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-----------------------------------------------------------------------------
Statistic identifier: St000016
-----------------------------------------------------------------------------
Collection: Standard tableaux
-----------------------------------------------------------------------------
Description: The number of attacking pairs of a standard tableau.
Note that this is actually a statistic on the underlying partition.
A pair of cells $(c, d)$ of a Young diagram (in English notation) is said to be attacking if one of the following conditions holds:
1. $c$ and $d$ lie in the same row with $c$ strictly to the west of $d$.
2. $c$ is in the row immediately to the south of $d$, and $c$ lies strictly east of $d$.
-----------------------------------------------------------------------------
References:
-----------------------------------------------------------------------------
Code:
def statistic(x):
return len(x.shape().attacking_pairs())
-----------------------------------------------------------------------------
Statistic values:
[[1]] => 0
[[1,2]] => 1
[[1],[2]] => 0
[[1,2,3]] => 3
[[1,3],[2]] => 1
[[1,2],[3]] => 1
[[1],[2],[3]] => 0
[[1,2,3,4]] => 6
[[1,3,4],[2]] => 3
[[1,2,4],[3]] => 3
[[1,2,3],[4]] => 3
[[1,3],[2,4]] => 3
[[1,2],[3,4]] => 3
[[1,4],[2],[3]] => 1
[[1,3],[2],[4]] => 1
[[1,2],[3],[4]] => 1
[[1],[2],[3],[4]] => 0
[[1,2,3,4,5]] => 10
[[1,3,4,5],[2]] => 6
[[1,2,4,5],[3]] => 6
[[1,2,3,5],[4]] => 6
[[1,2,3,4],[5]] => 6
[[1,3,5],[2,4]] => 5
[[1,2,5],[3,4]] => 5
[[1,3,4],[2,5]] => 5
[[1,2,4],[3,5]] => 5
[[1,2,3],[4,5]] => 5
[[1,4,5],[2],[3]] => 3
[[1,3,5],[2],[4]] => 3
[[1,2,5],[3],[4]] => 3
[[1,3,4],[2],[5]] => 3
[[1,2,4],[3],[5]] => 3
[[1,2,3],[4],[5]] => 3
[[1,4],[2,5],[3]] => 3
[[1,3],[2,5],[4]] => 3
[[1,2],[3,5],[4]] => 3
[[1,3],[2,4],[5]] => 3
[[1,2],[3,4],[5]] => 3
[[1,5],[2],[3],[4]] => 1
[[1,4],[2],[3],[5]] => 1
[[1,3],[2],[4],[5]] => 1
[[1,2],[3],[4],[5]] => 1
[[1],[2],[3],[4],[5]] => 0
[[1,2,3,4,5,6]] => 15
[[1,3,4,5,6],[2]] => 10
[[1,2,4,5,6],[3]] => 10
[[1,2,3,5,6],[4]] => 10
[[1,2,3,4,6],[5]] => 10
[[1,2,3,4,5],[6]] => 10
[[1,3,5,6],[2,4]] => 8
[[1,2,5,6],[3,4]] => 8
[[1,3,4,6],[2,5]] => 8
[[1,2,4,6],[3,5]] => 8
[[1,2,3,6],[4,5]] => 8
[[1,3,4,5],[2,6]] => 8
[[1,2,4,5],[3,6]] => 8
[[1,2,3,5],[4,6]] => 8
[[1,2,3,4],[5,6]] => 8
[[1,4,5,6],[2],[3]] => 6
[[1,3,5,6],[2],[4]] => 6
[[1,2,5,6],[3],[4]] => 6
[[1,3,4,6],[2],[5]] => 6
[[1,2,4,6],[3],[5]] => 6
[[1,2,3,6],[4],[5]] => 6
[[1,3,4,5],[2],[6]] => 6
[[1,2,4,5],[3],[6]] => 6
[[1,2,3,5],[4],[6]] => 6
[[1,2,3,4],[5],[6]] => 6
[[1,3,5],[2,4,6]] => 9
[[1,2,5],[3,4,6]] => 9
[[1,3,4],[2,5,6]] => 9
[[1,2,4],[3,5,6]] => 9
[[1,2,3],[4,5,6]] => 9
[[1,4,6],[2,5],[3]] => 5
[[1,3,6],[2,5],[4]] => 5
[[1,2,6],[3,5],[4]] => 5
[[1,3,6],[2,4],[5]] => 5
[[1,2,6],[3,4],[5]] => 5
[[1,4,5],[2,6],[3]] => 5
[[1,3,5],[2,6],[4]] => 5
[[1,2,5],[3,6],[4]] => 5
[[1,3,4],[2,6],[5]] => 5
[[1,2,4],[3,6],[5]] => 5
[[1,2,3],[4,6],[5]] => 5
[[1,3,5],[2,4],[6]] => 5
[[1,2,5],[3,4],[6]] => 5
[[1,3,4],[2,5],[6]] => 5
[[1,2,4],[3,5],[6]] => 5
[[1,2,3],[4,5],[6]] => 5
[[1,5,6],[2],[3],[4]] => 3
[[1,4,6],[2],[3],[5]] => 3
[[1,3,6],[2],[4],[5]] => 3
[[1,2,6],[3],[4],[5]] => 3
[[1,4,5],[2],[3],[6]] => 3
[[1,3,5],[2],[4],[6]] => 3
[[1,2,5],[3],[4],[6]] => 3
[[1,3,4],[2],[5],[6]] => 3
[[1,2,4],[3],[5],[6]] => 3
[[1,2,3],[4],[5],[6]] => 3
[[1,4],[2,5],[3,6]] => 5
[[1,3],[2,5],[4,6]] => 5
[[1,2],[3,5],[4,6]] => 5
[[1,3],[2,4],[5,6]] => 5
[[1,2],[3,4],[5,6]] => 5
[[1,5],[2,6],[3],[4]] => 3
[[1,4],[2,6],[3],[5]] => 3
[[1,3],[2,6],[4],[5]] => 3
[[1,2],[3,6],[4],[5]] => 3
[[1,4],[2,5],[3],[6]] => 3
[[1,3],[2,5],[4],[6]] => 3
[[1,2],[3,5],[4],[6]] => 3
[[1,3],[2,4],[5],[6]] => 3
[[1,2],[3,4],[5],[6]] => 3
[[1,6],[2],[3],[4],[5]] => 1
[[1,5],[2],[3],[4],[6]] => 1
[[1,4],[2],[3],[5],[6]] => 1
[[1,3],[2],[4],[5],[6]] => 1
[[1,2],[3],[4],[5],[6]] => 1
[[1],[2],[3],[4],[5],[6]] => 0
[[1,2,3,4,5,6,7]] => 21
[[1,3,4,5,6,7],[2]] => 15
[[1,2,4,5,6,7],[3]] => 15
[[1,2,3,5,6,7],[4]] => 15
[[1,2,3,4,6,7],[5]] => 15
[[1,2,3,4,5,7],[6]] => 15
[[1,2,3,4,5,6],[7]] => 15
[[1,3,5,6,7],[2,4]] => 12
[[1,2,5,6,7],[3,4]] => 12
[[1,3,4,6,7],[2,5]] => 12
[[1,2,4,6,7],[3,5]] => 12
[[1,2,3,6,7],[4,5]] => 12
[[1,3,4,5,7],[2,6]] => 12
[[1,2,4,5,7],[3,6]] => 12
[[1,2,3,5,7],[4,6]] => 12
