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* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
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-----------------------------------------------------------------------------
Statistic identifier: St001660
-----------------------------------------------------------------------------
Collection: Skew partitions
-----------------------------------------------------------------------------
Description: The number of ways to place as many non-attacking rooks as possible on a skew 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 next(v for v in reversed(rook_matrix.rook_vector()) if v)
-----------------------------------------------------------------------------
Statistic values:
[[1],[]] => 1
[[2],[]] => 2
[[1,1],[]] => 2
[[2,1],[1]] => 1
[[3],[]] => 3
[[2,1],[]] => 1
[[3,1],[1]] => 2
[[2,2],[1]] => 1
[[3,2],[2]] => 2
[[1,1,1],[]] => 3
[[2,2,1],[1,1]] => 2
[[2,1,1],[1]] => 2
[[3,2,1],[2,1]] => 1
[[4],[]] => 4
[[3,1],[]] => 2
[[4,1],[1]] => 3
[[2,2],[]] => 2
[[3,2],[1]] => 3
[[4,2],[2]] => 4
[[2,1,1],[]] => 2
[[3,2,1],[1,1]] => 1
[[3,1,1],[1]] => 4
[[4,2,1],[2,1]] => 2
[[3,3],[2]] => 2
[[4,3],[3]] => 3
[[2,2,1],[1]] => 3
[[3,3,1],[2,1]] => 1
[[3,2,1],[2]] => 1
[[4,3,1],[3,1]] => 2
[[2,2,2],[1,1]] => 2
[[3,3,2],[2,2]] => 4
[[3,2,2],[2,1]] => 1
[[4,3,2],[3,2]] => 2
[[1,1,1,1],[]] => 4
[[2,2,2,1],[1,1,1]] => 3
[[2,2,1,1],[1,1]] => 4
[[3,3,2,1],[2,2,1]] => 2
[[2,1,1,1],[1]] => 3
[[3,2,2,1],[2,1,1]] => 2
[[3,2,1,1],[2,1]] => 2
[[4,3,2,1],[3,2,1]] => 1
[[5],[]] => 5
[[4,1],[]] => 3
[[5,1],[1]] => 4
[[3,2],[]] => 4
[[4,2],[1]] => 5
[[5,2],[2]] => 6
[[3,1,1],[]] => 4
[[4,2,1],[1,1]] => 2
[[4,1,1],[1]] => 6
[[5,2,1],[2,1]] => 3
[[3,3],[1]] => 4
[[4,3],[2]] => 5
[[5,3],[3]] => 6
[[2,2,1],[]] => 4
[[3,3,1],[1,1]] => 2
[[3,2,1],[1]] => 1
[[4,3,1],[2,1]] => 3
[[4,2,1],[2]] => 2
[[5,3,1],[3,1]] => 4
[[3,2,2],[1,1]] => 1
[[4,3,2],[2,2]] => 2
[[4,2,2],[2,1]] => 2
[[5,3,2],[3,2]] => 4
[[2,1,1,1],[]] => 3
[[3,2,2,1],[1,1,1]] => 2
[[3,2,1,1],[1,1]] => 2
[[4,3,2,1],[2,2,1]] => 1
[[3,1,1,1],[1]] => 6
[[4,2,2,1],[2,1,1]] => 4
[[4,2,1,1],[2,1]] => 4
[[5,3,2,1],[3,2,1]] => 2
[[4,4],[3]] => 3
[[5,4],[4]] => 4
[[3,3,1],[2]] => 1
[[4,4,1],[3,1]] => 2
[[4,3,1],[3]] => 2
[[5,4,1],[4,1]] => 3
[[2,2,2],[1]] => 4
[[3,3,2],[2,1]] => 1
[[4,4,2],[3,2]] => 2
[[3,2,2],[2]] => 2
[[4,3,2],[3,1]] => 3
[[5,4,2],[4,2]] => 4
[[2,2,1,1],[1]] => 5
[[3,3,2,1],[2,1,1]] => 3
[[3,3,1,1],[2,1]] => 2
[[4,4,2,1],[3,2,1]] => 1
[[3,2,1,1],[2]] => 2
[[4,3,2,1],[3,1,1]] => 1
[[4,3,1,1],[3,1]] => 4
[[5,4,2,1],[4,2,1]] => 2
[[3,3,3],[2,2]] => 4
[[4,4,3],[3,3]] => 6
[[4,3,3],[3,2]] => 2
[[5,4,3],[4,3]] => 3
[[2,2,2,1],[1,1]] => 5
[[3,3,3,1],[2,2,1]] => 2
[[3,3,2,1],[2,2]] => 2
[[4,4,3,1],[3,3,1]] => 4
[[3,2,2,1],[2,1]] => 3
[[4,3,3,1],[3,2,1]] => 1
[[4,3,2,1],[3,2]] => 1
[[5,4,3,1],[4,3,1]] => 2
[[2,2,2,2],[1,1,1]] => 3
[[3,3,3,2],[2,2,2]] => 6
[[3,3,2,2],[2,2,1]] => 2
[[4,4,3,2],[3,3,2]] => 4
[[3,2,2,2],[2,1,1]] => 2
[[4,3,3,2],[3,2,2]] => 4
[[4,3,2,2],[3,2,1]] => 1
[[5,4,3,2],[4,3,2]] => 2
[[1,1,1,1,1],[]] => 5
[[2,2,2,2,1],[1,1,1,1]] => 4
[[2,2,2,1,1],[1,1,1]] => 6
[[3,3,3,2,1],[2,2,2,1]] => 3
[[2,2,1,1,1],[1,1]] => 6
[[3,3,2,2,1],[2,2,1,1]] => 4
[[3,3,2,1,1],[2,2,1]] => 4
[[4,4,3,2,1],[3,3,2,1]] => 2
[[2,1,1,1,1],[1]] => 4
[[3,2,2,2,1],[2,1,1,1]] => 3
[[3,2,2,1,1],[2,1,1]] => 4
[[4,3,3,2,1],[3,2,2,1]] => 2
[[3,2,1,1,1],[2,1]] => 3
[[4,3,2,2,1],[3,2,1,1]] => 2
[[4,3,2,1,1],[3,2,1]] => 2
[[5,4,3,2,1],[4,3,2,1]] => 1
[[6],[]] => 6
[[5,1],[]] => 4
[[6,1],[1]] => 5
[[4,2],[]] => 6
[[5,2],[1]] => 7
[[6,2],[2]] => 8
[[4,1,1],[]] => 6
[[5,2,1],[1,1]] => 3
[[5,1,1],[1]] => 8
[[6,2,1],[2,1]] => 4
[[3,3],[]] => 6
[[4,3],[1]] => 7
[[5,3],[2]] => 8
[[6,3],[3]] => 9
[[3,2,1],[]] => 1
[[4,3,1],[1,1]] => 4
[[4,2,1],[1]] => 2
[[5,3,1],[2,1]] => 5
[[5,2,1],[2]] => 3
[[6,3,1],[3,1]] => 6
[[4,2,2],[1,1]] => 2
[[5,3,2],[2,2]] => 4
[[5,2,2],[2,1]] => 3
[[6,3,2],[3,2]] => 6
[[3,1,1,1],[]] => 6
[[4,2,2,1],[1,1,1]] => 4
[[4,2,1,1],[1,1]] => 4
