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* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
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* This information is distributed in the hope that it will be useful, *
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. *
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-----------------------------------------------------------------------------
Statistic identifier: St001918
-----------------------------------------------------------------------------
Collection: Integer partitions
-----------------------------------------------------------------------------
Description: The degree of the cyclic sieving polynomial corresponding to an integer partition.
Let $\lambda$ be an integer partition of $n$ and let $N$ be the least common multiple of the parts of $\lambda$. Fix an arbitrary permutation $\pi$ of cycle type $\lambda$. Then $\pi$ induces a cyclic action of order $N$ on $\{1,\dots,n\}$.
The corresponding character can be identified with the cyclic sieving polynomial $C_\lambda(q)$ of this action, modulo $q^N-1$. Explicitly, it is
$$
\sum_{p\in\lambda} [p]_{q^{N/p}},
$$
where $[p]_q = 1+\dots+q^{p-1}$ is the $q$-integer.
This statistic records the degree of $C_\lambda(q)$. Equivalently, it equals
$$
\left(1 - \frac{1}{\lambda_1}\right) N,
$$
where $\lambda_1$ is the largest part of $\lambda$.
The statistic is undefined for the empty partition.
-----------------------------------------------------------------------------
References:
-----------------------------------------------------------------------------
Code:
def statistic(la):
return (la[0] - 1) * lcm(la) / la[0]
-----------------------------------------------------------------------------
Statistic values:
[1] => 0
[2] => 1
[1,1] => 0
[3] => 2
[2,1] => 1
[1,1,1] => 0
[4] => 3
[3,1] => 2
[2,2] => 1
[2,1,1] => 1
[1,1,1,1] => 0
[5] => 4
[4,1] => 3
[3,2] => 4
[3,1,1] => 2
[2,2,1] => 1
[2,1,1,1] => 1
[1,1,1,1,1] => 0
[6] => 5
[5,1] => 4
[4,2] => 3
[4,1,1] => 3
[3,3] => 2
[3,2,1] => 4
[3,1,1,1] => 2
[2,2,2] => 1
[2,2,1,1] => 1
[2,1,1,1,1] => 1
[1,1,1,1,1,1] => 0
[7] => 6
[6,1] => 5
[5,2] => 8
[5,1,1] => 4
[4,3] => 9
[4,2,1] => 3
[4,1,1,1] => 3
[3,3,1] => 2
[3,2,2] => 4
[3,2,1,1] => 4
[3,1,1,1,1] => 2
[2,2,2,1] => 1
[2,2,1,1,1] => 1
[2,1,1,1,1,1] => 1
[1,1,1,1,1,1,1] => 0
[8] => 7
[7,1] => 6
[6,2] => 5
[6,1,1] => 5
[5,3] => 12
[5,2,1] => 8
[5,1,1,1] => 4
[4,4] => 3
[4,3,1] => 9
[4,2,2] => 3
[4,2,1,1] => 3
[4,1,1,1,1] => 3
[3,3,2] => 4
[3,3,1,1] => 2
[3,2,2,1] => 4
[3,2,1,1,1] => 4
[3,1,1,1,1,1] => 2
[2,2,2,2] => 1
[2,2,2,1,1] => 1
[2,2,1,1,1,1] => 1
[2,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1] => 0
[9] => 8
[8,1] => 7
[7,2] => 12
[7,1,1] => 6
[6,3] => 5
[6,2,1] => 5
[6,1,1,1] => 5
[5,4] => 16
[5,3,1] => 12
[5,2,2] => 8
[5,2,1,1] => 8
[5,1,1,1,1] => 4
[4,4,1] => 3
[4,3,2] => 9
[4,3,1,1] => 9
[4,2,2,1] => 3
[4,2,1,1,1] => 3
[4,1,1,1,1,1] => 3
[3,3,3] => 2
[3,3,2,1] => 4
[3,3,1,1,1] => 2
[3,2,2,2] => 4
[3,2,2,1,1] => 4
[3,2,1,1,1,1] => 4
[3,1,1,1,1,1,1] => 2
[2,2,2,2,1] => 1
[2,2,2,1,1,1] => 1
[2,2,1,1,1,1,1] => 1