[[1,2,3,4,7],[5,6]] => 12
[[1,3,4,5,6],[2,7]] => 12
[[1,2,4,5,6],[3,7]] => 12
[[1,2,3,5,6],[4,7]] => 12
[[1,2,3,4,6],[5,7]] => 12
[[1,2,3,4,5],[6,7]] => 12
[[1,4,5,6,7],[2],[3]] => 10
[[1,3,5,6,7],[2],[4]] => 10
[[1,2,5,6,7],[3],[4]] => 10
[[1,3,4,6,7],[2],[5]] => 10
[[1,2,4,6,7],[3],[5]] => 10
[[1,2,3,6,7],[4],[5]] => 10
[[1,3,4,5,7],[2],[6]] => 10
[[1,2,4,5,7],[3],[6]] => 10
[[1,2,3,5,7],[4],[6]] => 10
[[1,2,3,4,7],[5],[6]] => 10
[[1,3,4,5,6],[2],[7]] => 10
[[1,2,4,5,6],[3],[7]] => 10
[[1,2,3,5,6],[4],[7]] => 10
[[1,2,3,4,6],[5],[7]] => 10
[[1,2,3,4,5],[6],[7]] => 10
[[1,3,5,7],[2,4,6]] => 12
[[1,2,5,7],[3,4,6]] => 12
[[1,3,4,7],[2,5,6]] => 12
[[1,2,4,7],[3,5,6]] => 12
[[1,2,3,7],[4,5,6]] => 12
[[1,3,5,6],[2,4,7]] => 12
[[1,2,5,6],[3,4,7]] => 12
[[1,3,4,6],[2,5,7]] => 12
[[1,2,4,6],[3,5,7]] => 12
[[1,2,3,6],[4,5,7]] => 12
[[1,3,4,5],[2,6,7]] => 12
[[1,2,4,5],[3,6,7]] => 12
[[1,2,3,5],[4,6,7]] => 12
[[1,2,3,4],[5,6,7]] => 12
[[1,4,6,7],[2,5],[3]] => 8
[[1,3,6,7],[2,5],[4]] => 8
[[1,2,6,7],[3,5],[4]] => 8
[[1,3,6,7],[2,4],[5]] => 8
[[1,2,6,7],[3,4],[5]] => 8
[[1,4,5,7],[2,6],[3]] => 8
[[1,3,5,7],[2,6],[4]] => 8
[[1,2,5,7],[3,6],[4]] => 8
[[1,3,4,7],[2,6],[5]] => 8
[[1,2,4,7],[3,6],[5]] => 8
[[1,2,3,7],[4,6],[5]] => 8
[[1,3,5,7],[2,4],[6]] => 8
[[1,2,5,7],[3,4],[6]] => 8
[[1,3,4,7],[2,5],[6]] => 8
[[1,2,4,7],[3,5],[6]] => 8
[[1,2,3,7],[4,5],[6]] => 8
[[1,4,5,6],[2,7],[3]] => 8
[[1,3,5,6],[2,7],[4]] => 8
[[1,2,5,6],[3,7],[4]] => 8
[[1,3,4,6],[2,7],[5]] => 8
[[1,2,4,6],[3,7],[5]] => 8
[[1,2,3,6],[4,7],[5]] => 8
[[1,3,4,5],[2,7],[6]] => 8
[[1,2,4,5],[3,7],[6]] => 8
[[1,2,3,5],[4,7],[6]] => 8
[[1,2,3,4],[5,7],[6]] => 8
[[1,3,5,6],[2,4],[7]] => 8
[[1,2,5,6],[3,4],[7]] => 8
[[1,3,4,6],[2,5],[7]] => 8
[[1,2,4,6],[3,5],[7]] => 8
[[1,2,3,6],[4,5],[7]] => 8
[[1,3,4,5],[2,6],[7]] => 8
[[1,2,4,5],[3,6],[7]] => 8
[[1,2,3,5],[4,6],[7]] => 8
[[1,2,3,4],[5,6],[7]] => 8
[[1,5,6,7],[2],[3],[4]] => 6
[[1,4,6,7],[2],[3],[5]] => 6
[[1,3,6,7],[2],[4],[5]] => 6
[[1,2,6,7],[3],[4],[5]] => 6
[[1,4,5,7],[2],[3],[6]] => 6
[[1,3,5,7],[2],[4],[6]] => 6
[[1,2,5,7],[3],[4],[6]] => 6
[[1,3,4,7],[2],[5],[6]] => 6
[[1,2,4,7],[3],[5],[6]] => 6
[[1,2,3,7],[4],[5],[6]] => 6
[[1,4,5,6],[2],[3],[7]] => 6
[[1,3,5,6],[2],[4],[7]] => 6
[[1,2,5,6],[3],[4],[7]] => 6
[[1,3,4,6],[2],[5],[7]] => 6
[[1,2,4,6],[3],[5],[7]] => 6
[[1,2,3,6],[4],[5],[7]] => 6
[[1,3,4,5],[2],[6],[7]] => 6
[[1,2,4,5],[3],[6],[7]] => 6
[[1,2,3,5],[4],[6],[7]] => 6
[[1,2,3,4],[5],[6],[7]] => 6
[[1,4,6],[2,5,7],[3]] => 9
[[1,3,6],[2,5,7],[4]] => 9
[[1,2,6],[3,5,7],[4]] => 9
[[1,3,6],[2,4,7],[5]] => 9
[[1,2,6],[3,4,7],[5]] => 9
[[1,4,5],[2,6,7],[3]] => 9
[[1,3,5],[2,6,7],[4]] => 9
[[1,2,5],[3,6,7],[4]] => 9
[[1,3,4],[2,6,7],[5]] => 9
[[1,2,4],[3,6,7],[5]] => 9
[[1,2,3],[4,6,7],[5]] => 9
[[1,3,5],[2,4,7],[6]] => 9
[[1,2,5],[3,4,7],[6]] => 9
[[1,3,4],[2,5,7],[6]] => 9
[[1,2,4],[3,5,7],[6]] => 9
[[1,2,3],[4,5,7],[6]] => 9
[[1,3,5],[2,4,6],[7]] => 9
[[1,2,5],[3,4,6],[7]] => 9
[[1,3,4],[2,5,6],[7]] => 9
[[1,2,4],[3,5,6],[7]] => 9
[[1,2,3],[4,5,6],[7]] => 9
[[1,4,7],[2,5],[3,6]] => 7
[[1,3,7],[2,5],[4,6]] => 7
[[1,2,7],[3,5],[4,6]] => 7
[[1,3,7],[2,4],[5,6]] => 7
[[1,2,7],[3,4],[5,6]] => 7
[[1,4,6],[2,5],[3,7]] => 7
[[1,3,6],[2,5],[4,7]] => 7
[[1,2,6],[3,5],[4,7]] => 7
[[1,3,6],[2,4],[5,7]] => 7
[[1,2,6],[3,4],[5,7]] => 7
[[1,4,5],[2,6],[3,7]] => 7
[[1,3,5],[2,6],[4,7]] => 7
[[1,2,5],[3,6],[4,7]] => 7
[[1,3,4],[2,6],[5,7]] => 7
[[1,2,4],[3,6],[5,7]] => 7
[[1,2,3],[4,6],[5,7]] => 7
[[1,3,5],[2,4],[6,7]] => 7
[[1,2,5],[3,4],[6,7]] => 7
[[1,3,4],[2,5],[6,7]] => 7
[[1,2,4],[3,5],[6,7]] => 7
[[1,2,3],[4,5],[6,7]] => 7
[[1,5,7],[2,6],[3],[4]] => 5
[[1,4,7],[2,6],[3],[5]] => 5
[[1,3,7],[2,6],[4],[5]] => 5
[[1,2,7],[3,6],[4],[5]] => 5
[[1,4,7],[2,5],[3],[6]] => 5
[[1,3,7],[2,5],[4],[6]] => 5
[[1,2,7],[3,5],[4],[6]] => 5
[[1,3,7],[2,4],[5],[6]] => 5
[[1,2,7],[3,4],[5],[6]] => 5
[[1,5,6],[2,7],[3],[4]] => 5
[[1,4,6],[2,7],[3],[5]] => 5
[[1,3,6],[2,7],[4],[5]] => 5
[[1,2,6],[3,7],[4],[5]] => 5
[[1,4,5],[2,7],[3],[6]] => 5
[[1,3,5],[2,7],[4],[6]] => 5
[[1,2,5],[3,7],[4],[6]] => 5
[[1,3,4],[2,7],[5],[6]] => 5
[[1,2,4],[3,7],[5],[6]] => 5
[[1,2,3],[4,7],[5],[6]] => 5
[[1,4,6],[2,5],[3],[7]] => 5
[[1,3,6],[2,5],[4],[7]] => 5
[[1,2,6],[3,5],[4],[7]] => 5
[[1,3,6],[2,4],[5],[7]] => 5
[[1,2,6],[3,4],[5],[7]] => 5