[[5,3,2,1],[2,2,1]] => 2
[[4,1,1,1],[1]] => 9
[[5,2,2,1],[2,1,1]] => 6
[[5,2,1,1],[2,1]] => 6
[[6,3,2,1],[3,2,1]] => 3
[[4,4],[2]] => 6
[[5,4],[3]] => 7
[[6,4],[4]] => 8
[[3,3,1],[1]] => 2
[[4,4,1],[2,1]] => 4
[[4,3,1],[2]] => 3
[[5,4,1],[3,1]] => 5
[[5,3,1],[3]] => 4
[[6,4,1],[4,1]] => 6
[[2,2,2],[]] => 6
[[3,3,2],[1,1]] => 2
[[4,4,2],[2,2]] => 4
[[3,2,2],[1]] => 2
[[4,3,2],[2,1]] => 4
[[5,4,2],[3,2]] => 6
[[4,2,2],[2]] => 4
[[5,3,2],[3,1]] => 6
[[6,4,2],[4,2]] => 8
[[2,2,1,1],[]] => 6
[[3,3,2,1],[1,1,1]] => 4
[[3,3,1,1],[1,1]] => 4
[[4,4,2,1],[2,2,1]] => 2
[[3,2,1,1],[1]] => 2
[[4,3,2,1],[2,1,1]] => 1
[[4,3,1,1],[2,1]] => 6
[[5,4,2,1],[3,2,1]] => 3
[[4,2,1,1],[2]] => 4
[[5,3,2,1],[3,1,1]] => 2
[[5,3,1,1],[3,1]] => 8
[[6,4,2,1],[4,2,1]] => 4
[[4,3,3],[2,2]] => 2
[[5,4,3],[3,3]] => 3
[[5,3,3],[3,2]] => 4
[[6,4,3],[4,3]] => 6
[[3,2,2,1],[1,1]] => 3
[[4,3,3,1],[2,2,1]] => 1
[[4,3,2,1],[2,2]] => 1
[[5,4,3,1],[3,3,1]] => 2
[[4,2,2,1],[2,1]] => 6
[[5,3,3,1],[3,2,1]] => 2
[[5,3,2,1],[3,2]] => 2
[[6,4,3,1],[4,3,1]] => 4
[[3,2,2,2],[1,1,1]] => 2
[[4,3,3,2],[2,2,2]] => 4
[[4,3,2,2],[2,2,1]] => 1
[[5,4,3,2],[3,3,2]] => 2
[[4,2,2,2],[2,1,1]] => 4
[[5,3,3,2],[3,2,2]] => 8
[[5,3,2,2],[3,2,1]] => 2
[[6,4,3,2],[4,3,2]] => 4
[[2,1,1,1,1],[]] => 4
[[3,2,2,2,1],[1,1,1,1]] => 3
[[3,2,2,1,1],[1,1,1]] => 4
[[4,3,3,2,1],[2,2,2,1]] => 2
[[3,2,1,1,1],[1,1]] => 3
[[4,3,2,2,1],[2,2,1,1]] => 2
[[4,3,2,1,1],[2,2,1]] => 2
[[5,4,3,2,1],[3,3,2,1]] => 1
[[3,1,1,1,1],[1]] => 8
[[4,2,2,2,1],[2,1,1,1]] => 6
[[4,2,2,1,1],[2,1,1]] => 8
[[5,3,3,2,1],[3,2,2,1]] => 4
[[4,2,1,1,1],[2,1]] => 6
[[5,3,2,2,1],[3,2,1,1]] => 4
[[5,3,2,1,1],[3,2,1]] => 4
[[6,4,3,2,1],[4,3,2,1]] => 2
[[5,5],[4]] => 4
[[6,5],[5]] => 5
[[4,4,1],[3]] => 2
[[5,5,1],[4,1]] => 3
[[5,4,1],[4]] => 3
[[6,5,1],[5,1]] => 4
[[3,3,2],[2]] => 2
[[4,4,2],[3,1]] => 3
[[5,5,2],[4,2]] => 4
[[4,3,2],[3]] => 4
[[5,4,2],[4,1]] => 5
[[6,5,2],[5,2]] => 6
[[3,3,1,1],[2]] => 2
[[4,4,2,1],[3,1,1]] => 1
[[4,4,1,1],[3,1]] => 4
[[5,5,2,1],[4,2,1]] => 2
[[4,3,1,1],[3]] => 4
[[5,4,2,1],[4,1,1]] => 2
[[5,4,1,1],[4,1]] => 6
[[6,5,2,1],[5,2,1]] => 3
[[3,3,3],[2,1]] => 1
[[4,4,3],[3,2]] => 2
[[5,5,3],[4,3]] => 3
[[4,3,3],[3,1]] => 4
[[5,4,3],[4,2]] => 5
[[6,5,3],[5,3]] => 6
[[2,2,2,1],[1]] => 7
[[3,3,3,1],[2,1,1]] => 4
[[3,3,2,1],[2,1]] => 4
[[4,4,3,1],[3,2,1]] => 1
[[4,4,2,1],[3,2]] => 1
[[5,5,3,1],[4,3,1]] => 2
[[3,2,2,1],[2]] => 4
[[4,3,3,1],[3,1,1]] => 2
[[4,3,2,1],[3,1]] => 1
[[5,4,3,1],[4,2,1]] => 3
[[5,4,2,1],[4,2]] => 2
[[6,5,3,1],[5,3,1]] => 4
[[3,3,2,2],[2,1,1]] => 3
[[4,4,3,2],[3,2,2]] => 6
[[4,4,2,2],[3,2,1]] => 1
[[5,5,3,2],[4,3,2]] => 2
[[4,3,2,2],[3,1,1]] => 1
[[5,4,3,2],[4,2,2]] => 2
[[5,4,2,2],[4,2,1]] => 2
[[6,5,3,2],[5,3,2]] => 4
[[2,2,1,1,1],[1]] => 7
[[3,3,2,2,1],[2,1,1,1]] => 5
[[3,3,2,1,1],[2,1,1]] => 6
[[4,4,3,2,1],[3,2,2,1]] => 3
[[3,3,1,1,1],[2,1]] => 3
[[4,4,2,2,1],[3,2,1,1]] => 2
[[4,4,2,1,1],[3,2,1]] => 2
[[5,5,3,2,1],[4,3,2,1]] => 1
[[3,2,1,1,1],[2]] => 3
[[4,3,2,2,1],[3,1,1,1]] => 2
[[4,3,2,1,1],[3,1,1]] => 2
[[5,4,3,2,1],[4,2,2,1]] => 1
[[4,3,1,1,1],[3,1]] => 6
[[5,4,2,2,1],[4,2,1,1]] => 4
[[5,4,2,1,1],[4,2,1]] => 4
[[6,5,3,2,1],[5,3,2,1]] => 2
[[4,4,4],[3,3]] => 6
[[5,5,4],[4,4]] => 8
[[5,4,4],[4,3]] => 3
[[6,5,4],[5,4]] => 4
[[3,3,3,1],[2,2]] => 2
[[4,4,4,1],[3,3,1]] => 4
[[4,4,3,1],[3,3]] => 4
[[5,5,4,1],[4,4,1]] => 6
[[4,3,3,1],[3,2]] => 1
[[5,4,4,1],[4,3,1]] => 2
[[5,4,3,1],[4,3]] => 2
[[6,5,4,1],[5,4,1]] => 3
[[2,2,2,2],[1,1]] => 6
[[3,3,3,2],[2,2,1]] => 2
[[4,4,4,2],[3,3,2]] => 4
[[3,3,2,2],[2,2]] => 4
[[4,4,3,2],[3,3,1]] => 6
[[5,5,4,2],[4,4,2]] => 8
[[3,2,2,2],[2,1]] => 4
[[4,3,3,2],[3,2,1]] => 1
[[5,4,4,2],[4,3,2]] => 2
[[4,3,2,2],[3,2]] => 2
[[5,4,3,2],[4,3,1]] => 3
[[6,5,4,2],[5,4,2]] => 4
[[2,2,2,1,1],[1,1]] => 8
[[3,3,3,2,1],[2,2,1,1]] => 5
[[3,3,3,1,1],[2,2,1]] => 4
[[4,4,4,2,1],[3,3,2,1]] => 2
[[3,3,2,1,1],[2,2]] => 4
[[4,4,3,2,1],[3,3,1,1]] => 2
[[4,4,3,1,1],[3,3,1]] => 8
[[5,5,4,2,1],[4,4,2,1]] => 4
[[3,2,2,1,1],[2,1]] => 5
[[4,3,3,2,1],[3,2,1,1]] => 3
[[4,3,3,1,1],[3,2,1]] => 2
