*****************************************************************************
* 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: St001658
-----------------------------------------------------------------------------
Collection: Skew partitions
-----------------------------------------------------------------------------
Description: The total number of rook placements on a Ferrers board.
-----------------------------------------------------------------------------
References: [1] [[wikipedia:Rook_polynomial]]
-----------------------------------------------------------------------------
Code:
def statistic(nu):
import itertools
rook_matrix = matrix([[0]*q + [1]*(p-q) + [0]*(nu[0][0]-p)
for p, q in itertools.zip_longest(*nu, fillvalue=0)])
return sum(rook_matrix.rook_vector())
-----------------------------------------------------------------------------
Statistic values:
[[1],[]] => 2
[[2],[]] => 3
[[1,1],[]] => 3
[[2,1],[1]] => 4
[[3],[]] => 4
[[2,1],[]] => 5
[[3,1],[1]] => 6
[[2,2],[1]] => 5
[[3,2],[2]] => 6
[[1,1,1],[]] => 4
[[2,2,1],[1,1]] => 6
[[2,1,1],[1]] => 6
[[3,2,1],[2,1]] => 8
[[4],[]] => 5
[[3,1],[]] => 7
[[4,1],[1]] => 8
[[2,2],[]] => 7
[[3,2],[1]] => 8
[[4,2],[2]] => 9
[[2,1,1],[]] => 7
[[3,2,1],[1,1]] => 10
[[3,1,1],[1]] => 9
[[4,2,1],[2,1]] => 12
[[3,3],[2]] => 7
[[4,3],[3]] => 8
[[2,2,1],[1]] => 8
[[3,3,1],[2,1]] => 10
[[3,2,1],[2]] => 10
[[4,3,1],[3,1]] => 12
[[2,2,2],[1,1]] => 7
[[3,3,2],[2,2]] => 9
[[3,2,2],[2,1]] => 10
[[4,3,2],[3,2]] => 12
[[1,1,1,1],[]] => 5
[[2,2,2,1],[1,1,1]] => 8
[[2,2,1,1],[1,1]] => 9
[[3,3,2,1],[2,2,1]] => 12
[[2,1,1,1],[1]] => 8
[[3,2,2,1],[2,1,1]] => 12
[[3,2,1,1],[2,1]] => 12
[[4,3,2,1],[3,2,1]] => 16
[[5],[]] => 6
[[4,1],[]] => 9
[[5,1],[1]] => 10
[[3,2],[]] => 10
[[4,2],[1]] => 11
[[5,2],[2]] => 12
[[3,1,1],[]] => 10
[[4,2,1],[1,1]] => 14
[[4,1,1],[1]] => 12
[[5,2,1],[2,1]] => 16
[[3,3],[1]] => 10
[[4,3],[2]] => 11
[[5,3],[3]] => 12
[[2,2,1],[]] => 10
[[3,3,1],[1,1]] => 14
[[3,2,1],[1]] => 13
[[4,3,1],[2,1]] => 16
[[4,2,1],[2]] => 15
[[5,3,1],[3,1]] => 18
[[3,2,2],[1,1]] => 12
[[4,3,2],[2,2]] => 15
[[4,2,2],[2,1]] => 15
[[5,3,2],[3,2]] => 18
[[2,1,1,1],[]] => 9
[[3,2,2,1],[1,1,1]] => 14
[[3,2,1,1],[1,1]] => 15
[[4,3,2,1],[2,2,1]] => 20
[[3,1,1,1],[1]] => 12
[[4,2,2,1],[2,1,1]] => 18
[[4,2,1,1],[2,1]] => 18
[[5,3,2,1],[3,2,1]] => 24
[[4,4],[3]] => 9
[[5,4],[4]] => 10
[[3,3,1],[2]] => 12
[[4,4,1],[3,1]] => 14
[[4,3,1],[3]] => 14
[[5,4,1],[4,1]] => 16
[[2,2,2],[1]] => 10
[[3,3,2],[2,1]] => 13
[[4,4,2],[3,2]] => 15
[[3,2,2],[2]] => 14
[[4,3,2],[3,1]] => 16
[[5,4,2],[4,2]] => 18
[[2,2,1,1],[1]] => 11
[[3,3,2,1],[2,1,1]] => 16
[[3,3,1,1],[2,1]] => 15
[[4,4,2,1],[3,2,1]] => 20
[[3,2,1,1],[2]] => 14
[[4,3,2,1],[3,1,1]] => 20
[[4,3,1,1],[3,1]] => 18
[[5,4,2,1],[4,2,1]] => 24
[[3,3,3],[2,2]] => 10
[[4,4,3],[3,3]] => 12
[[4,3,3],[3,2]] => 14
[[5,4,3],[4,3]] => 16
[[2,2,2,1],[1,1]] => 11
[[3,3,3,1],[2,2,1]] => 14
[[3,3,2,1],[2,2]] => 15
[[4,4,3,1],[3,3,1]] => 18
[[3,2,2,1],[2,1]] => 16
[[4,3,3,1],[3,2,1]] => 20
[[4,3,2,1],[3,2]] => 20
[[5,4,3,1],[4,3,1]] => 24
[[2,2,2,2],[1,1,1]] => 9
[[3,3,3,2],[2,2,2]] => 12
[[3,3,2,2],[2,2,1]] => 15
[[4,4,3,2],[3,3,2]] => 18
[[3,2,2,2],[2,1,1]] => 14
[[4,3,3,2],[3,2,2]] => 18
[[4,3,2,2],[3,2,1]] => 20
[[5,4,3,2],[4,3,2]] => 24
[[1,1,1,1,1],[]] => 6
[[2,2,2,2,1],[1,1,1,1]] => 10
[[2,2,2,1,1],[1,1,1]] => 12
[[3,3,3,2,1],[2,2,2,1]] => 16
[[2,2,1,1,1],[1,1]] => 12
[[3,3,2,2,1],[2,2,1,1]] => 18
[[3,3,2,1,1],[2,2,1]] => 18
[[4,4,3,2,1],[3,3,2,1]] => 24
[[2,1,1,1,1],[1]] => 10
[[3,2,2,2,1],[2,1,1,1]] => 16
[[3,2,2,1,1],[2,1,1]] => 18
[[4,3,3,2,1],[3,2,2,1]] => 24
[[3,2,1,1,1],[2,1]] => 16
[[4,3,2,2,1],[3,2,1,1]] => 24
[[4,3,2,1,1],[3,2,1]] => 24
[[5,4,3,2,1],[4,3,2,1]] => 32
[[6],[]] => 7
[[5,1],[]] => 11
[[6,1],[1]] => 12
[[4,2],[]] => 13
[[5,2],[1]] => 14
[[6,2],[2]] => 15
[[4,1,1],[]] => 13
[[5,2,1],[1,1]] => 18
[[5,1,1],[1]] => 15
[[6,2,1],[2,1]] => 20
[[3,3],[]] => 13
[[4,3],[1]] => 14
[[5,3],[2]] => 15
[[6,3],[3]] => 16
[[3,2,1],[]] => 15
[[4,3,1],[1,1]] => 20
[[4,2,1],[1]] => 18
[[5,3,1],[2,1]] => 22
[[5,2,1],[2]] => 20
[[6,3,1],[3,1]] => 24
[[4,2,2],[1,1]] => 17
[[5,3,2],[2,2]] => 21
[[5,2,2],[2,1]] => 20
