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-----------------------------------------------------------------------------
Statistic identifier: St001597
-----------------------------------------------------------------------------
Collection: Skew partitions
-----------------------------------------------------------------------------
Description: The Frobenius rank of a skew partition.
This is the minimal number of border strips in a border strip decomposition of the skew partition.
-----------------------------------------------------------------------------
References:
-----------------------------------------------------------------------------
Code:
def statistic(la):
return la.frobenius_rank()
-----------------------------------------------------------------------------
Statistic values:
[[1],[]] => 1
[[2],[]] => 1
[[1,1],[]] => 1
[[2,1],[1]] => 2
[[3],[]] => 1
[[2,1],[]] => 1
[[3,1],[1]] => 2
[[2,2],[1]] => 1
[[3,2],[2]] => 2
[[1,1,1],[]] => 1
[[2,2,1],[1,1]] => 2
[[2,1,1],[1]] => 2
[[3,2,1],[2,1]] => 3
[[4],[]] => 1
[[3,1],[]] => 1
[[4,1],[1]] => 2
[[2,2],[]] => 2
[[3,2],[1]] => 1
[[4,2],[2]] => 2
[[2,1,1],[]] => 1
[[3,2,1],[1,1]] => 2
[[3,1,1],[1]] => 2
[[4,2,1],[2,1]] => 3
[[3,3],[2]] => 1
[[4,3],[3]] => 2
[[2,2,1],[1]] => 1
[[3,3,1],[2,1]] => 2
[[3,2,1],[2]] => 2
[[4,3,1],[3,1]] => 3
[[2,2,2],[1,1]] => 1
[[3,3,2],[2,2]] => 2
[[3,2,2],[2,1]] => 2
[[4,3,2],[3,2]] => 3
[[1,1,1,1],[]] => 1
[[2,2,2,1],[1,1,1]] => 2
[[2,2,1,1],[1,1]] => 2
[[3,3,2,1],[2,2,1]] => 3
[[2,1,1,1],[1]] => 2
[[3,2,2,1],[2,1,1]] => 3
[[3,2,1,1],[2,1]] => 3
[[4,3,2,1],[3,2,1]] => 4
[[5],[]] => 1
[[4,1],[]] => 1
[[5,1],[1]] => 2
[[3,2],[]] => 2
[[4,2],[1]] => 1
[[5,2],[2]] => 2
[[3,1,1],[]] => 1
[[4,2,1],[1,1]] => 2
[[4,1,1],[1]] => 2
[[5,2,1],[2,1]] => 3
[[3,3],[1]] => 2
[[4,3],[2]] => 1
[[5,3],[3]] => 2
[[2,2,1],[]] => 2
[[3,3,1],[1,1]] => 3
[[3,2,1],[1]] => 1
[[4,3,1],[2,1]] => 2
[[4,2,1],[2]] => 2
[[5,3,1],[3,1]] => 3
[[3,2,2],[1,1]] => 1
[[4,3,2],[2,2]] => 2
[[4,2,2],[2,1]] => 2
[[5,3,2],[3,2]] => 3
[[2,1,1,1],[]] => 1
[[3,2,2,1],[1,1,1]] => 2
[[3,2,1,1],[1,1]] => 2
[[4,3,2,1],[2,2,1]] => 3
[[3,1,1,1],[1]] => 2
[[4,2,2,1],[2,1,1]] => 3
[[4,2,1,1],[2,1]] => 3
[[5,3,2,1],[3,2,1]] => 4
[[4,4],[3]] => 1
[[5,4],[4]] => 2
[[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]] => 2
[[3,3,2],[2,1]] => 1
[[4,4,2],[3,2]] => 2
[[3,2,2],[2]] => 3
[[4,3,2],[3,1]] => 2
[[5,4,2],[4,2]] => 3
[[2,2,1,1],[1]] => 1
[[3,3,2,1],[2,1,1]] => 2
[[3,3,1,1],[2,1]] => 2
[[4,4,2,1],[3,2,1]] => 3
[[3,2,1,1],[2]] => 2
[[4,3,2,1],[3,1,1]] => 3
[[4,3,1,1],[3,1]] => 3
[[5,4,2,1],[4,2,1]] => 4
[[3,3,3],[2,2]] => 1
[[4,4,3],[3,3]] => 2
[[4,3,3],[3,2]] => 2
[[5,4,3],[4,3]] => 3
[[2,2,2,1],[1,1]] => 1
[[3,3,3,1],[2,2,1]] => 2
[[3,3,2,1],[2,2]] => 2
[[4,4,3,1],[3,3,1]] => 3
[[3,2,2,1],[2,1]] => 2
[[4,3,3,1],[3,2,1]] => 3
[[4,3,2,1],[3,2]] => 3
[[5,4,3,1],[4,3,1]] => 4
[[2,2,2,2],[1,1,1]] => 1
[[3,3,3,2],[2,2,2]] => 2
[[3,3,2,2],[2,2,1]] => 2
[[4,4,3,2],[3,3,2]] => 3
[[3,2,2,2],[2,1,1]] => 2
[[4,3,3,2],[3,2,2]] => 3
[[4,3,2,2],[3,2,1]] => 3
[[5,4,3,2],[4,3,2]] => 4
[[1,1,1,1,1],[]] => 1
[[2,2,2,2,1],[1,1,1,1]] => 2
[[2,2,2,1,1],[1,1,1]] => 2
[[3,3,3,2,1],[2,2,2,1]] => 3
[[2,2,1,1,1],[1,1]] => 2
[[3,3,2,2,1],[2,2,1,1]] => 3
[[3,3,2,1,1],[2,2,1]] => 3
[[4,4,3,2,1],[3,3,2,1]] => 4
[[2,1,1,1,1],[1]] => 2
[[3,2,2,2,1],[2,1,1,1]] => 3
[[3,2,2,1,1],[2,1,1]] => 3
[[4,3,3,2,1],[3,2,2,1]] => 4
[[3,2,1,1,1],[2,1]] => 3
[[4,3,2,2,1],[3,2,1,1]] => 4
[[4,3,2,1,1],[3,2,1]] => 4
[[5,4,3,2,1],[4,3,2,1]] => 5
[[6],[]] => 1
[[5,1],[]] => 1
[[6,1],[1]] => 2