[[5,4,4,2,1],[4,3,2,1]] => 1
[[4,3,2,1,1],[3,2]] => 2
[[5,4,3,2,1],[4,3,1,1]] => 1
[[5,4,3,1,1],[4,3,1]] => 4
[[6,5,4,2,1],[5,4,2,1]] => 2
[[3,3,3,3],[2,2,2]] => 6
[[4,4,4,3],[3,3,3]] => 9
[[4,4,3,3],[3,3,2]] => 4
[[5,5,4,3],[4,4,3]] => 6
[[4,3,3,3],[3,2,2]] => 4
[[5,4,4,3],[4,3,3]] => 6
[[5,4,3,3],[4,3,2]] => 2
[[6,5,4,3],[5,4,3]] => 3
[[2,2,2,2,1],[1,1,1]] => 7
[[3,3,3,3,1],[2,2,2,1]] => 3
[[3,3,3,2,1],[2,2,2]] => 3
[[4,4,4,3,1],[3,3,3,1]] => 6
[[3,3,2,2,1],[2,2,1]] => 6
[[4,4,3,3,1],[3,3,2,1]] => 2
[[4,4,3,2,1],[3,3,2]] => 2
[[5,5,4,3,1],[4,4,3,1]] => 4
[[3,2,2,2,1],[2,1,1]] => 5
[[4,3,3,3,1],[3,2,2,1]] => 2
[[4,3,3,2,1],[3,2,2]] => 2
[[5,4,4,3,1],[4,3,3,1]] => 4
[[4,3,2,2,1],[3,2,1]] => 3
[[5,4,3,3,1],[4,3,2,1]] => 1
[[5,4,3,2,1],[4,3,2]] => 1
[[6,5,4,3,1],[5,4,3,1]] => 2
[[2,2,2,2,2],[1,1,1,1]] => 4
[[3,3,3,3,2],[2,2,2,2]] => 8
[[3,3,3,2,2],[2,2,2,1]] => 3
[[4,4,4,3,2],[3,3,3,2]] => 6
[[3,3,2,2,2],[2,2,1,1]] => 4
[[4,4,3,3,2],[3,3,2,2]] => 8
[[4,4,3,2,2],[3,3,2,1]] => 2
[[5,5,4,3,2],[4,4,3,2]] => 4
[[3,2,2,2,2],[2,1,1,1]] => 3
[[4,3,3,3,2],[3,2,2,2]] => 6
[[4,3,3,2,2],[3,2,2,1]] => 2
[[5,4,4,3,2],[4,3,3,2]] => 4
[[4,3,2,2,2],[3,2,1,1]] => 2
[[5,4,3,3,2],[4,3,2,2]] => 4
[[5,4,3,2,2],[4,3,2,1]] => 1
[[6,5,4,3,2],[5,4,3,2]] => 2
[[1,1,1,1,1,1],[]] => 6
[[2,2,2,2,2,1],[1,1,1,1,1]] => 5
[[2,2,2,2,1,1],[1,1,1,1]] => 8
[[3,3,3,3,2,1],[2,2,2,2,1]] => 4
[[2,2,2,1,1,1],[1,1,1]] => 9
[[3,3,3,2,2,1],[2,2,2,1,1]] => 6
[[3,3,3,2,1,1],[2,2,2,1]] => 6
[[4,4,4,3,2,1],[3,3,3,2,1]] => 3
[[2,2,1,1,1,1],[1,1]] => 8
[[3,3,2,2,2,1],[2,2,1,1,1]] => 6
[[3,3,2,2,1,1],[2,2,1,1]] => 8
[[4,4,3,3,2,1],[3,3,2,2,1]] => 4
[[3,3,2,1,1,1],[2,2,1]] => 6
[[4,4,3,2,2,1],[3,3,2,1,1]] => 4
[[4,4,3,2,1,1],[3,3,2,1]] => 4
[[5,5,4,3,2,1],[4,4,3,2,1]] => 2
[[2,1,1,1,1,1],[1]] => 5
[[3,2,2,2,2,1],[2,1,1,1,1]] => 4
[[3,2,2,2,1,1],[2,1,1,1]] => 6
[[4,3,3,3,2,1],[3,2,2,2,1]] => 3
[[3,2,2,1,1,1],[2,1,1]] => 6
[[4,3,3,2,2,1],[3,2,2,1,1]] => 4
[[4,3,3,2,1,1],[3,2,2,1]] => 4
[[5,4,4,3,2,1],[4,3,3,2,1]] => 2
[[3,2,1,1,1,1],[2,1]] => 4
[[4,3,2,2,2,1],[3,2,1,1,1]] => 3
[[4,3,2,2,1,1],[3,2,1,1]] => 4
[[5,4,3,3,2,1],[4,3,2,2,1]] => 2
[[4,3,2,1,1,1],[3,2,1]] => 3
[[5,4,3,2,2,1],[4,3,2,1,1]] => 2
[[5,4,3,2,1,1],[4,3,2,1]] => 2
[[6,5,4,3,2,1],[5,4,3,2,1]] => 1
[[7],[]] => 7
[[6,1],[]] => 5
[[7,1],[1]] => 6
[[5,2],[]] => 8
[[6,2],[1]] => 9
[[7,2],[2]] => 10
[[5,1,1],[]] => 8
[[6,2,1],[1,1]] => 4
[[6,1,1],[1]] => 10
[[7,2,1],[2,1]] => 5
[[4,3],[]] => 9
[[5,3],[1]] => 10
[[6,3],[2]] => 11
[[7,3],[3]] => 12
[[4,2,1],[]] => 2
[[5,3,1],[1,1]] => 6
[[5,2,1],[1]] => 3
[[6,3,1],[2,1]] => 7
[[6,2,1],[2]] => 4
[[7,3,1],[3,1]] => 8
[[5,2,2],[1,1]] => 3
[[6,3,2],[2,2]] => 6
[[6,2,2],[2,1]] => 4
[[7,3,2],[3,2]] => 8
[[4,1,1,1],[]] => 9
[[5,2,2,1],[1,1,1]] => 6
[[5,2,1,1],[1,1]] => 6
[[6,3,2,1],[2,2,1]] => 3
[[5,1,1,1],[1]] => 12
[[6,2,2,1],[2,1,1]] => 8
[[6,2,1,1],[2,1]] => 8
[[7,3,2,1],[3,2,1]] => 4
[[4,4],[1]] => 9
[[5,4],[2]] => 10
[[6,4],[3]] => 11
[[7,4],[4]] => 12
[[3,3,1],[]] => 2
[[4,4,1],[1,1]] => 6
[[4,3,1],[1]] => 4
[[5,4,1],[2,1]] => 7
[[5,3,1],[2]] => 5
[[6,4,1],[3,1]] => 8
[[6,3,1],[3]] => 6
[[7,4,1],[4,1]] => 9
[[3,2,2],[]] => 2
[[4,3,2],[1,1]] => 5
[[5,4,2],[2,2]] => 8
[[4,2,2],[1]] => 4
[[5,3,2],[2,1]] => 7
[[6,4,2],[3,2]] => 10
[[5,2,2],[2]] => 6
[[6,3,2],[3,1]] => 9
[[7,4,2],[4,2]] => 12
[[3,2,1,1],[]] => 2
[[4,3,2,1],[1,1,1]] => 1
[[4,3,1,1],[1,1]] => 8
[[5,4,2,1],[2,2,1]] => 4
[[4,2,1,1],[1]] => 4
[[5,3,2,1],[2,1,1]] => 2
[[5,3,1,1],[2,1]] => 10
[[6,4,2,1],[3,2,1]] => 5
[[5,2,1,1],[2]] => 6
[[6,3,2,1],[3,1,1]] => 3
[[6,3,1,1],[3,1]] => 12
[[7,4,2,1],[4,2,1]] => 6
[[5,3,3],[2,2]] => 4
[[6,4,3],[3,3]] => 6
[[6,3,3],[3,2]] => 6
[[7,4,3],[4,3]] => 9
[[4,2,2,1],[1,1]] => 6
[[5,3,3,1],[2,2,1]] => 2
[[5,3,2,1],[2,2]] => 2
[[6,4,3,1],[3,3,1]] => 4
[[5,2,2,1],[2,1]] => 9
[[6,3,3,1],[3,2,1]] => 3
[[6,3,2,1],[3,2]] => 3
[[7,4,3,1],[4,3,1]] => 6
[[4,2,2,2],[1,1,1]] => 4
[[5,3,3,2],[2,2,2]] => 8
[[5,3,2,2],[2,2,1]] => 2
[[6,4,3,2],[3,3,2]] => 4
[[5,2,2,2],[2,1,1]] => 6
[[6,3,3,2],[3,2,2]] => 12
