*****************************************************************************
*       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: St000188

-----------------------------------------------------------------------------
Collection: Parking functions

-----------------------------------------------------------------------------
Description: The area of the Dyck path corresponding to a parking function and the total displacement of a parking function.


The area Dyck path corresponding to a parking function for a parking function $p_1,\ldots,p_n$ of length $n$, is given by $\binom{n+1}{2} - \sum_i p_i$.


The total displacement of a parking function $ p \in PF_n $ is defined by
$$
\operatorname{disp}(p) := \sum_{i=1}^{n} d_i,
$$
where the displacement vector $ d := (d_1, d_2, \ldots, d_n) $ and $ d_i := \pi^{-1}(i) - p_i $ for all $ i \in [n] $, 
such that each $ d_i $ is the positive difference between the actual spot a car parks and its preferred spot.

-----------------------------------------------------------------------------
References: [1]   Triangle of coefficients of polynomials enumerating trees with n labeled nodes by inversions. [[OEIS:A052121]]
[2]   Kang, Y., Selig, T., Yang, G., Zhang, Y., Zhu, H. On friendship and cyclic parking functions [[arXiv:2310.06560]]

-----------------------------------------------------------------------------
Code:
def statistic(p):
    return p.area()

-----------------------------------------------------------------------------
Statistic values:

[1]         => 0
[1,1]       => 1
[1,2]       => 0
[2,1]       => 0
[1,1,1]     => 3
[1,1,2]     => 2
[1,2,1]     => 2
[2,1,1]     => 2
[1,1,3]     => 1
[1,3,1]     => 1
[3,1,1]     => 1
[1,2,2]     => 1
[2,1,2]     => 1
[2,2,1]     => 1
[1,2,3]     => 0
[1,3,2]     => 0
[2,1,3]     => 0
[2,3,1]     => 0
[3,1,2]     => 0
[3,2,1]     => 0
[1,1,1,1]   => 6
[1,1,1,2]   => 5
[1,1,2,1]   => 5
[1,2,1,1]   => 5
[2,1,1,1]   => 5
[1,1,1,3]   => 4
[1,1,3,1]   => 4
[1,3,1,1]   => 4
[3,1,1,1]   => 4
[1,1,1,4]   => 3
[1,1,4,1]   => 3
[1,4,1,1]   => 3
[4,1,1,1]   => 3
[1,1,2,2]   => 4
[1,2,1,2]   => 4
[1,2,2,1]   => 4
[2,1,1,2]   => 4
[2,1,2,1]   => 4
[2,2,1,1]   => 4
[1,1,2,3]   => 3
[1,1,3,2]   => 3
[1,2,1,3]   => 3
[1,2,3,1]   => 3
[1,3,1,2]   => 3
[1,3,2,1]   => 3
[2,1,1,3]   => 3
[2,1,3,1]   => 3
[2,3,1,1]   => 3
[3,1,1,2]   => 3
[3,1,2,1]   => 3
[3,2,1,1]   => 3
[1,1,2,4]   => 2
[1,1,4,2]   => 2
[1,2,1,4]   => 2
[1,2,4,1]   => 2
[1,4,1,2]   => 2
[1,4,2,1]   => 2
[2,1,1,4]   => 2
[2,1,4,1]   => 2
[2,4,1,1]   => 2
[4,1,1,2]   => 2
[4,1,2,1]   => 2
[4,2,1,1]   => 2
[1,1,3,3]   => 2
[1,3,1,3]   => 2
[1,3,3,1]   => 2
[3,1,1,3]   => 2
[3,1,3,1]   => 2