[[1,4,5],[2,6],[3],[7]] => 5
[[1,3,5],[2,6],[4],[7]] => 5
[[1,2,5],[3,6],[4],[7]] => 5
[[1,3,4],[2,6],[5],[7]] => 5
[[1,2,4],[3,6],[5],[7]] => 5
[[1,2,3],[4,6],[5],[7]] => 5
[[1,3,5],[2,4],[6],[7]] => 5
[[1,2,5],[3,4],[6],[7]] => 5
[[1,3,4],[2,5],[6],[7]] => 5
[[1,2,4],[3,5],[6],[7]] => 5
[[1,2,3],[4,5],[6],[7]] => 5
[[1,6,7],[2],[3],[4],[5]] => 3
[[1,5,7],[2],[3],[4],[6]] => 3
[[1,4,7],[2],[3],[5],[6]] => 3
[[1,3,7],[2],[4],[5],[6]] => 3
[[1,2,7],[3],[4],[5],[6]] => 3
[[1,5,6],[2],[3],[4],[7]] => 3
[[1,4,6],[2],[3],[5],[7]] => 3
[[1,3,6],[2],[4],[5],[7]] => 3
[[1,2,6],[3],[4],[5],[7]] => 3
[[1,4,5],[2],[3],[6],[7]] => 3
[[1,3,5],[2],[4],[6],[7]] => 3
[[1,2,5],[3],[4],[6],[7]] => 3
[[1,3,4],[2],[5],[6],[7]] => 3
[[1,2,4],[3],[5],[6],[7]] => 3
[[1,2,3],[4],[5],[6],[7]] => 3
[[1,5],[2,6],[3,7],[4]] => 5
[[1,4],[2,6],[3,7],[5]] => 5
[[1,3],[2,6],[4,7],[5]] => 5
[[1,2],[3,6],[4,7],[5]] => 5
[[1,4],[2,5],[3,7],[6]] => 5
[[1,3],[2,5],[4,7],[6]] => 5
[[1,2],[3,5],[4,7],[6]] => 5
[[1,3],[2,4],[5,7],[6]] => 5
[[1,2],[3,4],[5,7],[6]] => 5
[[1,4],[2,5],[3,6],[7]] => 5
[[1,3],[2,5],[4,6],[7]] => 5
[[1,2],[3,5],[4,6],[7]] => 5
[[1,3],[2,4],[5,6],[7]] => 5
[[1,2],[3,4],[5,6],[7]] => 5
[[1,6],[2,7],[3],[4],[5]] => 3
[[1,5],[2,7],[3],[4],[6]] => 3
[[1,4],[2,7],[3],[5],[6]] => 3
[[1,3],[2,7],[4],[5],[6]] => 3
[[1,2],[3,7],[4],[5],[6]] => 3
[[1,5],[2,6],[3],[4],[7]] => 3
[[1,4],[2,6],[3],[5],[7]] => 3
[[1,3],[2,6],[4],[5],[7]] => 3
[[1,2],[3,6],[4],[5],[7]] => 3
[[1,4],[2,5],[3],[6],[7]] => 3
[[1,3],[2,5],[4],[6],[7]] => 3
[[1,2],[3,5],[4],[6],[7]] => 3
[[1,3],[2,4],[5],[6],[7]] => 3
[[1,2],[3,4],[5],[6],[7]] => 3
[[1,7],[2],[3],[4],[5],[6]] => 1
[[1,6],[2],[3],[4],[5],[7]] => 1
[[1,5],[2],[3],[4],[6],[7]] => 1
[[1,4],[2],[3],[5],[6],[7]] => 1
[[1,3],[2],[4],[5],[6],[7]] => 1
[[1,2],[3],[4],[5],[6],[7]] => 1
[[1],[2],[3],[4],[5],[6],[7]] => 0
[[1,2,3,4,5,6,7,8]] => 28
[[1,3,4,5,6,7,8],[2]] => 21
[[1,2,4,5,6,7,8],[3]] => 21
[[1,2,3,5,6,7,8],[4]] => 21
[[1,2,3,4,6,7,8],[5]] => 21
[[1,2,3,4,5,7,8],[6]] => 21
[[1,2,3,4,5,6,8],[7]] => 21
[[1,2,3,4,5,6,7],[8]] => 21
[[1,3,5,6,7,8],[2,4]] => 17
[[1,2,5,6,7,8],[3,4]] => 17
[[1,3,4,6,7,8],[2,5]] => 17
[[1,2,4,6,7,8],[3,5]] => 17
[[1,2,3,6,7,8],[4,5]] => 17
[[1,3,4,5,7,8],[2,6]] => 17
[[1,2,4,5,7,8],[3,6]] => 17
[[1,2,3,5,7,8],[4,6]] => 17
[[1,2,3,4,7,8],[5,6]] => 17
[[1,3,4,5,6,8],[2,7]] => 17
[[1,2,4,5,6,8],[3,7]] => 17
[[1,2,3,5,6,8],[4,7]] => 17
[[1,2,3,4,6,8],[5,7]] => 17
[[1,2,3,4,5,8],[6,7]] => 17
[[1,3,4,5,6,7],[2,8]] => 17
[[1,2,4,5,6,7],[3,8]] => 17
[[1,2,3,5,6,7],[4,8]] => 17
[[1,2,3,4,6,7],[5,8]] => 17
[[1,2,3,4,5,7],[6,8]] => 17
[[1,2,3,4,5,6],[7,8]] => 17
[[1,4,5,6,7,8],[2],[3]] => 15
[[1,3,5,6,7,8],[2],[4]] => 15
[[1,2,5,6,7,8],[3],[4]] => 15
[[1,3,4,6,7,8],[2],[5]] => 15
[[1,2,4,6,7,8],[3],[5]] => 15
[[1,2,3,6,7,8],[4],[5]] => 15
[[1,3,4,5,7,8],[2],[6]] => 15
[[1,2,4,5,7,8],[3],[6]] => 15
[[1,2,3,5,7,8],[4],[6]] => 15
[[1,2,3,4,7,8],[5],[6]] => 15
[[1,3,4,5,6,8],[2],[7]] => 15
[[1,2,4,5,6,8],[3],[7]] => 15
[[1,2,3,5,6,8],[4],[7]] => 15
[[1,2,3,4,6,8],[5],[7]] => 15
[[1,2,3,4,5,8],[6],[7]] => 15
[[1,3,4,5,6,7],[2],[8]] => 15
[[1,2,4,5,6,7],[3],[8]] => 15
[[1,2,3,5,6,7],[4],[8]] => 15
[[1,2,3,4,6,7],[5],[8]] => 15
[[1,2,3,4,5,7],[6],[8]] => 15
[[1,2,3,4,5,6],[7],[8]] => 15
[[1,3,5,7,8],[2,4,6]] => 16
[[1,2,5,7,8],[3,4,6]] => 16
[[1,3,4,7,8],[2,5,6]] => 16
[[1,2,4,7,8],[3,5,6]] => 16
[[1,2,3,7,8],[4,5,6]] => 16
[[1,3,5,6,8],[2,4,7]] => 16
[[1,2,5,6,8],[3,4,7]] => 16
[[1,3,4,6,8],[2,5,7]] => 16
[[1,2,4,6,8],[3,5,7]] => 16
[[1,2,3,6,8],[4,5,7]] => 16
[[1,3,4,5,8],[2,6,7]] => 16
[[1,2,4,5,8],[3,6,7]] => 16
[[1,2,3,5,8],[4,6,7]] => 16
[[1,2,3,4,8],[5,6,7]] => 16
[[1,3,5,6,7],[2,4,8]] => 16
[[1,2,5,6,7],[3,4,8]] => 16
[[1,3,4,6,7],[2,5,8]] => 16
[[1,2,4,6,7],[3,5,8]] => 16
[[1,2,3,6,7],[4,5,8]] => 16
[[1,3,4,5,7],[2,6,8]] => 16
[[1,2,4,5,7],[3,6,8]] => 16
[[1,2,3,5,7],[4,6,8]] => 16
[[1,2,3,4,7],[5,6,8]] => 16
[[1,3,4,5,6],[2,7,8]] => 16
[[1,2,4,5,6],[3,7,8]] => 16
[[1,2,3,5,6],[4,7,8]] => 16
[[1,2,3,4,6],[5,7,8]] => 16
[[1,2,3,4,5],[6,7,8]] => 16
[[1,4,6,7,8],[2,5],[3]] => 12
[[1,3,6,7,8],[2,5],[4]] => 12
[[1,2,6,7,8],[3,5],[4]] => 12
[[1,3,6,7,8],[2,4],[5]] => 12
[[1,2,6,7,8],[3,4],[5]] => 12
[[1,4,5,7,8],[2,6],[3]] => 12
[[1,3,5,7,8],[2,6],[4]] => 12
[[1,2,5,7,8],[3,6],[4]] => 12