[[6,3,2],[3,2]] => 24
[[3,1,1,1],[]] => 13
[[4,2,2,1],[1,1,1]] => 20
[[4,2,1,1],[1,1]] => 21
[[5,3,2,1],[2,2,1]] => 28
[[4,1,1,1],[1]] => 16
[[5,2,2,1],[2,1,1]] => 24
[[5,2,1,1],[2,1]] => 24
[[6,3,2,1],[3,2,1]] => 32
[[4,4],[2]] => 13
[[5,4],[3]] => 14
[[6,4],[4]] => 15
[[3,3,1],[1]] => 17
[[4,4,1],[2,1]] => 20
[[4,3,1],[2]] => 19
[[5,4,1],[3,1]] => 22
[[5,3,1],[3]] => 21
[[6,4,1],[4,1]] => 24
[[2,2,2],[]] => 13
[[3,3,2],[1,1]] => 17
[[4,4,2],[2,2]] => 21
[[3,2,2],[1]] => 17
[[4,3,2],[2,1]] => 21
[[5,4,2],[3,2]] => 24
[[4,2,2],[2]] => 21
[[5,3,2],[3,1]] => 24
[[6,4,2],[4,2]] => 27
[[2,2,1,1],[]] => 13
[[3,3,2,1],[1,1,1]] => 20
[[3,3,1,1],[1,1]] => 21
[[4,4,2,1],[2,2,1]] => 28
[[3,2,1,1],[1]] => 18
[[4,3,2,1],[2,1,1]] => 26
[[4,3,1,1],[2,1]] => 24
[[5,4,2,1],[3,2,1]] => 32
[[4,2,1,1],[2]] => 21
[[5,3,2,1],[3,1,1]] => 30
[[5,3,1,1],[3,1]] => 27
[[6,4,2,1],[4,2,1]] => 36
[[4,3,3],[2,2]] => 17
[[5,4,3],[3,3]] => 20
[[5,3,3],[3,2]] => 21
[[6,4,3],[4,3]] => 24
[[3,2,2,1],[1,1]] => 19
[[4,3,3,1],[2,2,1]] => 24
[[4,3,2,1],[2,2]] => 25
[[5,4,3,1],[3,3,1]] => 30
[[4,2,2,1],[2,1]] => 24
[[5,3,3,1],[3,2,1]] => 30
[[5,3,2,1],[3,2]] => 30
[[6,4,3,1],[4,3,1]] => 36
[[3,2,2,2],[1,1,1]] => 16
[[4,3,3,2],[2,2,2]] => 21
[[4,3,2,2],[2,2,1]] => 25
[[5,4,3,2],[3,3,2]] => 30
[[4,2,2,2],[2,1,1]] => 21
[[5,3,3,2],[3,2,2]] => 27
[[5,3,2,2],[3,2,1]] => 30
[[6,4,3,2],[4,3,2]] => 36
[[2,1,1,1,1],[]] => 11
[[3,2,2,2,1],[1,1,1,1]] => 18
[[3,2,2,1,1],[1,1,1]] => 21
[[4,3,3,2,1],[2,2,2,1]] => 28
[[3,2,1,1,1],[1,1]] => 20
[[4,3,2,2,1],[2,2,1,1]] => 30
[[4,3,2,1,1],[2,2,1]] => 30
[[5,4,3,2,1],[3,3,2,1]] => 40
[[3,1,1,1,1],[1]] => 15
[[4,2,2,2,1],[2,1,1,1]] => 24
[[4,2,2,1,1],[2,1,1]] => 27
[[5,3,3,2,1],[3,2,2,1]] => 36
[[4,2,1,1,1],[2,1]] => 24
[[5,3,2,2,1],[3,2,1,1]] => 36
[[5,3,2,1,1],[3,2,1]] => 36
[[6,4,3,2,1],[4,3,2,1]] => 48
[[5,5],[4]] => 11
[[6,5],[5]] => 12
[[4,4,1],[3]] => 16
[[5,5,1],[4,1]] => 18
[[5,4,1],[4]] => 18
[[6,5,1],[5,1]] => 20
[[3,3,2],[2]] => 17
[[4,4,2],[3,1]] => 19
[[5,5,2],[4,2]] => 21
[[4,3,2],[3]] => 20
[[5,4,2],[4,1]] => 22
[[6,5,2],[5,2]] => 24
[[3,3,1,1],[2]] => 17
[[4,4,2,1],[3,1,1]] => 24
[[4,4,1,1],[3,1]] => 21
[[5,5,2,1],[4,2,1]] => 28
[[4,3,1,1],[3]] => 20
[[5,4,2,1],[4,1,1]] => 28
[[5,4,1,1],[4,1]] => 24
[[6,5,2,1],[5,2,1]] => 32
[[3,3,3],[2,1]] => 15
[[4,4,3],[3,2]] => 18
[[5,5,3],[4,3]] => 20
[[4,3,3],[3,1]] => 20
[[5,4,3],[4,2]] => 22
[[6,5,3],[5,3]] => 24
[[2,2,2,1],[1]] => 14
[[3,3,3,1],[2,1,1]] => 20
[[3,3,2,1],[2,1]] => 21
[[4,4,3,1],[3,2,1]] => 26
[[4,4,2,1],[3,2]] => 25
[[5,5,3,1],[4,3,1]] => 30
[[3,2,2,1],[2]] => 20
[[4,3,3,1],[3,1,1]] => 28
[[4,3,2,1],[3,1]] => 26
[[5,4,3,1],[4,2,1]] => 32
[[5,4,2,1],[4,2]] => 30
[[6,5,3,1],[5,3,1]] => 36
[[3,3,2,2],[2,1,1]] => 19
[[4,4,3,2],[3,2,2]] => 24
[[4,4,2,2],[3,2,1]] => 25
[[5,5,3,2],[4,3,2]] => 30
[[4,3,2,2],[3,1,1]] => 24
[[5,4,3,2],[4,2,2]] => 30
[[5,4,2,2],[4,2,1]] => 30
[[6,5,3,2],[5,3,2]] => 36
[[2,2,1,1,1],[1]] => 14
[[3,3,2,2,1],[2,1,1,1]] => 22
[[3,3,2,1,1],[2,1,1]] => 24
[[4,4,3,2,1],[3,2,2,1]] => 32
[[3,3,1,1,1],[2,1]] => 20
[[4,4,2,2,1],[3,2,1,1]] => 30
[[4,4,2,1,1],[3,2,1]] => 30
[[5,5,3,2,1],[4,3,2,1]] => 40
[[3,2,1,1,1],[2]] => 18
[[4,3,2,2,1],[3,1,1,1]] => 28
[[4,3,2,1,1],[3,1,1]] => 30
[[5,4,3,2,1],[4,2,2,1]] => 40
[[4,3,1,1,1],[3,1]] => 24
[[5,4,2,2,1],[4,2,1,1]] => 36
[[5,4,2,1,1],[4,2,1]] => 36
[[6,5,3,2,1],[5,3,2,1]] => 48
[[4,4,4],[3,3]] => 13
[[5,5,4],[4,4]] => 15
[[5,4,4],[4,3]] => 18
[[6,5,4],[5,4]] => 20
[[3,3,3,1],[2,2]] => 17
[[4,4,4,1],[3,3,1]] => 20
[[4,4,3,1],[3,3]] => 21
[[5,5,4,1],[4,4,1]] => 24
[[4,3,3,1],[3,2]] => 24
[[5,4,4,1],[4,3,1]] => 28
[[5,4,3,1],[4,3]] => 28
[[6,5,4,1],[5,4,1]] => 32
[[2,2,2,2],[1,1]] => 13
[[3,3,3,2],[2,2,1]] => 18
[[4,4,4,2],[3,3,2]] => 21
[[3,3,2,2],[2,2]] => 21
[[4,4,3,2],[3,3,1]] => 24
[[5,5,4,2],[4,4,2]] => 27
[[3,2,2,2],[2,1]] => 20
[[4,3,3,2],[3,2,1]] => 26
[[5,4,4,2],[4,3,2]] => 30
[[4,3,2,2],[3,2]] => 28
[[5,4,3,2],[4,3,1]] => 32
[[6,5,4,2],[5,4,2]] => 36
[[2,2,2,1,1],[1,1]] => 15
[[3,3,3,2,1],[2,2,1,1]] => 22
[[3,3,3,1,1],[2,2,1]] => 21
[[4,4,4,2,1],[3,3,2,1]] => 28
[[3,3,2,1,1],[2,2]] => 21
[[4,4,3,2,1],[3,3,1,1]] => 30
[[4,4,3,1,1],[3,3,1]] => 27