[3,3,1,1]   => 2
[1,1,3,4]   => 1
[1,1,4,3]   => 1
[1,3,1,4]   => 1
[1,3,4,1]   => 1
[1,4,1,3]   => 1
[1,4,3,1]   => 1
[3,1,1,4]   => 1
[3,1,4,1]   => 1
[3,4,1,1]   => 1
[4,1,1,3]   => 1
[4,1,3,1]   => 1
[4,3,1,1]   => 1
[1,2,2,2]   => 3
[2,1,2,2]   => 3
[2,2,1,2]   => 3
[2,2,2,1]   => 3
[1,2,2,3]   => 2
[1,2,3,2]   => 2
[1,3,2,2]   => 2
[2,1,2,3]   => 2
[2,1,3,2]   => 2
[2,2,1,3]   => 2
[2,2,3,1]   => 2
[2,3,1,2]   => 2
[2,3,2,1]   => 2
[3,1,2,2]   => 2
[3,2,1,2]   => 2
[3,2,2,1]   => 2
[1,2,2,4]   => 1
[1,2,4,2]   => 1
[1,4,2,2]   => 1
[2,1,2,4]   => 1
[2,1,4,2]   => 1
[2,2,1,4]   => 1
[2,2,4,1]   => 1
[2,4,1,2]   => 1
[2,4,2,1]   => 1
[4,1,2,2]   => 1
[4,2,1,2]   => 1
[4,2,2,1]   => 1
[1,2,3,3]   => 1
[1,3,2,3]   => 1
[1,3,3,2]   => 1
[2,1,3,3]   => 1
[2,3,1,3]   => 1
[2,3,3,1]   => 1
[3,1,2,3]   => 1
[3,1,3,2]   => 1
[3,2,1,3]   => 1
[3,2,3,1]   => 1
[3,3,1,2]   => 1
[3,3,2,1]   => 1
[1,2,3,4]   => 0
[1,2,4,3]   => 0
[1,3,2,4]   => 0
[1,3,4,2]   => 0
[1,4,2,3]   => 0
[1,4,3,2]   => 0
[2,1,3,4]   => 0
[2,1,4,3]   => 0
[2,3,1,4]   => 0
[2,3,4,1]   => 0
[2,4,1,3]   => 0
[2,4,3,1]   => 0
[3,1,2,4]   => 0
[3,1,4,2]   => 0
[3,2,1,4]   => 0
[3,2,4,1]   => 0
[3,4,1,2]   => 0
[3,4,2,1]   => 0
[4,1,2,3]   => 0
[4,1,3,2]   => 0
[4,2,1,3]   => 0
[4,2,3,1]   => 0
[4,3,1,2]   => 0
[4,3,2,1]   => 0
[1,1,1,1,1] => 10
[1,1,1,1,2] => 9
[1,1,1,2,1] => 9
[1,1,2,1,1] => 9
[1,2,1,1,1] => 9
[2,1,1,1,1] => 9
[1,1,1,1,3] => 8
[1,1,1,3,1] => 8
[1,1,3,1,1] => 8
[1,3,1,1,1] => 8
[3,1,1,1,1] => 8
[1,1,1,1,4] => 7
[1,1,1,4,1] => 7
[1,1,4,1,1] => 7
[1,4,1,1,1] => 7
[4,1,1,1,1] => 7
[1,1,1,1,5] => 6
[1,1,1,5,1] => 6
[1,1,5,1,1] => 6
[1,5,1,1,1] => 6
[5,1,1,1,1] => 6
[1,1,1,2,2] => 8
[1,1,2,1,2] => 8
[1,1,2,2,1] => 8
[1,2,1,1,2] => 8
[1,2,1,2,1] => 8
[1,2,2,1,1] => 8
[2,1,1,1,2] => 8
[2,1,1,2,1] => 8
[2,1,2,1,1] => 8
[2,2,1,1,1] => 8
[1,1,1,2,3] => 7
[1,1,1,3,2] => 7
[1,1,2,1,3] => 7
[1,1,2,3,1] => 7
[1,1,3,1,2] => 7
[1,1,3,2,1] => 7
[1,2,1,1,3] => 7
[1,2,1,3,1] => 7
[1,2,3,1,1] => 7
[1,3,1,1,2] => 7
[1,3,1,2,1] => 7
[1,3,2,1,1] => 7
[2,1,1,1,3] => 7
[2,1,1,3,1] => 7
[2,1,3,1,1] => 7
[2,3,1,1,1] => 7
[3,1,1,1,2] => 7
[3,1,1,2,1] => 7
[3,1,2,1,1] => 7
[3,2,1,1,1] => 7
[1,1,1,2,4] => 6
[1,1,1,4,2] => 6
[1,1,2,1,4] => 6
[1,1,2,4,1] => 6
[1,1,4,1,2] => 6
[1,1,4,2,1] => 6
[1,2,1,1,4] => 6
[1,2,1,4,1] => 6
[1,2,4,1,1] => 6
[1,4,1,1,2] => 6
[1,4,1,2,1] => 6
[1,4,2,1,1] => 6
[2,1,1,1,4] => 6
[2,1,1,4,1] => 6
[2,1,4,1,1] => 6
[2,4,1,1,1] => 6
[4,1,1,1,2] => 6
[4,1,1,2,1] => 6
[4,1,2,1,1] => 6
[4,2,1,1,1] => 6
[1,1,1,2,5] => 5
[1,1,1,5,2] => 5
[1,1,2,1,5] => 5
[1,1,2,5,1] => 5
[1,1,5,1,2] => 5
[1,1,5,2,1] => 5
[1,2,1,1,5] => 5
[1,2,1,5,1] => 5
[1,2,5,1,1] => 5