[[1,3,4,7,8],[2,6],[5]] => 12
[[1,2,4,7,8],[3,6],[5]] => 12
[[1,2,3,7,8],[4,6],[5]] => 12
[[1,3,5,7,8],[2,4],[6]] => 12
[[1,2,5,7,8],[3,4],[6]] => 12
[[1,3,4,7,8],[2,5],[6]] => 12
[[1,2,4,7,8],[3,5],[6]] => 12
[[1,2,3,7,8],[4,5],[6]] => 12
[[1,4,5,6,8],[2,7],[3]] => 12
[[1,3,5,6,8],[2,7],[4]] => 12
[[1,2,5,6,8],[3,7],[4]] => 12
[[1,3,4,6,8],[2,7],[5]] => 12
[[1,2,4,6,8],[3,7],[5]] => 12
[[1,2,3,6,8],[4,7],[5]] => 12
[[1,3,4,5,8],[2,7],[6]] => 12
[[1,2,4,5,8],[3,7],[6]] => 12
[[1,2,3,5,8],[4,7],[6]] => 12
[[1,2,3,4,8],[5,7],[6]] => 12
[[1,3,5,6,8],[2,4],[7]] => 12
[[1,2,5,6,8],[3,4],[7]] => 12
[[1,3,4,6,8],[2,5],[7]] => 12
[[1,2,4,6,8],[3,5],[7]] => 12
[[1,2,3,6,8],[4,5],[7]] => 12
[[1,3,4,5,8],[2,6],[7]] => 12
[[1,2,4,5,8],[3,6],[7]] => 12
[[1,2,3,5,8],[4,6],[7]] => 12
[[1,2,3,4,8],[5,6],[7]] => 12
[[1,4,5,6,7],[2,8],[3]] => 12
[[1,3,5,6,7],[2,8],[4]] => 12
[[1,2,5,6,7],[3,8],[4]] => 12
[[1,3,4,6,7],[2,8],[5]] => 12
[[1,2,4,6,7],[3,8],[5]] => 12
[[1,2,3,6,7],[4,8],[5]] => 12
[[1,3,4,5,7],[2,8],[6]] => 12
[[1,2,4,5,7],[3,8],[6]] => 12
[[1,2,3,5,7],[4,8],[6]] => 12
[[1,2,3,4,7],[5,8],[6]] => 12
[[1,3,4,5,6],[2,8],[7]] => 12
[[1,2,4,5,6],[3,8],[7]] => 12
[[1,2,3,5,6],[4,8],[7]] => 12
[[1,2,3,4,6],[5,8],[7]] => 12
[[1,2,3,4,5],[6,8],[7]] => 12
[[1,3,5,6,7],[2,4],[8]] => 12
[[1,2,5,6,7],[3,4],[8]] => 12
[[1,3,4,6,7],[2,5],[8]] => 12
[[1,2,4,6,7],[3,5],[8]] => 12
[[1,2,3,6,7],[4,5],[8]] => 12
[[1,3,4,5,7],[2,6],[8]] => 12
[[1,2,4,5,7],[3,6],[8]] => 12
[[1,2,3,5,7],[4,6],[8]] => 12
[[1,2,3,4,7],[5,6],[8]] => 12
[[1,3,4,5,6],[2,7],[8]] => 12
[[1,2,4,5,6],[3,7],[8]] => 12
[[1,2,3,5,6],[4,7],[8]] => 12
[[1,2,3,4,6],[5,7],[8]] => 12
[[1,2,3,4,5],[6,7],[8]] => 12
[[1,5,6,7,8],[2],[3],[4]] => 10
[[1,4,6,7,8],[2],[3],[5]] => 10
[[1,3,6,7,8],[2],[4],[5]] => 10
[[1,2,6,7,8],[3],[4],[5]] => 10
[[1,4,5,7,8],[2],[3],[6]] => 10
[[1,3,5,7,8],[2],[4],[6]] => 10
[[1,2,5,7,8],[3],[4],[6]] => 10
[[1,3,4,7,8],[2],[5],[6]] => 10
[[1,2,4,7,8],[3],[5],[6]] => 10
[[1,2,3,7,8],[4],[5],[6]] => 10
[[1,4,5,6,8],[2],[3],[7]] => 10
[[1,3,5,6,8],[2],[4],[7]] => 10
[[1,2,5,6,8],[3],[4],[7]] => 10
[[1,3,4,6,8],[2],[5],[7]] => 10
[[1,2,4,6,8],[3],[5],[7]] => 10
[[1,2,3,6,8],[4],[5],[7]] => 10
[[1,3,4,5,8],[2],[6],[7]] => 10
[[1,2,4,5,8],[3],[6],[7]] => 10
[[1,2,3,5,8],[4],[6],[7]] => 10
[[1,2,3,4,8],[5],[6],[7]] => 10
[[1,4,5,6,7],[2],[3],[8]] => 10
[[1,3,5,6,7],[2],[4],[8]] => 10
[[1,2,5,6,7],[3],[4],[8]] => 10
[[1,3,4,6,7],[2],[5],[8]] => 10
[[1,2,4,6,7],[3],[5],[8]] => 10
[[1,2,3,6,7],[4],[5],[8]] => 10
[[1,3,4,5,7],[2],[6],[8]] => 10
[[1,2,4,5,7],[3],[6],[8]] => 10
[[1,2,3,5,7],[4],[6],[8]] => 10
[[1,2,3,4,7],[5],[6],[8]] => 10
[[1,3,4,5,6],[2],[7],[8]] => 10
[[1,2,4,5,6],[3],[7],[8]] => 10
[[1,2,3,5,6],[4],[7],[8]] => 10
[[1,2,3,4,6],[5],[7],[8]] => 10
[[1,2,3,4,5],[6],[7],[8]] => 10
[[1,3,5,7],[2,4,6,8]] => 18
[[1,2,5,7],[3,4,6,8]] => 18
[[1,3,4,7],[2,5,6,8]] => 18
[[1,2,4,7],[3,5,6,8]] => 18
[[1,2,3,7],[4,5,6,8]] => 18
[[1,3,5,6],[2,4,7,8]] => 18
[[1,2,5,6],[3,4,7,8]] => 18
[[1,3,4,6],[2,5,7,8]] => 18
[[1,2,4,6],[3,5,7,8]] => 18
[[1,2,3,6],[4,5,7,8]] => 18
[[1,3,4,5],[2,6,7,8]] => 18
[[1,2,4,5],[3,6,7,8]] => 18
[[1,2,3,5],[4,6,7,8]] => 18
[[1,2,3,4],[5,6,7,8]] => 18
[[1,4,6,8],[2,5,7],[3]] => 12
[[1,3,6,8],[2,5,7],[4]] => 12
[[1,2,6,8],[3,5,7],[4]] => 12
[[1,3,6,8],[2,4,7],[5]] => 12
[[1,2,6,8],[3,4,7],[5]] => 12
[[1,4,5,8],[2,6,7],[3]] => 12
[[1,3,5,8],[2,6,7],[4]] => 12
[[1,2,5,8],[3,6,7],[4]] => 12
[[1,3,4,8],[2,6,7],[5]] => 12
[[1,2,4,8],[3,6,7],[5]] => 12
[[1,2,3,8],[4,6,7],[5]] => 12
[[1,3,5,8],[2,4,7],[6]] => 12
[[1,2,5,8],[3,4,7],[6]] => 12
[[1,3,4,8],[2,5,7],[6]] => 12
[[1,2,4,8],[3,5,7],[6]] => 12
[[1,2,3,8],[4,5,7],[6]] => 12
[[1,3,5,8],[2,4,6],[7]] => 12
[[1,2,5,8],[3,4,6],[7]] => 12
[[1,3,4,8],[2,5,6],[7]] => 12
[[1,2,4,8],[3,5,6],[7]] => 12
[[1,2,3,8],[4,5,6],[7]] => 12
[[1,4,6,7],[2,5,8],[3]] => 12
[[1,3,6,7],[2,5,8],[4]] => 12
[[1,2,6,7],[3,5,8],[4]] => 12
[[1,3,6,7],[2,4,8],[5]] => 12
[[1,2,6,7],[3,4,8],[5]] => 12
[[1,4,5,7],[2,6,8],[3]] => 12
[[1,3,5,7],[2,6,8],[4]] => 12
[[1,2,5,7],[3,6,8],[4]] => 12
[[1,3,4,7],[2,6,8],[5]] => 12
[[1,2,4,7],[3,6,8],[5]] => 12
[[1,2,3,7],[4,6,8],[5]] => 12
[[1,3,5,7],[2,4,8],[6]] => 12
[[1,2,5,7],[3,4,8],[6]] => 12
[[1,3,4,7],[2,5,8],[6]] => 12
[[1,2,4,7],[3,5,8],[6]] => 12
[[1,2,3,7],[4,5,8],[6]] => 12
[[1,4,5,6],[2,7,8],[3]] => 12