[[5,5,4,2,1],[4,4,2,1]] => 36
[[3,2,2,1,1],[2,1]] => 22
[[4,3,3,2,1],[3,2,1,1]] => 32
[[4,3,3,1,1],[3,2,1]] => 30
[[5,4,4,2,1],[4,3,2,1]] => 40
[[4,3,2,1,1],[3,2]] => 28
[[5,4,3,2,1],[4,3,1,1]] => 40
[[5,4,3,1,1],[4,3,1]] => 36
[[6,5,4,2,1],[5,4,2,1]] => 48
[[3,3,3,3],[2,2,2]] => 13
[[4,4,4,3],[3,3,3]] => 16
[[4,4,3,3],[3,3,2]] => 21
[[5,5,4,3],[4,4,3]] => 24
[[4,3,3,3],[3,2,2]] => 20
[[5,4,4,3],[4,3,3]] => 24
[[5,4,3,3],[4,3,2]] => 28
[[6,5,4,3],[5,4,3]] => 32
[[2,2,2,2,1],[1,1,1]] => 14
[[3,3,3,3,1],[2,2,2,1]] => 18
[[3,3,3,2,1],[2,2,2]] => 20
[[4,4,4,3,1],[3,3,3,1]] => 24
[[3,3,2,2,1],[2,2,1]] => 24
[[4,4,3,3,1],[3,3,2,1]] => 30
[[4,4,3,2,1],[3,3,2]] => 30
[[5,5,4,3,1],[4,4,3,1]] => 36
[[3,2,2,2,1],[2,1,1]] => 22
[[4,3,3,3,1],[3,2,2,1]] => 28
[[4,3,3,2,1],[3,2,2]] => 30
[[5,4,4,3,1],[4,3,3,1]] => 36
[[4,3,2,2,1],[3,2,1]] => 32
[[5,4,3,3,1],[4,3,2,1]] => 40
[[5,4,3,2,1],[4,3,2]] => 40
[[6,5,4,3,1],[5,4,3,1]] => 48
[[2,2,2,2,2],[1,1,1,1]] => 11
[[3,3,3,3,2],[2,2,2,2]] => 15
[[3,3,3,2,2],[2,2,2,1]] => 20
[[4,4,4,3,2],[3,3,3,2]] => 24
[[3,3,2,2,2],[2,2,1,1]] => 21
[[4,4,3,3,2],[3,3,2,2]] => 27
[[4,4,3,2,2],[3,3,2,1]] => 30
[[5,5,4,3,2],[4,4,3,2]] => 36
[[3,2,2,2,2],[2,1,1,1]] => 18
[[4,3,3,3,2],[3,2,2,2]] => 24
[[4,3,3,2,2],[3,2,2,1]] => 30
[[5,4,4,3,2],[4,3,3,2]] => 36
[[4,3,2,2,2],[3,2,1,1]] => 28
[[5,4,3,3,2],[4,3,2,2]] => 36
[[5,4,3,2,2],[4,3,2,1]] => 40
[[6,5,4,3,2],[5,4,3,2]] => 48
[[1,1,1,1,1,1],[]] => 7
[[2,2,2,2,2,1],[1,1,1,1,1]] => 12
[[2,2,2,2,1,1],[1,1,1,1]] => 15
[[3,3,3,3,2,1],[2,2,2,2,1]] => 20
[[2,2,2,1,1,1],[1,1,1]] => 16
[[3,3,3,2,2,1],[2,2,2,1,1]] => 24
[[3,3,3,2,1,1],[2,2,2,1]] => 24
[[4,4,4,3,2,1],[3,3,3,2,1]] => 32
[[2,2,1,1,1,1],[1,1]] => 15
[[3,3,2,2,2,1],[2,2,1,1,1]] => 24
[[3,3,2,2,1,1],[2,2,1,1]] => 27
[[4,4,3,3,2,1],[3,3,2,2,1]] => 36
[[3,3,2,1,1,1],[2,2,1]] => 24
[[4,4,3,2,2,1],[3,3,2,1,1]] => 36
[[4,4,3,2,1,1],[3,3,2,1]] => 36
[[5,5,4,3,2,1],[4,4,3,2,1]] => 48
[[2,1,1,1,1,1],[1]] => 12
[[3,2,2,2,2,1],[2,1,1,1,1]] => 20
[[3,2,2,2,1,1],[2,1,1,1]] => 24
[[4,3,3,3,2,1],[3,2,2,2,1]] => 32
[[3,2,2,1,1,1],[2,1,1]] => 24
[[4,3,3,2,2,1],[3,2,2,1,1]] => 36
[[4,3,3,2,1,1],[3,2,2,1]] => 36
[[5,4,4,3,2,1],[4,3,3,2,1]] => 48
[[3,2,1,1,1,1],[2,1]] => 20
[[4,3,2,2,2,1],[3,2,1,1,1]] => 32
[[4,3,2,2,1,1],[3,2,1,1]] => 36
[[5,4,3,3,2,1],[4,3,2,2,1]] => 48
[[4,3,2,1,1,1],[3,2,1]] => 32
[[5,4,3,2,2,1],[4,3,2,1,1]] => 48
[[5,4,3,2,1,1],[4,3,2,1]] => 48
[[6,5,4,3,2,1],[5,4,3,2,1]] => 64
[[7],[]] => 8
[[6,1],[]] => 13
[[7,1],[1]] => 14
[[5,2],[]] => 16
[[6,2],[1]] => 17
[[7,2],[2]] => 18
[[5,1,1],[]] => 16
[[6,2,1],[1,1]] => 22
[[6,1,1],[1]] => 18
[[7,2,1],[2,1]] => 24
[[4,3],[]] => 17
[[5,3],[1]] => 18
[[6,3],[2]] => 19
[[7,3],[3]] => 20
[[4,2,1],[]] => 20
[[5,3,1],[1,1]] => 26
[[5,2,1],[1]] => 23
[[6,3,1],[2,1]] => 28
[[6,2,1],[2]] => 25
[[7,3,1],[3,1]] => 30
[[5,2,2],[1,1]] => 22
[[6,3,2],[2,2]] => 27
[[6,2,2],[2,1]] => 25
[[7,3,2],[3,2]] => 30
[[4,1,1,1],[]] => 17
[[5,2,2,1],[1,1,1]] => 26
[[5,2,1,1],[1,1]] => 27
[[6,3,2,1],[2,2,1]] => 36
[[5,1,1,1],[1]] => 20
[[6,2,2,1],[2,1,1]] => 30
[[6,2,1,1],[2,1]] => 30
[[7,3,2,1],[3,2,1]] => 40
[[4,4],[1]] => 17
[[5,4],[2]] => 18
[[6,4],[3]] => 19
[[7,4],[4]] => 20
[[3,3,1],[]] => 20
[[4,4,1],[1,1]] => 26
[[4,3,1],[1]] => 24
[[5,4,1],[2,1]] => 28
[[5,3,1],[2]] => 26
[[6,4,1],[3,1]] => 30
[[6,3,1],[3]] => 28
[[7,4,1],[4,1]] => 32
[[3,2,2],[]] => 20
[[4,3,2],[1,1]] => 25
[[5,4,2],[2,2]] => 30
[[4,2,2],[1]] => 24
[[5,3,2],[2,1]] => 29
[[6,4,2],[3,2]] => 33
[[5,2,2],[2]] => 28
[[6,3,2],[3,1]] => 32
[[7,4,2],[4,2]] => 36
[[3,2,1,1],[]] => 20
[[4,3,2,1],[1,1,1]] => 30
[[4,3,1,1],[1,1]] => 30
[[5,4,2,1],[2,2,1]] => 40
[[4,2,1,1],[1]] => 25
[[5,3,2,1],[2,1,1]] => 36
[[5,3,1,1],[2,1]] => 33
[[6,4,2,1],[3,2,1]] => 44
[[5,2,1,1],[2]] => 28
[[6,3,2,1],[3,1,1]] => 40
[[6,3,1,1],[3,1]] => 36
[[7,4,2,1],[4,2,1]] => 48
[[5,3,3],[2,2]] => 24
[[6,4,3],[3,3]] => 28
[[6,3,3],[3,2]] => 28
[[7,4,3],[4,3]] => 32
[[4,2,2,1],[1,1]] => 27
[[5,3,3,1],[2,2,1]] => 34
[[5,3,2,1],[2,2]] => 35
[[6,4,3,1],[3,3,1]] => 42
[[5,2,2,1],[2,1]] => 32
[[6,3,3,1],[3,2,1]] => 40
[[6,3,2,1],[3,2]] => 40
[[7,4,3,1],[4,3,1]] => 48
[[4,2,2,2],[1,1,1]] => 23
[[5,3,3,2],[2,2,2]] => 30