[1,5,1,1,2] => 5
[1,5,1,2,1] => 5
[1,5,2,1,1] => 5
[2,1,1,1,5] => 5
[2,1,1,5,1] => 5
[2,1,5,1,1] => 5
[2,5,1,1,1] => 5
[5,1,1,1,2] => 5
[5,1,1,2,1] => 5
[5,1,2,1,1] => 5
[5,2,1,1,1] => 5
[1,1,1,3,3] => 6
[1,1,3,1,3] => 6
[1,1,3,3,1] => 6
[1,3,1,1,3] => 6
[1,3,1,3,1] => 6
[1,3,3,1,1] => 6
[3,1,1,1,3] => 6
[3,1,1,3,1] => 6
[3,1,3,1,1] => 6
[3,3,1,1,1] => 6
[1,1,1,3,4] => 5
[1,1,1,4,3] => 5
[1,1,3,1,4] => 5
[1,1,3,4,1] => 5
[1,1,4,1,3] => 5
[1,1,4,3,1] => 5
[1,3,1,1,4] => 5
[1,3,1,4,1] => 5
[1,3,4,1,1] => 5
[1,4,1,1,3] => 5
[1,4,1,3,1] => 5
[1,4,3,1,1] => 5
[3,1,1,1,4] => 5
[3,1,1,4,1] => 5
[3,1,4,1,1] => 5
[3,4,1,1,1] => 5
[4,1,1,1,3] => 5
[4,1,1,3,1] => 5
[4,1,3,1,1] => 5
[4,3,1,1,1] => 5
[1,1,1,3,5] => 4
[1,1,1,5,3] => 4
[1,1,3,1,5] => 4
[1,1,3,5,1] => 4
[1,1,5,1,3] => 4
[1,1,5,3,1] => 4
[1,3,1,1,5] => 4
[1,3,1,5,1] => 4
[1,3,5,1,1] => 4
[1,5,1,1,3] => 4
[1,5,1,3,1] => 4
[1,5,3,1,1] => 4
[3,1,1,1,5] => 4
[3,1,1,5,1] => 4
[3,1,5,1,1] => 4
[3,5,1,1,1] => 4
[5,1,1,1,3] => 4
[5,1,1,3,1] => 4
[5,1,3,1,1] => 4
[5,3,1,1,1] => 4
[1,1,1,4,4] => 4
[1,1,4,1,4] => 4
[1,1,4,4,1] => 4
[1,4,1,1,4] => 4
[1,4,1,4,1] => 4
[1,4,4,1,1] => 4
[4,1,1,1,4] => 4
[4,1,1,4,1] => 4
[4,1,4,1,1] => 4
[4,4,1,1,1] => 4
[1,1,1,4,5] => 3
[1,1,1,5,4] => 3
[1,1,4,1,5] => 3
[1,1,4,5,1] => 3
[1,1,5,1,4] => 3
[1,1,5,4,1] => 3
[1,4,1,1,5] => 3
[1,4,1,5,1] => 3
[1,4,5,1,1] => 3
[1,5,1,1,4] => 3
[1,5,1,4,1] => 3
[1,5,4,1,1] => 3
[4,1,1,1,5] => 3
[4,1,1,5,1] => 3
[4,1,5,1,1] => 3
[4,5,1,1,1] => 3
[5,1,1,1,4] => 3
[5,1,1,4,1] => 3
[5,1,4,1,1] => 3
[5,4,1,1,1] => 3
[1,1,2,2,2] => 7
[1,2,1,2,2] => 7
[1,2,2,1,2] => 7
[1,2,2,2,1] => 7
[2,1,1,2,2] => 7
[2,1,2,1,2] => 7
[2,1,2,2,1] => 7
[2,2,1,1,2] => 7
[2,2,1,2,1] => 7
[2,2,2,1,1] => 7
[1,1,2,2,3] => 6
[1,1,2,3,2] => 6
[1,1,3,2,2] => 6
[1,2,1,2,3] => 6
[1,2,1,3,2] => 6
[1,2,2,1,3] => 6
[1,2,2,3,1] => 6
[1,2,3,1,2] => 6
[1,2,3,2,1] => 6
[1,3,1,2,2] => 6
[1,3,2,1,2] => 6
[1,3,2,2,1] => 6
[2,1,1,2,3] => 6
[2,1,1,3,2] => 6
[2,1,2,1,3] => 6
[2,1,2,3,1] => 6
[2,1,3,1,2] => 6
[2,1,3,2,1] => 6
[2,2,1,1,3] => 6
[2,2,1,3,1] => 6
[2,2,3,1,1] => 6
[2,3,1,1,2] => 6
[2,3,1,2,1] => 6
[2,3,2,1,1] => 6
[3,1,1,2,2] => 6
[3,1,2,1,2] => 6
[3,1,2,2,1] => 6
[3,2,1,1,2] => 6
[3,2,1,2,1] => 6
[3,2,2,1,1] => 6
[1,1,2,2,4] => 5
[1,1,2,4,2] => 5
[1,1,4,2,2] => 5
[1,2,1,2,4] => 5
[1,2,1,4,2] => 5
[1,2,2,1,4] => 5
[1,2,2,4,1] => 5
[1,2,4,1,2] => 5
[1,2,4,2,1] => 5
[1,4,1,2,2] => 5
[1,4,2,1,2] => 5
[1,4,2,2,1] => 5
[2,1,1,2,4] => 5
[2,1,1,4,2] => 5
[2,1,2,1,4] => 5
[2,1,2,4,1] => 5
[2,1,4,1,2] => 5
[2,1,4,2,1] => 5
[2,2,1,1,4] => 5
[2,2,1,4,1] => 5
[2,2,4,1,1] => 5
[2,4,1,1,2] => 5
[2,4,1,2,1] => 5
[2,4,2,1,1] => 5
[4,1,1,2,2] => 5
[4,1,2,1,2] => 5
