1
[4,1,2,3] => 5
[4,1,3,2] => 3
[4,2,1,3] => 2
[4,2,3,1] => 2
[4,3,1,2] => 3
[4,3,2,1] => 0
[1,1,1,1,1] => 0
[1,1,1,1,2] => 1
[1,1,1,2,1] => 0
[1,1,2,1,1] => 0
[1,2,1,1,1] => 0
[2,1,1,1,1] => 0
[1,1,1,1,3] => 1
[1,1,1,3,1] => 1
[1,1,3,1,1] => 0
[1,3,1,1,1] => 0
[3,1,1,1,1] => 0
[1,1,1,1,4] => 1
[1,1,1,4,1] => 1
[1,1,4,1,1] => 1
[1,4,1,1,1] => 0
[4,1,1,1,1] => 0
[1,1,1,1,5] => 1
[1,1,1,5,1] => 1
[1,1,5,1,1] => 1
[1,5,1,1,1] => 1
[5,1,1,1,1] => 0
[1,1,1,2,2] => 2
[1,1,2,1,2] => 1
[1,1,2,2,1] => 0
[1,2,1,1,2] => 1
[1,2,1,2,1] => 0
[1,2,2,1,1] => 0
[2,1,1,1,2] => 1
[2,1,1,2,1] => 0
[2,1,2,1,1] => 0
[2,2,1,1,1] => 0
[1,1,1,2,3] => 2
[1,1,1,3,2] => 2
[1,1,2,1,3] => 1
[1,1,2,3,1] => 1
[1,1,3,1,2] => 2
[1,1,3,2,1] => 0
[1,2,1,1,3] => 1
[1,2,1,3,1] => 1
[1,2,3,1,1] => 0
[1,3,1,1,2] => 1
[1,3,1,2,1] => 0
[1,3,2,1,1] => 0
[2,1,1,1,3] => 1
[2,1,1,3,1] => 1
[2,1,3,1,1] => 0
[2,3,1,1,1] => 0
[3,1,1,1,2] => 1
[3,1,1,2,1] => 0
[3,1,2,1,1] => 0
[3,2,1,1,1] => 0
[1,1,1,2,4] => 2
[1,1,1,4,2] => 2
[1,1,2,1,4] => 1
[1,1,2,4,1] => 1
[1,1,4,1,2] => 2
[1,1,4,2,1] => 1
[1,2,1,1,4] => 1
[1,2,1,4,1] => 1
[1,2,4,1,1] => 1
[1,4,1,1,2] => 2
[1,4,1,2,1] => 0
[1,4,2,1,1] => 0
[2,1,1,1,4] => 1
[2,1,1,4,1] => 1
[2,1,4,1,1] => 1
[2,4,1,1,1] => 0
[4,1,1,1,2] => 1
[4,1,1,2,1] => 0
[4,1,2,1,1] => 0
[4,2,1,1,1] => 0
[1,1,1,2,5] => 3
[1,1,1,5,2] => 2
[1,1,2,1,5] => 1
[1,1,2,5,1] => 1
[1,1,5,1,2] => 2
[1,1,5,2,1] => 1
[1,2,1,1,5] => 1
[1,2,1,5,1] => 1
[1,2,5,1,1] => 1
[1,5,1,1,2] => 2
[1,5,1,2,1] => 1
[1,5,2,1,1] => 1
[2,1,1,1,5] => 1
[2,1,1,5,1] => 1
[2,1,5,1,1] => 1
[2,5,1,1,1] => 1
[5,1,1,1,2] => 2
[5,1,1,2,1] => 0
[5,1,2,1,1] => 0
[5,2,1,1,1] => 0
[1,1,1,3,3] => 2
[1,1,3,1,3] => 2
[1,1,3,3,1] => 2
[1,3,1,1,3] => 1
[1,3,1,3,1] => 1
[1,3,3,1,1] => 0
[3,1,1,1,3] => 1
[3,1,1,3,1] => 1
[3,1,3,1,1] => 0
[3,3,1,1,1] => 0
[1,1,1,3,4] => 2
[1,1,1,4,3] => 2
[1,1,3,1,4] => 2
[1,1,3,4,1] => 2
[1,1,4,1,3] => 2
[1,1,4,3,1] => 2
[1,3,1,1,4] => 1
[1,3,1,4,1] => 1
[1,3,4,1,1] => 1
[1,4,1,1,3] => 2
[1,4,1,3,1] => 2
[1,4,3,1,1] => 0
[3,1,1,1,4] => 1
[3,1,1,4,1] => 1
[3,1,4,1,1] => 1
[3,4,1,1,1] => 0
[4,1,1,1,3] => 1
[4,1,1,3,1] => 1
[4,1,3,1,1] => 0
[4,3,1,1,1] => 0
[1,1,1,3,5] => 3
[1,1,1,5,3] => 2
[1,1,3,1,5] => 3
[1,1,3,5,1] => 3
[1,1,5,1,3] => 2
[1,1,5,3,1] => 2
[1,3,1,1,5] => 1
[1,3,1,5,1] => 1