[[5,3,2,2],[2,2,1]] => 35
[[6,4,3,2],[3,3,2]] => 42
[[5,2,2,2],[2,1,1]] => 28
[[6,3,3,2],[3,2,2]] => 36
[[6,3,2,2],[3,2,1]] => 40
[[7,4,3,2],[4,3,2]] => 48
[[3,1,1,1,1],[]] => 16
[[4,2,2,2,1],[1,1,1,1]] => 26
[[4,2,2,1,1],[1,1,1]] => 30
[[5,3,3,2,1],[2,2,2,1]] => 40
[[4,2,1,1,1],[1,1]] => 28
[[5,3,2,2,1],[2,2,1,1]] => 42
[[5,3,2,1,1],[2,2,1]] => 42
[[6,4,3,2,1],[3,3,2,1]] => 56
[[4,1,1,1,1],[1]] => 20
[[5,2,2,2,1],[2,1,1,1]] => 32
[[5,2,2,1,1],[2,1,1]] => 36
[[6,3,3,2,1],[3,2,2,1]] => 48
[[5,2,1,1,1],[2,1]] => 32
[[6,3,2,2,1],[3,2,1,1]] => 48
[[6,3,2,1,1],[3,2,1]] => 48
[[7,4,3,2,1],[4,3,2,1]] => 64
[[5,5],[3]] => 16
[[6,5],[4]] => 17
[[7,5],[5]] => 18
[[4,4,1],[2]] => 23
[[5,5,1],[3,1]] => 26
[[5,4,1],[3]] => 25
[[6,5,1],[4,1]] => 28
[[6,4,1],[4]] => 27
[[7,5,1],[5,1]] => 30
[[3,3,2],[1]] => 22
[[4,4,2],[2,1]] => 27
[[5,5,2],[3,2]] => 30
[[4,3,2],[2]] => 27
[[5,4,2],[3,1]] => 30
[[6,5,2],[4,2]] => 33
[[5,3,2],[3]] => 30
[[6,4,2],[4,1]] => 33
[[7,5,2],[5,2]] => 36
[[3,3,1,1],[1]] => 24
[[4,4,2,1],[2,1,1]] => 34
[[4,4,1,1],[2,1]] => 30
[[5,5,2,1],[3,2,1]] => 40
[[4,3,1,1],[2]] => 27
[[5,4,2,1],[3,1,1]] => 38
[[5,4,1,1],[3,1]] => 33
[[6,5,2,1],[4,2,1]] => 44
[[5,3,1,1],[3]] => 30
[[6,4,2,1],[4,1,1]] => 42
[[6,4,1,1],[4,1]] => 36
[[7,5,2,1],[5,2,1]] => 48
[[3,3,3],[1,1]] => 20
[[4,4,3],[2,2]] => 24
[[5,5,3],[3,3]] => 28
[[4,3,3],[2,1]] => 25
[[5,4,3],[3,2]] => 29
[[6,5,3],[4,3]] => 32
[[5,3,3],[3,1]] => 30
[[6,4,3],[4,2]] => 33
[[7,5,3],[5,3]] => 36
[[2,2,2,1],[]] => 17
[[3,3,3,1],[1,1,1]] => 26
[[3,3,2,1],[1,1]] => 27
[[4,4,3,1],[2,2,1]] => 34
[[4,4,2,1],[2,2]] => 35
[[5,5,3,1],[3,3,1]] => 42
[[3,2,2,1],[1]] => 24
[[4,3,3,1],[2,1,1]] => 34
[[4,3,2,1],[2,1]] => 34
[[5,4,3,1],[3,2,1]] => 42
[[5,4,2,1],[3,2]] => 40
[[6,5,3,1],[4,3,1]] => 48
[[4,2,2,1],[2]] => 30
[[5,3,3,1],[3,1,1]] => 42
[[5,3,2,1],[3,1]] => 39
[[6,4,3,1],[4,2,1]] => 48
[[6,4,2,1],[4,2]] => 45
[[7,5,3,1],[5,3,1]] => 54
[[3,3,2,2],[1,1,1]] => 23
[[4,4,3,2],[2,2,2]] => 30
[[4,4,2,2],[2,2,1]] => 35
[[5,5,3,2],[3,3,2]] => 42
[[4,3,2,2],[2,1,1]] => 31
[[5,4,3,2],[3,2,2]] => 39
[[5,4,2,2],[3,2,1]] => 40
[[6,5,3,2],[4,3,2]] => 48
[[5,3,2,2],[3,1,1]] => 36
[[6,4,3,2],[4,2,2]] => 45
[[6,4,2,2],[4,2,1]] => 45
[[7,5,3,2],[5,3,2]] => 54
[[2,2,1,1,1],[]] => 16
[[3,3,2,2,1],[1,1,1,1]] => 26
[[3,3,2,1,1],[1,1,1]] => 30
[[4,4,3,2,1],[2,2,2,1]] => 40
[[3,3,1,1,1],[1,1]] => 28
[[4,4,2,2,1],[2,2,1,1]] => 42
[[4,4,2,1,1],[2,2,1]] => 42
[[5,5,3,2,1],[3,3,2,1]] => 56
[[3,2,1,1,1],[1]] => 23
[[4,3,2,2,1],[2,1,1,1]] => 36
[[4,3,2,1,1],[2,1,1]] => 39
[[5,4,3,2,1],[3,2,2,1]] => 52
[[4,3,1,1,1],[2,1]] => 32
[[5,4,2,2,1],[3,2,1,1]] => 48
[[5,4,2,1,1],[3,2,1]] => 48
[[6,5,3,2,1],[4,3,2,1]] => 64
[[4,2,1,1,1],[2]] => 27
[[5,3,2,2,1],[3,1,1,1]] => 42
[[5,3,2,1,1],[3,1,1]] => 45
[[6,4,3,2,1],[4,2,2,1]] => 60
[[5,3,1,1,1],[3,1]] => 36
[[6,4,2,2,1],[4,2,1,1]] => 54
[[6,4,2,1,1],[4,2,1]] => 54
[[7,5,3,2,1],[5,3,2,1]] => 72
[[5,4,4],[3,3]] => 22
[[6,5,4],[4,4]] => 25
[[6,4,4],[4,3]] => 27
[[7,5,4],[5,4]] => 30
[[4,3,3,1],[2,2]] => 29
[[5,4,4,1],[3,3,1]] => 34
[[5,4,3,1],[3,3]] => 35
[[6,5,4,1],[4,4,1]] => 40
[[5,3,3,1],[3,2]] => 36
[[6,4,4,1],[4,3,1]] => 42
[[6,4,3,1],[4,3]] => 42
[[7,5,4,1],[5,4,1]] => 48
[[3,2,2,2],[1,1]] => 23
[[4,3,3,2],[2,2,1]] => 31
[[5,4,4,2],[3,3,2]] => 36
[[4,3,2,2],[2,2]] => 35
[[5,4,3,2],[3,3,1]] => 40
[[6,5,4,2],[4,4,2]] => 45
[[4,2,2,2],[2,1]] => 30
[[5,3,3,2],[3,2,1]] => 39
[[6,4,4,2],[4,3,2]] => 45
[[5,3,2,2],[3,2]] => 42
[[6,4,3,2],[4,3,1]] => 48
[[7,5,4,2],[5,4,2]] => 54
[[3,2,2,1,1],[1,1]] => 26
[[4,3,3,2,1],[2,2,1,1]] => 38
[[4,3,3,1,1],[2,2,1]] => 36
[[5,4,4,2,1],[3,3,2,1]] => 48
[[4,3,2,1,1],[2,2]] => 35
[[5,4,3,2,1],[3,3,1,1]] => 50
[[5,4,3,1,1],[3,3,1]] => 45
[[6,5,4,2,1],[4,4,2,1]] => 60
[[4,2,2,1,1],[2,1]] => 33
[[5,3,3,2,1],[3,2,1,1]] => 48
[[5,3,3,1,1],[3,2,1]] => 45
[[6,4,4,2,1],[4,3,2,1]] => 60
[[5,3,2,1,1],[3,2]] => 42
[[6,4,3,2,1],[4,3,1,1]] => 60
[[6,4,3,1,1],[4,3,1]] => 54
[[7,5,4,2,1],[5,4,2,1]] => 72
[[4,3,3,3],[2,2,2]] => 23
[[5,4,4,3],[3,3,3]] => 28
[[5,4,3,3],[3,3,2]] => 35
[[6,5,4,3],[4,4,3]] => 40
[[5,3,3,3],[3,2,2]] => 30
[[6,4,4,3],[4,3,3]] => 36
[[6,4,3,3],[4,3,2]] => 42
[[7,5,4,3],[5,4,3]] => 48