[2,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1] => 0
[10] => 9
[9,1] => 8
[8,2] => 7
[8,1,1] => 7
[7,3] => 18
[7,2,1] => 12
[7,1,1,1] => 6
[6,4] => 10
[6,3,1] => 5
[6,2,2] => 5
[6,2,1,1] => 5
[6,1,1,1,1] => 5
[5,5] => 4
[5,4,1] => 16
[5,3,2] => 24
[5,3,1,1] => 12
[5,2,2,1] => 8
[5,2,1,1,1] => 8
[5,1,1,1,1,1] => 4
[4,4,2] => 3
[4,4,1,1] => 3
[4,3,3] => 9
[4,3,2,1] => 9
[4,3,1,1,1] => 9
[4,2,2,2] => 3
[4,2,2,1,1] => 3
[4,2,1,1,1,1] => 3
[4,1,1,1,1,1,1] => 3
[3,3,3,1] => 2
[3,3,2,2] => 4
[3,3,2,1,1] => 4
[3,3,1,1,1,1] => 2
[3,2,2,2,1] => 4
[3,2,2,1,1,1] => 4
[3,2,1,1,1,1,1] => 4
[3,1,1,1,1,1,1,1] => 2
[2,2,2,2,2] => 1
[2,2,2,2,1,1] => 1
[2,2,2,1,1,1,1] => 1
[2,2,1,1,1,1,1,1] => 1
[2,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,1] => 0
[11] => 10
[10,1] => 9
[9,2] => 16
[9,1,1] => 8
[8,3] => 21
[8,2,1] => 7
[8,1,1,1] => 7
[7,4] => 24
[7,3,1] => 18
[7,2,2] => 12
[7,2,1,1] => 12
[7,1,1,1,1] => 6
[6,5] => 25
[6,4,1] => 10
[6,3,2] => 5
[6,3,1,1] => 5
[6,2,2,1] => 5
[6,2,1,1,1] => 5
[6,1,1,1,1,1] => 5
[5,5,1] => 4
[5,4,2] => 16
[5,4,1,1] => 16
[5,3,3] => 12
[5,3,2,1] => 24
[5,3,1,1,1] => 12
[5,2,2,2] => 8
[5,2,2,1,1] => 8
[5,2,1,1,1,1] => 8
[5,1,1,1,1,1,1] => 4
[4,4,3] => 9
[4,4,2,1] => 3
[4,4,1,1,1] => 3
[4,3,3,1] => 9
[4,3,2,2] => 9
[4,3,2,1,1] => 9
[4,3,1,1,1,1] => 9
[4,2,2,2,1] => 3
[4,2,2,1,1,1] => 3
[4,2,1,1,1,1,1] => 3
[4,1,1,1,1,1,1,1] => 3
[3,3,3,2] => 4
[3,3,3,1,1] => 2
[3,3,2,2,1] => 4
[3,3,2,1,1,1] => 4
[3,3,1,1,1,1,1] => 2
[3,2,2,2,2] => 4
[3,2,2,2,1,1] => 4
[3,2,2,1,1,1,1] => 4
[3,2,1,1,1,1,1,1] => 4
[3,1,1,1,1,1,1,1,1] => 2
[2,2,2,2,2,1] => 1
[2,2,2,2,1,1,1] => 1
[2,2,2,1,1,1,1,1] => 1
[2,2,1,1,1,1,1,1,1] => 1
[2,1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,1,1] => 0
[12] => 11
[11,1] => 10
[10,2] => 9
[10,1,1] => 9
[9,3] => 8
[9,2,1] => 16
[9,1,1,1] => 8
[8,4] => 7
[8,3,1] => 21
[8,2,2] => 7
[8,2,1,1] => 7
[8,1,1,1,1] => 7
[7,5] => 30
[7,4,1] => 24
[7,3,2] => 36
[7,3,1,1] => 18
[7,2,2,1] => 12
[7,2,1,1,1] => 12
[7,1,1,1,1,1] => 6
[6,6] => 5
[6,5,1] => 25
[6,4,2] => 10
[6,4,1,1] => 10
[6,3,3] => 5
[6,3,2,1] => 5
[6,3,1,1,1] => 5
[6,2,2,2] => 5
[6,2,2,1,1] => 5
[6,2,1,1,1,1] => 5
[6,1,1,1,1,1,1] => 5
[5,5,2] => 8
[5,5,1,1] => 4
[5,4,3] => 48
[5,4,2,1] => 16
[5,4,1,1,1] => 16
[5,3,3,1] => 12
[5,3,2,2] => 24
[5,3,2,1,1] => 24
[5,3,1,1,1,1] => 12
[5,2,2,2,1] => 8
[5,2,2,1,1,1] => 8
[5,2,1,1,1,1,1] => 8
[5,1,1,1,1,1,1,1] => 4
[4,4,4] => 3
[4,4,3,1] => 9
[4,4,2,2] => 3
[4,4,2,1,1] => 3
[4,4,1,1,1,1] => 3
[4,3,3,2] => 9
[4,3,3,1,1] => 9
[4,3,2,2,1] => 9
[4,3,2,1,1,1] => 9
[4,3,1,1,1,1,1] => 9
[4,2,2,2,2] => 3
[4,2,2,2,1,1] => 3
[4,2,2,1,1,1,1] => 3
[4,2,1,1,1,1,1,1] => 3
[4,1,1,1,1,1,1,1,1] => 3
[3,3,3,3] => 2
[3,3,3,2,1] => 4
[3,3,3,1,1,1] => 2
[3,3,2,2,2] => 4
[3,3,2,2,1,1] => 4
[3,3,2,1,1,1,1] => 4
[3,3,1,1,1,1,1,1] => 2
[3,2,2,2,2,1] => 4
[3,2,2,2,1,1,1] => 4
[3,2,2,1,1,1,1,1] => 4
[3,2,1,1,1,1,1,1,1] => 4
[3,1,1,1,1,1,1,1,1,1] => 2
[2,2,2,2,2,2] => 1
[2,2,2,2,2,1,1] => 1
[2,2,2,2,1,1,1,1] => 1
[2,2,2,1,1,1,1,1,1] => 1
[2,2,1,1,1,1,1,1,1,1] => 1
[2,1,1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,1,1,1] => 0
[13] => 12
[12,1] => 11