[4,1,2,2,1] => 5
[4,2,1,1,2] => 5
[4,2,1,2,1] => 5
[4,2,2,1,1] => 5
[1,1,2,2,5] => 4
[1,1,2,5,2] => 4
[1,1,5,2,2] => 4
[1,2,1,2,5] => 4
[1,2,1,5,2] => 4
[1,2,2,1,5] => 4
[1,2,2,5,1] => 4
[1,2,5,1,2] => 4
[1,2,5,2,1] => 4
[1,5,1,2,2] => 4
[1,5,2,1,2] => 4
[1,5,2,2,1] => 4
[2,1,1,2,5] => 4
[2,1,1,5,2] => 4
[2,1,2,1,5] => 4
[2,1,2,5,1] => 4
[2,1,5,1,2] => 4
[2,1,5,2,1] => 4
[2,2,1,1,5] => 4
[2,2,1,5,1] => 4
[2,2,5,1,1] => 4
[2,5,1,1,2] => 4
[2,5,1,2,1] => 4
[2,5,2,1,1] => 4
[5,1,1,2,2] => 4
[5,1,2,1,2] => 4
[5,1,2,2,1] => 4
[5,2,1,1,2] => 4
[5,2,1,2,1] => 4
[5,2,2,1,1] => 4
[1,1,2,3,3] => 5
[1,1,3,2,3] => 5
[1,1,3,3,2] => 5
[1,2,1,3,3] => 5
[1,2,3,1,3] => 5
[1,2,3,3,1] => 5
[1,3,1,2,3] => 5
[1,3,1,3,2] => 5
[1,3,2,1,3] => 5
[1,3,2,3,1] => 5
[1,3,3,1,2] => 5
[1,3,3,2,1] => 5
[2,1,1,3,3] => 5
[2,1,3,1,3] => 5
[2,1,3,3,1] => 5
[2,3,1,1,3] => 5
[2,3,1,3,1] => 5
[2,3,3,1,1] => 5
[3,1,1,2,3] => 5
[3,1,1,3,2] => 5
[3,1,2,1,3] => 5
[3,1,2,3,1] => 5
[3,1,3,1,2] => 5
[3,1,3,2,1] => 5
[3,2,1,1,3] => 5
[3,2,1,3,1] => 5
[3,2,3,1,1] => 5
[3,3,1,1,2] => 5
[3,3,1,2,1] => 5
[3,3,2,1,1] => 5
[1,1,2,3,4] => 4
[1,1,2,4,3] => 4
[1,1,3,2,4] => 4
[1,1,3,4,2] => 4
[1,1,4,2,3] => 4
[1,1,4,3,2] => 4
[1,2,1,3,4] => 4
[1,2,1,4,3] => 4
[1,2,3,1,4] => 4
[1,2,3,4,1] => 4
[1,2,4,1,3] => 4
[1,2,4,3,1] => 4
[1,3,1,2,4] => 4
[1,3,1,4,2] => 4
[1,3,2,1,4] => 4
[1,3,2,4,1] => 4
[1,3,4,1,2] => 4
[1,3,4,2,1] => 4
[1,4,1,2,3] => 4
[1,4,1,3,2] => 4
[1,4,2,1,3] => 4
[1,4,2,3,1] => 4
[1,4,3,1,2] => 4
[1,4,3,2,1] => 4
[2,1,1,3,4] => 4
[2,1,1,4,3] => 4
[2,1,3,1,4] => 4
[2,1,3,4,1] => 4
[2,1,4,1,3] => 4
[2,1,4,3,1] => 4
[2,3,1,1,4] => 4
[2,3,1,4,1] => 4
[2,3,4,1,1] => 4
[2,4,1,1,3] => 4
[2,4,1,3,1] => 4
[2,4,3,1,1] => 4
[3,1,1,2,4] => 4
[3,1,1,4,2] => 4
[3,1,2,1,4] => 4
[3,1,2,4,1] => 4
[3,1,4,1,2] => 4
[3,1,4,2,1] => 4
[3,2,1,1,4] => 4
[3,2,1,4,1] => 4
[3,2,4,1,1] => 4
[3,4,1,1,2] => 4
[3,4,1,2,1] => 4
[3,4,2,1,1] => 4
[4,1,1,2,3] => 4
[4,1,1,3,2] => 4
[4,1,2,1,3] => 4
[4,1,2,3,1] => 4
[4,1,3,1,2] => 4
[4,1,3,2,1] => 4
[4,2,1,1,3] => 4
[4,2,1,3,1] => 4
[4,2,3,1,1] => 4
[4,3,1,1,2] => 4
[4,3,1,2,1] => 4
[4,3,2,1,1] => 4
[1,1,2,3,5] => 3
[1,1,2,5,3] => 3
[1,1,3,2,5] => 3
[1,1,3,5,2] => 3
[1,1,5,2,3] => 3
[1,1,5,3,2] => 3
[1,2,1,3,5] => 3
[1,2,1,5,3] => 3
[1,2,3,1,5] => 3
[1,2,3,5,1] => 3
[1,2,5,1,3] => 3
[1,2,5,3,1] => 3
[1,3,1,2,5] => 3
[1,3,1,5,2] => 3
[1,3,2,1,5] => 3
[1,3,2,5,1] => 3
[1,3,5,1,2] => 3
[1,3,5,2,1] => 3
[1,5,1,2,3] => 3
[1,5,1,3,2] => 3
[1,5,2,1,3] => 3
[1,5,2,3,1] => 3
[1,5,3,1,2] => 3
[1,5,3,2,1] => 3
[2,1,1,3,5] => 3
[2,1,1,5,3] => 3
[2,1,3,1,5] => 3
[2,1,3,5,1] => 3
[2,1,5,1,3] => 3
[2,1,5,3,1] => 3
[2,3,1,1,5] => 3
[2,3,1,5,1] => 3
[2,3,5,1,1] => 3