[[1,3,5,6],[2,7,8],[4]] => 12
[[1,2,5,6],[3,7,8],[4]] => 12
[[1,3,4,6],[2,7,8],[5]] => 12
[[1,2,4,6],[3,7,8],[5]] => 12
[[1,2,3,6],[4,7,8],[5]] => 12
[[1,3,4,5],[2,7,8],[6]] => 12
[[1,2,4,5],[3,7,8],[6]] => 12
[[1,2,3,5],[4,7,8],[6]] => 12
[[1,2,3,4],[5,7,8],[6]] => 12
[[1,3,5,6],[2,4,8],[7]] => 12
[[1,2,5,6],[3,4,8],[7]] => 12
[[1,3,4,6],[2,5,8],[7]] => 12
[[1,2,4,6],[3,5,8],[7]] => 12
[[1,2,3,6],[4,5,8],[7]] => 12
[[1,3,4,5],[2,6,8],[7]] => 12
[[1,2,4,5],[3,6,8],[7]] => 12
[[1,2,3,5],[4,6,8],[7]] => 12
[[1,2,3,4],[5,6,8],[7]] => 12
[[1,3,5,7],[2,4,6],[8]] => 12
[[1,2,5,7],[3,4,6],[8]] => 12
[[1,3,4,7],[2,5,6],[8]] => 12
[[1,2,4,7],[3,5,6],[8]] => 12
[[1,2,3,7],[4,5,6],[8]] => 12
[[1,3,5,6],[2,4,7],[8]] => 12
[[1,2,5,6],[3,4,7],[8]] => 12
[[1,3,4,6],[2,5,7],[8]] => 12
[[1,2,4,6],[3,5,7],[8]] => 12
[[1,2,3,6],[4,5,7],[8]] => 12
[[1,3,4,5],[2,6,7],[8]] => 12
[[1,2,4,5],[3,6,7],[8]] => 12
[[1,2,3,5],[4,6,7],[8]] => 12
[[1,2,3,4],[5,6,7],[8]] => 12
[[1,4,7,8],[2,5],[3,6]] => 10
[[1,3,7,8],[2,5],[4,6]] => 10
[[1,2,7,8],[3,5],[4,6]] => 10
[[1,3,7,8],[2,4],[5,6]] => 10
[[1,2,7,8],[3,4],[5,6]] => 10
[[1,4,6,8],[2,5],[3,7]] => 10
[[1,3,6,8],[2,5],[4,7]] => 10
[[1,2,6,8],[3,5],[4,7]] => 10
[[1,3,6,8],[2,4],[5,7]] => 10
[[1,2,6,8],[3,4],[5,7]] => 10
[[1,4,5,8],[2,6],[3,7]] => 10
[[1,3,5,8],[2,6],[4,7]] => 10
[[1,2,5,8],[3,6],[4,7]] => 10
[[1,3,4,8],[2,6],[5,7]] => 10
[[1,2,4,8],[3,6],[5,7]] => 10
[[1,2,3,8],[4,6],[5,7]] => 10
[[1,3,5,8],[2,4],[6,7]] => 10
[[1,2,5,8],[3,4],[6,7]] => 10
[[1,3,4,8],[2,5],[6,7]] => 10
[[1,2,4,8],[3,5],[6,7]] => 10
[[1,2,3,8],[4,5],[6,7]] => 10
[[1,4,6,7],[2,5],[3,8]] => 10
[[1,3,6,7],[2,5],[4,8]] => 10
[[1,2,6,7],[3,5],[4,8]] => 10
[[1,3,6,7],[2,4],[5,8]] => 10
[[1,2,6,7],[3,4],[5,8]] => 10
[[1,4,5,7],[2,6],[3,8]] => 10
[[1,3,5,7],[2,6],[4,8]] => 10
[[1,2,5,7],[3,6],[4,8]] => 10
[[1,3,4,7],[2,6],[5,8]] => 10
[[1,2,4,7],[3,6],[5,8]] => 10
[[1,2,3,7],[4,6],[5,8]] => 10
[[1,3,5,7],[2,4],[6,8]] => 10
[[1,2,5,7],[3,4],[6,8]] => 10
[[1,3,4,7],[2,5],[6,8]] => 10
[[1,2,4,7],[3,5],[6,8]] => 10
[[1,2,3,7],[4,5],[6,8]] => 10
[[1,4,5,6],[2,7],[3,8]] => 10
[[1,3,5,6],[2,7],[4,8]] => 10
[[1,2,5,6],[3,7],[4,8]] => 10
[[1,3,4,6],[2,7],[5,8]] => 10
[[1,2,4,6],[3,7],[5,8]] => 10
[[1,2,3,6],[4,7],[5,8]] => 10
[[1,3,4,5],[2,7],[6,8]] => 10
[[1,2,4,5],[3,7],[6,8]] => 10
[[1,2,3,5],[4,7],[6,8]] => 10
[[1,2,3,4],[5,7],[6,8]] => 10
[[1,3,5,6],[2,4],[7,8]] => 10
[[1,2,5,6],[3,4],[7,8]] => 10
[[1,3,4,6],[2,5],[7,8]] => 10
[[1,2,4,6],[3,5],[7,8]] => 10
[[1,2,3,6],[4,5],[7,8]] => 10
[[1,3,4,5],[2,6],[7,8]] => 10
[[1,2,4,5],[3,6],[7,8]] => 10
[[1,2,3,5],[4,6],[7,8]] => 10
[[1,2,3,4],[5,6],[7,8]] => 10
[[1,5,7,8],[2,6],[3],[4]] => 8
[[1,4,7,8],[2,6],[3],[5]] => 8
[[1,3,7,8],[2,6],[4],[5]] => 8
[[1,2,7,8],[3,6],[4],[5]] => 8
[[1,4,7,8],[2,5],[3],[6]] => 8
[[1,3,7,8],[2,5],[4],[6]] => 8
[[1,2,7,8],[3,5],[4],[6]] => 8
[[1,3,7,8],[2,4],[5],[6]] => 8
[[1,2,7,8],[3,4],[5],[6]] => 8
[[1,5,6,8],[2,7],[3],[4]] => 8
[[1,4,6,8],[2,7],[3],[5]] => 8
[[1,3,6,8],[2,7],[4],[5]] => 8
[[1,2,6,8],[3,7],[4],[5]] => 8
[[1,4,5,8],[2,7],[3],[6]] => 8
[[1,3,5,8],[2,7],[4],[6]] => 8
[[1,2,5,8],[3,7],[4],[6]] => 8
[[1,3,4,8],[2,7],[5],[6]] => 8
[[1,2,4,8],[3,7],[5],[6]] => 8
[[1,2,3,8],[4,7],[5],[6]] => 8
[[1,4,6,8],[2,5],[3],[7]] => 8
[[1,3,6,8],[2,5],[4],[7]] => 8
[[1,2,6,8],[3,5],[4],[7]] => 8
[[1,3,6,8],[2,4],[5],[7]] => 8
[[1,2,6,8],[3,4],[5],[7]] => 8
[[1,4,5,8],[2,6],[3],[7]] => 8
[[1,3,5,8],[2,6],[4],[7]] => 8
[[1,2,5,8],[3,6],[4],[7]] => 8
[[1,3,4,8],[2,6],[5],[7]] => 8
[[1,2,4,8],[3,6],[5],[7]] => 8
[[1,2,3,8],[4,6],[5],[7]] => 8
[[1,3,5,8],[2,4],[6],[7]] => 8
[[1,2,5,8],[3,4],[6],[7]] => 8
[[1,3,4,8],[2,5],[6],[7]] => 8
[[1,2,4,8],[3,5],[6],[7]] => 8
[[1,2,3,8],[4,5],[6],[7]] => 8
[[1,5,6,7],[2,8],[3],[4]] => 8
[[1,4,6,7],[2,8],[3],[5]] => 8
[[1,3,6,7],[2,8],[4],[5]] => 8
[[1,2,6,7],[3,8],[4],[5]] => 8
[[1,4,5,7],[2,8],[3],[6]] => 8
[[1,3,5,7],[2,8],[4],[6]] => 8
[[1,2,5,7],[3,8],[4],[6]] => 8
[[1,3,4,7],[2,8],[5],[6]] => 8
[[1,2,4,7],[3,8],[5],[6]] => 8
[[1,2,3,7],[4,8],[5],[6]] => 8
[[1,4,5,6],[2,8],[3],[7]] => 8
[[1,3,5,6],[2,8],[4],[7]] => 8
[[1,2,5,6],[3,8],[4],[7]] => 8
[[1,3,4,6],[2,8],[5],[7]] => 8
[[1,2,4,6],[3,8],[5],[7]] => 8
[[1,2,3,6],[4,8],[5],[7]] => 8
[[1,3,4,5],[2,8],[6],[7]] => 8
[[1,2,4,5],[3,8],[6],[7]] => 8