[11,2] => 20
[11,1,1] => 10
[10,3] => 27
[10,2,1] => 9
[10,1,1,1] => 9
[9,4] => 32
[9,3,1] => 8
[9,2,2] => 16
[9,2,1,1] => 16
[9,1,1,1,1] => 8
[8,5] => 35
[8,4,1] => 7
[8,3,2] => 21
[8,3,1,1] => 21
[8,2,2,1] => 7
[8,2,1,1,1] => 7
[8,1,1,1,1,1] => 7
[7,6] => 36
[7,5,1] => 30
[7,4,2] => 24
[7,4,1,1] => 24
[7,3,3] => 18
[7,3,2,1] => 36
[7,3,1,1,1] => 18
[7,2,2,2] => 12
[7,2,2,1,1] => 12
[7,2,1,1,1,1] => 12
[7,1,1,1,1,1,1] => 6
[6,6,1] => 5
[6,5,2] => 25
[6,5,1,1] => 25
[6,4,3] => 10
[6,4,2,1] => 10
[6,4,1,1,1] => 10
[6,3,3,1] => 5
[6,3,2,2] => 5
[6,3,2,1,1] => 5
[6,3,1,1,1,1] => 5
[6,2,2,2,1] => 5
[6,2,2,1,1,1] => 5
[6,2,1,1,1,1,1] => 5
[6,1,1,1,1,1,1,1] => 5
[5,5,3] => 12
[5,5,2,1] => 8
[5,5,1,1,1] => 4
[5,4,4] => 16
[5,4,3,1] => 48
[5,4,2,2] => 16
[5,4,2,1,1] => 16
[5,4,1,1,1,1] => 16
[5,3,3,2] => 24
[5,3,3,1,1] => 12
[5,3,2,2,1] => 24
[5,3,2,1,1,1] => 24
[5,3,1,1,1,1,1] => 12
[5,2,2,2,2] => 8
[5,2,2,2,1,1] => 8
[5,2,2,1,1,1,1] => 8
[5,2,1,1,1,1,1,1] => 8
[5,1,1,1,1,1,1,1,1] => 4
[4,4,4,1] => 3
[4,4,3,2] => 9
[4,4,3,1,1] => 9
[4,4,2,2,1] => 3
[4,4,2,1,1,1] => 3
[4,4,1,1,1,1,1] => 3
[4,3,3,3] => 9
[4,3,3,2,1] => 9
[4,3,3,1,1,1] => 9
[4,3,2,2,2] => 9
[4,3,2,2,1,1] => 9
[4,3,2,1,1,1,1] => 9
[4,3,1,1,1,1,1,1] => 9
[4,2,2,2,2,1] => 3
[4,2,2,2,1,1,1] => 3
[4,2,2,1,1,1,1,1] => 3
[4,2,1,1,1,1,1,1,1] => 3
[4,1,1,1,1,1,1,1,1,1] => 3
[3,3,3,3,1] => 2
[3,3,3,2,2] => 4
[3,3,3,2,1,1] => 4
[3,3,3,1,1,1,1] => 2
[3,3,2,2,2,1] => 4
[3,3,2,2,1,1,1] => 4
[3,3,2,1,1,1,1,1] => 4
[3,3,1,1,1,1,1,1,1] => 2
[3,2,2,2,2,2] => 4
[3,2,2,2,2,1,1] => 4
[3,2,2,2,1,1,1,1] => 4
[3,2,2,1,1,1,1,1,1] => 4
[3,2,1,1,1,1,1,1,1,1] => 4
[3,1,1,1,1,1,1,1,1,1,1] => 2
[2,2,2,2,2,2,1] => 1
[2,2,2,2,2,1,1,1] => 1
[2,2,2,2,1,1,1,1,1] => 1
[2,2,2,1,1,1,1,1,1,1] => 1
[2,2,1,1,1,1,1,1,1,1,1] => 1
[2,1,1,1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,1,1,1,1] => 0
[14] => 13
[13,1] => 12
[12,2] => 11
[12,1,1] => 11
[11,3] => 30
[11,2,1] => 20
[11,1,1,1] => 10
[10,4] => 18
[10,3,1] => 27
[10,2,2] => 9
[10,2,1,1] => 9
[10,1,1,1,1] => 9
[9,5] => 40
[9,4,1] => 32
[9,3,2] => 16
[9,3,1,1] => 8
[9,2,2,1] => 16
[9,2,1,1,1] => 16
[9,1,1,1,1,1] => 8
[8,6] => 21
[8,5,1] => 35
[8,4,2] => 7
[8,4,1,1] => 7
[8,3,3] => 21
[8,3,2,1] => 21
[8,3,1,1,1] => 21
[8,2,2,2] => 7
[8,2,2,1,1] => 7
[8,2,1,1,1,1] => 7
[8,1,1,1,1,1,1] => 7
[7,7] => 6
[7,6,1] => 36
[7,5,2] => 60
[7,5,1,1] => 30
[7,4,3] => 72
[7,4,2,1] => 24
[7,4,1,1,1] => 24
[7,3,3,1] => 18
[7,3,2,2] => 36
[7,3,2,1,1] => 36
[7,3,1,1,1,1] => 18
[7,2,2,2,1] => 12
[7,2,2,1,1,1] => 12
[7,2,1,1,1,1,1] => 12
[7,1,1,1,1,1,1,1] => 6
[6,6,2] => 5
[6,6,1,1] => 5
[6,5,3] => 25
[6,5,2,1] => 25
[6,5,1,1,1] => 25
[6,4,4] => 10
[6,4,3,1] => 10
[6,4,2,2] => 10
[6,4,2,1,1] => 10
[6,4,1,1,1,1] => 10
[6,3,3,2] => 5
[6,3,3,1,1] => 5
[6,3,2,2,1] => 5
[6,3,2,1,1,1] => 5
[6,3,1,1,1,1,1] => 5
[6,2,2,2,2] => 5
[6,2,2,2,1,1] => 5
[6,2,2,1,1,1,1] => 5
[6,2,1,1,1,1,1,1] => 5
[6,1,1,1,1,1,1,1,1] => 5
[5,5,4] => 16
[5,5,3,1] => 12
[5,5,2,2] => 8
[5,5,2,1,1] => 8
[5,5,1,1,1,1] => 4
[5,4,4,1] => 16
[5,4,3,2] => 48
[5,4,3,1,1] => 48
[5,4,2,2,1] => 16
[5,4,2,1,1,1] => 16
[5,4,1,1,1,1,1] => 16
[5,3,3,3] => 12