[2,5,1,1,3] => 3
[2,5,1,3,1] => 3
[2,5,3,1,1] => 3
[3,1,1,2,5] => 3
[3,1,1,5,2] => 3
[3,1,2,1,5] => 3
[3,1,2,5,1] => 3
[3,1,5,1,2] => 3
[3,1,5,2,1] => 3
[3,2,1,1,5] => 3
[3,2,1,5,1] => 3
[3,2,5,1,1] => 3
[3,5,1,1,2] => 3
[3,5,1,2,1] => 3
[3,5,2,1,1] => 3
[5,1,1,2,3] => 3
[5,1,1,3,2] => 3
[5,1,2,1,3] => 3
[5,1,2,3,1] => 3
[5,1,3,1,2] => 3
[5,1,3,2,1] => 3
[5,2,1,1,3] => 3
[5,2,1,3,1] => 3
[5,2,3,1,1] => 3
[5,3,1,1,2] => 3
[5,3,1,2,1] => 3
[5,3,2,1,1] => 3
[1,1,2,4,4] => 3
[1,1,4,2,4] => 3
[1,1,4,4,2] => 3
[1,2,1,4,4] => 3
[1,2,4,1,4] => 3
[1,2,4,4,1] => 3
[1,4,1,2,4] => 3
[1,4,1,4,2] => 3
[1,4,2,1,4] => 3
[1,4,2,4,1] => 3
[1,4,4,1,2] => 3
[1,4,4,2,1] => 3
[2,1,1,4,4] => 3
[2,1,4,1,4] => 3
[2,1,4,4,1] => 3
[2,4,1,1,4] => 3
[2,4,1,4,1] => 3
[2,4,4,1,1] => 3
[4,1,1,2,4] => 3
[4,1,1,4,2] => 3
[4,1,2,1,4] => 3
[4,1,2,4,1] => 3
[4,1,4,1,2] => 3
[4,1,4,2,1] => 3
[4,2,1,1,4] => 3
[4,2,1,4,1] => 3
[4,2,4,1,1] => 3
[4,4,1,1,2] => 3
[4,4,1,2,1] => 3
[4,4,2,1,1] => 3
[1,1,2,4,5] => 2
[1,1,2,5,4] => 2
[1,1,4,2,5] => 2
[1,1,4,5,2] => 2
[1,1,5,2,4] => 2
[1,1,5,4,2] => 2
[1,2,1,4,5] => 2
[1,2,1,5,4] => 2
[1,2,4,1,5] => 2
[1,2,4,5,1] => 2
[1,2,5,1,4] => 2
[1,2,5,4,1] => 2
[1,4,1,2,5] => 2
[1,4,1,5,2] => 2
[1,4,2,1,5] => 2
[1,4,2,5,1] => 2
[1,4,5,1,2] => 2
[1,4,5,2,1] => 2
[1,5,1,2,4] => 2
[1,5,1,4,2] => 2
[1,5,2,1,4] => 2
[1,5,2,4,1] => 2
[1,5,4,1,2] => 2
[1,5,4,2,1] => 2
[2,1,1,4,5] => 2
[2,1,1,5,4] => 2
[2,1,4,1,5] => 2
[2,1,4,5,1] => 2
[2,1,5,1,4] => 2
[2,1,5,4,1] => 2
[2,4,1,1,5] => 2
[2,4,1,5,1] => 2
[2,4,5,1,1] => 2
[2,5,1,1,4] => 2
[2,5,1,4,1] => 2
[2,5,4,1,1] => 2
[4,1,1,2,5] => 2
[4,1,1,5,2] => 2
[4,1,2,1,5] => 2
[4,1,2,5,1] => 2
[4,1,5,1,2] => 2
[4,1,5,2,1] => 2
[4,2,1,1,5] => 2
[4,2,1,5,1] => 2
[4,2,5,1,1] => 2
[4,5,1,1,2] => 2
[4,5,1,2,1] => 2
[4,5,2,1,1] => 2
[5,1,1,2,4] => 2
[5,1,1,4,2] => 2
[5,1,2,1,4] => 2
[5,1,2,4,1] => 2
[5,1,4,1,2] => 2
[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] => 2
[5,4,1,2,1] => 2
[5,4,2,1,1] => 2
[1,1,3,3,3] => 4
[1,3,1,3,3] => 4
[1,3,3,1,3] => 4
[1,3,3,3,1] => 4
[3,1,1,3,3] => 4
[3,1,3,1,3] => 4
[3,1,3,3,1] => 4
[3,3,1,1,3] => 4
[3,3,1,3,1] => 4
[3,3,3,1,1] => 4
[1,1,3,3,4] => 3
[1,1,3,4,3] => 3
[1,1,4,3,3] => 3
[1,3,1,3,4] => 3
[1,3,1,4,3] => 3
[1,3,3,1,4] => 3
[1,3,3,4,1] => 3
[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] => 3
[3,1,1,4,3] => 3
[3,1,3,1,4] => 3
[3,1,3,4,1] => 3
[3,1,4,1,3] => 3
[3,1,4,3,1] => 3
[3,3,1,1,4] => 3
[3,3,1,4,1] => 3
[3,3,4,1,1] => 3
[3,4,1,1,3] => 3
[3,4,1,3,1] => 3
[3,4,3,1,1] => 3
[4,1,1,3,3] => 3
[4,1,3,1,3] => 3
[4,1,3,3,1] => 3
[4,3,1,1,3] => 3
[4,3,1,3,1] => 3
[4,3,3,1,1] => 3
[1,1,3,3,5] => 2
[1,1,3,5,3] => 2
[1,1,5,3,3] => 2
[1,3,1,3,5] => 2
[1,3,1,5,3] => 2