[[4,2],[]] => 2
[[5,2],[1]] => 1
[[6,2],[2]] => 2
[[4,1,1],[]] => 1
[[5,2,1],[1,1]] => 2
[[5,1,1],[1]] => 2
[[6,2,1],[2,1]] => 3
[[3,3],[]] => 2
[[4,3],[1]] => 2
[[5,3],[2]] => 1
[[6,3],[3]] => 2
[[3,2,1],[]] => 2
[[4,3,1],[1,1]] => 3
[[4,2,1],[1]] => 1
[[5,3,1],[2,1]] => 2
[[5,2,1],[2]] => 2
[[6,3,1],[3,1]] => 3
[[4,2,2],[1,1]] => 1
[[5,3,2],[2,2]] => 2
[[5,2,2],[2,1]] => 2
[[6,3,2],[3,2]] => 3
[[3,1,1,1],[]] => 1
[[4,2,2,1],[1,1,1]] => 2
[[4,2,1,1],[1,1]] => 2
[[5,3,2,1],[2,2,1]] => 3
[[4,1,1,1],[1]] => 2
[[5,2,2,1],[2,1,1]] => 3
[[5,2,1,1],[2,1]] => 3
[[6,3,2,1],[3,2,1]] => 4
[[4,4],[2]] => 2
[[5,4],[3]] => 1
[[6,4],[4]] => 2
[[3,3,1],[1]] => 2
[[4,4,1],[2,1]] => 3
[[4,3,1],[2]] => 1
[[5,4,1],[3,1]] => 2
[[5,3,1],[3]] => 2
[[6,4,1],[4,1]] => 3
[[2,2,2],[]] => 2
[[3,3,2],[1,1]] => 2
[[4,4,2],[2,2]] => 3
[[3,2,2],[1]] => 2
[[4,3,2],[2,1]] => 1
[[5,4,2],[3,2]] => 2
[[4,2,2],[2]] => 3
[[5,3,2],[3,1]] => 2
[[6,4,2],[4,2]] => 3
[[2,2,1,1],[]] => 2
[[3,3,2,1],[1,1,1]] => 3
[[3,3,1,1],[1,1]] => 3
[[4,4,2,1],[2,2,1]] => 4
[[3,2,1,1],[1]] => 1
[[4,3,2,1],[2,1,1]] => 2
[[4,3,1,1],[2,1]] => 2
[[5,4,2,1],[3,2,1]] => 3
[[4,2,1,1],[2]] => 2
[[5,3,2,1],[3,1,1]] => 3
[[5,3,1,1],[3,1]] => 3
[[6,4,2,1],[4,2,1]] => 4
[[4,3,3],[2,2]] => 1
[[5,4,3],[3,3]] => 2
[[5,3,3],[3,2]] => 2
[[6,4,3],[4,3]] => 3
[[3,2,2,1],[1,1]] => 1
[[4,3,3,1],[2,2,1]] => 2
[[4,3,2,1],[2,2]] => 2
[[5,4,3,1],[3,3,1]] => 3
[[4,2,2,1],[2,1]] => 2
[[5,3,3,1],[3,2,1]] => 3
[[5,3,2,1],[3,2]] => 3
[[6,4,3,1],[4,3,1]] => 4
[[3,2,2,2],[1,1,1]] => 1
[[4,3,3,2],[2,2,2]] => 2
[[4,3,2,2],[2,2,1]] => 2
[[5,4,3,2],[3,3,2]] => 3
[[4,2,2,2],[2,1,1]] => 2
[[5,3,3,2],[3,2,2]] => 3
[[5,3,2,2],[3,2,1]] => 3
[[6,4,3,2],[4,3,2]] => 4
[[2,1,1,1,1],[]] => 1
[[3,2,2,2,1],[1,1,1,1]] => 2
[[3,2,2,1,1],[1,1,1]] => 2
[[4,3,3,2,1],[2,2,2,1]] => 3
[[3,2,1,1,1],[1,1]] => 2
[[4,3,2,2,1],[2,2,1,1]] => 3
[[4,3,2,1,1],[2,2,1]] => 3
[[5,4,3,2,1],[3,3,2,1]] => 4
[[3,1,1,1,1],[1]] => 2
[[4,2,2,2,1],[2,1,1,1]] => 3
[[4,2,2,1,1],[2,1,1]] => 3
[[5,3,3,2,1],[3,2,2,1]] => 4
[[4,2,1,1,1],[2,1]] => 3
[[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]] => 5
[[5,5],[4]] => 1
[[6,5],[5]] => 2
[[4,4,1],[3]] => 1
[[5,5,1],[4,1]] => 2
[[5,4,1],[4]] => 2
[[6,5,1],[5,1]] => 3
[[3,3,2],[2]] => 2
[[4,4,2],[3,1]] => 1
[[5,5,2],[4,2]] => 2
[[4,3,2],[3]] => 3
[[5,4,2],[4,1]] => 2
[[6,5,2],[5,2]] => 3
[[3,3,1,1],[2]] => 1
[[4,4,2,1],[3,1,1]] => 2
[[4,4,1,1],[3,1]] => 2
[[5,5,2,1],[4,2,1]] => 3
[[4,3,1,1],[3]] => 2
[[5,4,2,1],[4,1,1]] => 3
[[5,4,1,1],[4,1]] => 3
[[6,5,2,1],[5,2,1]] => 4
[[3,3,3],[2,1]] => 2
[[4,4,3],[3,2]] => 1
[[5,5,3],[4,3]] => 2
[[4,3,3],[3,1]] => 3
[[5,4,3],[4,2]] => 2
[[6,5,3],[5,3]] => 3
[[2,2,2,1],[1]] => 2
[[3,3,3,1],[2,1,1]] => 3
[[3,3,2,1],[2,1]] => 1
[[4,4,3,1],[3,2,1]] => 2
[[4,4,2,1],[3,2]] => 2
[[5,5,3,1],[4,3,1]] => 3
[[3,2,2,1],[2]] => 3
[[4,3,3,1],[3,1,1]] => 4
[[4,3,2,1],[3,1]] => 2
[[5,4,3,1],[4,2,1]] => 3
[[5,4,2,1],[4,2]] => 3
[[6,5,3,1],[5,3,1]] => 4
[[3,3,2,2],[2,1,1]] => 1
[[4,4,3,2],[3,2,2]] => 2
[[4,4,2,2],[3,2,1]] => 2
[[5,5,3,2],[4,3,2]] => 3
[[4,3,2,2],[3,1,1]] => 2
[[5,4,3,2],[4,2,2]] => 3
[[5,4,2,2],[4,2,1]] => 3
[[6,5,3,2],[5,3,2]] => 4
[[2,2,1,1,1],[1]] => 1
[[3,3,2,2,1],[2,1,1,1]] => 2
[[3,3,2,1,1],[2,1,1]] => 2
[[4,4,3,2,1],[3,2,2,1]] => 3
[[3,3,1,1,1],[2,1]] => 2
[[4,4,2,2,1],[3,2,1,1]] => 3
[[4,4,2,1,1],[3,2,1]] => 3
[[5,5,3,2,1],[4,3,2,1]] => 4
[[3,2,1,1,1],[2]] => 2
[[4,3,2,2,1],[3,1,1,1]] => 3
[[4,3,2,1,1],[3,1,1]] => 3
[[5,4,3,2,1],[4,2,2,1]] => 4
[[4,3,1,1,1],[3,1]] => 3
[[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]] => 5