[5,3,3,2,1] => 24
[5,3,3,1,1,1] => 12
[5,3,2,2,2] => 24
[5,3,2,2,1,1] => 24
[5,3,2,1,1,1,1] => 24
[5,3,1,1,1,1,1,1] => 12
[5,2,2,2,2,1] => 8
[5,2,2,2,1,1,1] => 8
[5,2,2,1,1,1,1,1] => 8
[5,2,1,1,1,1,1,1,1] => 8
[5,1,1,1,1,1,1,1,1,1] => 4
[4,4,4,2] => 3
[4,4,4,1,1] => 3
[4,4,3,3] => 9
[4,4,3,2,1] => 9
[4,4,3,1,1,1] => 9
[4,4,2,2,2] => 3
[4,4,2,2,1,1] => 3
[4,4,2,1,1,1,1] => 3
[4,4,1,1,1,1,1,1] => 3
[4,3,3,3,1] => 9
[4,3,3,2,2] => 9
[4,3,3,2,1,1] => 9
[4,3,3,1,1,1,1] => 9
[4,3,2,2,2,1] => 9
[4,3,2,2,1,1,1] => 9
[4,3,2,1,1,1,1,1] => 9
[4,3,1,1,1,1,1,1,1] => 9
[4,2,2,2,2,2] => 3
[4,2,2,2,2,1,1] => 3
[4,2,2,2,1,1,1,1] => 3
[4,2,2,1,1,1,1,1,1] => 3
[4,2,1,1,1,1,1,1,1,1] => 3
[4,1,1,1,1,1,1,1,1,1,1] => 3
[3,3,3,3,2] => 4
[3,3,3,3,1,1] => 2
[3,3,3,2,2,1] => 4
[3,3,3,2,1,1,1] => 4
[3,3,3,1,1,1,1,1] => 2
[3,3,2,2,2,2] => 4
[3,3,2,2,2,1,1] => 4
[3,3,2,2,1,1,1,1] => 4
[3,3,2,1,1,1,1,1,1] => 4
[3,3,1,1,1,1,1,1,1,1] => 2
[3,2,2,2,2,2,1] => 4
[3,2,2,2,2,1,1,1] => 4
[3,2,2,2,1,1,1,1,1] => 4
[3,2,2,1,1,1,1,1,1,1] => 4
[3,2,1,1,1,1,1,1,1,1,1] => 4
[3,1,1,1,1,1,1,1,1,1,1,1] => 2
[2,2,2,2,2,2,2] => 1
[2,2,2,2,2,2,1,1] => 1
[2,2,2,2,2,1,1,1,1] => 1
[2,2,2,2,1,1,1,1,1,1] => 1
[2,2,2,1,1,1,1,1,1,1,1] => 1
[2,2,1,1,1,1,1,1,1,1,1,1] => 1
[2,1,1,1,1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0
[15] => 14
[14,1] => 13
[13,2] => 24
[13,1,1] => 12
[12,3] => 11
[12,2,1] => 11
[12,1,1,1] => 11
[11,4] => 40
[11,3,1] => 30
[11,2,2] => 20
[11,2,1,1] => 20
[11,1,1,1,1] => 10
[10,5] => 9
[10,4,1] => 18
[10,3,2] => 27
[10,3,1,1] => 27
[10,2,2,1] => 9
[10,2,1,1,1] => 9
[10,1,1,1,1,1] => 9
[9,6] => 16
[9,5,1] => 40
[9,4,2] => 32
[9,4,1,1] => 32
[9,3,3] => 8
[9,3,2,1] => 16
[9,3,1,1,1] => 8
[9,2,2,2] => 16
[9,2,2,1,1] => 16
[9,2,1,1,1,1] => 16
[9,1,1,1,1,1,1] => 8
[8,7] => 49
[8,6,1] => 21
[8,5,2] => 35
[8,5,1,1] => 35
[8,4,3] => 21
[8,4,2,1] => 7
[8,4,1,1,1] => 7
[8,3,3,1] => 21
[8,3,2,2] => 21
[8,3,2,1,1] => 21
[8,3,1,1,1,1] => 21
[8,2,2,2,1] => 7
[8,2,2,1,1,1] => 7
[8,2,1,1,1,1,1] => 7
[8,1,1,1,1,1,1,1] => 7
[7,7,1] => 6
[7,6,2] => 36
[7,6,1,1] => 36
[7,5,3] => 90
[7,5,2,1] => 60
[7,5,1,1,1] => 30
[7,4,4] => 24
[7,4,3,1] => 72
[7,4,2,2] => 24
[7,4,2,1,1] => 24
[7,4,1,1,1,1] => 24
[7,3,3,2] => 36
[7,3,3,1,1] => 18
[7,3,2,2,1] => 36
[7,3,2,1,1,1] => 36
[7,3,1,1,1,1,1] => 18
[7,2,2,2,2] => 12
[7,2,2,2,1,1] => 12
[7,2,2,1,1,1,1] => 12
[7,2,1,1,1,1,1,1] => 12
[7,1,1,1,1,1,1,1,1] => 6
[6,6,3] => 5
[6,6,2,1] => 5
[6,6,1,1,1] => 5
[6,5,4] => 50
[6,5,3,1] => 25
[6,5,2,2] => 25
[6,5,2,1,1] => 25
[6,5,1,1,1,1] => 25
[6,4,4,1] => 10
[6,4,3,2] => 10
[6,4,3,1,1] => 10
[6,4,2,2,1] => 10
[6,4,2,1,1,1] => 10
[6,4,1,1,1,1,1] => 10
[6,3,3,3] => 5
[6,3,3,2,1] => 5
[6,3,3,1,1,1] => 5
[6,3,2,2,2] => 5
[6,3,2,2,1,1] => 5
[6,3,2,1,1,1,1] => 5
[6,3,1,1,1,1,1,1] => 5
[6,2,2,2,2,1] => 5
[6,2,2,2,1,1,1] => 5
[6,2,2,1,1,1,1,1] => 5
[6,2,1,1,1,1,1,1,1] => 5
[6,1,1,1,1,1,1,1,1,1] => 5
[5,5,5] => 4
[5,5,4,1] => 16
[5,5,3,2] => 24
[5,5,3,1,1] => 12
[5,5,2,2,1] => 8
[5,5,2,1,1,1] => 8
[5,5,1,1,1,1,1] => 4
[5,4,4,2] => 16
[5,4,4,1,1] => 16
[5,4,3,3] => 48
[5,4,3,2,1] => 48
[5,4,3,1,1,1] => 48
[5,4,2,2,2] => 16
[5,4,2,2,1,1] => 16