[1,3,3,1,5] => 2
[1,3,3,5,1] => 2
[1,3,5,1,3] => 2
[1,3,5,3,1] => 2
[1,5,1,3,3] => 2
[1,5,3,1,3] => 2
[1,5,3,3,1] => 2
[3,1,1,3,5] => 2
[3,1,1,5,3] => 2
[3,1,3,1,5] => 2
[3,1,3,5,1] => 2
[3,1,5,1,3] => 2
[3,1,5,3,1] => 2
[3,3,1,1,5] => 2
[3,3,1,5,1] => 2
[3,3,5,1,1] => 2
[3,5,1,1,3] => 2
[3,5,1,3,1] => 2
[3,5,3,1,1] => 2
[5,1,1,3,3] => 2
[5,1,3,1,3] => 2
[5,1,3,3,1] => 2
[5,3,1,1,3] => 2
[5,3,1,3,1] => 2
[5,3,3,1,1] => 2
[1,1,3,4,4] => 2
[1,1,4,3,4] => 2
[1,1,4,4,3] => 2
[1,3,1,4,4] => 2
[1,3,4,1,4] => 2
[1,3,4,4,1] => 2
[1,4,1,3,4] => 2
[1,4,1,4,3] => 2
[1,4,3,1,4] => 2
[1,4,3,4,1] => 2
[1,4,4,1,3] => 2
[1,4,4,3,1] => 2
[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] => 2
[4,1,1,4,3] => 2
[4,1,3,1,4] => 2
[4,1,3,4,1] => 2
[4,1,4,1,3] => 2
[4,1,4,3,1] => 2
[4,3,1,1,4] => 2
[4,3,1,4,1] => 2
[4,3,4,1,1] => 2
[4,4,1,1,3] => 2
[4,4,1,3,1] => 2
[4,4,3,1,1] => 2
[1,1,3,4,5] => 1
[1,1,3,5,4] => 1
[1,1,4,3,5] => 1
[1,1,4,5,3] => 1
[1,1,5,3,4] => 1
[1,1,5,4,3] => 1
[1,3,1,4,5] => 1
[1,3,1,5,4] => 1
[1,3,4,1,5] => 1
[1,3,4,5,1] => 1
[1,3,5,1,4] => 1
[1,3,5,4,1] => 1
[1,4,1,3,5] => 1
[1,4,1,5,3] => 1
[1,4,3,1,5] => 1
[1,4,3,5,1] => 1
[1,4,5,1,3] => 1
[1,4,5,3,1] => 1
[1,5,1,3,4] => 1
[1,5,1,4,3] => 1
[1,5,3,1,4] => 1
[1,5,3,4,1] => 1
[1,5,4,1,3] => 1
[1,5,4,3,1] => 1
[3,1,1,4,5] => 1
[3,1,1,5,4] => 1
[3,1,4,1,5] => 1
[3,1,4,5,1] => 1
[3,1,5,1,4] => 1
[3,1,5,4,1] => 1
[3,4,1,1,5] => 1
[3,4,1,5,1] => 1
[3,4,5,1,1] => 1
[3,5,1,1,4] => 1
[3,5,1,4,1] => 1
[3,5,4,1,1] => 1
[4,1,1,3,5] => 1
[4,1,1,5,3] => 1
[4,1,3,1,5] => 1
[4,1,3,5,1] => 1
[4,1,5,1,3] => 1
[4,1,5,3,1] => 1
[4,3,1,1,5] => 1
[4,3,1,5,1] => 1
[4,3,5,1,1] => 1
[4,5,1,1,3] => 1
[4,5,1,3,1] => 1
[4,5,3,1,1] => 1
[5,1,1,3,4] => 1
[5,1,1,4,3] => 1
[5,1,3,1,4] => 1
[5,1,3,4,1] => 1
[5,1,4,1,3] => 1
[5,1,4,3,1] => 1
[5,3,1,1,4] => 1
[5,3,1,4,1] => 1
[5,3,4,1,1] => 1
[5,4,1,1,3] => 1
[5,4,1,3,1] => 1
[5,4,3,1,1] => 1
[1,2,2,2,2] => 6
[2,1,2,2,2] => 6
[2,2,1,2,2] => 6
[2,2,2,1,2] => 6
[2,2,2,2,1] => 6
[1,2,2,2,3] => 5
[1,2,2,3,2] => 5
[1,2,3,2,2] => 5
[1,3,2,2,2] => 5
[2,1,2,2,3] => 5
[2,1,2,3,2] => 5
[2,1,3,2,2] => 5
[2,2,1,2,3] => 5
[2,2,1,3,2] => 5
[2,2,2,1,3] => 5
[2,2,2,3,1] => 5
[2,2,3,1,2] => 5
[2,2,3,2,1] => 5
[2,3,1,2,2] => 5
[2,3,2,1,2] => 5
[2,3,2,2,1] => 5
[3,1,2,2,2] => 5
[3,2,1,2,2] => 5
[3,2,2,1,2] => 5
[3,2,2,2,1] => 5
[1,2,2,2,4] => 4
[1,2,2,4,2] => 4
[1,2,4,2,2] => 4
[1,4,2,2,2] => 4
[2,1,2,2,4] => 4
[2,1,2,4,2] => 4
[2,1,4,2,2] => 4
[2,2,1,2,4] => 4
[2,2,1,4,2] => 4
[2,2,2,1,4] => 4
[2,2,2,4,1] => 4
[2,2,4,1,2] => 4
[2,2,4,2,1] => 4
[2,4,1,2,2] => 4
[2,4,2,1,2] => 4
[2,4,2,2,1] => 4
[4,1,2,2,2] => 4
[4,2,1,2,2] => 4
[4,2,2,1,2] => 4
[4,2,2,2,1] => 4