[[4,4,4],[3,3]] => 1
[[5,5,4],[4,4]] => 2
[[5,4,4],[4,3]] => 2
[[6,5,4],[5,4]] => 3
[[3,3,3,1],[2,2]] => 1
[[4,4,4,1],[3,3,1]] => 2
[[4,4,3,1],[3,3]] => 2
[[5,5,4,1],[4,4,1]] => 3
[[4,3,3,1],[3,2]] => 2
[[5,4,4,1],[4,3,1]] => 3
[[5,4,3,1],[4,3]] => 3
[[6,5,4,1],[5,4,1]] => 4
[[2,2,2,2],[1,1]] => 2
[[3,3,3,2],[2,2,1]] => 1
[[4,4,4,2],[3,3,2]] => 2
[[3,3,2,2],[2,2]] => 3
[[4,4,3,2],[3,3,1]] => 2
[[5,5,4,2],[4,4,2]] => 3
[[3,2,2,2],[2,1]] => 3
[[4,3,3,2],[3,2,1]] => 2
[[5,4,4,2],[4,3,2]] => 3
[[4,3,2,2],[3,2]] => 4
[[5,4,3,2],[4,3,1]] => 3
[[6,5,4,2],[5,4,2]] => 4
[[2,2,2,1,1],[1,1]] => 1
[[3,3,3,2,1],[2,2,1,1]] => 2
[[3,3,3,1,1],[2,2,1]] => 2
[[4,4,4,2,1],[3,3,2,1]] => 3
[[3,3,2,1,1],[2,2]] => 2
[[4,4,3,2,1],[3,3,1,1]] => 3
[[4,4,3,1,1],[3,3,1]] => 3
[[5,5,4,2,1],[4,4,2,1]] => 4
[[3,2,2,1,1],[2,1]] => 2
[[4,3,3,2,1],[3,2,1,1]] => 3
[[4,3,3,1,1],[3,2,1]] => 3
[[5,4,4,2,1],[4,3,2,1]] => 4
[[4,3,2,1,1],[3,2]] => 3
[[5,4,3,2,1],[4,3,1,1]] => 4
[[5,4,3,1,1],[4,3,1]] => 4
[[6,5,4,2,1],[5,4,2,1]] => 5
[[3,3,3,3],[2,2,2]] => 1
[[4,4,4,3],[3,3,3]] => 2
[[4,4,3,3],[3,3,2]] => 2
[[5,5,4,3],[4,4,3]] => 3
[[4,3,3,3],[3,2,2]] => 2
[[5,4,4,3],[4,3,3]] => 3
[[5,4,3,3],[4,3,2]] => 3
[[6,5,4,3],[5,4,3]] => 4
[[2,2,2,2,1],[1,1,1]] => 1
[[3,3,3,3,1],[2,2,2,1]] => 2
[[3,3,3,2,1],[2,2,2]] => 2
[[4,4,4,3,1],[3,3,3,1]] => 3
[[3,3,2,2,1],[2,2,1]] => 2
[[4,4,3,3,1],[3,3,2,1]] => 3
[[4,4,3,2,1],[3,3,2]] => 3
[[5,5,4,3,1],[4,4,3,1]] => 4
[[3,2,2,2,1],[2,1,1]] => 2
[[4,3,3,3,1],[3,2,2,1]] => 3
[[4,3,3,2,1],[3,2,2]] => 3
[[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]] => 4
[[5,4,3,2,1],[4,3,2]] => 4
[[6,5,4,3,1],[5,4,3,1]] => 5
[[2,2,2,2,2],[1,1,1,1]] => 1
[[3,3,3,3,2],[2,2,2,2]] => 2
[[3,3,3,2,2],[2,2,2,1]] => 2
[[4,4,4,3,2],[3,3,3,2]] => 3
[[3,3,2,2,2],[2,2,1,1]] => 2
[[4,4,3,3,2],[3,3,2,2]] => 3
[[4,4,3,2,2],[3,3,2,1]] => 3
[[5,5,4,3,2],[4,4,3,2]] => 4
[[3,2,2,2,2],[2,1,1,1]] => 2
[[4,3,3,3,2],[3,2,2,2]] => 3
[[4,3,3,2,2],[3,2,2,1]] => 3
[[5,4,4,3,2],[4,3,3,2]] => 4
[[4,3,2,2,2],[3,2,1,1]] => 3
[[5,4,3,3,2],[4,3,2,2]] => 4
[[5,4,3,2,2],[4,3,2,1]] => 4
[[6,5,4,3,2],[5,4,3,2]] => 5
[[1,1,1,1,1,1],[]] => 1
[[2,2,2,2,2,1],[1,1,1,1,1]] => 2
[[2,2,2,2,1,1],[1,1,1,1]] => 2
[[3,3,3,3,2,1],[2,2,2,2,1]] => 3
[[2,2,2,1,1,1],[1,1,1]] => 2
[[3,3,3,2,2,1],[2,2,2,1,1]] => 3
[[3,3,3,2,1,1],[2,2,2,1]] => 3
[[4,4,4,3,2,1],[3,3,3,2,1]] => 4
[[2,2,1,1,1,1],[1,1]] => 2
[[3,3,2,2,2,1],[2,2,1,1,1]] => 3
[[3,3,2,2,1,1],[2,2,1,1]] => 3
[[4,4,3,3,2,1],[3,3,2,2,1]] => 4
[[3,3,2,1,1,1],[2,2,1]] => 3
[[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]] => 5
[[2,1,1,1,1,1],[1]] => 2
[[3,2,2,2,2,1],[2,1,1,1,1]] => 3
[[3,2,2,2,1,1],[2,1,1,1]] => 3
[[4,3,3,3,2,1],[3,2,2,2,1]] => 4
[[3,2,2,1,1,1],[2,1,1]] => 3
[[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]] => 5
[[3,2,1,1,1,1],[2,1]] => 3
[[4,3,2,2,2,1],[3,2,1,1,1]] => 4
[[4,3,2,2,1,1],[3,2,1,1]] => 4
[[5,4,3,3,2,1],[4,3,2,2,1]] => 5
[[4,3,2,1,1,1],[3,2,1]] => 4
[[5,4,3,2,2,1],[4,3,2,1,1]] => 5
[[5,4,3,2,1,1],[4,3,2,1]] => 5
[[6,5,4,3,2,1],[5,4,3,2,1]] => 6
[[7],[]] => 1
[[6,1],[]] => 1
[[7,1],[1]] => 2
[[5,2],[]] => 2
[[6,2],[1]] => 1
[[7,2],[2]] => 2
[[5,1,1],[]] => 1
[[6,2,1],[1,1]] => 2
[[6,1,1],[1]] => 2
[[7,2,1],[2,1]] => 3
[[4,3],[]] => 2
[[5,3],[1]] => 2
[[6,3],[2]] => 1
[[7,3],[3]] => 2
[[4,2,1],[]] => 2
[[5,3,1],[1,1]] => 3
[[5,2,1],[1]] => 1
[[6,3,1],[2,1]] => 2
[[6,2,1],[2]] => 2
[[7,3,1],[3,1]] => 3
[[5,2,2],[1,1]] => 1
[[6,3,2],[2,2]] => 2
[[6,2,2],[2,1]] => 2
[[7,3,2],[3,2]] => 3
[[4,1,1,1],[]] => 1
[[5,2,2,1],[1,1,1]] => 2
[[5,2,1,1],[1,1]] => 2
[[6,3,2,1],[2,2,1]] => 3