[[3,2,2,2,1],[1,1,1]] => 25
[[4,3,3,3,1],[2,2,2,1]] => 32
[[4,3,3,2,1],[2,2,2]] => 35
[[5,4,4,3,1],[3,3,3,1]] => 42
[[4,3,2,2,1],[2,2,1]] => 40
[[5,4,3,3,1],[3,3,2,1]] => 50
[[5,4,3,2,1],[3,3,2]] => 50
[[6,5,4,3,1],[4,4,3,1]] => 60
[[4,2,2,2,1],[2,1,1]] => 33
[[5,3,3,3,1],[3,2,2,1]] => 42
[[5,3,3,2,1],[3,2,2]] => 45
[[6,4,4,3,1],[4,3,3,1]] => 54
[[5,3,2,2,1],[3,2,1]] => 48
[[6,4,3,3,1],[4,3,2,1]] => 60
[[6,4,3,2,1],[4,3,2]] => 60
[[7,5,4,3,1],[5,4,3,1]] => 72
[[3,2,2,2,2],[1,1,1,1]] => 20
[[4,3,3,3,2],[2,2,2,2]] => 27
[[4,3,3,2,2],[2,2,2,1]] => 35
[[5,4,4,3,2],[3,3,3,2]] => 42
[[4,3,2,2,2],[2,2,1,1]] => 35
[[5,4,3,3,2],[3,3,2,2]] => 45
[[5,4,3,2,2],[3,3,2,1]] => 50
[[6,5,4,3,2],[4,4,3,2]] => 60
[[4,2,2,2,2],[2,1,1,1]] => 27
[[5,3,3,3,2],[3,2,2,2]] => 36
[[5,3,3,2,2],[3,2,2,1]] => 45
[[6,4,4,3,2],[4,3,3,2]] => 54
[[5,3,2,2,2],[3,2,1,1]] => 42
[[6,4,3,3,2],[4,3,2,2]] => 54
[[6,4,3,2,2],[4,3,2,1]] => 60
[[7,5,4,3,2],[5,4,3,2]] => 72
[[2,1,1,1,1,1],[]] => 13
[[3,2,2,2,2,1],[1,1,1,1,1]] => 22
[[3,2,2,2,1,1],[1,1,1,1]] => 27
[[4,3,3,3,2,1],[2,2,2,2,1]] => 36
[[3,2,2,1,1,1],[1,1,1]] => 28
[[4,3,3,2,2,1],[2,2,2,1,1]] => 42
[[4,3,3,2,1,1],[2,2,2,1]] => 42
[[5,4,4,3,2,1],[3,3,3,2,1]] => 56
[[3,2,1,1,1,1],[1,1]] => 25
[[4,3,2,2,2,1],[2,2,1,1,1]] => 40
[[4,3,2,2,1,1],[2,2,1,1]] => 45
[[5,4,3,3,2,1],[3,3,2,2,1]] => 60
[[4,3,2,1,1,1],[2,2,1]] => 40
[[5,4,3,2,2,1],[3,3,2,1,1]] => 60
[[5,4,3,2,1,1],[3,3,2,1]] => 60
[[6,5,4,3,2,1],[4,4,3,2,1]] => 80
[[3,1,1,1,1,1],[1]] => 18
[[4,2,2,2,2,1],[2,1,1,1,1]] => 30
[[4,2,2,2,1,1],[2,1,1,1]] => 36
[[5,3,3,3,2,1],[3,2,2,2,1]] => 48
[[4,2,2,1,1,1],[2,1,1]] => 36
[[5,3,3,2,2,1],[3,2,2,1,1]] => 54
[[5,3,3,2,1,1],[3,2,2,1]] => 54
[[6,4,4,3,2,1],[4,3,3,2,1]] => 72
[[4,2,1,1,1,1],[2,1]] => 30
[[5,3,2,2,2,1],[3,2,1,1,1]] => 48
[[5,3,2,2,1,1],[3,2,1,1]] => 54
[[6,4,3,3,2,1],[4,3,2,2,1]] => 72
[[5,3,2,1,1,1],[3,2,1]] => 48
[[6,4,3,2,2,1],[4,3,2,1,1]] => 72
[[6,4,3,2,1,1],[4,3,2,1]] => 72
[[7,5,4,3,2,1],[5,4,3,2,1]] => 96
[[6,6],[5]] => 13
[[7,6],[6]] => 14
[[5,5,1],[4]] => 20
[[6,6,1],[5,1]] => 22
[[6,5,1],[5]] => 22
[[7,6,1],[6,1]] => 24
[[4,4,2],[3]] => 23
[[5,5,2],[4,1]] => 25
[[6,6,2],[5,2]] => 27
[[5,4,2],[4]] => 26
[[6,5,2],[5,1]] => 28
[[7,6,2],[6,2]] => 30
[[4,4,1,1],[3]] => 23
[[5,5,2,1],[4,1,1]] => 32
[[5,5,1,1],[4,1]] => 27
[[6,6,2,1],[5,2,1]] => 36
[[5,4,1,1],[4]] => 26
[[6,5,2,1],[5,1,1]] => 36
[[6,5,1,1],[5,1]] => 30
[[7,6,2,1],[6,2,1]] => 40
[[3,3,3],[2]] => 20
[[4,4,3],[3,1]] => 24
[[5,5,3],[4,2]] => 26
[[6,6,3],[5,3]] => 28
[[4,3,3],[3]] => 26
[[5,4,3],[4,1]] => 28
[[6,5,3],[5,2]] => 30
[[7,6,3],[6,3]] => 32
[[3,3,2,1],[2]] => 25
[[4,4,3,1],[3,1,1]] => 34
[[4,4,2,1],[3,1]] => 31
[[5,5,3,1],[4,2,1]] => 38
[[5,5,2,1],[4,2]] => 35
[[6,6,3,1],[5,3,1]] => 42
[[4,3,2,1],[3]] => 30
[[5,4,3,1],[4,1,1]] => 40
[[5,4,2,1],[4,1]] => 36
[[6,5,3,1],[5,2,1]] => 44
[[6,5,2,1],[5,2]] => 40
[[7,6,3,1],[6,3,1]] => 48
[[4,4,2,2],[3,1,1]] => 29
[[5,5,3,2],[4,2,2]] => 36
[[5,5,2,2],[4,2,1]] => 35
[[6,6,3,2],[5,3,2]] => 42
[[5,4,2,2],[4,1,1]] => 34
[[6,5,3,2],[5,2,2]] => 42
[[6,5,2,2],[5,2,1]] => 40
[[7,6,3,2],[6,3,2]] => 48
[[3,3,1,1,1],[2]] => 22
[[4,4,2,2,1],[3,1,1,1]] => 34
[[4,4,2,1,1],[3,1,1]] => 36
[[5,5,3,2,1],[4,2,2,1]] => 48
[[4,4,1,1,1],[3,1]] => 28
[[5,5,2,2,1],[4,2,1,1]] => 42
[[5,5,2,1,1],[4,2,1]] => 42
[[6,6,3,2,1],[5,3,2,1]] => 56
[[4,3,1,1,1],[3]] => 26
[[5,4,2,2,1],[4,1,1,1]] => 40
[[5,4,2,1,1],[4,1,1]] => 42
[[6,5,3,2,1],[5,2,2,1]] => 56
[[5,4,1,1,1],[4,1]] => 32
[[6,5,2,2,1],[5,2,1,1]] => 48
[[6,5,2,1,1],[5,2,1]] => 48
[[7,6,3,2,1],[6,3,2,1]] => 64
[[4,4,4],[3,2]] => 20
[[5,5,4],[4,3]] => 23
[[6,6,4],[5,4]] => 25
[[5,4,4],[4,2]] => 26
[[6,5,4],[5,3]] => 28
[[7,6,4],[6,4]] => 30
[[3,3,3,1],[2,1]] => 25
[[4,4,4,1],[3,2,1]] => 30
[[4,4,3,1],[3,2]] => 31
[[5,5,4,1],[4,3,1]] => 36
[[5,5,3,1],[4,3]] => 35
[[6,6,4,1],[5,4,1]] => 40
[[4,3,3,1],[3,1]] => 34
[[5,4,4,1],[4,2,1]] => 40
[[5,4,3,1],[4,2]] => 38
[[6,5,4,1],[5,3,1]] => 44
[[6,5,3,1],[5,3]] => 42
[[7,6,4,1],[6,4,1]] => 48
[[2,2,2,2],[1]] => 17
[[3,3,3,2],[2,1,1]] => 24
[[4,4,4,2],[3,2,2]] => 30
[[3,3,2,2],[2,1]] => 27
[[4,4,3,2],[3,2,1]] => 34
[[5,5,4,2],[4,3,2]] => 39
[[4,4,2,2],[3,2]] => 35
[[5,5,3,2],[4,3,1]] => 40