[1,3,5,1,1] => 1
[1,5,1,1,3] => 2
[1,5,1,3,1] => 2
[1,5,3,1,1] => 1
[3,1,1,1,5] => 1
[3,1,1,5,1] => 1
[3,1,5,1,1] => 1
[3,5,1,1,1] => 1
[5,1,1,1,3] => 2
[5,1,1,3,1] => 2
[5,1,3,1,1] => 0
[5,3,1,1,1] => 0
[1,1,1,4,4] => 2
[1,1,4,1,4] => 2
[1,1,4,4,1] => 2
[1,4,1,1,4] => 2
[1,4,1,4,1] => 2
[1,4,4,1,1] => 2
[4,1,1,1,4] => 1
[4,1,1,4,1] => 1
[4,1,4,1,1] => 1
[4,4,1,1,1] => 0
[1,1,1,4,5] => 3
[1,1,1,5,4] => 2
[1,1,4,1,5] => 3
[1,1,4,5,1] => 3
[1,1,5,1,4] => 2
[1,1,5,4,1] => 2
[1,4,1,1,5] => 3
[1,4,1,5,1] => 3
[1,4,5,1,1] => 3
[1,5,1,1,4] => 2
[1,5,1,4,1] => 2
[1,5,4,1,1] => 2
[4,1,1,1,5] => 1
[4,1,1,5,1] => 1
[4,1,5,1,1] => 1
[4,5,1,1,1] => 1
[5,1,1,1,4] => 2
[5,1,1,4,1] => 2
[5,1,4,1,1] => 2
[5,4,1,1,1] => 0
[1,1,2,2,2] => 3
[1,2,1,2,2] => 2
[1,2,2,1,2] => 1
[1,2,2,2,1] => 0
[2,1,1,2,2] => 2
[2,1,2,1,2] => 1
[2,1,2,2,1] => 0
[2,2,1,1,2] => 1
[2,2,1,2,1] => 0
[2,2,2,1,1] => 0
[1,1,2,2,3] => 3
[1,1,2,3,2] => 3
[1,1,3,2,2] => 3
[1,2,1,2,3] => 2
[1,2,1,3,2] => 2
[1,2,2,1,3] => 1
[1,2,2,3,1] => 1
[1,2,3,1,2] => 2
[1,2,3,2,1] => 0
[1,3,1,2,2] => 3
[1,3,2,1,2] => 1
[1,3,2,2,1] => 0
[2,1,1,2,3] => 2
[2,1,1,3,2] => 2
[2,1,2,1,3] => 1
[2,1,2,3,1] => 1
[2,1,3,1,2] => 2
[2,1,3,2,1] => 0
[2,2,1,1,3] => 1
[2,2,1,3,1] => 1
[2,2,3,1,1] => 0
[2,3,1,1,2] => 1
[2,3,1,2,1] => 0
[2,3,2,1,1] => 0
[3,1,1,2,2] => 2
[3,1,2,1,2] => 1
[3,1,2,2,1] => 0
[3,2,1,1,2] => 1
[3,2,1,2,1] => 0
[3,2,2,1,1] => 0
[1,1,2,2,4] => 4
[1,1,2,4,2] => 3
[1,1,4,2,2] => 3
[1,2,1,2,4] => 2
[1,2,1,4,2] => 2
[1,2,2,1,4] => 1
[1,2,2,4,1] => 1
[1,2,4,1,2] => 2
[1,2,4,2,1] => 1
[1,4,1,2,2] => 3
[1,4,2,1,2] => 2
[1,4,2,2,1] => 0
[2,1,1,2,4] => 2
[2,1,1,4,2] => 2
[2,1,2,1,4] => 1
[2,1,2,4,1] => 1
[2,1,4,1,2] => 2
[2,1,4,2,1] => 1
[2,2,1,1,4] => 1
[2,2,1,4,1] => 1
[2,2,4,1,1] => 1
[2,4,1,1,2] => 2
[2,4,1,2,1] => 0
[2,4,2,1,1] => 0
[4,1,1,2,2] => 3
[4,1,2,1,2] => 1
[4,1,2,2,1] => 0
[4,2,1,1,2] => 1
[4,2,1,2,1] => 0
[4,2,2,1,1] => 0
[1,1,2,2,5] => 4
[1,1,2,5,2] => 4
[1,1,5,2,2] => 3
[1,2,1,2,5] => 3
[1,2,1,5,2] => 2
[1,2,2,1,5] => 1
[1,2,2,5,1] => 1
[1,2,5,1,2] => 2
[1,2,5,2,1] => 1
[1,5,1,2,2] => 3
[1,5,2,1,2] => 2
[1,5,2,2,1] => 1
[2,1,1,2,5] => 3
[2,1,1,5,2] => 2
[2,1,2,1,5] => 1
[2,1,2,5,1] => 1
[2,1,5,1,2] => 2
[2,1,5,2,1] => 1
[2,2,1,1,5] => 1
[2,2,1,5,1] => 1
[2,2,5,1,1] => 1
[2,5,1,1,2] => 2
[2,5,1,2,1] => 1