[5,4,2,1,1,1,1] => 16
[5,4,1,1,1,1,1,1] => 16
[5,3,3,3,1] => 12
[5,3,3,2,2] => 24
[5,3,3,2,1,1] => 24
[5,3,3,1,1,1,1] => 12
[5,3,2,2,2,1] => 24
[5,3,2,2,1,1,1] => 24
[5,3,2,1,1,1,1,1] => 24
[5,3,1,1,1,1,1,1,1] => 12
[5,2,2,2,2,2] => 8
[5,2,2,2,2,1,1] => 8
[5,2,2,2,1,1,1,1] => 8
[5,2,2,1,1,1,1,1,1] => 8
[5,2,1,1,1,1,1,1,1,1] => 8
[5,1,1,1,1,1,1,1,1,1,1] => 4
[4,4,4,3] => 9
[4,4,4,2,1] => 3
[4,4,4,1,1,1] => 3
[4,4,3,3,1] => 9
[4,4,3,2,2] => 9
[4,4,3,2,1,1] => 9
[4,4,3,1,1,1,1] => 9
[4,4,2,2,2,1] => 3
[4,4,2,2,1,1,1] => 3
[4,4,2,1,1,1,1,1] => 3
[4,4,1,1,1,1,1,1,1] => 3
[4,3,3,3,2] => 9
[4,3,3,3,1,1] => 9
[4,3,3,2,2,1] => 9
[4,3,3,2,1,1,1] => 9
[4,3,3,1,1,1,1,1] => 9
[4,3,2,2,2,2] => 9
[4,3,2,2,2,1,1] => 9
[4,3,2,2,1,1,1,1] => 9
[4,3,2,1,1,1,1,1,1] => 9
[4,3,1,1,1,1,1,1,1,1] => 9
[4,2,2,2,2,2,1] => 3
[4,2,2,2,2,1,1,1] => 3
[4,2,2,2,1,1,1,1,1] => 3
[4,2,2,1,1,1,1,1,1,1] => 3
[4,2,1,1,1,1,1,1,1,1,1] => 3
[4,1,1,1,1,1,1,1,1,1,1,1] => 3
[3,3,3,3,3] => 2
[3,3,3,3,2,1] => 4
[3,3,3,3,1,1,1] => 2
[3,3,3,2,2,2] => 4
[3,3,3,2,2,1,1] => 4
[3,3,3,2,1,1,1,1] => 4
[3,3,3,1,1,1,1,1,1] => 2
[3,3,2,2,2,2,1] => 4
[3,3,2,2,2,1,1,1] => 4
[3,3,2,2,1,1,1,1,1] => 4
[3,3,2,1,1,1,1,1,1,1] => 4
[3,3,1,1,1,1,1,1,1,1,1] => 2
[3,2,2,2,2,2,2] => 4
[3,2,2,2,2,2,1,1] => 4
[3,2,2,2,2,1,1,1,1] => 4
[3,2,2,2,1,1,1,1,1,1] => 4
[3,2,2,1,1,1,1,1,1,1,1] => 4
[3,2,1,1,1,1,1,1,1,1,1,1] => 4
[3,1,1,1,1,1,1,1,1,1,1,1,1] => 2
[2,2,2,2,2,2,2,1] => 1
[2,2,2,2,2,2,1,1,1] => 1
[2,2,2,2,2,1,1,1,1,1] => 1
[2,2,2,2,1,1,1,1,1,1,1] => 1
[2,2,2,1,1,1,1,1,1,1,1,1] => 1
[2,2,1,1,1,1,1,1,1,1,1,1,1] => 1
[2,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0
[16] => 15
[15,1] => 14
[14,2] => 13
[14,1,1] => 13
[13,3] => 36
[13,2,1] => 24
[13,1,1,1] => 12
[12,4] => 11
[12,3,1] => 11
[12,2,2] => 11
[12,2,1,1] => 11
[12,1,1,1,1] => 11
[11,5] => 50
[11,4,1] => 40
[11,3,2] => 60
[11,3,1,1] => 30
[11,2,2,1] => 20
[11,2,1,1,1] => 20
[11,1,1,1,1,1] => 10
[10,6] => 27
[10,5,1] => 9
[10,4,2] => 18
[10,4,1,1] => 18
[10,3,3] => 27
[10,3,2,1] => 27
[10,3,1,1,1] => 27
[10,2,2,2] => 9
[10,2,2,1,1] => 9
[10,2,1,1,1,1] => 9
[10,1,1,1,1,1,1] => 9
[9,7] => 56
[9,6,1] => 16
[9,5,2] => 80
[9,5,1,1] => 40
[9,4,3] => 32
[9,4,2,1] => 32
[9,4,1,1,1] => 32
[9,3,3,1] => 8
[9,3,2,2] => 16
[9,3,2,1,1] => 16
[9,3,1,1,1,1] => 8
[9,2,2,2,1] => 16
[9,2,2,1,1,1] => 16
[9,2,1,1,1,1,1] => 16
[9,1,1,1,1,1,1,1] => 8
[8,8] => 7
[8,7,1] => 49
[8,6,2] => 21
[8,6,1,1] => 21
[8,5,3] => 105
[8,5,2,1] => 35
[8,5,1,1,1] => 35
[8,4,4] => 7
[8,4,3,1] => 21
[8,4,2,2] => 7
[8,4,2,1,1] => 7
[8,4,1,1,1,1] => 7
[8,3,3,2] => 21
[8,3,3,1,1] => 21
[8,3,2,2,1] => 21
[8,3,2,1,1,1] => 21
[8,3,1,1,1,1,1] => 21
[8,2,2,2,2] => 7
[8,2,2,2,1,1] => 7
[8,2,2,1,1,1,1] => 7
[8,2,1,1,1,1,1,1] => 7
[8,1,1,1,1,1,1,1,1] => 7
[7,7,2] => 12
[7,7,1,1] => 6
[7,6,3] => 36
[7,6,2,1] => 36
[7,6,1,1,1] => 36
[7,5,4] => 120
[7,5,3,1] => 90
[7,5,2,2] => 60
[7,5,2,1,1] => 60
[7,5,1,1,1,1] => 30
[7,4,4,1] => 24
[7,4,3,2] => 72
[7,4,3,1,1] => 72
[7,4,2,2,1] => 24
[7,4,2,1,1,1] => 24
[7,4,1,1,1,1,1] => 24
[7,3,3,3] => 18
[7,3,3,2,1] => 36
[7,3,3,1,1,1] => 18
[7,3,2,2,2] => 36
[7,3,2,2,1,1] => 36