[[1,2,3,5],[4,8],[6],[7]] => 8
[[1,2,3,4],[5,8],[6],[7]] => 8
[[1,4,6,7],[2,5],[3],[8]] => 8
[[1,3,6,7],[2,5],[4],[8]] => 8
[[1,2,6,7],[3,5],[4],[8]] => 8
[[1,3,6,7],[2,4],[5],[8]] => 8
[[1,2,6,7],[3,4],[5],[8]] => 8
[[1,4,5,7],[2,6],[3],[8]] => 8
[[1,3,5,7],[2,6],[4],[8]] => 8
[[1,2,5,7],[3,6],[4],[8]] => 8
[[1,3,4,7],[2,6],[5],[8]] => 8
[[1,2,4,7],[3,6],[5],[8]] => 8
[[1,2,3,7],[4,6],[5],[8]] => 8
[[1,3,5,7],[2,4],[6],[8]] => 8
[[1,2,5,7],[3,4],[6],[8]] => 8
[[1,3,4,7],[2,5],[6],[8]] => 8
[[1,2,4,7],[3,5],[6],[8]] => 8
[[1,2,3,7],[4,5],[6],[8]] => 8
[[1,4,5,6],[2,7],[3],[8]] => 8
[[1,3,5,6],[2,7],[4],[8]] => 8
[[1,2,5,6],[3,7],[4],[8]] => 8
[[1,3,4,6],[2,7],[5],[8]] => 8
[[1,2,4,6],[3,7],[5],[8]] => 8
[[1,2,3,6],[4,7],[5],[8]] => 8
[[1,3,4,5],[2,7],[6],[8]] => 8
[[1,2,4,5],[3,7],[6],[8]] => 8
[[1,2,3,5],[4,7],[6],[8]] => 8
[[1,2,3,4],[5,7],[6],[8]] => 8
[[1,3,5,6],[2,4],[7],[8]] => 8
[[1,2,5,6],[3,4],[7],[8]] => 8
[[1,3,4,6],[2,5],[7],[8]] => 8
[[1,2,4,6],[3,5],[7],[8]] => 8
[[1,2,3,6],[4,5],[7],[8]] => 8
[[1,3,4,5],[2,6],[7],[8]] => 8
[[1,2,4,5],[3,6],[7],[8]] => 8
[[1,2,3,5],[4,6],[7],[8]] => 8
[[1,2,3,4],[5,6],[7],[8]] => 8
[[1,6,7,8],[2],[3],[4],[5]] => 6
[[1,5,7,8],[2],[3],[4],[6]] => 6
[[1,4,7,8],[2],[3],[5],[6]] => 6
[[1,3,7,8],[2],[4],[5],[6]] => 6
[[1,2,7,8],[3],[4],[5],[6]] => 6
[[1,5,6,8],[2],[3],[4],[7]] => 6
[[1,4,6,8],[2],[3],[5],[7]] => 6
[[1,3,6,8],[2],[4],[5],[7]] => 6
[[1,2,6,8],[3],[4],[5],[7]] => 6
[[1,4,5,8],[2],[3],[6],[7]] => 6
[[1,3,5,8],[2],[4],[6],[7]] => 6
[[1,2,5,8],[3],[4],[6],[7]] => 6
[[1,3,4,8],[2],[5],[6],[7]] => 6
[[1,2,4,8],[3],[5],[6],[7]] => 6
[[1,2,3,8],[4],[5],[6],[7]] => 6
[[1,5,6,7],[2],[3],[4],[8]] => 6
[[1,4,6,7],[2],[3],[5],[8]] => 6
[[1,3,6,7],[2],[4],[5],[8]] => 6
[[1,2,6,7],[3],[4],[5],[8]] => 6
[[1,4,5,7],[2],[3],[6],[8]] => 6
[[1,3,5,7],[2],[4],[6],[8]] => 6
[[1,2,5,7],[3],[4],[6],[8]] => 6
[[1,3,4,7],[2],[5],[6],[8]] => 6
[[1,2,4,7],[3],[5],[6],[8]] => 6
[[1,2,3,7],[4],[5],[6],[8]] => 6
[[1,4,5,6],[2],[3],[7],[8]] => 6
[[1,3,5,6],[2],[4],[7],[8]] => 6
[[1,2,5,6],[3],[4],[7],[8]] => 6
[[1,3,4,6],[2],[5],[7],[8]] => 6
[[1,2,4,6],[3],[5],[7],[8]] => 6
[[1,2,3,6],[4],[5],[7],[8]] => 6
[[1,3,4,5],[2],[6],[7],[8]] => 6
[[1,2,4,5],[3],[6],[7],[8]] => 6
[[1,2,3,5],[4],[6],[7],[8]] => 6
[[1,2,3,4],[5],[6],[7],[8]] => 6
[[1,4,7],[2,5,8],[3,6]] => 11
[[1,3,7],[2,5,8],[4,6]] => 11
[[1,2,7],[3,5,8],[4,6]] => 11
[[1,3,7],[2,4,8],[5,6]] => 11
[[1,2,7],[3,4,8],[5,6]] => 11
[[1,4,6],[2,5,8],[3,7]] => 11
[[1,3,6],[2,5,8],[4,7]] => 11
[[1,2,6],[3,5,8],[4,7]] => 11
[[1,3,6],[2,4,8],[5,7]] => 11
[[1,2,6],[3,4,8],[5,7]] => 11
[[1,4,5],[2,6,8],[3,7]] => 11
[[1,3,5],[2,6,8],[4,7]] => 11
[[1,2,5],[3,6,8],[4,7]] => 11
[[1,3,4],[2,6,8],[5,7]] => 11
[[1,2,4],[3,6,8],[5,7]] => 11
[[1,2,3],[4,6,8],[5,7]] => 11
[[1,3,5],[2,4,8],[6,7]] => 11
[[1,2,5],[3,4,8],[6,7]] => 11
[[1,3,4],[2,5,8],[6,7]] => 11
[[1,2,4],[3,5,8],[6,7]] => 11
[[1,2,3],[4,5,8],[6,7]] => 11
[[1,4,6],[2,5,7],[3,8]] => 11
[[1,3,6],[2,5,7],[4,8]] => 11
[[1,2,6],[3,5,7],[4,8]] => 11
[[1,3,6],[2,4,7],[5,8]] => 11
[[1,2,6],[3,4,7],[5,8]] => 11
[[1,4,5],[2,6,7],[3,8]] => 11
[[1,3,5],[2,6,7],[4,8]] => 11
[[1,2,5],[3,6,7],[4,8]] => 11
[[1,3,4],[2,6,7],[5,8]] => 11
[[1,2,4],[3,6,7],[5,8]] => 11
[[1,2,3],[4,6,7],[5,8]] => 11
[[1,3,5],[2,4,7],[6,8]] => 11
[[1,2,5],[3,4,7],[6,8]] => 11
[[1,3,4],[2,5,7],[6,8]] => 11
[[1,2,4],[3,5,7],[6,8]] => 11
[[1,2,3],[4,5,7],[6,8]] => 11
[[1,3,5],[2,4,6],[7,8]] => 11
[[1,2,5],[3,4,6],[7,8]] => 11
[[1,3,4],[2,5,6],[7,8]] => 11
[[1,2,4],[3,5,6],[7,8]] => 11
[[1,2,3],[4,5,6],[7,8]] => 11
[[1,5,7],[2,6,8],[3],[4]] => 9
[[1,4,7],[2,6,8],[3],[5]] => 9
[[1,3,7],[2,6,8],[4],[5]] => 9
[[1,2,7],[3,6,8],[4],[5]] => 9
[[1,4,7],[2,5,8],[3],[6]] => 9
[[1,3,7],[2,5,8],[4],[6]] => 9
[[1,2,7],[3,5,8],[4],[6]] => 9
[[1,3,7],[2,4,8],[5],[6]] => 9
[[1,2,7],[3,4,8],[5],[6]] => 9
[[1,5,6],[2,7,8],[3],[4]] => 9
[[1,4,6],[2,7,8],[3],[5]] => 9
[[1,3,6],[2,7,8],[4],[5]] => 9
[[1,2,6],[3,7,8],[4],[5]] => 9
[[1,4,5],[2,7,8],[3],[6]] => 9
[[1,3,5],[2,7,8],[4],[6]] => 9
[[1,2,5],[3,7,8],[4],[6]] => 9
[[1,3,4],[2,7,8],[5],[6]] => 9
[[1,2,4],[3,7,8],[5],[6]] => 9
[[1,2,3],[4,7,8],[5],[6]] => 9
[[1,4,6],[2,5,8],[3],[7]] => 9
[[1,3,6],[2,5,8],[4],[7]] => 9
[[1,2,6],[3,5,8],[4],[7]] => 9
[[1,3,6],[2,4,8],[5],[7]] => 9
[[1,2,6],[3,4,8],[5],[7]] => 9