[2,5,2,1,1] => 1
[5,1,1,2,2] => 3
[5,1,2,1,2] => 2
[5,1,2,2,1] => 0
[5,2,1,1,2] => 2
[5,2,1,2,1] => 0
[5,2,2,1,1] => 0
[1,1,2,3,3] => 3
[1,1,3,2,3] => 3
[1,1,3,3,2] => 3
[1,2,1,3,3] => 2
[1,2,3,1,3] => 2
[1,2,3,3,1] => 2
[1,3,1,2,3] => 3
[1,3,1,3,2] => 3
[1,3,2,1,3] => 1
[1,3,2,3,1] => 1
[1,3,3,1,2] => 3
[1,3,3,2,1] => 0
[2,1,1,3,3] => 2
[2,1,3,1,3] => 2
[2,1,3,3,1] => 2
[2,3,1,1,3] => 1
[2,3,1,3,1] => 1
[2,3,3,1,1] => 0
[3,1,1,2,3] => 2
[3,1,1,3,2] => 2
[3,1,2,1,3] => 1
[3,1,2,3,1] => 1
[3,1,3,1,2] => 2
[3,1,3,2,1] => 0
[3,2,1,1,3] => 1
[3,2,1,3,1] => 1
[3,2,3,1,1] => 0
[3,3,1,1,2] => 1
[3,3,1,2,1] => 0
[3,3,2,1,1] => 0
[1,1,2,3,4] => 4
[1,1,2,4,3] => 3
[1,1,3,2,4] => 4
[1,1,3,4,2] => 3
[1,1,4,2,3] => 3
[1,1,4,3,2] => 3
[1,2,1,3,4] => 2
[1,2,1,4,3] => 2
[1,2,3,1,4] => 2
[1,2,3,4,1] => 2
[1,2,4,1,3] => 2
[1,2,4,3,1] => 2
[1,3,1,2,4] => 4
[1,3,1,4,2] => 3
[1,3,2,1,4] => 1
[1,3,2,4,1] => 1
[1,3,4,1,2] => 3
[1,3,4,2,1] => 1
[1,4,1,2,3] => 3
[1,4,1,3,2] => 3
[1,4,2,1,3] => 2
[1,4,2,3,1] => 2
[1,4,3,1,2] => 3
[1,4,3,2,1] => 0
[2,1,1,3,4] => 2
[2,1,1,4,3] => 2
[2,1,3,1,4] => 2
[2,1,3,4,1] => 2
[2,1,4,1,3] => 2
[2,1,4,3,1] => 2
[2,3,1,1,4] => 1
[2,3,1,4,1] => 1
[2,3,4,1,1] => 1
[2,4,1,1,3] => 2
[2,4,1,3,1] => 2
[2,4,3,1,1] => 0
[3,1,1,2,4] => 2
[3,1,1,4,2] => 2
[3,1,2,1,4] => 1
[3,1,2,4,1] => 1
[3,1,4,1,2] => 2
[3,1,4,2,1] => 1
[3,2,1,1,4] => 1
[3,2,1,4,1] => 1
[3,2,4,1,1] => 1
[3,4,1,1,2] => 2
[3,4,1,2,1] => 0
[3,4,2,1,1] => 0
[4,1,1,2,3] => 3
[4,1,1,3,2] => 3
[4,1,2,1,3] => 1
[4,1,2,3,1] => 1
[4,1,3,1,2] => 3
[4,1,3,2,1] => 0
[4,2,1,1,3] => 1
[4,2,1,3,1] => 1
[4,2,3,1,1] => 0
[4,3,1,1,2] => 1
[4,3,1,2,1] => 0
[4,3,2,1,1] => 0
[1,1,2,3,5] => 4
[1,1,2,5,3] => 4
[1,1,3,2,5] => 4
[1,1,3,5,2] => 4
[1,1,5,2,3] => 3
[1,1,5,3,2] => 3
[1,2,1,3,5] => 3
[1,2,1,5,3] => 2
[1,2,3,1,5] => 3
[1,2,3,5,1] => 3
[1,2,5,1,3] => 2
[1,2,5,3,1] => 2
[1,3,1,2,5] => 4
[1,3,1,5,2] => 4
[1,3,2,1,5] => 1
[1,3,2,5,1] => 1
[1,3,5,1,2] => 4
[1,3,5,2,1] => 1
[1,5,1,2,3] => 3
[1,5,1,3,2] => 3
[1,5,2,1,3] => 2
[1,5,2,3,1] => 2
[1,5,3,1,2] => 3
[1,5,3,2,1] => 1
[2,1,1,3,5] => 3
[2,1,1,5,3] => 2
[2,1,3,1,5] => 3
[2,1,3,5,1] => 3
[2,1,5,1,3] => 2
[2,1,5,3,1] => 2
[2,3,1,1,5] => 1
[2,3,1,5,1] => 1
[2,3,5,1,1] => 1
[2,5,1,1,3] => 2
[2,5,1,3,1] => 2
[2,5,3,1,1] => 1
[3,1,1,2,5] => 3