[[6,3,2,2],[3,2,1]] => 3
[[7,4,3,2],[4,3,2]] => 6
[[3,1,1,1,1],[]] => 8
[[4,2,2,2,1],[1,1,1,1]] => 6
[[4,2,2,1,1],[1,1,1]] => 8
[[5,3,3,2,1],[2,2,2,1]] => 4
[[4,2,1,1,1],[1,1]] => 6
[[5,3,2,2,1],[2,2,1,1]] => 4
[[5,3,2,1,1],[2,2,1]] => 4
[[6,4,3,2,1],[3,3,2,1]] => 2
[[4,1,1,1,1],[1]] => 12
[[5,2,2,2,1],[2,1,1,1]] => 9
[[5,2,2,1,1],[2,1,1]] => 12
[[6,3,3,2,1],[3,2,2,1]] => 6
[[5,2,1,1,1],[2,1]] => 9
[[6,3,2,2,1],[3,2,1,1]] => 6
[[6,3,2,1,1],[3,2,1]] => 6
[[7,4,3,2,1],[4,3,2,1]] => 3
[[5,5],[3]] => 8
[[6,5],[4]] => 9
[[7,5],[5]] => 10
[[4,4,1],[2]] => 4
[[5,5,1],[3,1]] => 6
[[5,4,1],[3]] => 5
[[6,5,1],[4,1]] => 7
[[6,4,1],[4]] => 6
[[7,5,1],[5,1]] => 8
[[3,3,2],[1]] => 3
[[4,4,2],[2,1]] => 6
[[5,5,2],[3,2]] => 8
[[4,3,2],[2]] => 6
[[5,4,2],[3,1]] => 8
[[6,5,2],[4,2]] => 10
[[5,3,2],[3]] => 8
[[6,4,2],[4,1]] => 10
[[7,5,2],[5,2]] => 12
[[3,3,1,1],[1]] => 4
[[4,4,2,1],[2,1,1]] => 2
[[4,4,1,1],[2,1]] => 8
[[5,5,2,1],[3,2,1]] => 4
[[4,3,1,1],[2]] => 6
[[5,4,2,1],[3,1,1]] => 3
[[5,4,1,1],[3,1]] => 10
[[6,5,2,1],[4,2,1]] => 5
[[5,3,1,1],[3]] => 8
[[6,4,2,1],[4,1,1]] => 4
[[6,4,1,1],[4,1]] => 12
[[7,5,2,1],[5,2,1]] => 6
[[3,3,3],[1,1]] => 2
[[4,4,3],[2,2]] => 4
[[5,5,3],[3,3]] => 6
[[4,3,3],[2,1]] => 5
[[5,4,3],[3,2]] => 7
[[6,5,3],[4,3]] => 9
[[5,3,3],[3,1]] => 8
[[6,4,3],[4,2]] => 10
[[7,5,3],[5,3]] => 12
[[2,2,2,1],[]] => 9
[[3,3,3,1],[1,1,1]] => 6
[[3,3,2,1],[1,1]] => 6
[[4,4,3,1],[2,2,1]] => 2
[[4,4,2,1],[2,2]] => 2
[[5,5,3,1],[3,3,1]] => 4
[[3,2,2,1],[1]] => 4
[[4,3,3,1],[2,1,1]] => 2
[[4,3,2,1],[2,1]] => 1
[[5,4,3,1],[3,2,1]] => 4
[[5,4,2,1],[3,2]] => 3
[[6,5,3,1],[4,3,1]] => 6
[[4,2,2,1],[2]] => 8
[[5,3,3,1],[3,1,1]] => 4
[[5,3,2,1],[3,1]] => 2
[[6,4,3,1],[4,2,1]] => 6
[[6,4,2,1],[4,2]] => 4
[[7,5,3,1],[5,3,1]] => 8
[[3,3,2,2],[1,1,1]] => 4
[[4,4,3,2],[2,2,2]] => 8
[[4,4,2,2],[2,2,1]] => 2
[[5,5,3,2],[3,3,2]] => 4
[[4,3,2,2],[2,1,1]] => 1
[[5,4,3,2],[3,2,2]] => 2
[[5,4,2,2],[3,2,1]] => 3
[[6,5,3,2],[4,3,2]] => 6
[[5,3,2,2],[3,1,1]] => 2
[[6,4,3,2],[4,2,2]] => 4
[[6,4,2,2],[4,2,1]] => 4
[[7,5,3,2],[5,3,2]] => 8
[[2,2,1,1,1],[]] => 8
[[3,3,2,2,1],[1,1,1,1]] => 6
[[3,3,2,1,1],[1,1,1]] => 8
[[4,4,3,2,1],[2,2,2,1]] => 4
[[3,3,1,1,1],[1,1]] => 6
[[4,4,2,2,1],[2,2,1,1]] => 4
[[4,4,2,1,1],[2,2,1]] => 4
[[5,5,3,2,1],[3,3,2,1]] => 2
[[3,2,1,1,1],[1]] => 3
[[4,3,2,2,1],[2,1,1,1]] => 2
[[4,3,2,1,1],[2,1,1]] => 2
[[5,4,3,2,1],[3,2,2,1]] => 1
[[4,3,1,1,1],[2,1]] => 9
[[5,4,2,2,1],[3,2,1,1]] => 6
[[5,4,2,1,1],[3,2,1]] => 6
[[6,5,3,2,1],[4,3,2,1]] => 3
[[4,2,1,1,1],[2]] => 6
[[5,3,2,2,1],[3,1,1,1]] => 4
[[5,3,2,1,1],[3,1,1]] => 4
[[6,4,3,2,1],[4,2,2,1]] => 2
[[5,3,1,1,1],[3,1]] => 12
[[6,4,2,2,1],[4,2,1,1]] => 8
[[6,4,2,1,1],[4,2,1]] => 8
[[7,5,3,2,1],[5,3,2,1]] => 4
[[5,4,4],[3,3]] => 3
[[6,5,4],[4,4]] => 4
[[6,4,4],[4,3]] => 6
[[7,5,4],[5,4]] => 8
[[4,3,3,1],[2,2]] => 1
[[5,4,4,1],[3,3,1]] => 2
[[5,4,3,1],[3,3]] => 2
[[6,5,4,1],[4,4,1]] => 3
[[5,3,3,1],[3,2]] => 2
[[6,4,4,1],[4,3,1]] => 4
[[6,4,3,1],[4,3]] => 4
[[7,5,4,1],[5,4,1]] => 6
[[3,2,2,2],[1,1]] => 4
[[4,3,3,2],[2,2,1]] => 1
[[5,4,4,2],[3,3,2]] => 2
[[4,3,2,2],[2,2]] => 2
[[5,4,3,2],[3,3,1]] => 3
[[6,5,4,2],[4,4,2]] => 4
[[4,2,2,2],[2,1]] => 8
[[5,3,3,2],[3,2,1]] => 2
[[6,4,4,2],[4,3,2]] => 4
[[5,3,2,2],[3,2]] => 4
[[6,4,3,2],[4,3,1]] => 6
[[7,5,4,2],[5,4,2]] => 8
[[3,2,2,1,1],[1,1]] => 5
[[4,3,3,2,1],[2,2,1,1]] => 3
[[4,3,3,1,1],[2,2,1]] => 2
[[5,4,4,2,1],[3,3,2,1]] => 1
[[4,3,2,1,1],[2,2]] => 2
[[5,4,3,2,1],[3,3,1,1]] => 1
[[5,4,3,1,1],[3,3,1]] => 4
[[6,5,4,2,1],[4,4,2,1]] => 2
[[4,2,2,1,1],[2,1]] => 10
[[5,3,3,2,1],[3,2,1,1]] => 6
[[5,3,3,1,1],[3,2,1]] => 4
[[6,4,4,2,1],[4,3,2,1]] => 2
[[5,3,2,1,1],[3,2]] => 4
[[6,4,3,2,1],[4,3,1,1]] => 2
[[6,4,3,1,1],[4,3,1]] => 8
[[7,5,4,2,1],[5,4,2,1]] => 4
[[4,3,3,3],[2,2,2]] => 4
[[5,4,4,3],[3,3,3]] => 6
[[5,4,3,3],[3,3,2]] => 2
[[6,5,4,3],[4,4,3]] => 3
[[5,3,3,3],[3,2,2]] => 8
[[6,4,4,3],[4,3,3]] => 12
[[6,4,3,3],[4,3,2]] => 4
[[7,5,4,3],[5,4,3]] => 6
[[3,2,2,2,1],[1,1,1]] => 5
[[4,3,3,3,1],[2,2,2,1]] => 2
[[4,3,3,2,1],[2,2,2]] => 2
[[5,4,4,3,1],[3,3,3,1]] => 4