[[6,6,4,2],[5,4,2]] => 45
[[3,2,2,2],[2]] => 26
[[4,3,3,2],[3,1,1]] => 34
[[5,4,4,2],[4,2,2]] => 42
[[4,3,2,2],[3,1]] => 34
[[5,4,3,2],[4,2,1]] => 42
[[6,5,4,2],[5,3,2]] => 48
[[5,4,2,2],[4,2]] => 42
[[6,5,3,2],[5,3,1]] => 48
[[7,6,4,2],[6,4,2]] => 54
[[2,2,2,1,1],[1]] => 18
[[3,3,3,2,1],[2,1,1,1]] => 28
[[3,3,3,1,1],[2,1,1]] => 30
[[4,4,4,2,1],[3,2,2,1]] => 40
[[3,3,2,1,1],[2,1]] => 29
[[4,4,3,2,1],[3,2,1,1]] => 42
[[4,4,3,1,1],[3,2,1]] => 39
[[5,5,4,2,1],[4,3,2,1]] => 52
[[4,4,2,1,1],[3,2]] => 35
[[5,5,3,2,1],[4,3,1,1]] => 50
[[5,5,3,1,1],[4,3,1]] => 45
[[6,6,4,2,1],[5,4,2,1]] => 60
[[3,2,2,1,1],[2]] => 26
[[4,3,3,2,1],[3,1,1,1]] => 40
[[4,3,3,1,1],[3,1,1]] => 42
[[5,4,4,2,1],[4,2,2,1]] => 56
[[4,3,2,1,1],[3,1]] => 36
[[5,4,3,2,1],[4,2,1,1]] => 52
[[5,4,3,1,1],[4,2,1]] => 48
[[6,5,4,2,1],[5,3,2,1]] => 64
[[5,4,2,1,1],[4,2]] => 42
[[6,5,3,2,1],[5,3,1,1]] => 60
[[6,5,3,1,1],[5,3,1]] => 54
[[7,6,4,2,1],[6,4,2,1]] => 72
[[4,4,3,3],[3,2,2]] => 27
[[5,5,4,3],[4,3,3]] => 32
[[5,5,3,3],[4,3,2]] => 35
[[6,6,4,3],[5,4,3]] => 40
[[5,4,3,3],[4,2,2]] => 34
[[6,5,4,3],[5,3,3]] => 40
[[6,5,3,3],[5,3,2]] => 42
[[7,6,4,3],[6,4,3]] => 48
[[3,3,2,2,1],[2,1,1]] => 30
[[4,4,3,3,1],[3,2,2,1]] => 38
[[4,4,3,2,1],[3,2,2]] => 40
[[5,5,4,3,1],[4,3,3,1]] => 48
[[4,4,2,2,1],[3,2,1]] => 40
[[5,5,3,3,1],[4,3,2,1]] => 50
[[5,5,3,2,1],[4,3,2]] => 50
[[6,6,4,3,1],[5,4,3,1]] => 60
[[4,3,2,2,1],[3,1,1]] => 38
[[5,4,3,3,1],[4,2,2,1]] => 48
[[5,4,3,2,1],[4,2,2]] => 50
[[6,5,4,3,1],[5,3,3,1]] => 60
[[5,4,2,2,1],[4,2,1]] => 48
[[6,5,3,3,1],[5,3,2,1]] => 60
[[6,5,3,2,1],[5,3,2]] => 60
[[7,6,4,3,1],[6,4,3,1]] => 72
[[3,3,2,2,2],[2,1,1,1]] => 25
[[4,4,3,3,2],[3,2,2,2]] => 33
[[4,4,3,2,2],[3,2,2,1]] => 40
[[5,5,4,3,2],[4,3,3,2]] => 48
[[4,4,2,2,2],[3,2,1,1]] => 35
[[5,5,3,3,2],[4,3,2,2]] => 45
[[5,5,3,2,2],[4,3,2,1]] => 50
[[6,6,4,3,2],[5,4,3,2]] => 60
[[4,3,2,2,2],[3,1,1,1]] => 32
[[5,4,3,3,2],[4,2,2,2]] => 42
[[5,4,3,2,2],[4,2,2,1]] => 50
[[6,5,4,3,2],[5,3,3,2]] => 60
[[5,4,2,2,2],[4,2,1,1]] => 42
[[6,5,3,3,2],[5,3,2,2]] => 54
[[6,5,3,2,2],[5,3,2,1]] => 60
[[7,6,4,3,2],[6,4,3,2]] => 72
[[2,2,1,1,1,1],[1]] => 17
[[3,3,2,2,2,1],[2,1,1,1,1]] => 28
[[3,3,2,2,1,1],[2,1,1,1]] => 33
[[4,4,3,3,2,1],[3,2,2,2,1]] => 44
[[3,3,2,1,1,1],[2,1,1]] => 32
[[4,4,3,2,2,1],[3,2,2,1,1]] => 48
[[4,4,3,2,1,1],[3,2,2,1]] => 48
[[5,5,4,3,2,1],[4,3,3,2,1]] => 64
[[3,3,1,1,1,1],[2,1]] => 25
[[4,4,2,2,2,1],[3,2,1,1,1]] => 40
[[4,4,2,2,1,1],[3,2,1,1]] => 45
[[5,5,3,3,2,1],[4,3,2,2,1]] => 60
[[4,4,2,1,1,1],[3,2,1]] => 40
[[5,5,3,2,2,1],[4,3,2,1,1]] => 60
[[5,5,3,2,1,1],[4,3,2,1]] => 60
[[6,6,4,3,2,1],[5,4,3,2,1]] => 80
[[3,2,1,1,1,1],[2]] => 22
[[4,3,2,2,2,1],[3,1,1,1,1]] => 36
[[4,3,2,2,1,1],[3,1,1,1]] => 42
[[5,4,3,3,2,1],[4,2,2,2,1]] => 56
[[4,3,2,1,1,1],[3,1,1]] => 40
[[5,4,3,2,2,1],[4,2,2,1,1]] => 60
[[5,4,3,2,1,1],[4,2,2,1]] => 60
[[6,5,4,3,2,1],[5,3,3,2,1]] => 80
[[4,3,1,1,1,1],[3,1]] => 30
[[5,4,2,2,2,1],[4,2,1,1,1]] => 48
[[5,4,2,2,1,1],[4,2,1,1]] => 54
[[6,5,3,3,2,1],[5,3,2,2,1]] => 72
[[5,4,2,1,1,1],[4,2,1]] => 48
[[6,5,3,2,2,1],[5,3,2,1,1]] => 72
[[6,5,3,2,1,1],[5,3,2,1]] => 72
[[7,6,4,3,2,1],[6,4,3,2,1]] => 96
[[5,5,5],[4,4]] => 16
[[6,6,5],[5,5]] => 18
[[6,5,5],[5,4]] => 22
[[7,6,5],[6,5]] => 24
[[4,4,4,1],[3,3]] => 23
[[5,5,5,1],[4,4,1]] => 26
[[5,5,4,1],[4,4]] => 27
[[6,6,5,1],[5,5,1]] => 30
[[5,4,4,1],[4,3]] => 32
[[6,5,5,1],[5,4,1]] => 36
[[6,5,4,1],[5,4]] => 36
[[7,6,5,1],[6,5,1]] => 40
[[3,3,3,2],[2,2]] => 24
[[4,4,4,2],[3,3,1]] => 27
[[5,5,5,2],[4,4,2]] => 30
[[4,4,3,2],[3,3]] => 30
[[5,5,4,2],[4,4,1]] => 33
[[6,6,5,2],[5,5,2]] => 36
[[4,3,3,2],[3,2]] => 34
[[5,4,4,2],[4,3,1]] => 38
[[6,5,5,2],[5,4,2]] => 42
[[5,4,3,2],[4,3]] => 40
[[6,5,4,2],[5,4,1]] => 44
[[7,6,5,2],[6,5,2]] => 48
[[3,3,3,1,1],[2,2]] => 24
[[4,4,4,2,1],[3,3,1,1]] => 34
[[4,4,4,1,1],[3,3,1]] => 30
[[5,5,5,2,1],[4,4,2,1]] => 40
[[4,4,3,1,1],[3,3]] => 30
[[5,5,4,2,1],[4,4,1,1]] => 42
[[5,5,4,1,1],[4,4,1]] => 36
[[6,6,5,2,1],[5,5,2,1]] => 48
[[4,3,3,1,1],[3,2]] => 34
[[5,4,4,2,1],[4,3,1,1]] => 48
[[5,4,4,1,1],[4,3,1]] => 42
[[6,5,5,2,1],[5,4,2,1]] => 56
[[5,4,3,1,1],[4,3]] => 40
[[6,5,4,2,1],[5,4,1,1]] => 56
[[6,5,4,1,1],[5,4,1]] => 48
[[7,6,5,2,1],[6,5,2,1]] => 64