[3,1,1,5,2] => 2
[3,1,2,1,5] => 1
[3,1,2,5,1] => 1
[3,1,5,1,2] => 2
[3,1,5,2,1] => 1
[3,2,1,1,5] => 1
[3,2,1,5,1] => 1
[3,2,5,1,1] => 1
[3,5,1,1,2] => 2
[3,5,1,2,1] => 1
[3,5,2,1,1] => 1
[5,1,1,2,3] => 3
[5,1,1,3,2] => 3
[5,1,2,1,3] => 2
[5,1,2,3,1] => 2
[5,1,3,1,2] => 3
[5,1,3,2,1] => 0
[5,2,1,1,3] => 2
[5,2,1,3,1] => 2
[5,2,3,1,1] => 0
[5,3,1,1,2] => 2
[5,3,1,2,1] => 0
[5,3,2,1,1] => 0
[1,1,2,4,4] => 5
[1,1,4,2,4] => 4
[1,1,4,4,2] => 3
[1,2,1,4,4] => 2
[1,2,4,1,4] => 2
[1,2,4,4,1] => 2
[1,4,1,2,4] => 4
[1,4,1,4,2] => 3
[1,4,2,1,4] => 2
[1,4,2,4,1] => 2
[1,4,4,1,2] => 3
[1,4,4,2,1] => 2
[2,1,1,4,4] => 2
[2,1,4,1,4] => 2
[2,1,4,4,1] => 2
[2,4,1,1,4] => 2
[2,4,1,4,1] => 2
[2,4,4,1,1] => 2
[4,1,1,2,4] => 4
[4,1,1,4,2] => 3
[4,1,2,1,4] => 1
[4,1,2,4,1] => 1
[4,1,4,1,2] => 3
[4,1,4,2,1] => 1
[4,2,1,1,4] => 1
[4,2,1,4,1] => 1
[4,2,4,1,1] => 1
[4,4,1,1,2] => 3
[4,4,1,2,1] => 0
[4,4,2,1,1] => 0
[1,1,2,4,5] => 6
[1,1,2,5,4] => 5
[1,1,4,2,5] => 4
[1,1,4,5,2] => 4
[1,1,5,2,4] => 5
[1,1,5,4,2] => 3
[1,2,1,4,5] => 3
[1,2,1,5,4] => 2
[1,2,4,1,5] => 3
[1,2,4,5,1] => 3
[1,2,5,1,4] => 2
[1,2,5,4,1] => 2
[1,4,1,2,5] => 4
[1,4,1,5,2] => 4
[1,4,2,1,5] => 3
[1,4,2,5,1] => 3
[1,4,5,1,2] => 4
[1,4,5,2,1] => 3
[1,5,1,2,4] => 5
[1,5,1,4,2] => 3
[1,5,2,1,4] => 2
[1,5,2,4,1] => 2
[1,5,4,1,2] => 3
[1,5,4,2,1] => 2
[2,1,1,4,5] => 3
[2,1,1,5,4] => 2
[2,1,4,1,5] => 3
[2,1,4,5,1] => 3
[2,1,5,1,4] => 2
[2,1,5,4,1] => 2
[2,4,1,1,5] => 3
[2,4,1,5,1] => 3
[2,4,5,1,1] => 3
[2,5,1,1,4] => 2
[2,5,1,4,1] => 2
[2,5,4,1,1] => 2
[4,1,1,2,5] => 4
[4,1,1,5,2] => 4
[4,1,2,1,5] => 1
[4,1,2,5,1] => 1
[4,1,5,1,2] => 4
[4,1,5,2,1] => 1
[4,2,1,1,5] => 1
[4,2,1,5,1] => 1
[4,2,5,1,1] => 1
[4,5,1,1,2] => 4
[4,5,1,2,1] => 1
[4,5,2,1,1] => 1
[5,1,1,2,4] => 5
[5,1,1,4,2] => 3
[5,1,2,1,4] => 2
[5,1,2,4,1] => 2
[5,1,4,1,2] => 3
[5,1,4,2,1] => 2
[5,2,1,1,4] => 2
[5,2,1,4,1] => 2
[5,2,4,1,1] => 2
[5,4,1,1,2] => 3
[5,4,1,2,1] => 0
[5,4,2,1,1] => 0
[1,1,3,3,3] => 3
[1,3,1,3,3] => 3
[1,3,3,1,3] => 3
[1,3,3,3,1] => 3
[3,1,1,3,3] => 2
[3,1,3,1,3] => 2
[3,1,3,3,1] => 2
[3,3,1,1,3] => 1
[3,3,1,3,1] => 1
[3,3,3,1,1] => 0
[1,1,3,3,4] => 4
[1,1,3,4,3] => 3
[1,1,4,3,3] => 3
[1,3,1,3,4] => 4
[1,3,1,4,3] => 3
[1,3,3,1,4] => 4
[1,3,3,4,1] => 4
[1,3,4,1,3] => 3
[1,3,4,3,1] => 3
[1,4,1,3,3] => 3
[1,4,3,1,3] => 3