[[4,3,2,2,1],[2,2,1]] => 3
[[5,4,3,3,1],[3,3,2,1]] => 1
[[5,4,3,2,1],[3,3,2]] => 1
[[6,5,4,3,1],[4,4,3,1]] => 2
[[4,2,2,2,1],[2,1,1]] => 10
[[5,3,3,3,1],[3,2,2,1]] => 4
[[5,3,3,2,1],[3,2,2]] => 4
[[6,4,4,3,1],[4,3,3,1]] => 8
[[5,3,2,2,1],[3,2,1]] => 6
[[6,4,3,3,1],[4,3,2,1]] => 2
[[6,4,3,2,1],[4,3,2]] => 2
[[7,5,4,3,1],[5,4,3,1]] => 4
[[3,2,2,2,2],[1,1,1,1]] => 3
[[4,3,3,3,2],[2,2,2,2]] => 6
[[4,3,3,2,2],[2,2,2,1]] => 2
[[5,4,4,3,2],[3,3,3,2]] => 4
[[4,3,2,2,2],[2,2,1,1]] => 2
[[5,4,3,3,2],[3,3,2,2]] => 4
[[5,4,3,2,2],[3,3,2,1]] => 1
[[6,5,4,3,2],[4,4,3,2]] => 2
[[4,2,2,2,2],[2,1,1,1]] => 6
[[5,3,3,3,2],[3,2,2,2]] => 12
[[5,3,3,2,2],[3,2,2,1]] => 4
[[6,4,4,3,2],[4,3,3,2]] => 8
[[5,3,2,2,2],[3,2,1,1]] => 4
[[6,4,3,3,2],[4,3,2,2]] => 8
[[6,4,3,2,2],[4,3,2,1]] => 2
[[7,5,4,3,2],[5,4,3,2]] => 4
[[2,1,1,1,1,1],[]] => 5
[[3,2,2,2,2,1],[1,1,1,1,1]] => 4
[[3,2,2,2,1,1],[1,1,1,1]] => 6
[[4,3,3,3,2,1],[2,2,2,2,1]] => 3
[[3,2,2,1,1,1],[1,1,1]] => 6
[[4,3,3,2,2,1],[2,2,2,1,1]] => 4
[[4,3,3,2,1,1],[2,2,2,1]] => 4
[[5,4,4,3,2,1],[3,3,3,2,1]] => 2
[[3,2,1,1,1,1],[1,1]] => 4
[[4,3,2,2,2,1],[2,2,1,1,1]] => 3
[[4,3,2,2,1,1],[2,2,1,1]] => 4
[[5,4,3,3,2,1],[3,3,2,2,1]] => 2
[[4,3,2,1,1,1],[2,2,1]] => 3
[[5,4,3,2,2,1],[3,3,2,1,1]] => 2
[[5,4,3,2,1,1],[3,3,2,1]] => 2
[[6,5,4,3,2,1],[4,4,3,2,1]] => 1
[[3,1,1,1,1,1],[1]] => 10
[[4,2,2,2,2,1],[2,1,1,1,1]] => 8
[[4,2,2,2,1,1],[2,1,1,1]] => 12
[[5,3,3,3,2,1],[3,2,2,2,1]] => 6
[[4,2,2,1,1,1],[2,1,1]] => 12
[[5,3,3,2,2,1],[3,2,2,1,1]] => 8
[[5,3,3,2,1,1],[3,2,2,1]] => 8
[[6,4,4,3,2,1],[4,3,3,2,1]] => 4
[[4,2,1,1,1,1],[2,1]] => 8
[[5,3,2,2,2,1],[3,2,1,1,1]] => 6
[[5,3,2,2,1,1],[3,2,1,1]] => 8
[[6,4,3,3,2,1],[4,3,2,2,1]] => 4
[[5,3,2,1,1,1],[3,2,1]] => 6
[[6,4,3,2,2,1],[4,3,2,1,1]] => 4
[[6,4,3,2,1,1],[4,3,2,1]] => 4
[[7,5,4,3,2,1],[5,4,3,2,1]] => 2
[[6,6],[5]] => 5
[[7,6],[6]] => 6
[[5,5,1],[4]] => 3
[[6,6,1],[5,1]] => 4
[[6,5,1],[5]] => 4
[[7,6,1],[6,1]] => 5
[[4,4,2],[3]] => 4
[[5,5,2],[4,1]] => 5
[[6,6,2],[5,2]] => 6
[[5,4,2],[4]] => 6
[[6,5,2],[5,1]] => 7
[[7,6,2],[6,2]] => 8
[[4,4,1,1],[3]] => 4
[[5,5,2,1],[4,1,1]] => 2
[[5,5,1,1],[4,1]] => 6
[[6,6,2,1],[5,2,1]] => 3
[[5,4,1,1],[4]] => 6
[[6,5,2,1],[5,1,1]] => 3
[[6,5,1,1],[5,1]] => 8
[[7,6,2,1],[6,2,1]] => 4
[[3,3,3],[2]] => 2
[[4,4,3],[3,1]] => 4
[[5,5,3],[4,2]] => 5
[[6,6,3],[5,3]] => 6
[[4,3,3],[3]] => 6
[[5,4,3],[4,1]] => 7
[[6,5,3],[5,2]] => 8
[[7,6,3],[6,3]] => 9
[[3,3,2,1],[2]] => 5
[[4,4,3,1],[3,1,1]] => 2
[[4,4,2,1],[3,1]] => 1
[[5,5,3,1],[4,2,1]] => 3
[[5,5,2,1],[4,2]] => 2
[[6,6,3,1],[5,3,1]] => 4
[[4,3,2,1],[3]] => 1
[[5,4,3,1],[4,1,1]] => 4
[[5,4,2,1],[4,1]] => 2
[[6,5,3,1],[5,2,1]] => 5
[[6,5,2,1],[5,2]] => 3
[[7,6,3,1],[6,3,1]] => 6
[[4,4,2,2],[3,1,1]] => 1
[[5,5,3,2],[4,2,2]] => 2
[[5,5,2,2],[4,2,1]] => 2
[[6,6,3,2],[5,3,2]] => 4
[[5,4,2,2],[4,1,1]] => 2
[[6,5,3,2],[5,2,2]] => 4
[[6,5,2,2],[5,2,1]] => 3
[[7,6,3,2],[6,3,2]] => 6
[[3,3,1,1,1],[2]] => 3
[[4,4,2,2,1],[3,1,1,1]] => 2
[[4,4,2,1,1],[3,1,1]] => 2
[[5,5,3,2,1],[4,2,2,1]] => 1
[[4,4,1,1,1],[3,1]] => 6
[[5,5,2,2,1],[4,2,1,1]] => 4
[[5,5,2,1,1],[4,2,1]] => 4
[[6,6,3,2,1],[5,3,2,1]] => 2
[[4,3,1,1,1],[3]] => 6
[[5,4,2,2,1],[4,1,1,1]] => 4
[[5,4,2,1,1],[4,1,1]] => 4
[[6,5,3,2,1],[5,2,2,1]] => 2
[[5,4,1,1,1],[4,1]] => 9
[[6,5,2,2,1],[5,2,1,1]] => 6
[[6,5,2,1,1],[5,2,1]] => 6
[[7,6,3,2,1],[6,3,2,1]] => 3
[[4,4,4],[3,2]] => 2
[[5,5,4],[4,3]] => 3
[[6,6,4],[5,4]] => 4
[[5,4,4],[4,2]] => 6
[[6,5,4],[5,3]] => 7
[[7,6,4],[6,4]] => 8
[[3,3,3,1],[2,1]] => 5
[[4,4,4,1],[3,2,1]] => 1
[[4,4,3,1],[3,2]] => 1
[[5,5,4,1],[4,3,1]] => 2
[[5,5,3,1],[4,3]] => 2
[[6,6,4,1],[5,4,1]] => 3
[[4,3,3,1],[3,1]] => 2
[[5,4,4,1],[4,2,1]] => 4
[[5,4,3,1],[4,2]] => 3
[[6,5,4,1],[5,3,1]] => 5
[[6,5,3,1],[5,3]] => 4
[[7,6,4,1],[6,4,1]] => 6
[[2,2,2,2],[1]] => 9
[[3,3,3,2],[2,1,1]] => 4
[[4,4,4,2],[3,2,2]] => 8
[[3,3,2,2],[2,1]] => 6
[[4,4,3,2],[3,2,1]] => 1
[[5,5,4,2],[4,3,2]] => 2
[[4,4,2,2],[3,2]] => 2
[[5,5,3,2],[4,3,1]] => 3
[[6,6,4,2],[5,4,2]] => 4
[[3,2,2,2],[2]] => 6
[[4,3,3,2],[3,1,1]] => 2