[[1,4,5],[2,6,8],[3],[7]] => 9
[[1,3,5],[2,6,8],[4],[7]] => 9
[[1,2,5],[3,6,8],[4],[7]] => 9
[[1,3,4],[2,6,8],[5],[7]] => 9
[[1,2,4],[3,6,8],[5],[7]] => 9
[[1,2,3],[4,6,8],[5],[7]] => 9
[[1,3,5],[2,4,8],[6],[7]] => 9
[[1,2,5],[3,4,8],[6],[7]] => 9
[[1,3,4],[2,5,8],[6],[7]] => 9
[[1,2,4],[3,5,8],[6],[7]] => 9
[[1,2,3],[4,5,8],[6],[7]] => 9
[[1,4,6],[2,5,7],[3],[8]] => 9
[[1,3,6],[2,5,7],[4],[8]] => 9
[[1,2,6],[3,5,7],[4],[8]] => 9
[[1,3,6],[2,4,7],[5],[8]] => 9
[[1,2,6],[3,4,7],[5],[8]] => 9
[[1,4,5],[2,6,7],[3],[8]] => 9
[[1,3,5],[2,6,7],[4],[8]] => 9
[[1,2,5],[3,6,7],[4],[8]] => 9
[[1,3,4],[2,6,7],[5],[8]] => 9
[[1,2,4],[3,6,7],[5],[8]] => 9
[[1,2,3],[4,6,7],[5],[8]] => 9
[[1,3,5],[2,4,7],[6],[8]] => 9
[[1,2,5],[3,4,7],[6],[8]] => 9
[[1,3,4],[2,5,7],[6],[8]] => 9
[[1,2,4],[3,5,7],[6],[8]] => 9
[[1,2,3],[4,5,7],[6],[8]] => 9
[[1,3,5],[2,4,6],[7],[8]] => 9
[[1,2,5],[3,4,6],[7],[8]] => 9
[[1,3,4],[2,5,6],[7],[8]] => 9
[[1,2,4],[3,5,6],[7],[8]] => 9
[[1,2,3],[4,5,6],[7],[8]] => 9
[[1,5,8],[2,6],[3,7],[4]] => 7
[[1,4,8],[2,6],[3,7],[5]] => 7
[[1,3,8],[2,6],[4,7],[5]] => 7
[[1,2,8],[3,6],[4,7],[5]] => 7
[[1,4,8],[2,5],[3,7],[6]] => 7
[[1,3,8],[2,5],[4,7],[6]] => 7
[[1,2,8],[3,5],[4,7],[6]] => 7
[[1,3,8],[2,4],[5,7],[6]] => 7
[[1,2,8],[3,4],[5,7],[6]] => 7
[[1,4,8],[2,5],[3,6],[7]] => 7
[[1,3,8],[2,5],[4,6],[7]] => 7
[[1,2,8],[3,5],[4,6],[7]] => 7
[[1,3,8],[2,4],[5,6],[7]] => 7
[[1,2,8],[3,4],[5,6],[7]] => 7
[[1,5,7],[2,6],[3,8],[4]] => 7
[[1,4,7],[2,6],[3,8],[5]] => 7
[[1,3,7],[2,6],[4,8],[5]] => 7
[[1,2,7],[3,6],[4,8],[5]] => 7
[[1,4,7],[2,5],[3,8],[6]] => 7
[[1,3,7],[2,5],[4,8],[6]] => 7
[[1,2,7],[3,5],[4,8],[6]] => 7
[[1,3,7],[2,4],[5,8],[6]] => 7
[[1,2,7],[3,4],[5,8],[6]] => 7
[[1,5,6],[2,7],[3,8],[4]] => 7
[[1,4,6],[2,7],[3,8],[5]] => 7
[[1,3,6],[2,7],[4,8],[5]] => 7
[[1,2,6],[3,7],[4,8],[5]] => 7
[[1,4,5],[2,7],[3,8],[6]] => 7
[[1,3,5],[2,7],[4,8],[6]] => 7
[[1,2,5],[3,7],[4,8],[6]] => 7
[[1,3,4],[2,7],[5,8],[6]] => 7
[[1,2,4],[3,7],[5,8],[6]] => 7
[[1,2,3],[4,7],[5,8],[6]] => 7
[[1,4,6],[2,5],[3,8],[7]] => 7
[[1,3,6],[2,5],[4,8],[7]] => 7
[[1,2,6],[3,5],[4,8],[7]] => 7
[[1,3,6],[2,4],[5,8],[7]] => 7
[[1,2,6],[3,4],[5,8],[7]] => 7
[[1,4,5],[2,6],[3,8],[7]] => 7
[[1,3,5],[2,6],[4,8],[7]] => 7
[[1,2,5],[3,6],[4,8],[7]] => 7
[[1,3,4],[2,6],[5,8],[7]] => 7
[[1,2,4],[3,6],[5,8],[7]] => 7
[[1,2,3],[4,6],[5,8],[7]] => 7
[[1,3,5],[2,4],[6,8],[7]] => 7
[[1,2,5],[3,4],[6,8],[7]] => 7
[[1,3,4],[2,5],[6,8],[7]] => 7
[[1,2,4],[3,5],[6,8],[7]] => 7
[[1,2,3],[4,5],[6,8],[7]] => 7
[[1,4,7],[2,5],[3,6],[8]] => 7
[[1,3,7],[2,5],[4,6],[8]] => 7
[[1,2,7],[3,5],[4,6],[8]] => 7
[[1,3,7],[2,4],[5,6],[8]] => 7
[[1,2,7],[3,4],[5,6],[8]] => 7
[[1,4,6],[2,5],[3,7],[8]] => 7
[[1,3,6],[2,5],[4,7],[8]] => 7
[[1,2,6],[3,5],[4,7],[8]] => 7
[[1,3,6],[2,4],[5,7],[8]] => 7
[[1,2,6],[3,4],[5,7],[8]] => 7
[[1,4,5],[2,6],[3,7],[8]] => 7
[[1,3,5],[2,6],[4,7],[8]] => 7
[[1,2,5],[3,6],[4,7],[8]] => 7
[[1,3,4],[2,6],[5,7],[8]] => 7
[[1,2,4],[3,6],[5,7],[8]] => 7
[[1,2,3],[4,6],[5,7],[8]] => 7
[[1,3,5],[2,4],[6,7],[8]] => 7
[[1,2,5],[3,4],[6,7],[8]] => 7
[[1,3,4],[2,5],[6,7],[8]] => 7
[[1,2,4],[3,5],[6,7],[8]] => 7
[[1,2,3],[4,5],[6,7],[8]] => 7
[[1,6,8],[2,7],[3],[4],[5]] => 5
[[1,5,8],[2,7],[3],[4],[6]] => 5
[[1,4,8],[2,7],[3],[5],[6]] => 5
[[1,3,8],[2,7],[4],[5],[6]] => 5
[[1,2,8],[3,7],[4],[5],[6]] => 5
[[1,5,8],[2,6],[3],[4],[7]] => 5
[[1,4,8],[2,6],[3],[5],[7]] => 5
[[1,3,8],[2,6],[4],[5],[7]] => 5
[[1,2,8],[3,6],[4],[5],[7]] => 5
[[1,4,8],[2,5],[3],[6],[7]] => 5
[[1,3,8],[2,5],[4],[6],[7]] => 5
[[1,2,8],[3,5],[4],[6],[7]] => 5
[[1,3,8],[2,4],[5],[6],[7]] => 5
[[1,2,8],[3,4],[5],[6],[7]] => 5
[[1,6,7],[2,8],[3],[4],[5]] => 5
[[1,5,7],[2,8],[3],[4],[6]] => 5
[[1,4,7],[2,8],[3],[5],[6]] => 5
[[1,3,7],[2,8],[4],[5],[6]] => 5
[[1,2,7],[3,8],[4],[5],[6]] => 5
[[1,5,6],[2,8],[3],[4],[7]] => 5
[[1,4,6],[2,8],[3],[5],[7]] => 5
[[1,3,6],[2,8],[4],[5],[7]] => 5
[[1,2,6],[3,8],[4],[5],[7]] => 5
[[1,4,5],[2,8],[3],[6],[7]] => 5
[[1,3,5],[2,8],[4],[6],[7]] => 5
[[1,2,5],[3,8],[4],[6],[7]] => 5
[[1,3,4],[2,8],[5],[6],[7]] => 5
[[1,2,4],[3,8],[5],[6],[7]] => 5
[[1,2,3],[4,8],[5],[6],[7]] => 5
[[1,5,7],[2,6],[3],[4],[8]] => 5
[[1,4,7],[2,6],[3],[5],[8]] => 5
[[1,3,7],[2,6],[4],[5],[8]] => 5
[[1,2,7],[3,6],[4],[5],[8]] => 5
[[1,4,7],[2,5],[3],[6],[8]] => 5
[[1,3,7],[2,5],[4],[6],[8]] => 5