[7,3,2,1,1,1,1] => 36
[7,3,1,1,1,1,1,1] => 18
[7,2,2,2,2,1] => 12
[7,2,2,2,1,1,1] => 12
[7,2,2,1,1,1,1,1] => 12
[7,2,1,1,1,1,1,1,1] => 12
[7,1,1,1,1,1,1,1,1,1] => 6
[6,6,4] => 10
[6,6,3,1] => 5
[6,6,2,2] => 5
[6,6,2,1,1] => 5
[6,6,1,1,1,1] => 5
[6,5,5] => 25
[6,5,4,1] => 50
[6,5,3,2] => 25
[6,5,3,1,1] => 25
[6,5,2,2,1] => 25
[6,5,2,1,1,1] => 25
[6,5,1,1,1,1,1] => 25
[6,4,4,2] => 10
[6,4,4,1,1] => 10
[6,4,3,3] => 10
[6,4,3,2,1] => 10
[6,4,3,1,1,1] => 10
[6,4,2,2,2] => 10
[6,4,2,2,1,1] => 10
[6,4,2,1,1,1,1] => 10
[6,4,1,1,1,1,1,1] => 10
[6,3,3,3,1] => 5
[6,3,3,2,2] => 5
[6,3,3,2,1,1] => 5
[6,3,3,1,1,1,1] => 5
[6,3,2,2,2,1] => 5
[6,3,2,2,1,1,1] => 5
[6,3,2,1,1,1,1,1] => 5
[6,3,1,1,1,1,1,1,1] => 5
[6,2,2,2,2,2] => 5
[6,2,2,2,2,1,1] => 5
[6,2,2,2,1,1,1,1] => 5
[6,2,2,1,1,1,1,1,1] => 5
[6,2,1,1,1,1,1,1,1,1] => 5
[6,1,1,1,1,1,1,1,1,1,1] => 5
[5,5,5,1] => 4
[5,5,4,2] => 16
[5,5,4,1,1] => 16
[5,5,3,3] => 12
[5,5,3,2,1] => 24
[5,5,3,1,1,1] => 12
[5,5,2,2,2] => 8
[5,5,2,2,1,1] => 8
[5,5,2,1,1,1,1] => 8
[5,5,1,1,1,1,1,1] => 4
[5,4,4,3] => 48
[5,4,4,2,1] => 16
[5,4,4,1,1,1] => 16
[5,4,3,3,1] => 48
[5,4,3,2,2] => 48
[5,4,3,2,1,1] => 48
[5,4,3,1,1,1,1] => 48
[5,4,2,2,2,1] => 16
[5,4,2,2,1,1,1] => 16
[5,4,2,1,1,1,1,1] => 16
[5,4,1,1,1,1,1,1,1] => 16
[5,3,3,3,2] => 24
[5,3,3,3,1,1] => 12
[5,3,3,2,2,1] => 24
[5,3,3,2,1,1,1] => 24
[5,3,3,1,1,1,1,1] => 12
[5,3,2,2,2,2] => 24
[5,3,2,2,2,1,1] => 24
[5,3,2,2,1,1,1,1] => 24
[5,3,2,1,1,1,1,1,1] => 24
[5,3,1,1,1,1,1,1,1,1] => 12
[5,2,2,2,2,2,1] => 8
[5,2,2,2,2,1,1,1] => 8
[5,2,2,2,1,1,1,1,1] => 8
[5,2,2,1,1,1,1,1,1,1] => 8
[5,2,1,1,1,1,1,1,1,1,1] => 8
[5,1,1,1,1,1,1,1,1,1,1,1] => 4
[4,4,4,4] => 3
[4,4,4,3,1] => 9
[4,4,4,2,2] => 3
[4,4,4,2,1,1] => 3
[4,4,4,1,1,1,1] => 3
[4,4,3,3,2] => 9
[4,4,3,3,1,1] => 9
[4,4,3,2,2,1] => 9
[4,4,3,2,1,1,1] => 9
[4,4,3,1,1,1,1,1] => 9
[4,4,2,2,2,2] => 3
[4,4,2,2,2,1,1] => 3
[4,4,2,2,1,1,1,1] => 3
[4,4,2,1,1,1,1,1,1] => 3
[4,4,1,1,1,1,1,1,1,1] => 3
[4,3,3,3,3] => 9
[4,3,3,3,2,1] => 9
[4,3,3,3,1,1,1] => 9
[4,3,3,2,2,2] => 9
[4,3,3,2,2,1,1] => 9
[4,3,3,2,1,1,1,1] => 9
[4,3,3,1,1,1,1,1,1] => 9
[4,3,2,2,2,2,1] => 9
[4,3,2,2,2,1,1,1] => 9
[4,3,2,2,1,1,1,1,1] => 9
[4,3,2,1,1,1,1,1,1,1] => 9
[4,3,1,1,1,1,1,1,1,1,1] => 9
[4,2,2,2,2,2,2] => 3
[4,2,2,2,2,2,1,1] => 3
[4,2,2,2,2,1,1,1,1] => 3
[4,2,2,2,1,1,1,1,1,1] => 3
[4,2,2,1,1,1,1,1,1,1,1] => 3
[4,2,1,1,1,1,1,1,1,1,1,1] => 3
[4,1,1,1,1,1,1,1,1,1,1,1,1] => 3
[3,3,3,3,3,1] => 2
[3,3,3,3,2,2] => 4
[3,3,3,3,2,1,1] => 4
[3,3,3,3,1,1,1,1] => 2
[3,3,3,2,2,2,1] => 4
[3,3,3,2,2,1,1,1] => 4
[3,3,3,2,1,1,1,1,1] => 4
[3,3,3,1,1,1,1,1,1,1] => 2
[3,3,2,2,2,2,2] => 4
[3,3,2,2,2,2,1,1] => 4
[3,3,2,2,2,1,1,1,1] => 4
[3,3,2,2,1,1,1,1,1,1] => 4
[3,3,2,1,1,1,1,1,1,1,1] => 4
[3,3,1,1,1,1,1,1,1,1,1,1] => 2
[3,2,2,2,2,2,2,1] => 4
[3,2,2,2,2,2,1,1,1] => 4
[3,2,2,2,2,1,1,1,1,1] => 4
[3,2,2,2,1,1,1,1,1,1,1] => 4
[3,2,2,1,1,1,1,1,1,1,1,1] => 4
[3,2,1,1,1,1,1,1,1,1,1,1,1] => 4
[3,1,1,1,1,1,1,1,1,1,1,1,1,1] => 2
[2,2,2,2,2,2,2,2] => 1
[2,2,2,2,2,2,2,1,1] => 1
[2,2,2,2,2,2,1,1,1,1] => 1
[2,2,2,2,2,1,1,1,1,1,1] => 1
[2,2,2,2,1,1,1,1,1,1,1,1] => 1
[2,2,2,1,1,1,1,1,1,1,1,1,1] => 1
[2,2,1,1,1,1,1,1,1,1,1,1,1,1] => 1