[[5,4,4,2],[4,2,2]] => 4
[[4,3,2,2],[3,1]] => 2
[[5,4,3,2],[4,2,1]] => 4
[[6,5,4,2],[5,3,2]] => 6
[[5,4,2,2],[4,2]] => 4
[[6,5,3,2],[5,3,1]] => 6
[[7,6,4,2],[6,4,2]] => 8
[[2,2,2,1,1],[1]] => 10
[[3,3,3,2,1],[2,1,1,1]] => 7
[[3,3,3,1,1],[2,1,1]] => 8
[[4,4,4,2,1],[3,2,2,1]] => 4
[[3,3,2,1,1],[2,1]] => 7
[[4,4,3,2,1],[3,2,1,1]] => 4
[[4,4,3,1,1],[3,2,1]] => 2
[[5,5,4,2,1],[4,3,2,1]] => 1
[[4,4,2,1,1],[3,2]] => 2
[[5,5,3,2,1],[4,3,1,1]] => 1
[[5,5,3,1,1],[4,3,1]] => 4
[[6,6,4,2,1],[5,4,2,1]] => 2
[[3,2,2,1,1],[2]] => 6
[[4,3,3,2,1],[3,1,1,1]] => 4
[[4,3,3,1,1],[3,1,1]] => 4
[[5,4,4,2,1],[4,2,2,1]] => 2
[[4,3,2,1,1],[3,1]] => 2
[[5,4,3,2,1],[4,2,1,1]] => 1
[[5,4,3,1,1],[4,2,1]] => 6
[[6,5,4,2,1],[5,3,2,1]] => 3
[[5,4,2,1,1],[4,2]] => 4
[[6,5,3,2,1],[5,3,1,1]] => 2
[[6,5,3,1,1],[5,3,1]] => 8
[[7,6,4,2,1],[6,4,2,1]] => 4
[[4,4,3,3],[3,2,2]] => 6
[[5,5,4,3],[4,3,3]] => 9
[[5,5,3,3],[4,3,2]] => 2
[[6,6,4,3],[5,4,3]] => 3
[[5,4,3,3],[4,2,2]] => 2
[[6,5,4,3],[5,3,3]] => 3
[[6,5,3,3],[5,3,2]] => 4
[[7,6,4,3],[6,4,3]] => 6
[[3,3,2,2,1],[2,1,1]] => 8
[[4,4,3,3,1],[3,2,2,1]] => 3
[[4,4,3,2,1],[3,2,2]] => 3
[[5,5,4,3,1],[4,3,3,1]] => 6
[[4,4,2,2,1],[3,2,1]] => 3
[[5,5,3,3,1],[4,3,2,1]] => 1
[[5,5,3,2,1],[4,3,2]] => 1
[[6,6,4,3,1],[5,4,3,1]] => 2
[[4,3,2,2,1],[3,1,1]] => 3
[[5,4,3,3,1],[4,2,2,1]] => 1
[[5,4,3,2,1],[4,2,2]] => 1
[[6,5,4,3,1],[5,3,3,1]] => 2
[[5,4,2,2,1],[4,2,1]] => 6
[[6,5,3,3,1],[5,3,2,1]] => 2
[[6,5,3,2,1],[5,3,2]] => 2
[[7,6,4,3,1],[6,4,3,1]] => 4
[[3,3,2,2,2],[2,1,1,1]] => 5
[[4,4,3,3,2],[3,2,2,2]] => 10
[[4,4,3,2,2],[3,2,2,1]] => 3
[[5,5,4,3,2],[4,3,3,2]] => 6
[[4,4,2,2,2],[3,2,1,1]] => 2
[[5,5,3,3,2],[4,3,2,2]] => 4
[[5,5,3,2,2],[4,3,2,1]] => 1
[[6,6,4,3,2],[5,4,3,2]] => 2
[[4,3,2,2,2],[3,1,1,1]] => 2
[[5,4,3,3,2],[4,2,2,2]] => 4
[[5,4,3,2,2],[4,2,2,1]] => 1
[[6,5,4,3,2],[5,3,3,2]] => 2
[[5,4,2,2,2],[4,2,1,1]] => 4
[[6,5,3,3,2],[5,3,2,2]] => 8
[[6,5,3,2,2],[5,3,2,1]] => 2
[[7,6,4,3,2],[6,4,3,2]] => 4
[[2,2,1,1,1,1],[1]] => 9
[[3,3,2,2,2,1],[2,1,1,1,1]] => 7
[[3,3,2,2,1,1],[2,1,1,1]] => 10
[[4,4,3,3,2,1],[3,2,2,2,1]] => 5
[[3,3,2,1,1,1],[2,1,1]] => 9
[[4,4,3,2,2,1],[3,2,2,1,1]] => 6
[[4,4,3,2,1,1],[3,2,2,1]] => 6
[[5,5,4,3,2,1],[4,3,3,2,1]] => 3
[[3,3,1,1,1,1],[2,1]] => 4
[[4,4,2,2,2,1],[3,2,1,1,1]] => 3
[[4,4,2,2,1,1],[3,2,1,1]] => 4
[[5,5,3,3,2,1],[4,3,2,2,1]] => 2
[[4,4,2,1,1,1],[3,2,1]] => 3
[[5,5,3,2,2,1],[4,3,2,1,1]] => 2
[[5,5,3,2,1,1],[4,3,2,1]] => 2
[[6,6,4,3,2,1],[5,4,3,2,1]] => 1
[[3,2,1,1,1,1],[2]] => 4
[[4,3,2,2,2,1],[3,1,1,1,1]] => 3
[[4,3,2,2,1,1],[3,1,1,1]] => 4
[[5,4,3,3,2,1],[4,2,2,2,1]] => 2
[[4,3,2,1,1,1],[3,1,1]] => 3
[[5,4,3,2,2,1],[4,2,2,1,1]] => 2
[[5,4,3,2,1,1],[4,2,2,1]] => 2
[[6,5,4,3,2,1],[5,3,3,2,1]] => 1
[[4,3,1,1,1,1],[3,1]] => 8
[[5,4,2,2,2,1],[4,2,1,1,1]] => 6
[[5,4,2,2,1,1],[4,2,1,1]] => 8
[[6,5,3,3,2,1],[5,3,2,2,1]] => 4
[[5,4,2,1,1,1],[4,2,1]] => 6
[[6,5,3,2,2,1],[5,3,2,1,1]] => 4
[[6,5,3,2,1,1],[5,3,2,1]] => 4
[[7,6,4,3,2,1],[6,4,3,2,1]] => 2
[[5,5,5],[4,4]] => 8
[[6,6,5],[5,5]] => 10
[[6,5,5],[5,4]] => 4
[[7,6,5],[6,5]] => 5
[[4,4,4,1],[3,3]] => 4
[[5,5,5,1],[4,4,1]] => 6
[[5,5,4,1],[4,4]] => 6
[[6,6,5,1],[5,5,1]] => 8
[[5,4,4,1],[4,3]] => 2
[[6,5,5,1],[5,4,1]] => 3
[[6,5,4,1],[5,4]] => 3
[[7,6,5,1],[6,5,1]] => 4
[[3,3,3,2],[2,2]] => 4
[[4,4,4,2],[3,3,1]] => 6
[[5,5,5,2],[4,4,2]] => 8
[[4,4,3,2],[3,3]] => 8
[[5,5,4,2],[4,4,1]] => 10
[[6,6,5,2],[5,5,2]] => 12
[[4,3,3,2],[3,2]] => 2
[[5,4,4,2],[4,3,1]] => 3
[[6,5,5,2],[5,4,2]] => 4
[[5,4,3,2],[4,3]] => 4
[[6,5,4,2],[5,4,1]] => 5
[[7,6,5,2],[6,5,2]] => 6
[[3,3,3,1,1],[2,2]] => 4
[[4,4,4,2,1],[3,3,1,1]] => 2
[[4,4,4,1,1],[3,3,1]] => 8
[[5,5,5,2,1],[4,4,2,1]] => 4
[[4,4,3,1,1],[3,3]] => 8
[[5,5,4,2,1],[4,4,1,1]] => 4
[[5,5,4,1,1],[4,4,1]] => 12
[[6,6,5,2,1],[5,5,2,1]] => 6
[[4,3,3,1,1],[3,2]] => 2
[[5,4,4,2,1],[4,3,1,1]] => 1
[[5,4,4,1,1],[4,3,1]] => 4
[[6,5,5,2,1],[5,4,2,1]] => 2
[[5,4,3,1,1],[4,3]] => 4
[[6,5,4,2,1],[5,4,1,1]] => 2
[[6,5,4,1,1],[5,4,1]] => 6
[[7,6,5,2,1],[6,5,2,1]] => 3
[[3,3,3,3],[2,2,1]] => 2
[[4,4,4,3],[3,3,2]] => 4