[1,2,2,2,5] => 3
[1,2,2,5,2] => 3
[1,2,5,2,2] => 3
[1,5,2,2,2] => 3
[2,1,2,2,5] => 3
[2,1,2,5,2] => 3
[2,1,5,2,2] => 3
[2,2,1,2,5] => 3
[2,2,1,5,2] => 3
[2,2,2,1,5] => 3
[2,2,2,5,1] => 3
[2,2,5,1,2] => 3
[2,2,5,2,1] => 3
[2,5,1,2,2] => 3
[2,5,2,1,2] => 3
[2,5,2,2,1] => 3
[5,1,2,2,2] => 3
[5,2,1,2,2] => 3
[5,2,2,1,2] => 3
[5,2,2,2,1] => 3
[1,2,2,3,3] => 4
[1,2,3,2,3] => 4
[1,2,3,3,2] => 4
[1,3,2,2,3] => 4
[1,3,2,3,2] => 4
[1,3,3,2,2] => 4
[2,1,2,3,3] => 4
[2,1,3,2,3] => 4
[2,1,3,3,2] => 4
[2,2,1,3,3] => 4
[2,2,3,1,3] => 4
[2,2,3,3,1] => 4
[2,3,1,2,3] => 4
[2,3,1,3,2] => 4
[2,3,2,1,3] => 4
[2,3,2,3,1] => 4
[2,3,3,1,2] => 4
[2,3,3,2,1] => 4
[3,1,2,2,3] => 4
[3,1,2,3,2] => 4
[3,1,3,2,2] => 4
[3,2,1,2,3] => 4
[3,2,1,3,2] => 4
[3,2,2,1,3] => 4
[3,2,2,3,1] => 4
[3,2,3,1,2] => 4
[3,2,3,2,1] => 4
[3,3,1,2,2] => 4
[3,3,2,1,2] => 4
[3,3,2,2,1] => 4
[1,2,2,3,4] => 3
[1,2,2,4,3] => 3
[1,2,3,2,4] => 3
[1,2,3,4,2] => 3
[1,2,4,2,3] => 3
[1,2,4,3,2] => 3
[1,3,2,2,4] => 3
[1,3,2,4,2] => 3
[1,3,4,2,2] => 3
[1,4,2,2,3] => 3
[1,4,2,3,2] => 3
[1,4,3,2,2] => 3
[2,1,2,3,4] => 3
[2,1,2,4,3] => 3
[2,1,3,2,4] => 3
[2,1,3,4,2] => 3
[2,1,4,2,3] => 3
[2,1,4,3,2] => 3
[2,2,1,3,4] => 3
[2,2,1,4,3] => 3
[2,2,3,1,4] => 3
[2,2,3,4,1] => 3
[2,2,4,1,3] => 3
[2,2,4,3,1] => 3
[2,3,1,2,4] => 3
[2,3,1,4,2] => 3
[2,3,2,1,4] => 3
[2,3,2,4,1] => 3
[2,3,4,1,2] => 3
[2,3,4,2,1] => 3
[2,4,1,2,3] => 3
[2,4,1,3,2] => 3
[2,4,2,1,3] => 3
[2,4,2,3,1] => 3
[2,4,3,1,2] => 3
[2,4,3,2,1] => 3
[3,1,2,2,4] => 3
[3,1,2,4,2] => 3
[3,1,4,2,2] => 3
[3,2,1,2,4] => 3
[3,2,1,4,2] => 3
[3,2,2,1,4] => 3
[3,2,2,4,1] => 3
[3,2,4,1,2] => 3
[3,2,4,2,1] => 3
[3,4,1,2,2] => 3
[3,4,2,1,2] => 3
[3,4,2,2,1] => 3
[4,1,2,2,3] => 3
[4,1,2,3,2] => 3
[4,1,3,2,2] => 3
[4,2,1,2,3] => 3
[4,2,1,3,2] => 3
[4,2,2,1,3] => 3
[4,2,2,3,1] => 3
[4,2,3,1,2] => 3
[4,2,3,2,1] => 3
[4,3,1,2,2] => 3
[4,3,2,1,2] => 3
[4,3,2,2,1] => 3
[1,2,2,3,5] => 2
[1,2,2,5,3] => 2
[1,2,3,2,5] => 2
[1,2,3,5,2] => 2
[1,2,5,2,3] => 2
[1,2,5,3,2] => 2
[1,3,2,2,5] => 2
[1,3,2,5,2] => 2
[1,3,5,2,2] => 2
[1,5,2,2,3] => 2
[1,5,2,3,2] => 2
[1,5,3,2,2] => 2
[2,1,2,3,5] => 2
[2,1,2,5,3] => 2
[2,1,3,2,5] => 2
[2,1,3,5,2] => 2
[2,1,5,2,3] => 2
[2,1,5,3,2] => 2
[2,2,1,3,5] => 2
[2,2,1,5,3] => 2
[2,2,3,1,5] => 2
[2,2,3,5,1] => 2
[2,2,5,1,3] => 2
[2,2,5,3,1] => 2
[2,3,1,2,5] => 2
[2,3,1,5,2] => 2
[2,3,2,1,5] => 2
[2,3,2,5,1] => 2
[2,3,5,1,2] => 2
[2,3,5,2,1] => 2
[2,5,1,2,3] => 2
[2,5,1,3,2] => 2
[2,5,2,1,3] => 2
[2,5,2,3,1] => 2
[2,5,3,1,2] => 2
[2,5,3,2,1] => 2
[3,1,2,2,5] => 2
[3,1,2,5,2] => 2
[3,1,5,2,2] => 2
[3,2,1,2,5] => 2
[3,2,1,5,2] => 2
[3,2,2,1,5] => 2
[3,2,2,5,1] => 2
[3,2,5,1,2] => 2
[3,2,5,2,1] => 2
[3,5,1,2,2] => 2
[3,5,2,1,2] => 2
[3,5,2,2,1] => 2