[1,4,3,3,1] => 3
[3,1,1,3,4] => 2
[3,1,1,4,3] => 2
[3,1,3,1,4] => 2
[3,1,3,4,1] => 2
[3,1,4,1,3] => 2
[3,1,4,3,1] => 2
[3,3,1,1,4] => 1
[3,3,1,4,1] => 1
[3,3,4,1,1] => 1
[3,4,1,1,3] => 2
[3,4,1,3,1] => 2
[3,4,3,1,1] => 0
[4,1,1,3,3] => 3
[4,1,3,1,3] => 3
[4,1,3,3,1] => 3
[4,3,1,1,3] => 1
[4,3,1,3,1] => 1
[4,3,3,1,1] => 0
[1,1,3,3,5] => 4
[1,1,3,5,3] => 4
[1,1,5,3,3] => 3
[1,3,1,3,5] => 4
[1,3,1,5,3] => 4
[1,3,3,1,5] => 4
[1,3,3,5,1] => 4
[1,3,5,1,3] => 4
[1,3,5,3,1] => 4
[1,5,1,3,3] => 3
[1,5,3,1,3] => 3
[1,5,3,3,1] => 3
[3,1,1,3,5] => 3
[3,1,1,5,3] => 2
[3,1,3,1,5] => 3
[3,1,3,5,1] => 3
[3,1,5,1,3] => 2
[3,1,5,3,1] => 2
[3,3,1,1,5] => 1
[3,3,1,5,1] => 1
[3,3,5,1,1] => 1
[3,5,1,1,3] => 2
[3,5,1,3,1] => 2
[3,5,3,1,1] => 1
[5,1,1,3,3] => 3
[5,1,3,1,3] => 3
[5,1,3,3,1] => 3
[5,3,1,1,3] => 2
[5,3,1,3,1] => 2
[5,3,3,1,1] => 0
[1,1,3,4,4] => 5
[1,1,4,3,4] => 4
[1,1,4,4,3] => 3
[1,3,1,4,4] => 5
[1,3,4,1,4] => 5
[1,3,4,4,1] => 5
[1,4,1,3,4] => 4
[1,4,1,4,3] => 3
[1,4,3,1,4] => 4
[1,4,3,4,1] => 4
[1,4,4,1,3] => 3
[1,4,4,3,1] => 3
[3,1,1,4,4] => 2
[3,1,4,1,4] => 2
[3,1,4,4,1] => 2
[3,4,1,1,4] => 2
[3,4,1,4,1] => 2
[3,4,4,1,1] => 2
[4,1,1,3,4] => 4
[4,1,1,4,3] => 3
[4,1,3,1,4] => 4
[4,1,3,4,1] => 4
[4,1,4,1,3] => 3
[4,1,4,3,1] => 3
[4,3,1,1,4] => 1
[4,3,1,4,1] => 1
[4,3,4,1,1] => 1
[4,4,1,1,3] => 3
[4,4,1,3,1] => 3
[4,4,3,1,1] => 0
[1,1,3,4,5] => 6
[1,1,3,5,4] => 5
[1,1,4,3,5] => 4
[1,1,4,5,3] => 4
[1,1,5,3,4] => 5
[1,1,5,4,3] => 3
[1,3,1,4,5] => 6
[1,3,1,5,4] => 5
[1,3,4,1,5] => 6
[1,3,4,5,1] => 6
[1,3,5,1,4] => 5
[1,3,5,4,1] => 5
[1,4,1,3,5] => 4
[1,4,1,5,3] => 4
[1,4,3,1,5] => 4
[1,4,3,5,1] => 4
[1,4,5,1,3] => 4
[1,4,5,3,1] => 4
[1,5,1,3,4] => 5
[1,5,1,4,3] => 3
[1,5,3,1,4] => 5
[1,5,3,4,1] => 5
[1,5,4,1,3] => 3
[1,5,4,3,1] => 3
[3,1,1,4,5] => 3
[3,1,1,5,4] => 2
[3,1,4,1,5] => 3
[3,1,4,5,1] => 3
[3,1,5,1,4] => 2
[3,1,5,4,1] => 2
[3,4,1,1,5] => 3
[3,4,1,5,1] => 3
[3,4,5,1,1] => 3
[3,5,1,1,4] => 2
[3,5,1,4,1] => 2
[3,5,4,1,1] => 2
[4,1,1,3,5] => 4
[4,1,1,5,3] => 4
[4,1,3,1,5] => 4
[4,1,3,5,1] => 4
[4,1,5,1,3] => 4
[4,1,5,3,1] => 4
[4,3,1,1,5] => 1
[4,3,1,5,1] => 1
[4,3,5,1,1] => 1
[4,5,1,1,3] => 4
[4,5,1,3,1] => 4
[4,5,3,1,1] => 1
[5,1,1,3,4] => 5
[5,1,1,4,3] => 3
[5,1,3,1,4] => 5
[5,1,3,4,1] => 5
[5,1,4,1,3] => 3
[5,1,4,3,1] => 3
[5,3,1,1,4] => 2
[5,3,1,4,1] => 2