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 1
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0
[17] => 16
[16,1] => 15
[15,2] => 28
[15,1,1] => 14
[14,3] => 39
[14,2,1] => 13
[14,1,1,1] => 13
[13,4] => 48
[13,3,1] => 36
[13,2,2] => 24
[13,2,1,1] => 24
[13,1,1,1,1] => 12
[12,5] => 55
[12,4,1] => 11
[12,3,2] => 11
[12,3,1,1] => 11
[12,2,2,1] => 11
[12,2,1,1,1] => 11
[12,1,1,1,1,1] => 11
[11,6] => 60
[11,5,1] => 50
[11,4,2] => 40
[11,4,1,1] => 40
[11,3,3] => 30
[11,3,2,1] => 60
[11,3,1,1,1] => 30
[11,2,2,2] => 20
[11,2,2,1,1] => 20
[11,2,1,1,1,1] => 20
[11,1,1,1,1,1,1] => 10
[10,7] => 63
[10,6,1] => 27
[10,5,2] => 9
[10,5,1,1] => 9
[10,4,3] => 54
[10,4,2,1] => 18
[10,4,1,1,1] => 18
[10,3,3,1] => 27
[10,3,2,2] => 27
[10,3,2,1,1] => 27
[10,3,1,1,1,1] => 27
[10,2,2,2,1] => 9
[10,2,2,1,1,1] => 9
[10,2,1,1,1,1,1] => 9
[10,1,1,1,1,1,1,1] => 9
[9,8] => 64
[9,7,1] => 56
[9,6,2] => 16
[9,6,1,1] => 16
[9,5,3] => 40
[9,5,2,1] => 80
[9,5,1,1,1] => 40
[9,4,4] => 32
[9,4,3,1] => 32
[9,4,2,2] => 32
[9,4,2,1,1] => 32
[9,4,1,1,1,1] => 32
[9,3,3,2] => 16
[9,3,3,1,1] => 8
[9,3,2,2,1] => 16
[9,3,2,1,1,1] => 16
[9,3,1,1,1,1,1] => 8
[9,2,2,2,2] => 16
[9,2,2,2,1,1] => 16
[9,2,2,1,1,1,1] => 16
[9,2,1,1,1,1,1,1] => 16
[9,1,1,1,1,1,1,1,1] => 8
[8,8,1] => 7
[8,7,2] => 49
[8,7,1,1] => 49
[8,6,3] => 21
[8,6,2,1] => 21
[8,6,1,1,1] => 21
[8,5,4] => 35
[8,5,3,1] => 105
[8,5,2,2] => 35
[8,5,2,1,1] => 35
[8,5,1,1,1,1] => 35
[8,4,4,1] => 7
[8,4,3,2] => 21
[8,4,3,1,1] => 21
[8,4,2,2,1] => 7
[8,4,2,1,1,1] => 7
[8,4,1,1,1,1,1] => 7
[8,3,3,3] => 21
[8,3,3,2,1] => 21
[8,3,3,1,1,1] => 21
[8,3,2,2,2] => 21
[8,3,2,2,1,1] => 21
[8,3,2,1,1,1,1] => 21
[8,3,1,1,1,1,1,1] => 21
[8,2,2,2,2,1] => 7
[8,2,2,2,1,1,1] => 7
[8,2,2,1,1,1,1,1] => 7
[8,2,1,1,1,1,1,1,1] => 7
[8,1,1,1,1,1,1,1,1,1] => 7
[7,7,3] => 18
[7,7,2,1] => 12
[7,7,1,1,1] => 6
[7,6,4] => 72
[7,6,3,1] => 36
[7,6,2,2] => 36
[7,6,2,1,1] => 36
[7,6,1,1,1,1] => 36
[7,5,5] => 30
[7,5,4,1] => 120
[7,5,3,2] => 180
[7,5,3,1,1] => 90
[7,5,2,2,1] => 60
[7,5,2,1,1,1] => 60
[7,5,1,1,1,1,1] => 30
[7,4,4,2] => 24
[7,4,4,1,1] => 24
[7,4,3,3] => 72
[7,4,3,2,1] => 72
[7,4,3,1,1,1] => 72
[7,4,2,2,2] => 24
[7,4,2,2,1,1] => 24
[7,4,2,1,1,1,1] => 24
[7,4,1,1,1,1,1,1] => 24
[7,3,3,3,1] => 18
[7,3,3,2,2] => 36
[7,3,3,2,1,1] => 36
[7,3,3,1,1,1,1] => 18
[7,3,2,2,2,1] => 36
[7,3,2,2,1,1,1] => 36
[7,3,2,1,1,1,1,1] => 36
[7,3,1,1,1,1,1,1,1] => 18
[7,2,2,2,2,2] => 12
[7,2,2,2,2,1,1] => 12
[7,2,2,2,1,1,1,1] => 12
[7,2,2,1,1,1,1,1,1] => 12
[7,2,1,1,1,1,1,1,1,1] => 12
[7,1,1,1,1,1,1,1,1,1,1] => 6
[6,6,5] => 25
[6,6,4,1] => 10
[6,6,3,2] => 5
[6,6,3,1,1] => 5
[6,6,2,2,1] => 5
[6,6,2,1,1,1] => 5
[6,6,1,1,1,1,1] => 5
[6,5,5,1] => 25
[6,5,4,2] => 50
[6,5,4,1,1] => 50
[6,5,3,3] => 25
[6,5,3,2,1] => 25
[6,5,3,1,1,1] => 25
[6,5,2,2,2] => 25
[6,5,2,2,1,1] => 25
[6,5,2,1,1,1,1] => 25
[6,5,1,1,1,1,1,1] => 25
[6,4,4,3] => 10
[6,4,4,2,1] => 10
[6,4,4,1,1,1] => 10
[6,4,3,3,1] => 10
[6,4,3,2,2] => 10
[6,4,3,2,1,1] => 10
[6,4,3,1,1,1,1] => 10
[6,4,2,2,2,1] => 10
[6,4,2,2,1,1,1] => 10
[6,4,2,1,1,1,1,1] => 10
[6,4,1,1,1,1,1,1,1] => 10
[6,3,3,3,2] => 5
[6,3,3,3,1,1] => 5