[[5,5,5,3],[4,4,3]] => 6
[[4,4,3,3],[3,3,1]] => 8
[[5,5,4,3],[4,4,2]] => 10
[[6,6,5,3],[5,5,3]] => 12
[[4,3,3,3],[3,2,1]] => 1
[[5,4,4,3],[4,3,2]] => 2
[[6,5,5,3],[5,4,3]] => 3
[[5,4,3,3],[4,3,1]] => 4
[[6,5,4,3],[5,4,2]] => 5
[[7,6,5,3],[6,5,3]] => 6
[[2,2,2,2,1],[1,1]] => 10
[[3,3,3,3,1],[2,2,1,1]] => 6
[[3,3,3,2,1],[2,2,1]] => 7
[[4,4,4,3,1],[3,3,2,1]] => 2
[[4,4,4,2,1],[3,3,2]] => 2
[[5,5,5,3,1],[4,4,3,1]] => 4
[[3,3,2,2,1],[2,2]] => 8
[[4,4,3,3,1],[3,3,1,1]] => 4
[[4,4,3,2,1],[3,3,1]] => 2
[[5,5,4,3,1],[4,4,2,1]] => 6
[[5,5,4,2,1],[4,4,2]] => 4
[[6,6,5,3,1],[5,5,3,1]] => 8
[[3,2,2,2,1],[2,1]] => 7
[[4,3,3,3,1],[3,2,1,1]] => 4
[[4,3,3,2,1],[3,2,1]] => 4
[[5,4,4,3,1],[4,3,2,1]] => 1
[[5,4,4,2,1],[4,3,2]] => 1
[[6,5,5,3,1],[5,4,3,1]] => 2
[[4,3,2,2,1],[3,2]] => 4
[[5,4,3,3,1],[4,3,1,1]] => 2
[[5,4,3,2,1],[4,3,1]] => 1
[[6,5,4,3,1],[5,4,2,1]] => 3
[[6,5,4,2,1],[5,4,2]] => 2
[[7,6,5,3,1],[6,5,3,1]] => 4
[[3,3,3,2,2],[2,2,1,1]] => 5
[[4,4,4,3,2],[3,3,2,2]] => 10
[[4,4,4,2,2],[3,3,2,1]] => 2
[[5,5,5,3,2],[4,4,3,2]] => 4
[[4,4,3,2,2],[3,3,1,1]] => 2
[[5,5,4,3,2],[4,4,2,2]] => 4
[[5,5,4,2,2],[4,4,2,1]] => 4
[[6,6,5,3,2],[5,5,3,2]] => 8
[[4,3,3,2,2],[3,2,1,1]] => 3
[[5,4,4,3,2],[4,3,2,2]] => 6
[[5,4,4,2,2],[4,3,2,1]] => 1
[[6,5,5,3,2],[5,4,3,2]] => 2
[[5,4,3,2,2],[4,3,1,1]] => 1
[[6,5,4,3,2],[5,4,2,2]] => 2
[[6,5,4,2,2],[5,4,2,1]] => 2
[[7,6,5,3,2],[6,5,3,2]] => 4
[[2,2,2,1,1,1],[1,1]] => 11
[[3,3,3,2,2,1],[2,2,1,1,1]] => 8
[[3,3,3,2,1,1],[2,2,1,1]] => 10
[[4,4,4,3,2,1],[3,3,2,2,1]] => 5
[[3,3,3,1,1,1],[2,2,1]] => 6
[[4,4,4,2,2,1],[3,3,2,1,1]] => 4
[[4,4,4,2,1,1],[3,3,2,1]] => 4
[[5,5,5,3,2,1],[4,4,3,2,1]] => 2
[[3,3,2,1,1,1],[2,2]] => 6
[[4,4,3,2,2,1],[3,3,1,1,1]] => 4
[[4,4,3,2,1,1],[3,3,1,1]] => 4
[[5,5,4,3,2,1],[4,4,2,2,1]] => 2
[[4,4,3,1,1,1],[3,3,1]] => 12
[[5,5,4,2,2,1],[4,4,2,1,1]] => 8
[[5,5,4,2,1,1],[4,4,2,1]] => 8
[[6,6,5,3,2,1],[5,5,3,2,1]] => 4
[[3,2,2,1,1,1],[2,1]] => 7
[[4,3,3,2,2,1],[3,2,1,1,1]] => 5
[[4,3,3,2,1,1],[3,2,1,1]] => 6
[[5,4,4,3,2,1],[4,3,2,2,1]] => 3
[[4,3,3,1,1,1],[3,2,1]] => 3
[[5,4,4,2,2,1],[4,3,2,1,1]] => 2
[[5,4,4,2,1,1],[4,3,2,1]] => 2
[[6,5,5,3,2,1],[5,4,3,2,1]] => 1
[[4,3,2,1,1,1],[3,2]] => 3
[[5,4,3,2,2,1],[4,3,1,1,1]] => 2
[[5,4,3,2,1,1],[4,3,1,1]] => 2
[[6,5,4,3,2,1],[5,4,2,2,1]] => 1
[[5,4,3,1,1,1],[4,3,1]] => 6
[[6,5,4,2,2,1],[5,4,2,1,1]] => 4
[[6,5,4,2,1,1],[5,4,2,1]] => 4
[[7,6,5,3,2,1],[6,5,3,2,1]] => 2
[[4,4,4,4],[3,3,3]] => 9
[[5,5,5,4],[4,4,4]] => 12
[[5,5,4,4],[4,4,3]] => 6
[[6,6,5,4],[5,5,4]] => 8
[[5,4,4,4],[4,3,3]] => 6
[[6,5,5,4],[5,4,4]] => 8
[[6,5,4,4],[5,4,3]] => 3
[[7,6,5,4],[6,5,4]] => 4
[[3,3,3,3,1],[2,2,2]] => 3
[[4,4,4,4,1],[3,3,3,1]] => 6
[[4,4,4,3,1],[3,3,3]] => 6
[[5,5,5,4,1],[4,4,4,1]] => 9
[[4,4,3,3,1],[3,3,2]] => 2
[[5,5,4,4,1],[4,4,3,1]] => 4
[[5,5,4,3,1],[4,4,3]] => 4
[[6,6,5,4,1],[5,5,4,1]] => 6
[[4,3,3,3,1],[3,2,2]] => 2
[[5,4,4,4,1],[4,3,3,1]] => 4
[[5,4,4,3,1],[4,3,3]] => 4
[[6,5,5,4,1],[5,4,4,1]] => 6
[[5,4,3,3,1],[4,3,2]] => 1
[[6,5,4,4,1],[5,4,3,1]] => 2
[[6,5,4,3,1],[5,4,3]] => 2
[[7,6,5,4,1],[6,5,4,1]] => 3
[[2,2,2,2,2],[1,1,1]] => 8
[[3,3,3,3,2],[2,2,2,1]] => 3
[[4,4,4,4,2],[3,3,3,2]] => 6
[[3,3,3,2,2],[2,2,2]] => 6
[[4,4,4,3,2],[3,3,3,1]] => 9
[[5,5,5,4,2],[4,4,4,2]] => 12
[[3,3,2,2,2],[2,2,1]] => 8
[[4,4,3,3,2],[3,3,2,1]] => 2
[[5,5,4,4,2],[4,4,3,2]] => 4
[[4,4,3,2,2],[3,3,2]] => 4
[[5,5,4,3,2],[4,4,3,1]] => 6
[[6,6,5,4,2],[5,5,4,2]] => 8
[[3,2,2,2,2],[2,1,1]] => 6
[[4,3,3,3,2],[3,2,2,1]] => 2
[[5,4,4,4,2],[4,3,3,2]] => 4
[[4,3,3,2,2],[3,2,2]] => 4
[[5,4,4,3,2],[4,3,3,1]] => 6
[[6,5,5,4,2],[5,4,4,2]] => 8
[[4,3,2,2,2],[3,2,1]] => 4
[[5,4,3,3,2],[4,3,2,1]] => 1
[[6,5,4,4,2],[5,4,3,2]] => 2
[[5,4,3,2,2],[4,3,2]] => 2
[[6,5,4,3,2],[5,4,3,1]] => 3
[[7,6,5,4,2],[6,5,4,2]] => 4
[[2,2,2,2,1,1],[1,1,1]] => 11
[[3,3,3,3,2,1],[2,2,2,1,1]] => 7
[[3,3,3,3,1,1],[2,2,2,1]] => 6
[[4,4,4,4,2,1],[3,3,3,2,1]] => 3
[[3,3,3,2,1,1],[2,2,2]] => 6
[[4,4,4,3,2,1],[3,3,3,1,1]] => 3
[[4,4,4,3,1,1],[3,3,3,1]] => 12
[[5,5,5,4,2,1],[4,4,4,2,1]] => 6
[[3,3,2,2,1,1],[2,2,1]] => 10
[[4,4,3,3,2,1],[3,3,2,1,1]] => 6