[[3,3,3,3],[2,2,1]] => 20
[[4,4,4,3],[3,3,2]] => 25
[[5,5,5,3],[4,4,3]] => 28
[[4,4,3,3],[3,3,1]] => 30
[[5,5,4,3],[4,4,2]] => 33
[[6,6,5,3],[5,5,3]] => 36
[[4,3,3,3],[3,2,1]] => 30
[[5,4,4,3],[4,3,2]] => 36
[[6,5,5,3],[5,4,3]] => 40
[[5,4,3,3],[4,3,1]] => 40
[[6,5,4,3],[5,4,2]] => 44
[[7,6,5,3],[6,5,3]] => 48
[[2,2,2,2,1],[1,1]] => 18
[[3,3,3,3,1],[2,2,1,1]] => 26
[[3,3,3,2,1],[2,2,1]] => 29
[[4,4,4,3,1],[3,3,2,1]] => 36
[[4,4,4,2,1],[3,3,2]] => 35
[[5,5,5,3,1],[4,4,3,1]] => 42
[[3,3,2,2,1],[2,2]] => 30
[[4,4,3,3,1],[3,3,1,1]] => 42
[[4,4,3,2,1],[3,3,1]] => 39
[[5,5,4,3,1],[4,4,2,1]] => 48
[[5,5,4,2,1],[4,4,2]] => 45
[[6,6,5,3,1],[5,5,3,1]] => 54
[[3,2,2,2,1],[2,1]] => 28
[[4,3,3,3,1],[3,2,1,1]] => 40
[[4,3,3,2,1],[3,2,1]] => 42
[[5,4,4,3,1],[4,3,2,1]] => 52
[[5,4,4,2,1],[4,3,2]] => 50
[[6,5,5,3,1],[5,4,3,1]] => 60
[[4,3,2,2,1],[3,2]] => 40
[[5,4,3,3,1],[4,3,1,1]] => 56
[[5,4,3,2,1],[4,3,1]] => 52
[[6,5,4,3,1],[5,4,2,1]] => 64
[[6,5,4,2,1],[5,4,2]] => 60
[[7,6,5,3,1],[6,5,3,1]] => 72
[[3,3,3,2,2],[2,2,1,1]] => 26
[[4,4,4,3,2],[3,3,2,2]] => 33
[[4,4,4,2,2],[3,3,2,1]] => 35
[[5,5,5,3,2],[4,4,3,2]] => 42
[[4,4,3,2,2],[3,3,1,1]] => 36
[[5,5,4,3,2],[4,4,2,2]] => 45
[[5,5,4,2,2],[4,4,2,1]] => 45
[[6,6,5,3,2],[5,5,3,2]] => 54
[[4,3,3,2,2],[3,2,1,1]] => 38
[[5,4,4,3,2],[4,3,2,2]] => 48
[[5,4,4,2,2],[4,3,2,1]] => 50
[[6,5,5,3,2],[5,4,3,2]] => 60
[[5,4,3,2,2],[4,3,1,1]] => 48
[[6,5,4,3,2],[5,4,2,2]] => 60
[[6,5,4,2,2],[5,4,2,1]] => 60
[[7,6,5,3,2],[6,5,3,2]] => 72
[[2,2,2,1,1,1],[1,1]] => 19
[[3,3,3,2,2,1],[2,2,1,1,1]] => 30
[[3,3,3,2,1,1],[2,2,1,1]] => 33
[[4,4,4,3,2,1],[3,3,2,2,1]] => 44
[[3,3,3,1,1,1],[2,2,1]] => 28
[[4,4,4,2,2,1],[3,3,2,1,1]] => 42
[[4,4,4,2,1,1],[3,3,2,1]] => 42
[[5,5,5,3,2,1],[4,4,3,2,1]] => 56
[[3,3,2,1,1,1],[2,2]] => 27
[[4,4,3,2,2,1],[3,3,1,1,1]] => 42
[[4,4,3,2,1,1],[3,3,1,1]] => 45
[[5,5,4,3,2,1],[4,4,2,2,1]] => 60
[[4,4,3,1,1,1],[3,3,1]] => 36
[[5,5,4,2,2,1],[4,4,2,1,1]] => 54
[[5,5,4,2,1,1],[4,4,2,1]] => 54
[[6,6,5,3,2,1],[5,5,3,2,1]] => 72
[[3,2,2,1,1,1],[2,1]] => 28
[[4,3,3,2,2,1],[3,2,1,1,1]] => 44
[[4,3,3,2,1,1],[3,2,1,1]] => 48
[[5,4,4,3,2,1],[4,3,2,2,1]] => 64
[[4,3,3,1,1,1],[3,2,1]] => 40
[[5,4,4,2,2,1],[4,3,2,1,1]] => 60
[[5,4,4,2,1,1],[4,3,2,1]] => 60
[[6,5,5,3,2,1],[5,4,3,2,1]] => 80
[[4,3,2,1,1,1],[3,2]] => 36
[[5,4,3,2,2,1],[4,3,1,1,1]] => 56
[[5,4,3,2,1,1],[4,3,1,1]] => 60
[[6,5,4,3,2,1],[5,4,2,2,1]] => 80
[[5,4,3,1,1,1],[4,3,1]] => 48
[[6,5,4,2,2,1],[5,4,2,1,1]] => 72
[[6,5,4,2,1,1],[5,4,2,1]] => 72
[[7,6,5,3,2,1],[6,5,3,2,1]] => 96
[[4,4,4,4],[3,3,3]] => 17
[[5,5,5,4],[4,4,4]] => 20
[[5,5,4,4],[4,4,3]] => 27
[[6,6,5,4],[5,5,4]] => 30
[[5,4,4,4],[4,3,3]] => 26
[[6,5,5,4],[5,4,4]] => 30
[[6,5,4,4],[5,4,3]] => 36
[[7,6,5,4],[6,5,4]] => 40
[[3,3,3,3,1],[2,2,2]] => 22
[[4,4,4,4,1],[3,3,3,1]] => 26
[[4,4,4,3,1],[3,3,3]] => 28
[[5,5,5,4,1],[4,4,4,1]] => 32
[[4,4,3,3,1],[3,3,2]] => 36
[[5,5,4,4,1],[4,4,3,1]] => 42
[[5,5,4,3,1],[4,4,3]] => 42
[[6,6,5,4,1],[5,5,4,1]] => 48
[[4,3,3,3,1],[3,2,2]] => 34
[[5,4,4,4,1],[4,3,3,1]] => 40
[[5,4,4,3,1],[4,3,3]] => 42
[[6,5,5,4,1],[5,4,4,1]] => 48
[[5,4,3,3,1],[4,3,2]] => 48
[[6,5,4,4,1],[5,4,3,1]] => 56
[[6,5,4,3,1],[5,4,3]] => 56
[[7,6,5,4,1],[6,5,4,1]] => 64
[[2,2,2,2,2],[1,1,1]] => 16
[[3,3,3,3,2],[2,2,2,1]] => 23
[[4,4,4,4,2],[3,3,3,2]] => 27
[[3,3,3,2,2],[2,2,2]] => 28
[[4,4,4,3,2],[3,3,3,1]] => 32
[[5,5,5,4,2],[4,4,4,2]] => 36
[[3,3,2,2,2],[2,2,1]] => 30
[[4,4,3,3,2],[3,3,2,1]] => 39
[[5,5,4,4,2],[4,4,3,2]] => 45
[[4,4,3,2,2],[3,3,2]] => 42
[[5,5,4,3,2],[4,4,3,1]] => 48
[[6,6,5,4,2],[5,5,4,2]] => 54
[[3,2,2,2,2],[2,1,1]] => 26
[[4,3,3,3,2],[3,2,2,1]] => 36
[[5,4,4,4,2],[4,3,3,2]] => 42
[[4,3,3,2,2],[3,2,2]] => 42
[[5,4,4,3,2],[4,3,3,1]] => 48
[[6,5,5,4,2],[5,4,4,2]] => 54
[[4,3,2,2,2],[3,2,1]] => 40
[[5,4,3,3,2],[4,3,2,1]] => 52
[[6,5,4,4,2],[5,4,3,2]] => 60
[[5,4,3,2,2],[4,3,2]] => 56
[[6,5,4,3,2],[5,4,3,1]] => 64
[[7,6,5,4,2],[6,5,4,2]] => 72
[[2,2,2,2,1,1],[1,1,1]] => 19
[[3,3,3,3,2,1],[2,2,2,1,1]] => 28
[[3,3,3,3,1,1],[2,2,2,1]] => 27
[[4,4,4,4,2,1],[3,3,3,2,1]] => 36
[[3,3,3,2,1,1],[2,2,2]] => 28
[[4,4,4,3,2,1],[3,3,3,1,1]] => 40
[[4,4,4,3,1,1],[3,3,3,1]] => 36
[[5,5,5,4,2,1],[4,4,4,2,1]] => 48