[6,3,3,2,2,1] => 5
[6,3,3,2,1,1,1] => 5
[6,3,3,1,1,1,1,1] => 5
[6,3,2,2,2,2] => 5
[6,3,2,2,2,1,1] => 5
[6,3,2,2,1,1,1,1] => 5
[6,3,2,1,1,1,1,1,1] => 5
[6,3,1,1,1,1,1,1,1,1] => 5
[6,2,2,2,2,2,1] => 5
[6,2,2,2,2,1,1,1] => 5
[6,2,2,2,1,1,1,1,1] => 5
[6,2,2,1,1,1,1,1,1,1] => 5
[6,2,1,1,1,1,1,1,1,1,1] => 5
[6,1,1,1,1,1,1,1,1,1,1,1] => 5
[5,5,5,2] => 8
[5,5,5,1,1] => 4
[5,5,4,3] => 48
[5,5,4,2,1] => 16
[5,5,4,1,1,1] => 16
[5,5,3,3,1] => 12
[5,5,3,2,2] => 24
[5,5,3,2,1,1] => 24
[5,5,3,1,1,1,1] => 12
[5,5,2,2,2,1] => 8
[5,5,2,2,1,1,1] => 8
[5,5,2,1,1,1,1,1] => 8
[5,5,1,1,1,1,1,1,1] => 4
[5,4,4,4] => 16
[5,4,4,3,1] => 48
[5,4,4,2,2] => 16
[5,4,4,2,1,1] => 16
[5,4,4,1,1,1,1] => 16
[5,4,3,3,2] => 48
[5,4,3,3,1,1] => 48
[5,4,3,2,2,1] => 48
[5,4,3,2,1,1,1] => 48
[5,4,3,1,1,1,1,1] => 48
[5,4,2,2,2,2] => 16
[5,4,2,2,2,1,1] => 16
[5,4,2,2,1,1,1,1] => 16
[5,4,2,1,1,1,1,1,1] => 16
[5,4,1,1,1,1,1,1,1,1] => 16
[5,3,3,3,3] => 12
[5,3,3,3,2,1] => 24
[5,3,3,3,1,1,1] => 12
[5,3,3,2,2,2] => 24
[5,3,3,2,2,1,1] => 24
[5,3,3,2,1,1,1,1] => 24
[5,3,3,1,1,1,1,1,1] => 12
[5,3,2,2,2,2,1] => 24
[5,3,2,2,2,1,1,1] => 24
[5,3,2,2,1,1,1,1,1] => 24
[5,3,2,1,1,1,1,1,1,1] => 24
[5,3,1,1,1,1,1,1,1,1,1] => 12
[5,2,2,2,2,2,2] => 8
[5,2,2,2,2,2,1,1] => 8
[5,2,2,2,2,1,1,1,1] => 8
[5,2,2,2,1,1,1,1,1,1] => 8
[5,2,2,1,1,1,1,1,1,1,1] => 8
[5,2,1,1,1,1,1,1,1,1,1,1] => 8
[5,1,1,1,1,1,1,1,1,1,1,1,1] => 4
[4,4,4,4,1] => 3
[4,4,4,3,2] => 9
[4,4,4,3,1,1] => 9
[4,4,4,2,2,1] => 3
[4,4,4,2,1,1,1] => 3
[4,4,4,1,1,1,1,1] => 3
[4,4,3,3,3] => 9
[4,4,3,3,2,1] => 9
[4,4,3,3,1,1,1] => 9
[4,4,3,2,2,2] => 9
[4,4,3,2,2,1,1] => 9
[4,4,3,2,1,1,1,1] => 9
[4,4,3,1,1,1,1,1,1] => 9
[4,4,2,2,2,2,1] => 3
[4,4,2,2,2,1,1,1] => 3
[4,4,2,2,1,1,1,1,1] => 3
[4,4,2,1,1,1,1,1,1,1] => 3
[4,4,1,1,1,1,1,1,1,1,1] => 3
[4,3,3,3,3,1] => 9
[4,3,3,3,2,2] => 9
[4,3,3,3,2,1,1] => 9
[4,3,3,3,1,1,1,1] => 9
[4,3,3,2,2,2,1] => 9
[4,3,3,2,2,1,1,1] => 9
[4,3,3,2,1,1,1,1,1] => 9
[4,3,3,1,1,1,1,1,1,1] => 9
[4,3,2,2,2,2,2] => 9
[4,3,2,2,2,2,1,1] => 9
[4,3,2,2,2,1,1,1,1] => 9
[4,3,2,2,1,1,1,1,1,1] => 9
[4,3,2,1,1,1,1,1,1,1,1] => 9
[4,3,1,1,1,1,1,1,1,1,1,1] => 9
[4,2,2,2,2,2,2,1] => 3
[4,2,2,2,2,2,1,1,1] => 3
[4,2,2,2,2,1,1,1,1,1] => 3
[4,2,2,2,1,1,1,1,1,1,1] => 3
[4,2,2,1,1,1,1,1,1,1,1,1] => 3
[4,2,1,1,1,1,1,1,1,1,1,1,1] => 3
[4,1,1,1,1,1,1,1,1,1,1,1,1,1] => 3
[3,3,3,3,3,2] => 4
[3,3,3,3,3,1,1] => 2
[3,3,3,3,2,2,1] => 4
[3,3,3,3,2,1,1,1] => 4
[3,3,3,3,1,1,1,1,1] => 2
[3,3,3,2,2,2,2] => 4
[3,3,3,2,2,2,1,1] => 4
[3,3,3,2,2,1,1,1,1] => 4
[3,3,3,2,1,1,1,1,1,1] => 4
[3,3,3,1,1,1,1,1,1,1,1] => 2
[3,3,2,2,2,2,2,1] => 4
[3,3,2,2,2,2,1,1,1] => 4
[3,3,2,2,2,1,1,1,1,1] => 4
[3,3,2,2,1,1,1,1,1,1,1] => 4
[3,3,2,1,1,1,1,1,1,1,1,1] => 4
[3,3,1,1,1,1,1,1,1,1,1,1,1] => 2
[3,2,2,2,2,2,2,2] => 4
[3,2,2,2,2,2,2,1,1] => 4
[3,2,2,2,2,2,1,1,1,1] => 4
[3,2,2,2,2,1,1,1,1,1,1] => 4
[3,2,2,2,1,1,1,1,1,1,1,1] => 4
[3,2,2,1,1,1,1,1,1,1,1,1,1] => 4
-----------------------------------------------------------------------------
Created: Aug 21, 2023 at 14:19 by Martin Rubey
-----------------------------------------------------------------------------
Last Updated: Aug 21, 2023 at 14:19 by Martin Rubey