[[5,1,1,1],[1]] => 2
[[6,2,2,1],[2,1,1]] => 3
[[6,2,1,1],[2,1]] => 3
[[7,3,2,1],[3,2,1]] => 4
[[4,4],[1]] => 2
[[5,4],[2]] => 2
[[6,4],[3]] => 1
[[7,4],[4]] => 2
[[3,3,1],[]] => 2
[[4,4,1],[1,1]] => 3
[[4,3,1],[1]] => 2
[[5,4,1],[2,1]] => 3
[[5,3,1],[2]] => 1
[[6,4,1],[3,1]] => 2
[[6,3,1],[3]] => 2
[[7,4,1],[4,1]] => 3
[[3,2,2],[]] => 2
[[4,3,2],[1,1]] => 2
[[5,4,2],[2,2]] => 3
[[4,2,2],[1]] => 2
[[5,3,2],[2,1]] => 1
[[6,4,2],[3,2]] => 2
[[5,2,2],[2]] => 3
[[6,3,2],[3,1]] => 2
[[7,4,2],[4,2]] => 3
[[3,2,1,1],[]] => 2
[[4,3,2,1],[1,1,1]] => 3
[[4,3,1,1],[1,1]] => 3
[[5,4,2,1],[2,2,1]] => 4
[[4,2,1,1],[1]] => 1
[[5,3,2,1],[2,1,1]] => 2
[[5,3,1,1],[2,1]] => 2
[[6,4,2,1],[3,2,1]] => 3
[[5,2,1,1],[2]] => 2
[[6,3,2,1],[3,1,1]] => 3
[[6,3,1,1],[3,1]] => 3
[[7,4,2,1],[4,2,1]] => 4
[[5,3,3],[2,2]] => 1
[[6,4,3],[3,3]] => 2
[[6,3,3],[3,2]] => 2
[[7,4,3],[4,3]] => 3
[[4,2,2,1],[1,1]] => 1
[[5,3,3,1],[2,2,1]] => 2
[[5,3,2,1],[2,2]] => 2
[[6,4,3,1],[3,3,1]] => 3
[[5,2,2,1],[2,1]] => 2
[[6,3,3,1],[3,2,1]] => 3
[[6,3,2,1],[3,2]] => 3
[[7,4,3,1],[4,3,1]] => 4
[[4,2,2,2],[1,1,1]] => 1
[[5,3,3,2],[2,2,2]] => 2
[[5,3,2,2],[2,2,1]] => 2
[[6,4,3,2],[3,3,2]] => 3
[[5,2,2,2],[2,1,1]] => 2
[[6,3,3,2],[3,2,2]] => 3
[[6,3,2,2],[3,2,1]] => 3
[[7,4,3,2],[4,3,2]] => 4
[[3,1,1,1,1],[]] => 1
[[4,2,2,2,1],[1,1,1,1]] => 2
[[4,2,2,1,1],[1,1,1]] => 2
[[5,3,3,2,1],[2,2,2,1]] => 3
[[4,2,1,1,1],[1,1]] => 2
[[5,3,2,2,1],[2,2,1,1]] => 3
[[5,3,2,1,1],[2,2,1]] => 3
[[6,4,3,2,1],[3,3,2,1]] => 4
[[4,1,1,1,1],[1]] => 2
[[5,2,2,2,1],[2,1,1,1]] => 3
[[5,2,2,1,1],[2,1,1]] => 3
[[6,3,3,2,1],[3,2,2,1]] => 4
[[5,2,1,1,1],[2,1]] => 3
[[6,3,2,2,1],[3,2,1,1]] => 4
[[6,3,2,1,1],[3,2,1]] => 4
[[7,4,3,2,1],[4,3,2,1]] => 5
[[5,5],[3]] => 2
[[6,5],[4]] => 1
[[7,5],[5]] => 2
[[4,4,1],[2]] => 2
[[5,5,1],[3,1]] => 3
[[5,4,1],[3]] => 1
[[6,5,1],[4,1]] => 2
[[6,4,1],[4]] => 2
[[7,5,1],[5,1]] => 3
[[3,3,2],[1]] => 3
[[4,4,2],[2,1]] => 2
[[5,5,2],[3,2]] => 3
[[4,3,2],[2]] => 2
[[5,4,2],[3,1]] => 1
[[6,5,2],[4,2]] => 2
[[5,3,2],[3]] => 3
[[6,4,2],[4,1]] => 2
[[7,5,2],[5,2]] => 3
[[3,3,1,1],[1]] => 2
[[4,4,2,1],[2,1,1]] => 3
[[4,4,1,1],[2,1]] => 3
[[5,5,2,1],[3,2,1]] => 4
[[4,3,1,1],[2]] => 1
[[5,4,2,1],[3,1,1]] => 2
[[5,4,1,1],[3,1]] => 2
[[6,5,2,1],[4,2,1]] => 3
[[5,3,1,1],[3]] => 2
[[6,4,2,1],[4,1,1]] => 3
[[6,4,1,1],[4,1]] => 3
[[7,5,2,1],[5,2,1]] => 4
[[3,3,3],[1,1]] => 2
[[4,4,3],[2,2]] => 2
[[5,5,3],[3,3]] => 3
[[4,3,3],[2,1]] => 2
[[5,4,3],[3,2]] => 1
[[6,5,3],[4,3]] => 2
[[5,3,3],[3,1]] => 3
[[6,4,3],[4,2]] => 2
[[7,5,3],[5,3]] => 3
[[2,2,2,1],[]] => 2
[[3,3,3,1],[1,1,1]] => 3
[[3,3,2,1],[1,1]] => 2
[[4,4,3,1],[2,2,1]] => 3
[[4,4,2,1],[2,2]] => 3
[[5,5,3,1],[3,3,1]] => 4
[[3,2,2,1],[1]] => 2
[[4,3,3,1],[2,1,1]] => 3
[[4,3,2,1],[2,1]] => 1
[[5,4,3,1],[3,2,1]] => 2
[[5,4,2,1],[3,2]] => 2
[[6,5,3,1],[4,3,1]] => 3
[[4,2,2,1],[2]] => 3
[[5,3,3,1],[3,1,1]] => 4
[[5,3,2,1],[3,1]] => 2
[[6,4,3,1],[4,2,1]] => 3
[[6,4,2,1],[4,2]] => 3
[[7,5,3,1],[5,3,1]] => 4
[[3,3,2,2],[1,1,1]] => 2
[[4,4,3,2],[2,2,2]] => 3
[[4,4,2,2],[2,2,1]] => 3
[[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]] => 2
[[6,5,3,2],[4,3,2]] => 3
[[5,3,2,2],[3,1,1]] => 2
[[6,4,3,2],[4,2,2]] => 3
[[6,4,2,2],[4,2,1]] => 3
[[7,5,3,2],[5,3,2]] => 4
[[2,2,1,1,1],[]] => 2
[[3,3,2,2,1],[1,1,1,1]] => 3
[[3,3,2,1,1],[1,1,1]] => 3
[[4,4,3,2,1],[2,2,2,1]] => 4
[[3,3,1,1,1],[1,1]] => 3
[[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]] => 5
[[3,2,1,1,1],[1]] => 1
[[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]] => 3
[[4,3,1,1,1],[2,1]] => 2
[[5,4,2,2,1],[3,2,1,1]] => 3