[[3,3,2,2,1,1],[2,2,1]] => 33
[[4,4,3,3,2,1],[3,3,2,1,1]] => 48
[[4,4,3,3,1,1],[3,3,2,1]] => 45
[[5,5,4,4,2,1],[4,4,3,2,1]] => 60
[[4,4,3,2,1,1],[3,3,2]] => 42
[[5,5,4,3,2,1],[4,4,3,1,1]] => 60
[[5,5,4,3,1,1],[4,4,3,1]] => 54
[[6,6,5,4,2,1],[5,5,4,2,1]] => 72
[[3,2,2,2,1,1],[2,1,1]] => 30
[[4,3,3,3,2,1],[3,2,2,1,1]] => 44
[[4,3,3,3,1,1],[3,2,2,1]] => 42
[[5,4,4,4,2,1],[4,3,3,2,1]] => 56
[[4,3,3,2,1,1],[3,2,2]] => 42
[[5,4,4,3,2,1],[4,3,3,1,1]] => 60
[[5,4,4,3,1,1],[4,3,3,1]] => 54
[[6,5,5,4,2,1],[5,4,4,2,1]] => 72
[[4,3,2,2,1,1],[3,2,1]] => 44
[[5,4,3,3,2,1],[4,3,2,1,1]] => 64
[[5,4,3,3,1,1],[4,3,2,1]] => 60
[[6,5,4,4,2,1],[5,4,3,2,1]] => 80
[[5,4,3,2,1,1],[4,3,2]] => 56
[[6,5,4,3,2,1],[5,4,3,1,1]] => 80
[[6,5,4,3,1,1],[5,4,3,1]] => 72
[[7,6,5,4,2,1],[6,5,4,2,1]] => 96
[[3,3,3,3,3],[2,2,2,2]] => 16
[[4,4,4,4,3],[3,3,3,3]] => 20
[[4,4,4,3,3],[3,3,3,2]] => 28
[[5,5,5,4,3],[4,4,4,3]] => 32
[[4,4,3,3,3],[3,3,2,2]] => 30
[[5,5,4,4,3],[4,4,3,3]] => 36
[[5,5,4,3,3],[4,4,3,2]] => 42
[[6,6,5,4,3],[5,5,4,3]] => 48
[[4,3,3,3,3],[3,2,2,2]] => 26
[[5,4,4,4,3],[4,3,3,3]] => 32
[[5,4,4,3,3],[4,3,3,2]] => 42
[[6,5,5,4,3],[5,4,4,3]] => 48
[[5,4,3,3,3],[4,3,2,2]] => 40
[[6,5,4,4,3],[5,4,3,3]] => 48
[[6,5,4,3,3],[5,4,3,2]] => 56
[[7,6,5,4,3],[6,5,4,3]] => 64
[[2,2,2,2,2,1],[1,1,1,1]] => 17
[[3,3,3,3,3,1],[2,2,2,2,1]] => 22
[[3,3,3,3,2,1],[2,2,2,2]] => 25
[[4,4,4,4,3,1],[3,3,3,3,1]] => 30
[[3,3,3,2,2,1],[2,2,2,1]] => 32
[[4,4,4,3,3,1],[3,3,3,2,1]] => 40
[[4,4,4,3,2,1],[3,3,3,2]] => 40
[[5,5,5,4,3,1],[4,4,4,3,1]] => 48
[[3,3,2,2,2,1],[2,2,1,1]] => 33
[[4,4,3,3,3,1],[3,3,2,2,1]] => 42
[[4,4,3,3,2,1],[3,3,2,2]] => 45
[[5,5,4,4,3,1],[4,4,3,3,1]] => 54
[[4,4,3,2,2,1],[3,3,2,1]] => 48
[[5,5,4,3,3,1],[4,4,3,2,1]] => 60
[[5,5,4,3,2,1],[4,4,3,2]] => 60
[[6,6,5,4,3,1],[5,5,4,3,1]] => 72
[[3,2,2,2,2,1],[2,1,1,1]] => 28
[[4,3,3,3,3,1],[3,2,2,2,1]] => 36
[[4,3,3,3,2,1],[3,2,2,2]] => 40
[[5,4,4,4,3,1],[4,3,3,3,1]] => 48
[[4,3,3,2,2,1],[3,2,2,1]] => 48
[[5,4,4,3,3,1],[4,3,3,2,1]] => 60
[[5,4,4,3,2,1],[4,3,3,2]] => 60
[[6,5,5,4,3,1],[5,4,4,3,1]] => 72
[[4,3,2,2,2,1],[3,2,1,1]] => 44
[[5,4,3,3,3,1],[4,3,2,2,1]] => 56
[[5,4,3,3,2,1],[4,3,2,2]] => 60
[[6,5,4,4,3,1],[5,4,3,3,1]] => 72
[[5,4,3,2,2,1],[4,3,2,1]] => 64
[[6,5,4,3,3,1],[5,4,3,2,1]] => 80
[[6,5,4,3,2,1],[5,4,3,2]] => 80
[[7,6,5,4,3,1],[6,5,4,3,1]] => 96
[[2,2,2,2,2,2],[1,1,1,1,1]] => 13
[[3,3,3,3,3,2],[2,2,2,2,2]] => 18
[[3,3,3,3,2,2],[2,2,2,2,1]] => 25
[[4,4,4,4,3,2],[3,3,3,3,2]] => 30
[[3,3,3,2,2,2],[2,2,2,1,1]] => 28
[[4,4,4,3,3,2],[3,3,3,2,2]] => 36
[[4,4,4,3,2,2],[3,3,3,2,1]] => 40
[[5,5,5,4,3,2],[4,4,4,3,2]] => 48
[[3,3,2,2,2,2],[2,2,1,1,1]] => 27
[[4,4,3,3,3,2],[3,3,2,2,2]] => 36
[[4,4,3,3,2,2],[3,3,2,2,1]] => 45
[[5,5,4,4,3,2],[4,4,3,3,2]] => 54
[[4,4,3,2,2,2],[3,3,2,1,1]] => 42
[[5,5,4,3,3,2],[4,4,3,2,2]] => 54
[[5,5,4,3,2,2],[4,4,3,2,1]] => 60
[[6,6,5,4,3,2],[5,5,4,3,2]] => 72
[[3,2,2,2,2,2],[2,1,1,1,1]] => 22
[[4,3,3,3,3,2],[3,2,2,2,2]] => 30
[[4,3,3,3,2,2],[3,2,2,2,1]] => 40
[[5,4,4,4,3,2],[4,3,3,3,2]] => 48
[[4,3,3,2,2,2],[3,2,2,1,1]] => 42
[[5,4,4,3,3,2],[4,3,3,2,2]] => 54
[[5,4,4,3,2,2],[4,3,3,2,1]] => 60
[[6,5,5,4,3,2],[5,4,4,3,2]] => 72
[[4,3,2,2,2,2],[3,2,1,1,1]] => 36
[[5,4,3,3,3,2],[4,3,2,2,2]] => 48
[[5,4,3,3,2,2],[4,3,2,2,1]] => 60
[[6,5,4,4,3,2],[5,4,3,3,2]] => 72
[[5,4,3,2,2,2],[4,3,2,1,1]] => 56
[[6,5,4,3,3,2],[5,4,3,2,2]] => 72
[[6,5,4,3,2,2],[5,4,3,2,1]] => 80
[[7,6,5,4,3,2],[6,5,4,3,2]] => 96
[[1,1,1,1,1,1,1],[]] => 8
[[2,2,2,2,2,2,1],[1,1,1,1,1,1]] => 14
[[2,2,2,2,2,1,1],[1,1,1,1,1]] => 18
[[3,3,3,3,3,2,1],[2,2,2,2,2,1]] => 24
[[2,2,2,2,1,1,1],[1,1,1,1]] => 20
[[3,3,3,3,2,2,1],[2,2,2,2,1,1]] => 30
[[3,3,3,3,2,1,1],[2,2,2,2,1]] => 30
[[4,4,4,4,3,2,1],[3,3,3,3,2,1]] => 40
[[2,2,2,1,1,1,1],[1,1,1]] => 20
[[3,3,3,2,2,2,1],[2,2,2,1,1,1]] => 32
[[3,3,3,2,2,1,1],[2,2,2,1,1]] => 36
[[4,4,4,3,3,2,1],[3,3,3,2,2,1]] => 48
[[3,3,3,2,1,1,1],[2,2,2,1]] => 32
[[4,4,4,3,2,2,1],[3,3,3,2,1,1]] => 48
-----------------------------------------------------------------------------
Created: Dec 22, 2020 at 14:13 by Martin Rubey
-----------------------------------------------------------------------------
Last Updated: Dec 22, 2020 at 14:13 by Martin Rubey