[[1,2,7],[3,5],[4],[6],[8]] => 5
[[1,3,7],[2,4],[5],[6],[8]] => 5
[[1,2,7],[3,4],[5],[6],[8]] => 5
[[1,5,6],[2,7],[3],[4],[8]] => 5
[[1,4,6],[2,7],[3],[5],[8]] => 5
[[1,3,6],[2,7],[4],[5],[8]] => 5
[[1,2,6],[3,7],[4],[5],[8]] => 5
[[1,4,5],[2,7],[3],[6],[8]] => 5
[[1,3,5],[2,7],[4],[6],[8]] => 5
[[1,2,5],[3,7],[4],[6],[8]] => 5
[[1,3,4],[2,7],[5],[6],[8]] => 5
[[1,2,4],[3,7],[5],[6],[8]] => 5
[[1,2,3],[4,7],[5],[6],[8]] => 5
[[1,4,6],[2,5],[3],[7],[8]] => 5
[[1,3,6],[2,5],[4],[7],[8]] => 5
[[1,2,6],[3,5],[4],[7],[8]] => 5
[[1,3,6],[2,4],[5],[7],[8]] => 5
[[1,2,6],[3,4],[5],[7],[8]] => 5
[[1,4,5],[2,6],[3],[7],[8]] => 5
[[1,3,5],[2,6],[4],[7],[8]] => 5
[[1,2,5],[3,6],[4],[7],[8]] => 5
[[1,3,4],[2,6],[5],[7],[8]] => 5
[[1,2,4],[3,6],[5],[7],[8]] => 5
[[1,2,3],[4,6],[5],[7],[8]] => 5
[[1,3,5],[2,4],[6],[7],[8]] => 5
[[1,2,5],[3,4],[6],[7],[8]] => 5
[[1,3,4],[2,5],[6],[7],[8]] => 5
[[1,2,4],[3,5],[6],[7],[8]] => 5
[[1,2,3],[4,5],[6],[7],[8]] => 5
[[1,7,8],[2],[3],[4],[5],[6]] => 3
[[1,6,8],[2],[3],[4],[5],[7]] => 3
[[1,5,8],[2],[3],[4],[6],[7]] => 3
[[1,4,8],[2],[3],[5],[6],[7]] => 3
[[1,3,8],[2],[4],[5],[6],[7]] => 3
[[1,2,8],[3],[4],[5],[6],[7]] => 3
[[1,6,7],[2],[3],[4],[5],[8]] => 3
[[1,5,7],[2],[3],[4],[6],[8]] => 3
[[1,4,7],[2],[3],[5],[6],[8]] => 3
[[1,3,7],[2],[4],[5],[6],[8]] => 3
[[1,2,7],[3],[4],[5],[6],[8]] => 3
[[1,5,6],[2],[3],[4],[7],[8]] => 3
[[1,4,6],[2],[3],[5],[7],[8]] => 3
[[1,3,6],[2],[4],[5],[7],[8]] => 3
[[1,2,6],[3],[4],[5],[7],[8]] => 3
[[1,4,5],[2],[3],[6],[7],[8]] => 3
[[1,3,5],[2],[4],[6],[7],[8]] => 3
[[1,2,5],[3],[4],[6],[7],[8]] => 3
[[1,3,4],[2],[5],[6],[7],[8]] => 3
[[1,2,4],[3],[5],[6],[7],[8]] => 3
[[1,2,3],[4],[5],[6],[7],[8]] => 3
[[1,5],[2,6],[3,7],[4,8]] => 7
[[1,4],[2,6],[3,7],[5,8]] => 7
[[1,3],[2,6],[4,7],[5,8]] => 7
[[1,2],[3,6],[4,7],[5,8]] => 7
[[1,4],[2,5],[3,7],[6,8]] => 7
[[1,3],[2,5],[4,7],[6,8]] => 7
[[1,2],[3,5],[4,7],[6,8]] => 7
[[1,3],[2,4],[5,7],[6,8]] => 7
[[1,2],[3,4],[5,7],[6,8]] => 7
[[1,4],[2,5],[3,6],[7,8]] => 7
[[1,3],[2,5],[4,6],[7,8]] => 7
[[1,2],[3,5],[4,6],[7,8]] => 7
[[1,3],[2,4],[5,6],[7,8]] => 7
[[1,2],[3,4],[5,6],[7,8]] => 7
[[1,6],[2,7],[3,8],[4],[5]] => 5
[[1,5],[2,7],[3,8],[4],[6]] => 5
[[1,4],[2,7],[3,8],[5],[6]] => 5
[[1,3],[2,7],[4,8],[5],[6]] => 5
[[1,2],[3,7],[4,8],[5],[6]] => 5
[[1,5],[2,6],[3,8],[4],[7]] => 5
[[1,4],[2,6],[3,8],[5],[7]] => 5
[[1,3],[2,6],[4,8],[5],[7]] => 5
[[1,2],[3,6],[4,8],[5],[7]] => 5
[[1,4],[2,5],[3,8],[6],[7]] => 5
[[1,3],[2,5],[4,8],[6],[7]] => 5
[[1,2],[3,5],[4,8],[6],[7]] => 5
[[1,3],[2,4],[5,8],[6],[7]] => 5
[[1,2],[3,4],[5,8],[6],[7]] => 5
[[1,5],[2,6],[3,7],[4],[8]] => 5
[[1,4],[2,6],[3,7],[5],[8]] => 5
[[1,3],[2,6],[4,7],[5],[8]] => 5
[[1,2],[3,6],[4,7],[5],[8]] => 5
[[1,4],[2,5],[3,7],[6],[8]] => 5
[[1,3],[2,5],[4,7],[6],[8]] => 5
[[1,2],[3,5],[4,7],[6],[8]] => 5
[[1,3],[2,4],[5,7],[6],[8]] => 5
[[1,2],[3,4],[5,7],[6],[8]] => 5
[[1,4],[2,5],[3,6],[7],[8]] => 5
[[1,3],[2,5],[4,6],[7],[8]] => 5
[[1,2],[3,5],[4,6],[7],[8]] => 5
[[1,3],[2,4],[5,6],[7],[8]] => 5
[[1,2],[3,4],[5,6],[7],[8]] => 5
[[1,7],[2,8],[3],[4],[5],[6]] => 3
[[1,6],[2,8],[3],[4],[5],[7]] => 3
[[1,5],[2,8],[3],[4],[6],[7]] => 3
[[1,4],[2,8],[3],[5],[6],[7]] => 3
[[1,3],[2,8],[4],[5],[6],[7]] => 3
[[1,2],[3,8],[4],[5],[6],[7]] => 3
[[1,6],[2,7],[3],[4],[5],[8]] => 3
[[1,5],[2,7],[3],[4],[6],[8]] => 3
[[1,4],[2,7],[3],[5],[6],[8]] => 3
[[1,3],[2,7],[4],[5],[6],[8]] => 3
[[1,2],[3,7],[4],[5],[6],[8]] => 3
[[1,5],[2,6],[3],[4],[7],[8]] => 3
[[1,4],[2,6],[3],[5],[7],[8]] => 3
[[1,3],[2,6],[4],[5],[7],[8]] => 3
[[1,2],[3,6],[4],[5],[7],[8]] => 3
[[1,4],[2,5],[3],[6],[7],[8]] => 3
[[1,3],[2,5],[4],[6],[7],[8]] => 3
[[1,2],[3,5],[4],[6],[7],[8]] => 3
[[1,3],[2,4],[5],[6],[7],[8]] => 3
[[1,2],[3,4],[5],[6],[7],[8]] => 3
[[1,8],[2],[3],[4],[5],[6],[7]] => 1
[[1,7],[2],[3],[4],[5],[6],[8]] => 1
[[1,6],[2],[3],[4],[5],[7],[8]] => 1
[[1,5],[2],[3],[4],[6],[7],[8]] => 1
[[1,4],[2],[3],[5],[6],[7],[8]] => 1
[[1,3],[2],[4],[5],[6],[7],[8]] => 1
[[1,2],[3],[4],[5],[6],[7],[8]] => 1
[[1],[2],[3],[4],[5],[6],[7],[8]] => 0
-----------------------------------------------------------------------------
Created: Sep 27, 2011 at 20:00 by Chris Berg
-----------------------------------------------------------------------------
Last Updated: Oct 16, 2015 at 11:08 by Christian Stump