[[5,4,2,1,1],[3,2,1]] => 3
[[6,5,3,2,1],[4,3,2,1]] => 4
[[4,2,1,1,1],[2]] => 2
[[5,3,2,2,1],[3,1,1,1]] => 3
[[5,3,2,1,1],[3,1,1]] => 3
[[6,4,3,2,1],[4,2,2,1]] => 4
[[5,3,1,1,1],[3,1]] => 3
[[6,4,2,2,1],[4,2,1,1]] => 4
[[6,4,2,1,1],[4,2,1]] => 4
[[7,5,3,2,1],[5,3,2,1]] => 5
[[5,4,4],[3,3]] => 1
[[6,5,4],[4,4]] => 2
[[6,4,4],[4,3]] => 2
[[7,5,4],[5,4]] => 3
[[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]] => 3
[[6,4,3,1],[4,3]] => 3
[[7,5,4,1],[5,4,1]] => 4
[[3,2,2,2],[1,1]] => 2
[[4,3,3,2],[2,2,1]] => 1
[[5,4,4,2],[3,3,2]] => 2
[[4,3,2,2],[2,2]] => 3
[[5,4,3,2],[3,3,1]] => 2
[[6,5,4,2],[4,4,2]] => 3
[[4,2,2,2],[2,1]] => 3
[[5,3,3,2],[3,2,1]] => 2
[[6,4,4,2],[4,3,2]] => 3
[[5,3,2,2],[3,2]] => 4
[[6,4,3,2],[4,3,1]] => 3
[[7,5,4,2],[5,4,2]] => 4
[[3,2,2,1,1],[1,1]] => 1
[[4,3,3,2,1],[2,2,1,1]] => 2
[[4,3,3,1,1],[2,2,1]] => 2
[[5,4,4,2,1],[3,3,2,1]] => 3
[[4,3,2,1,1],[2,2]] => 2
[[5,4,3,2,1],[3,3,1,1]] => 3
[[5,4,3,1,1],[3,3,1]] => 3
[[6,5,4,2,1],[4,4,2,1]] => 4
[[4,2,2,1,1],[2,1]] => 2
[[5,3,3,2,1],[3,2,1,1]] => 3
[[5,3,3,1,1],[3,2,1]] => 3
[[6,4,4,2,1],[4,3,2,1]] => 4
[[5,3,2,1,1],[3,2]] => 3
[[6,4,3,2,1],[4,3,1,1]] => 4
[[6,4,3,1,1],[4,3,1]] => 4
[[7,5,4,2,1],[5,4,2,1]] => 5
[[4,3,3,3],[2,2,2]] => 1
[[5,4,4,3],[3,3,3]] => 2
[[5,4,3,3],[3,3,2]] => 2
[[6,5,4,3],[4,4,3]] => 3
[[5,3,3,3],[3,2,2]] => 2
[[6,4,4,3],[4,3,3]] => 3
[[6,4,3,3],[4,3,2]] => 3
[[7,5,4,3],[5,4,3]] => 4
[[3,2,2,2,1],[1,1,1]] => 1
[[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]] => 3
[[4,3,2,2,1],[2,2,1]] => 2
[[5,4,3,3,1],[3,3,2,1]] => 3
[[5,4,3,2,1],[3,3,2]] => 3
[[6,5,4,3,1],[4,4,3,1]] => 4
[[4,2,2,2,1],[2,1,1]] => 2
[[5,3,3,3,1],[3,2,2,1]] => 3
[[5,3,3,2,1],[3,2,2]] => 3
[[6,4,4,3,1],[4,3,3,1]] => 4
[[5,3,2,2,1],[3,2,1]] => 3
[[6,4,3,3,1],[4,3,2,1]] => 4
[[6,4,3,2,1],[4,3,2]] => 4
[[7,5,4,3,1],[5,4,3,1]] => 5
[[3,2,2,2,2],[1,1,1,1]] => 1
[[4,3,3,3,2],[2,2,2,2]] => 2
[[4,3,3,2,2],[2,2,2,1]] => 2
[[5,4,4,3,2],[3,3,3,2]] => 3
[[4,3,2,2,2],[2,2,1,1]] => 2
[[5,4,3,3,2],[3,3,2,2]] => 3
[[5,4,3,2,2],[3,3,2,1]] => 3
[[6,5,4,3,2],[4,4,3,2]] => 4
[[4,2,2,2,2],[2,1,1,1]] => 2
[[5,3,3,3,2],[3,2,2,2]] => 3
[[5,3,3,2,2],[3,2,2,1]] => 3
[[6,4,4,3,2],[4,3,3,2]] => 4
[[5,3,2,2,2],[3,2,1,1]] => 3
[[6,4,3,3,2],[4,3,2,2]] => 4
[[6,4,3,2,2],[4,3,2,1]] => 4
[[7,5,4,3,2],[5,4,3,2]] => 5
[[2,1,1,1,1,1],[]] => 1
[[3,2,2,2,2,1],[1,1,1,1,1]] => 2
[[3,2,2,2,1,1],[1,1,1,1]] => 2
[[4,3,3,3,2,1],[2,2,2,2,1]] => 3
[[3,2,2,1,1,1],[1,1,1]] => 2
[[4,3,3,2,2,1],[2,2,2,1,1]] => 3
[[4,3,3,2,1,1],[2,2,2,1]] => 3
[[5,4,4,3,2,1],[3,3,3,2,1]] => 4
[[3,2,1,1,1,1],[1,1]] => 2
[[4,3,2,2,2,1],[2,2,1,1,1]] => 3
[[4,3,2,2,1,1],[2,2,1,1]] => 3
[[5,4,3,3,2,1],[3,3,2,2,1]] => 4
[[4,3,2,1,1,1],[2,2,1]] => 3
[[5,4,3,2,2,1],[3,3,2,1,1]] => 4
[[5,4,3,2,1,1],[3,3,2,1]] => 4
[[6,5,4,3,2,1],[4,4,3,2,1]] => 5
[[3,1,1,1,1,1],[1]] => 2
[[4,2,2,2,2,1],[2,1,1,1,1]] => 3
[[4,2,2,2,1,1],[2,1,1,1]] => 3
[[5,3,3,3,2,1],[3,2,2,2,1]] => 4
[[4,2,2,1,1,1],[2,1,1]] => 3
[[5,3,3,2,2,1],[3,2,2,1,1]] => 4
[[5,3,3,2,1,1],[3,2,2,1]] => 4
[[6,4,4,3,2,1],[4,3,3,2,1]] => 5
[[4,2,1,1,1,1],[2,1]] => 3
[[5,3,2,2,2,1],[3,2,1,1,1]] => 4
[[5,3,2,2,1,1],[3,2,1,1]] => 4
[[6,4,3,3,2,1],[4,3,2,2,1]] => 5
[[5,3,2,1,1,1],[3,2,1]] => 4
[[6,4,3,2,2,1],[4,3,2,1,1]] => 5
[[6,4,3,2,1,1],[4,3,2,1]] => 5
[[7,5,4,3,2,1],[5,4,3,2,1]] => 6
[[6,6],[5]] => 1
[[7,6],[6]] => 2
[[5,5,1],[4]] => 1
[[6,6,1],[5,1]] => 2
[[6,5,1],[5]] => 2
[[7,6,1],[6,1]] => 3
[[4,4,2],[3]] => 2
[[5,5,2],[4,1]] => 1
[[6,6,2],[5,2]] => 2
[[5,4,2],[4]] => 3
[[6,5,2],[5,1]] => 2
[[7,6,2],[6,2]] => 3
[[4,4,1,1],[3]] => 1
[[5,5,2,1],[4,1,1]] => 2