[5,1,2,2,3] => 2
[5,1,2,3,2] => 2
[5,1,3,2,2] => 2
[5,2,1,2,3] => 2
[5,2,1,3,2] => 2
[5,2,2,1,3] => 2
[5,2,2,3,1] => 2
[5,2,3,1,2] => 2
[5,2,3,2,1] => 2
[5,3,1,2,2] => 2
[5,3,2,1,2] => 2
[5,3,2,2,1] => 2
[1,2,2,4,4] => 2
[1,2,4,2,4] => 2
[1,2,4,4,2] => 2
[1,4,2,2,4] => 2
[1,4,2,4,2] => 2
[1,4,4,2,2] => 2
[2,1,2,4,4] => 2
[2,1,4,2,4] => 2
[2,1,4,4,2] => 2
[2,2,1,4,4] => 2
[2,2,4,1,4] => 2
[2,2,4,4,1] => 2
[2,4,1,2,4] => 2
[2,4,1,4,2] => 2
[2,4,2,1,4] => 2
[2,4,2,4,1] => 2
[2,4,4,1,2] => 2
[2,4,4,2,1] => 2
[4,1,2,2,4] => 2
[4,1,2,4,2] => 2
[4,1,4,2,2] => 2
[4,2,1,2,4] => 2
[4,2,1,4,2] => 2
[4,2,2,1,4] => 2
[4,2,2,4,1] => 2
[4,2,4,1,2] => 2
[4,2,4,2,1] => 2
[4,4,1,2,2] => 2
[4,4,2,1,2] => 2
[4,4,2,2,1] => 2
[1,2,2,4,5] => 1
[1,2,2,5,4] => 1
[1,2,4,2,5] => 1
[1,2,4,5,2] => 1
[1,2,5,2,4] => 1
[1,2,5,4,2] => 1
[1,4,2,2,5] => 1
[1,4,2,5,2] => 1
[1,4,5,2,2] => 1
[1,5,2,2,4] => 1
[1,5,2,4,2] => 1
[1,5,4,2,2] => 1
[2,1,2,4,5] => 1
[2,1,2,5,4] => 1
[2,1,4,2,5] => 1
[2,1,4,5,2] => 1
[2,1,5,2,4] => 1
[2,1,5,4,2] => 1
[2,2,1,4,5] => 1
[2,2,1,5,4] => 1
[2,2,4,1,5] => 1
[2,2,4,5,1] => 1
[2,2,5,1,4] => 1
[2,2,5,4,1] => 1
[2,4,1,2,5] => 1
[2,4,1,5,2] => 1
[2,4,2,1,5] => 1
[2,4,2,5,1] => 1
[2,4,5,1,2] => 1
[2,4,5,2,1] => 1
[2,5,1,2,4] => 1
[2,5,1,4,2] => 1
[2,5,2,1,4] => 1
[2,5,2,4,1] => 1
[2,5,4,1,2] => 1
[2,5,4,2,1] => 1
[4,1,2,2,5] => 1
[4,1,2,5,2] => 1
[4,1,5,2,2] => 1
[4,2,1,2,5] => 1
[4,2,1,5,2] => 1
[4,2,2,1,5] => 1
[4,2,2,5,1] => 1
[4,2,5,1,2] => 1
[4,2,5,2,1] => 1
[4,5,1,2,2] => 1
[4,5,2,1,2] => 1
[4,5,2,2,1] => 1
[5,1,2,2,4] => 1
[5,1,2,4,2] => 1
[5,1,4,2,2] => 1
[5,2,1,2,4] => 1
[5,2,1,4,2] => 1
[5,2,2,1,4] => 1
[5,2,2,4,1] => 1
[5,2,4,1,2] => 1
[5,2,4,2,1] => 1
[5,4,1,2,2] => 1
[5,4,2,1,2] => 1
[5,4,2,2,1] => 1
[1,2,3,3,3] => 3
[1,3,2,3,3] => 3
[1,3,3,2,3] => 3
[1,3,3,3,2] => 3
[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] => 3
[3,1,3,2,3] => 3
[3,1,3,3,2] => 3
[3,2,1,3,3] => 3
[3,2,3,1,3] => 3
[3,2,3,3,1] => 3
[3,3,1,2,3] => 3
[3,3,1,3,2] => 3
[3,3,2,1,3] => 3
[3,3,2,3,1] => 3
[3,3,3,1,2] => 3
[3,3,3,2,1] => 3
[1,2,3,3,4] => 2
[1,2,3,4,3] => 2
[1,2,4,3,3] => 2
[1,3,2,3,4] => 2
[1,3,2,4,3] => 2
[1,3,3,2,4] => 2
[1,3,3,4,2] => 2
[1,3,4,2,3] => 2
[1,3,4,3,2] => 2
[1,4,2,3,3] => 2
[1,4,3,2,3] => 2
[1,4,3,3,2] => 2
[2,1,3,3,4] => 2
[2,1,3,4,3] => 2
[2,1,4,3,3] => 2
[2,3,1,3,4] => 2
[2,3,1,4,3] => 2
[2,3,3,1,4] => 2
[2,3,3,4,1] => 2
[2,3,4,1,3] => 2
[2,3,4,3,1] => 2
[2,4,1,3,3] => 2
[2,4,3,1,3] => 2
[2,4,3,3,1] => 2

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Created: May 08, 2014 at 23:40 by Joanna Heppner

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Last Updated: Jul 16, 2024 at 20:06 by Marvin Gandhi