[5,3,4,1,1] => 2
[5,4,1,1,3] => 3
[5,4,1,3,1] => 3
[5,4,3,1,1] => 0
[1,2,2,2,2] => 4
[2,1,2,2,2] => 3
[2,2,1,2,2] => 2
[2,2,2,1,2] => 1
[2,2,2,2,1] => 0
[1,2,2,2,3] => 5
[1,2,2,3,2] => 4
[1,2,3,2,2] => 4
[1,3,2,2,2] => 4
[2,1,2,2,3] => 3
[2,1,2,3,2] => 3
[2,1,3,2,2] => 3
[2,2,1,2,3] => 2
[2,2,1,3,2] => 2
[2,2,2,1,3] => 1
[2,2,2,3,1] => 1
[2,2,3,1,2] => 2
[2,2,3,2,1] => 0
[2,3,1,2,2] => 3
[2,3,2,1,2] => 1
[2,3,2,2,1] => 0
[3,1,2,2,2] => 4
[3,2,1,2,2] => 2
[3,2,2,1,2] => 1
[3,2,2,2,1] => 0
[1,2,2,2,4] => 5
[1,2,2,4,2] => 5
[1,2,4,2,2] => 4
[1,4,2,2,2] => 4
[2,1,2,2,4] => 4
[2,1,2,4,2] => 3
[2,1,4,2,2] => 3
[2,2,1,2,4] => 2
[2,2,1,4,2] => 2
[2,2,2,1,4] => 1
[2,2,2,4,1] => 1
[2,2,4,1,2] => 2
[2,2,4,2,1] => 1
[2,4,1,2,2] => 3
[2,4,2,1,2] => 2
[2,4,2,2,1] => 0
[4,1,2,2,2] => 4
[4,2,1,2,2] => 3
[4,2,2,1,2] => 1
[4,2,2,2,1] => 0
[1,2,2,2,5] => 5
[1,2,2,5,2] => 5
[1,2,5,2,2] => 5
[1,5,2,2,2] => 4
[2,1,2,2,5] => 4
[2,1,2,5,2] => 4
[2,1,5,2,2] => 3
[2,2,1,2,5] => 3
[2,2,1,5,2] => 2
[2,2,2,1,5] => 1
[2,2,2,5,1] => 1
[2,2,5,1,2] => 2
[2,2,5,2,1] => 1
[2,5,1,2,2] => 3
[2,5,2,1,2] => 2
[2,5,2,2,1] => 1
[5,1,2,2,2] => 4
[5,2,1,2,2] => 3
[5,2,2,1,2] => 2
[5,2,2,2,1] => 0
[1,2,2,3,3] => 6
[1,2,3,2,3] => 5
[1,2,3,3,2] => 4
[1,3,2,2,3] => 5
[1,3,2,3,2] => 4
[1,3,3,2,2] => 4
[2,1,2,3,3] => 3
[2,1,3,2,3] => 3
[2,1,3,3,2] => 3
[2,2,1,3,3] => 2
[2,2,3,1,3] => 2
[2,2,3,3,1] => 2
[2,3,1,2,3] => 3
[2,3,1,3,2] => 3
[2,3,2,1,3] => 1
[2,3,2,3,1] => 1
[2,3,3,1,2] => 3
[2,3,3,2,1] => 0
[3,1,2,2,3] => 5
[3,1,2,3,2] => 4
[3,1,3,2,2] => 4
[3,2,1,2,3] => 2
[3,2,1,3,2] => 2
[3,2,2,1,3] => 1
[3,2,2,3,1] => 1
[3,2,3,1,2] => 2
[3,2,3,2,1] => 0
[3,3,1,2,2] => 4
[3,3,2,1,2] => 1
[3,3,2,2,1] => 0
[1,2,2,3,4] => 6
[1,2,2,4,3] => 6
[1,2,3,2,4] => 5
[1,2,3,4,2] => 5
[1,2,4,2,3] => 6
[1,2,4,3,2] => 4
[1,3,2,2,4] => 5
[1,3,2,4,2] => 5
[1,3,4,2,2] => 4
[1,4,2,2,3] => 5
[1,4,2,3,2] => 4
[1,4,3,2,2] => 4
[2,1,2,3,4] => 4
[2,1,2,4,3] => 3
[2,1,3,2,4] => 4
[2,1,3,4,2] => 3
[2,1,4,2,3] => 3
[2,1,4,3,2] => 3
[2,2,1,3,4] => 2
[2,2,1,4,3] => 2
[2,2,3,1,4] => 2
[2,2,3,4,1] => 2
[2,2,4,1,3] => 2
[2,2,4,3,1] => 2
[2,3,1,2,4] => 4
[2,3,1,4,2] => 3
[2,3,2,1,4] => 1
[2,3,2,4,1] => 1
[2,3,4,1,2] => 3
[2,3,4,2,1] => 1
[2,4,1,2,3] => 3
[2,4,1,3,2] => 3
[2,4,2,1,3] => 2
[2,4,2,3,1] => 2
[2,4,3,1,2] => 3