[[5,5,1,1],[4,1]] => 2
[[6,6,2,1],[5,2,1]] => 3
[[5,4,1,1],[4]] => 2
[[6,5,2,1],[5,1,1]] => 3
[[6,5,1,1],[5,1]] => 3
[[7,6,2,1],[6,2,1]] => 4
[[3,3,3],[2]] => 2
[[4,4,3],[3,1]] => 2
[[5,5,3],[4,2]] => 1
[[6,6,3],[5,3]] => 2
[[4,3,3],[3]] => 3
[[5,4,3],[4,1]] => 3
[[6,5,3],[5,2]] => 2
[[7,6,3],[6,3]] => 3
[[3,3,2,1],[2]] => 2
[[4,4,3,1],[3,1,1]] => 3
[[4,4,2,1],[3,1]] => 1
[[5,5,3,1],[4,2,1]] => 2
[[5,5,2,1],[4,2]] => 2
[[6,6,3,1],[5,3,1]] => 3
[[4,3,2,1],[3]] => 3
[[5,4,3,1],[4,1,1]] => 4
[[5,4,2,1],[4,1]] => 2
[[6,5,3,1],[5,2,1]] => 3
[[6,5,2,1],[5,2]] => 3
[[7,6,3,1],[6,3,1]] => 4
[[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]] => 3
[[5,4,2,2],[4,1,1]] => 2
[[6,5,3,2],[5,2,2]] => 3
[[6,5,2,2],[5,2,1]] => 3
[[7,6,3,2],[6,3,2]] => 4
[[3,3,1,1,1],[2]] => 1
[[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]] => 3
[[4,4,1,1,1],[3,1]] => 2
[[5,5,2,2,1],[4,2,1,1]] => 3
[[5,5,2,1,1],[4,2,1]] => 3
[[6,6,3,2,1],[5,3,2,1]] => 4
[[4,3,1,1,1],[3]] => 2
[[5,4,2,2,1],[4,1,1,1]] => 3
[[5,4,2,1,1],[4,1,1]] => 3
[[6,5,3,2,1],[5,2,2,1]] => 4
[[5,4,1,1,1],[4,1]] => 3
[[6,5,2,2,1],[5,2,1,1]] => 4
[[6,5,2,1,1],[5,2,1]] => 4
[[7,6,3,2,1],[6,3,2,1]] => 5
[[4,4,4],[3,2]] => 2
[[5,5,4],[4,3]] => 1
[[6,6,4],[5,4]] => 2
[[5,4,4],[4,2]] => 3
[[6,5,4],[5,3]] => 2
[[7,6,4],[6,4]] => 3
[[3,3,3,1],[2,1]] => 2
[[4,4,4,1],[3,2,1]] => 3
[[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]] => 3
[[5,4,4,1],[4,2,1]] => 4
[[5,4,3,1],[4,2]] => 2
[[6,5,4,1],[5,3,1]] => 3
[[6,5,3,1],[5,3]] => 3
[[7,6,4,1],[6,4,1]] => 4
[[2,2,2,2],[1]] => 2
[[3,3,3,2],[2,1,1]] => 2
[[4,4,4,2],[3,2,2]] => 3
[[3,3,2,2],[2,1]] => 2
[[4,4,3,2],[3,2,1]] => 1
[[5,5,4,2],[4,3,2]] => 2
[[4,4,2,2],[3,2]] => 3
[[5,5,3,2],[4,3,1]] => 2
[[6,6,4,2],[5,4,2]] => 3
[[3,2,2,2],[2]] => 3
[[4,3,3,2],[3,1,1]] => 3
[[5,4,4,2],[4,2,2]] => 4
[[4,3,2,2],[3,1]] => 3
[[5,4,3,2],[4,2,1]] => 2
[[6,5,4,2],[5,3,2]] => 3
[[5,4,2,2],[4,2]] => 4
[[6,5,3,2],[5,3,1]] => 3
[[7,6,4,2],[6,4,2]] => 4
[[2,2,2,1,1],[1]] => 2
[[3,3,3,2,1],[2,1,1,1]] => 3
[[3,3,3,1,1],[2,1,1]] => 3
[[4,4,4,2,1],[3,2,2,1]] => 4
[[3,3,2,1,1],[2,1]] => 1
[[4,4,3,2,1],[3,2,1,1]] => 2
[[4,4,3,1,1],[3,2,1]] => 2
[[5,5,4,2,1],[4,3,2,1]] => 3
[[4,4,2,1,1],[3,2]] => 2
[[5,5,3,2,1],[4,3,1,1]] => 3
[[5,5,3,1,1],[4,3,1]] => 3
[[6,6,4,2,1],[5,4,2,1]] => 4
[[3,2,2,1,1],[2]] => 3
[[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]] => 5
[[4,3,2,1,1],[3,1]] => 2
[[5,4,3,2,1],[4,2,1,1]] => 3
[[5,4,3,1,1],[4,2,1]] => 3
[[6,5,4,2,1],[5,3,2,1]] => 4
[[5,4,2,1,1],[4,2]] => 3
[[6,5,3,2,1],[5,3,1,1]] => 4
[[6,5,3,1,1],[5,3,1]] => 4
[[7,6,4,2,1],[6,4,2,1]] => 5
[[4,4,3,3],[3,2,2]] => 1
[[5,5,4,3],[4,3,3]] => 2
[[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]] => 3
[[7,6,4,3],[6,4,3]] => 4
[[3,3,2,2,1],[2,1,1]] => 1
[[4,4,3,3,1],[3,2,2,1]] => 2
[[4,4,3,2,1],[3,2,2]] => 2
[[5,5,4,3,1],[4,3,3,1]] => 3
[[4,4,2,2,1],[3,2,1]] => 2
[[5,5,3,3,1],[4,3,2,1]] => 3
[[5,5,3,2,1],[4,3,2]] => 3
[[6,6,4,3,1],[5,4,3,1]] => 4
[[4,3,2,2,1],[3,1,1]] => 2
[[5,4,3,3,1],[4,2,2,1]] => 3
[[5,4,3,2,1],[4,2,2]] => 3
[[6,5,4,3,1],[5,3,3,1]] => 4
[[5,4,2,2,1],[4,2,1]] => 3
[[6,5,3,3,1],[5,3,2,1]] => 4
[[6,5,3,2,1],[5,3,2]] => 4
[[7,6,4,3,1],[6,4,3,1]] => 5
[[3,3,2,2,2],[2,1,1,1]] => 1
[[4,4,3,3,2],[3,2,2,2]] => 2
[[4,4,3,2,2],[3,2,2,1]] => 2
[[5,5,4,3,2],[4,3,3,2]] => 3
[[4,4,2,2,2],[3,2,1,1]] => 2
[[5,5,3,3,2],[4,3,2,2]] => 3
[[5,5,3,2,2],[4,3,2,1]] => 3
[[6,6,4,3,2],[5,4,3,2]] => 4
[[4,3,2,2,2],[3,1,1,1]] => 2
[[5,4,3,3,2],[4,2,2,2]] => 3
[[5,4,3,2,2],[4,2,2,1]] => 3
[[6,5,4,3,2],[5,3,3,2]] => 4
[[5,4,2,2,2],[4,2,1,1]] => 3