[[4,4,3,3,1,1],[3,3,2,1]] => 4
[[5,5,4,4,2,1],[4,4,3,2,1]] => 2
[[4,4,3,2,1,1],[3,3,2]] => 4
[[5,5,4,3,2,1],[4,4,3,1,1]] => 2
[[5,5,4,3,1,1],[4,4,3,1]] => 8
[[6,6,5,4,2,1],[5,5,4,2,1]] => 4
[[3,2,2,2,1,1],[2,1,1]] => 8
[[4,3,3,3,2,1],[3,2,2,1,1]] => 5
[[4,3,3,3,1,1],[3,2,2,1]] => 4
[[5,4,4,4,2,1],[4,3,3,2,1]] => 2
[[4,3,3,2,1,1],[3,2,2]] => 4
[[5,4,4,3,2,1],[4,3,3,1,1]] => 2
[[5,4,4,3,1,1],[4,3,3,1]] => 8
[[6,5,5,4,2,1],[5,4,4,2,1]] => 4
[[4,3,2,2,1,1],[3,2,1]] => 5
[[5,4,3,3,2,1],[4,3,2,1,1]] => 3
[[5,4,3,3,1,1],[4,3,2,1]] => 2
[[6,5,4,4,2,1],[5,4,3,2,1]] => 1
[[5,4,3,2,1,1],[4,3,2]] => 2
[[6,5,4,3,2,1],[5,4,3,1,1]] => 1
[[6,5,4,3,1,1],[5,4,3,1]] => 4
[[7,6,5,4,2,1],[6,5,4,2,1]] => 2
[[3,3,3,3,3],[2,2,2,2]] => 8
[[4,4,4,4,3],[3,3,3,3]] => 12
[[4,4,4,3,3],[3,3,3,2]] => 6
[[5,5,5,4,3],[4,4,4,3]] => 9
[[4,4,3,3,3],[3,3,2,2]] => 8
[[5,5,4,4,3],[4,4,3,3]] => 12
[[5,5,4,3,3],[4,4,3,2]] => 4
[[6,6,5,4,3],[5,5,4,3]] => 6
[[4,3,3,3,3],[3,2,2,2]] => 6
[[5,4,4,4,3],[4,3,3,3]] => 9
[[5,4,4,3,3],[4,3,3,2]] => 4
[[6,5,5,4,3],[5,4,4,3]] => 6
[[5,4,3,3,3],[4,3,2,2]] => 4
[[6,5,4,4,3],[5,4,3,3]] => 6
[[6,5,4,3,3],[5,4,3,2]] => 2
[[7,6,5,4,3],[6,5,4,3]] => 3
[[2,2,2,2,2,1],[1,1,1,1]] => 9
[[3,3,3,3,3,1],[2,2,2,2,1]] => 4
[[3,3,3,3,2,1],[2,2,2,2]] => 4
[[4,4,4,4,3,1],[3,3,3,3,1]] => 8
[[3,3,3,2,2,1],[2,2,2,1]] => 9
[[4,4,4,3,3,1],[3,3,3,2,1]] => 3
[[4,4,4,3,2,1],[3,3,3,2]] => 3
[[5,5,5,4,3,1],[4,4,4,3,1]] => 6
[[3,3,2,2,2,1],[2,2,1,1]] => 10
[[4,4,3,3,3,1],[3,3,2,2,1]] => 4
[[4,4,3,3,2,1],[3,3,2,2]] => 4
[[5,5,4,4,3,1],[4,4,3,3,1]] => 8
[[4,4,3,2,2,1],[3,3,2,1]] => 6
[[5,5,4,3,3,1],[4,4,3,2,1]] => 2
[[5,5,4,3,2,1],[4,4,3,2]] => 2
[[6,6,5,4,3,1],[5,5,4,3,1]] => 4
[[3,2,2,2,2,1],[2,1,1,1]] => 7
[[4,3,3,3,3,1],[3,2,2,2,1]] => 3
[[4,3,3,3,2,1],[3,2,2,2]] => 3
[[5,4,4,4,3,1],[4,3,3,3,1]] => 6
[[4,3,3,2,2,1],[3,2,2,1]] => 6
[[5,4,4,3,3,1],[4,3,3,2,1]] => 2
[[5,4,4,3,2,1],[4,3,3,2]] => 2
[[6,5,5,4,3,1],[5,4,4,3,1]] => 4
[[4,3,2,2,2,1],[3,2,1,1]] => 5
[[5,4,3,3,3,1],[4,3,2,2,1]] => 2
[[5,4,3,3,2,1],[4,3,2,2]] => 2
[[6,5,4,4,3,1],[5,4,3,3,1]] => 4
[[5,4,3,2,2,1],[4,3,2,1]] => 3
[[6,5,4,3,3,1],[5,4,3,2,1]] => 1
[[6,5,4,3,2,1],[5,4,3,2]] => 1
[[7,6,5,4,3,1],[6,5,4,3,1]] => 2
[[2,2,2,2,2,2],[1,1,1,1,1]] => 5
[[3,3,3,3,3,2],[2,2,2,2,2]] => 10
[[3,3,3,3,2,2],[2,2,2,2,1]] => 4
[[4,4,4,4,3,2],[3,3,3,3,2]] => 8
[[3,3,3,2,2,2],[2,2,2,1,1]] => 6
[[4,4,4,3,3,2],[3,3,3,2,2]] => 12
[[4,4,4,3,2,2],[3,3,3,2,1]] => 3
[[5,5,5,4,3,2],[4,4,4,3,2]] => 6
[[3,3,2,2,2,2],[2,2,1,1,1]] => 6
[[4,4,3,3,3,2],[3,3,2,2,2]] => 12
[[4,4,3,3,2,2],[3,3,2,2,1]] => 4
[[5,5,4,4,3,2],[4,4,3,3,2]] => 8
[[4,4,3,2,2,2],[3,3,2,1,1]] => 4
[[5,5,4,3,3,2],[4,4,3,2,2]] => 8
[[5,5,4,3,2,2],[4,4,3,2,1]] => 2
[[6,6,5,4,3,2],[5,5,4,3,2]] => 4
[[3,2,2,2,2,2],[2,1,1,1,1]] => 4
[[4,3,3,3,3,2],[3,2,2,2,2]] => 8
[[4,3,3,3,2,2],[3,2,2,2,1]] => 3
[[5,4,4,4,3,2],[4,3,3,3,2]] => 6
[[4,3,3,2,2,2],[3,2,2,1,1]] => 4
[[5,4,4,3,3,2],[4,3,3,2,2]] => 8
[[5,4,4,3,2,2],[4,3,3,2,1]] => 2
[[6,5,5,4,3,2],[5,4,4,3,2]] => 4
[[4,3,2,2,2,2],[3,2,1,1,1]] => 3
[[5,4,3,3,3,2],[4,3,2,2,2]] => 6
[[5,4,3,3,2,2],[4,3,2,2,1]] => 2
[[6,5,4,4,3,2],[5,4,3,3,2]] => 4
[[5,4,3,2,2,2],[4,3,2,1,1]] => 2
[[6,5,4,3,3,2],[5,4,3,2,2]] => 4
[[6,5,4,3,2,2],[5,4,3,2,1]] => 1
[[7,6,5,4,3,2],[6,5,4,3,2]] => 2
[[1,1,1,1,1,1,1],[]] => 7
[[2,2,2,2,2,2,1],[1,1,1,1,1,1]] => 6
[[2,2,2,2,2,1,1],[1,1,1,1,1]] => 10
[[3,3,3,3,3,2,1],[2,2,2,2,2,1]] => 5
[[2,2,2,2,1,1,1],[1,1,1,1]] => 12
[[3,3,3,3,2,2,1],[2,2,2,2,1,1]] => 8
[[3,3,3,3,2,1,1],[2,2,2,2,1]] => 8
[[4,4,4,4,3,2,1],[3,3,3,3,2,1]] => 4
[[2,2,2,1,1,1,1],[1,1,1]] => 12
[[3,3,3,2,2,2,1],[2,2,2,1,1,1]] => 9
[[3,3,3,2,2,1,1],[2,2,2,1,1]] => 12
[[4,4,4,3,3,2,1],[3,3,3,2,2,1]] => 6
[[3,3,3,2,1,1,1],[2,2,2,1]] => 9
[[4,4,4,3,2,2,1],[3,3,3,2,1,1]] => 6
-----------------------------------------------------------------------------
Created: Dec 22, 2020 at 14:22 by Martin Rubey
-----------------------------------------------------------------------------
Last Updated: Dec 22, 2020 at 14:22 by Martin Rubey