[2,4,3,2,1] => 0
[3,1,2,2,4] => 5
[3,1,2,4,2] => 5
[3,1,4,2,2] => 4
[3,2,1,2,4] => 2
[3,2,1,4,2] => 2
[3,2,2,1,4] => 1
[3,2,2,4,1] => 1
[3,2,4,1,2] => 2
[3,2,4,2,1] => 1
[3,4,1,2,2] => 4
[3,4,2,1,2] => 2
[3,4,2,2,1] => 0
[4,1,2,2,3] => 5
[4,1,2,3,2] => 4
[4,1,3,2,2] => 4
[4,2,1,2,3] => 3
[4,2,1,3,2] => 3
[4,2,2,1,3] => 1
[4,2,2,3,1] => 1
[4,2,3,1,2] => 3
[4,2,3,2,1] => 0
[4,3,1,2,2] => 4
[4,3,2,1,2] => 1
[4,3,2,2,1] => 0
[1,2,2,3,5] => 7
[1,2,2,5,3] => 6
[1,2,3,2,5] => 5
[1,2,3,5,2] => 5
[1,2,5,2,3] => 6
[1,2,5,3,2] => 5
[1,3,2,2,5] => 5
[1,3,2,5,2] => 5
[1,3,5,2,2] => 5
[1,5,2,2,3] => 6
[1,5,2,3,2] => 4
[1,5,3,2,2] => 4
[2,1,2,3,5] => 4
[2,1,2,5,3] => 4
[2,1,3,2,5] => 4
[2,1,3,5,2] => 4
[2,1,5,2,3] => 3
[2,1,5,3,2] => 3
[2,2,1,3,5] => 3
[2,2,1,5,3] => 2
[2,2,3,1,5] => 3
[2,2,3,5,1] => 3
[2,2,5,1,3] => 2
[2,2,5,3,1] => 2
[2,3,1,2,5] => 4
[2,3,1,5,2] => 4
[2,3,2,1,5] => 1
[2,3,2,5,1] => 1
[2,3,5,1,2] => 4
[2,3,5,2,1] => 1
[2,5,1,2,3] => 3
[2,5,1,3,2] => 3
[2,5,2,1,3] => 2
[2,5,2,3,1] => 2
[2,5,3,1,2] => 3
[2,5,3,2,1] => 1
[3,1,2,2,5] => 5
[3,1,2,5,2] => 5
[3,1,5,2,2] => 5
[3,2,1,2,5] => 3
[3,2,1,5,2] => 2
[3,2,2,1,5] => 1
[3,2,2,5,1] => 1
[3,2,5,1,2] => 2
[3,2,5,2,1] => 1
[3,5,1,2,2] => 5
[3,5,2,1,2] => 2
[3,5,2,2,1] => 1
[5,1,2,2,3] => 6
[5,1,2,3,2] => 4
[5,1,3,2,2] => 4
[5,2,1,2,3] => 3
[5,2,1,3,2] => 3
[5,2,2,1,3] => 2
[5,2,2,3,1] => 2
[5,2,3,1,2] => 3
[5,2,3,2,1] => 0
[5,3,1,2,2] => 4
[5,3,2,1,2] => 2
[5,3,2,2,1] => 0
[1,2,2,4,4] => 6
[1,2,4,2,4] => 6
[1,2,4,4,2] => 6
[1,4,2,2,4] => 5
[1,4,2,4,2] => 5
[1,4,4,2,2] => 4
[2,1,2,4,4] => 5
[2,1,4,2,4] => 4
[2,1,4,4,2] => 3
[2,2,1,4,4] => 2
[2,2,4,1,4] => 2
[2,2,4,4,1] => 2
[2,4,1,2,4] => 4
[2,4,1,4,2] => 3
[2,4,2,1,4] => 2
[2,4,2,4,1] => 2
[2,4,4,1,2] => 3
[2,4,4,2,1] => 2
[4,1,2,2,4] => 5
[4,1,2,4,2] => 5
[4,1,4,2,2] => 4
[4,2,1,2,4] => 4
[4,2,1,4,2] => 3
[4,2,2,1,4] => 1
[4,2,2,4,1] => 1
[4,2,4,1,2] => 3
[4,2,4,2,1] => 1
[4,4,1,2,2] => 4
[4,4,2,1,2] => 3
[4,4,2,2,1] => 0
[1,2,2,4,5] => 7
[1,2,2,5,4] => 6
[1,2,4,2,5] => 7
[1,2,4,5,2] => 7
[1,2,5,2,4] => 6
[1,2,5,4,2] => 6
[1,4,2,2,5] => 5
[1,4,2,5,2] => 5
[1,4,5,2,2] => 5
[1,5,2,2,4] => 6
[1,5,2,4,2] => 6
[1,5,4,2,2] => 4
[2,1,2,4,5] => 6
[2,1,2,5,4] => 5
[2,1,4,2,5] => 4
[2,1,4,5,2] => 4
[2,1,5,2,4] => 5
[2,1,5,4,2] => 3
[2,2,1,4,5] => 3
[2,2,1,5,4] => 2