[[6,5,3,3,2],[5,3,2,2]] => 4
[[6,5,3,2,2],[5,3,2,1]] => 4
[[7,6,4,3,2],[6,4,3,2]] => 5
[[2,2,1,1,1,1],[1]] => 1
[[3,3,2,2,2,1],[2,1,1,1,1]] => 2
[[3,3,2,2,1,1],[2,1,1,1]] => 2
[[4,4,3,3,2,1],[3,2,2,2,1]] => 3
[[3,3,2,1,1,1],[2,1,1]] => 2
[[4,4,3,2,2,1],[3,2,2,1,1]] => 3
[[4,4,3,2,1,1],[3,2,2,1]] => 3
[[5,5,4,3,2,1],[4,3,3,2,1]] => 4
[[3,3,1,1,1,1],[2,1]] => 2
[[4,4,2,2,2,1],[3,2,1,1,1]] => 3
[[4,4,2,2,1,1],[3,2,1,1]] => 3
[[5,5,3,3,2,1],[4,3,2,2,1]] => 4
[[4,4,2,1,1,1],[3,2,1]] => 3
[[5,5,3,2,2,1],[4,3,2,1,1]] => 4
[[5,5,3,2,1,1],[4,3,2,1]] => 4
[[6,6,4,3,2,1],[5,4,3,2,1]] => 5
[[3,2,1,1,1,1],[2]] => 2
[[4,3,2,2,2,1],[3,1,1,1,1]] => 3
[[4,3,2,2,1,1],[3,1,1,1]] => 3
[[5,4,3,3,2,1],[4,2,2,2,1]] => 4
[[4,3,2,1,1,1],[3,1,1]] => 3
[[5,4,3,2,2,1],[4,2,2,1,1]] => 4
[[5,4,3,2,1,1],[4,2,2,1]] => 4
[[6,5,4,3,2,1],[5,3,3,2,1]] => 5
[[4,3,1,1,1,1],[3,1]] => 3
[[5,4,2,2,2,1],[4,2,1,1,1]] => 4
[[5,4,2,2,1,1],[4,2,1,1]] => 4
[[6,5,3,3,2,1],[5,3,2,2,1]] => 5
[[5,4,2,1,1,1],[4,2,1]] => 4
[[6,5,3,2,2,1],[5,3,2,1,1]] => 5
[[6,5,3,2,1,1],[5,3,2,1]] => 5
[[7,6,4,3,2,1],[6,4,3,2,1]] => 6
[[5,5,5],[4,4]] => 1
[[6,6,5],[5,5]] => 2
[[6,5,5],[5,4]] => 2
[[7,6,5],[6,5]] => 3
[[4,4,4,1],[3,3]] => 1
[[5,5,5,1],[4,4,1]] => 2
[[5,5,4,1],[4,4]] => 2
[[6,6,5,1],[5,5,1]] => 3
[[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]] => 2
[[4,4,4,2],[3,3,1]] => 1
[[5,5,5,2],[4,4,2]] => 2
[[4,4,3,2],[3,3]] => 3
[[5,5,4,2],[4,4,1]] => 2
[[6,6,5,2],[5,5,2]] => 3
[[4,3,3,2],[3,2]] => 3
[[5,4,4,2],[4,3,1]] => 2
[[6,5,5,2],[5,4,2]] => 3
[[5,4,3,2],[4,3]] => 4
[[6,5,4,2],[5,4,1]] => 3
[[7,6,5,2],[6,5,2]] => 4
[[3,3,3,1,1],[2,2]] => 1
[[4,4,4,2,1],[3,3,1,1]] => 2
[[4,4,4,1,1],[3,3,1]] => 2
[[5,5,5,2,1],[4,4,2,1]] => 3
[[4,4,3,1,1],[3,3]] => 2
[[5,5,4,2,1],[4,4,1,1]] => 3
[[5,5,4,1,1],[4,4,1]] => 3
[[6,6,5,2,1],[5,5,2,1]] => 4
[[4,3,3,1,1],[3,2]] => 2
[[5,4,4,2,1],[4,3,1,1]] => 3
[[5,4,4,1,1],[4,3,1]] => 3
[[6,5,5,2,1],[5,4,2,1]] => 4
[[5,4,3,1,1],[4,3]] => 3
[[6,5,4,2,1],[5,4,1,1]] => 4
[[6,5,4,1,1],[5,4,1]] => 4
[[7,6,5,2,1],[6,5,2,1]] => 5
[[3,3,3,3],[2,2,1]] => 2
[[4,4,4,3],[3,3,2]] => 1
[[5,5,5,3],[4,4,3]] => 2
[[4,4,3,3],[3,3,1]] => 3
[[5,5,4,3],[4,4,2]] => 2
[[6,6,5,3],[5,5,3]] => 3
[[4,3,3,3],[3,2,1]] => 3
[[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]] => 3
[[7,6,5,3],[6,5,3]] => 4
[[2,2,2,2,1],[1,1]] => 2
[[3,3,3,3,1],[2,2,1,1]] => 3
[[3,3,3,2,1],[2,2,1]] => 1
[[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]] => 3
[[3,3,2,2,1],[2,2]] => 3
[[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]] => 3
[[5,5,4,2,1],[4,4,2]] => 3
[[6,6,5,3,1],[5,5,3,1]] => 4
[[3,2,2,2,1],[2,1]] => 3
[[4,3,3,3,1],[3,2,1,1]] => 4
[[4,3,3,2,1],[3,2,1]] => 2
[[5,4,4,3,1],[4,3,2,1]] => 3
[[5,4,4,2,1],[4,3,2]] => 3
[[6,5,5,3,1],[5,4,3,1]] => 4
[[4,3,2,2,1],[3,2]] => 4
[[5,4,3,3,1],[4,3,1,1]] => 5
[[5,4,3,2,1],[4,3,1]] => 3
[[6,5,4,3,1],[5,4,2,1]] => 4
[[6,5,4,2,1],[5,4,2]] => 4
[[7,6,5,3,1],[6,5,3,1]] => 5
[[3,3,3,2,2],[2,2,1,1]] => 1
[[4,4,4,3,2],[3,3,2,2]] => 2
[[4,4,4,2,2],[3,3,2,1]] => 2
[[5,5,5,3,2],[4,4,3,2]] => 3
[[4,4,3,2,2],[3,3,1,1]] => 2
[[5,5,4,3,2],[4,4,2,2]] => 3
[[5,5,4,2,2],[4,4,2,1]] => 3
[[6,6,5,3,2],[5,5,3,2]] => 4
[[4,3,3,2,2],[3,2,1,1]] => 2
[[5,4,4,3,2],[4,3,2,2]] => 3
[[5,4,4,2,2],[4,3,2,1]] => 3
[[6,5,5,3,2],[5,4,3,2]] => 4
[[5,4,3,2,2],[4,3,1,1]] => 3
[[6,5,4,3,2],[5,4,2,2]] => 4
[[6,5,4,2,2],[5,4,2,1]] => 4
[[7,6,5,3,2],[6,5,3,2]] => 5
[[2,2,2,1,1,1],[1,1]] => 1
[[3,3,3,2,2,1],[2,2,1,1,1]] => 2
[[3,3,3,2,1,1],[2,2,1,1]] => 2
[[4,4,4,3,2,1],[3,3,2,2,1]] => 3
[[3,3,3,1,1,1],[2,2,1]] => 2
[[4,4,4,2,2,1],[3,3,2,1,1]] => 3