[2,2,4,1,5] => 3
[2,2,4,5,1] => 3
[2,2,5,1,4] => 2
[2,2,5,4,1] => 2
[2,4,1,2,5] => 4
[2,4,1,5,2] => 4
[2,4,2,1,5] => 3
[2,4,2,5,1] => 3
[2,4,5,1,2] => 4
[2,4,5,2,1] => 3
[2,5,1,2,4] => 5
[2,5,1,4,2] => 3
[2,5,2,1,4] => 2
[2,5,2,4,1] => 2
[2,5,4,1,2] => 3
[2,5,4,2,1] => 2
[4,1,2,2,5] => 5
[4,1,2,5,2] => 5
[4,1,5,2,2] => 5
[4,2,1,2,5] => 4
[4,2,1,5,2] => 4
[4,2,2,1,5] => 1
[4,2,2,5,1] => 1
[4,2,5,1,2] => 4
[4,2,5,2,1] => 1
[4,5,1,2,2] => 5
[4,5,2,1,2] => 4
[4,5,2,2,1] => 1
[5,1,2,2,4] => 6
[5,1,2,4,2] => 6
[5,1,4,2,2] => 4
[5,2,1,2,4] => 5
[5,2,1,4,2] => 3
[5,2,2,1,4] => 2
[5,2,2,4,1] => 2
[5,2,4,1,2] => 3
[5,2,4,2,1] => 2
[5,4,1,2,2] => 4
[5,4,2,1,2] => 3
[5,4,2,2,1] => 0
[1,2,3,3,3] => 7
[1,3,2,3,3] => 6
[1,3,3,2,3] => 5
[1,3,3,3,2] => 4
[2,1,3,3,3] => 3
[2,3,1,3,3] => 3
[2,3,3,1,3] => 3
[2,3,3,3,1] => 3
[3,1,2,3,3] => 6
[3,1,3,2,3] => 5
[3,1,3,3,2] => 4
[3,2,1,3,3] => 2
[3,2,3,1,3] => 2
[3,2,3,3,1] => 2
[3,3,1,2,3] => 5
[3,3,1,3,2] => 4
[3,3,2,1,3] => 1
[3,3,2,3,1] => 1
[3,3,3,1,2] => 4
[3,3,3,2,1] => 0
[1,2,3,3,4] => 8
[1,2,3,4,3] => 7
[1,2,4,3,3] => 7
[1,3,2,3,4] => 6
[1,3,2,4,3] => 6
[1,3,3,2,4] => 5
[1,3,3,4,2] => 5
[1,3,4,2,3] => 6
[1,3,4,3,2] => 4
[1,4,2,3,3] => 7
[1,4,3,2,3] => 5
[1,4,3,3,2] => 4
[2,1,3,3,4] => 4
[2,1,3,4,3] => 3
[2,1,4,3,3] => 3
[2,3,1,3,4] => 4
[2,3,1,4,3] => 3
[2,3,3,1,4] => 4
[2,3,3,4,1] => 4
[2,3,4,1,3] => 3
[2,3,4,3,1] => 3
[2,4,1,3,3] => 3
[2,4,3,1,3] => 3
[2,4,3,3,1] => 3
[3,1,2,3,4] => 6
[3,1,2,4,3] => 6
[3,1,3,2,4] => 5
[3,1,3,4,2] => 5
[3,1,4,2,3] => 6
[3,1,4,3,2] => 4
[3,2,1,3,4] => 2
[3,2,1,4,3] => 2
[3,2,3,1,4] => 2
[3,2,3,4,1] => 2
[3,2,4,1,3] => 2
[3,2,4,3,1] => 2
[3,3,1,2,4] => 5
[3,3,1,4,2] => 5
[3,3,2,1,4] => 1
[3,3,2,4,1] => 1
[3,3,4,1,2] => 5
[3,3,4,2,1] => 1
[3,4,1,2,3] => 6
[3,4,1,3,2] => 4
[3,4,2,1,3] => 2
[3,4,2,3,1] => 2
[3,4,3,1,2] => 4
[3,4,3,2,1] => 0
[4,1,2,3,3] => 7
[4,1,3,2,3] => 5
[4,1,3,3,2] => 4
[4,2,1,3,3] => 3
[4,2,3,1,3] => 3
[4,2,3,3,1] => 3
[4,3,1,2,3] => 5
[4,3,1,3,2] => 4
[4,3,2,1,3] => 1
[4,3,2,3,1] => 1
[4,3,3,1,2] => 4
-----------------------------------------------------------------------------
Created: Jun 14, 2018 at 11:31 by Christian Stump
-----------------------------------------------------------------------------
Last Updated: Jun 14, 2018 at 11:31 by Christian Stump