[[4,4,4,2,1,1],[3,3,2,1]] => 3
[[5,5,5,3,2,1],[4,4,3,2,1]] => 4
[[3,3,2,1,1,1],[2,2]] => 2
[[4,4,3,2,2,1],[3,3,1,1,1]] => 3
[[4,4,3,2,1,1],[3,3,1,1]] => 3
[[5,5,4,3,2,1],[4,4,2,2,1]] => 4
[[4,4,3,1,1,1],[3,3,1]] => 3
[[5,5,4,2,2,1],[4,4,2,1,1]] => 4
[[5,5,4,2,1,1],[4,4,2,1]] => 4
[[6,6,5,3,2,1],[5,5,3,2,1]] => 5
[[3,2,2,1,1,1],[2,1]] => 2
[[4,3,3,2,2,1],[3,2,1,1,1]] => 3
[[4,3,3,2,1,1],[3,2,1,1]] => 3
[[5,4,4,3,2,1],[4,3,2,2,1]] => 4
[[4,3,3,1,1,1],[3,2,1]] => 3
[[5,4,4,2,2,1],[4,3,2,1,1]] => 4
[[5,4,4,2,1,1],[4,3,2,1]] => 4
[[6,5,5,3,2,1],[5,4,3,2,1]] => 5
[[4,3,2,1,1,1],[3,2]] => 3
[[5,4,3,2,2,1],[4,3,1,1,1]] => 4
[[5,4,3,2,1,1],[4,3,1,1]] => 4
[[6,5,4,3,2,1],[5,4,2,2,1]] => 5
[[5,4,3,1,1,1],[4,3,1]] => 4
[[6,5,4,2,2,1],[5,4,2,1,1]] => 5
[[6,5,4,2,1,1],[5,4,2,1]] => 5
[[7,6,5,3,2,1],[6,5,3,2,1]] => 6
[[4,4,4,4],[3,3,3]] => 1
[[5,5,5,4],[4,4,4]] => 2
[[5,5,4,4],[4,4,3]] => 2
[[6,6,5,4],[5,5,4]] => 3
[[5,4,4,4],[4,3,3]] => 2
[[6,5,5,4],[5,4,4]] => 3
[[6,5,4,4],[5,4,3]] => 3
[[7,6,5,4],[6,5,4]] => 4
[[3,3,3,3,1],[2,2,2]] => 1
[[4,4,4,4,1],[3,3,3,1]] => 2
[[4,4,4,3,1],[3,3,3]] => 2
[[5,5,5,4,1],[4,4,4,1]] => 3
[[4,4,3,3,1],[3,3,2]] => 2
[[5,5,4,4,1],[4,4,3,1]] => 3
[[5,5,4,3,1],[4,4,3]] => 3
[[6,6,5,4,1],[5,5,4,1]] => 4
[[4,3,3,3,1],[3,2,2]] => 2
[[5,4,4,4,1],[4,3,3,1]] => 3
[[5,4,4,3,1],[4,3,3]] => 3
[[6,5,5,4,1],[5,4,4,1]] => 4
[[5,4,3,3,1],[4,3,2]] => 3
[[6,5,4,4,1],[5,4,3,1]] => 4
[[6,5,4,3,1],[5,4,3]] => 4
[[7,6,5,4,1],[6,5,4,1]] => 5
[[2,2,2,2,2],[1,1,1]] => 2
[[3,3,3,3,2],[2,2,2,1]] => 1
[[4,4,4,4,2],[3,3,3,2]] => 2
[[3,3,3,2,2],[2,2,2]] => 3
[[4,4,4,3,2],[3,3,3,1]] => 2
[[5,5,5,4,2],[4,4,4,2]] => 3
[[3,3,2,2,2],[2,2,1]] => 3
[[4,4,3,3,2],[3,3,2,1]] => 2
[[5,5,4,4,2],[4,4,3,2]] => 3
[[4,4,3,2,2],[3,3,2]] => 4
[[5,5,4,3,2],[4,4,3,1]] => 3
[[6,6,5,4,2],[5,5,4,2]] => 4
[[3,2,2,2,2],[2,1,1]] => 3
[[4,3,3,3,2],[3,2,2,1]] => 2
[[5,4,4,4,2],[4,3,3,2]] => 3
[[4,3,3,2,2],[3,2,2]] => 4
[[5,4,4,3,2],[4,3,3,1]] => 3
[[6,5,5,4,2],[5,4,4,2]] => 4
[[4,3,2,2,2],[3,2,1]] => 4
[[5,4,3,3,2],[4,3,2,1]] => 3
[[6,5,4,4,2],[5,4,3,2]] => 4
[[5,4,3,2,2],[4,3,2]] => 5
[[6,5,4,3,2],[5,4,3,1]] => 4
[[7,6,5,4,2],[6,5,4,2]] => 5
[[2,2,2,2,1,1],[1,1,1]] => 1
[[3,3,3,3,2,1],[2,2,2,1,1]] => 2
[[3,3,3,3,1,1],[2,2,2,1]] => 2
[[4,4,4,4,2,1],[3,3,3,2,1]] => 3
[[3,3,3,2,1,1],[2,2,2]] => 2
[[4,4,4,3,2,1],[3,3,3,1,1]] => 3
[[4,4,4,3,1,1],[3,3,3,1]] => 3
[[5,5,5,4,2,1],[4,4,4,2,1]] => 4
[[3,3,2,2,1,1],[2,2,1]] => 2
[[4,4,3,3,2,1],[3,3,2,1,1]] => 3
[[4,4,3,3,1,1],[3,3,2,1]] => 3
[[5,5,4,4,2,1],[4,4,3,2,1]] => 4
[[4,4,3,2,1,1],[3,3,2]] => 3
[[5,5,4,3,2,1],[4,4,3,1,1]] => 4
[[5,5,4,3,1,1],[4,4,3,1]] => 4
[[6,6,5,4,2,1],[5,5,4,2,1]] => 5
[[3,2,2,2,1,1],[2,1,1]] => 2
[[4,3,3,3,2,1],[3,2,2,1,1]] => 3
[[4,3,3,3,1,1],[3,2,2,1]] => 3
[[5,4,4,4,2,1],[4,3,3,2,1]] => 4
[[4,3,3,2,1,1],[3,2,2]] => 3
[[5,4,4,3,2,1],[4,3,3,1,1]] => 4
[[5,4,4,3,1,1],[4,3,3,1]] => 4
[[6,5,5,4,2,1],[5,4,4,2,1]] => 5
[[4,3,2,2,1,1],[3,2,1]] => 3
[[5,4,3,3,2,1],[4,3,2,1,1]] => 4
[[5,4,3,3,1,1],[4,3,2,1]] => 4
[[6,5,4,4,2,1],[5,4,3,2,1]] => 5
[[5,4,3,2,1,1],[4,3,2]] => 4
[[6,5,4,3,2,1],[5,4,3,1,1]] => 5
[[6,5,4,3,1,1],[5,4,3,1]] => 5
[[7,6,5,4,2,1],[6,5,4,2,1]] => 6
[[3,3,3,3,3],[2,2,2,2]] => 1
[[4,4,4,4,3],[3,3,3,3]] => 2
[[4,4,4,3,3],[3,3,3,2]] => 2
[[5,5,5,4,3],[4,4,4,3]] => 3
[[4,4,3,3,3],[3,3,2,2]] => 2
[[5,5,4,4,3],[4,4,3,3]] => 3
[[5,5,4,3,3],[4,4,3,2]] => 3
[[6,6,5,4,3],[5,5,4,3]] => 4
[[4,3,3,3,3],[3,2,2,2]] => 2
[[5,4,4,4,3],[4,3,3,3]] => 3
[[5,4,4,3,3],[4,3,3,2]] => 3
[[6,5,5,4,3],[5,4,4,3]] => 4
[[5,4,3,3,3],[4,3,2,2]] => 3
[[6,5,4,4,3],[5,4,3,3]] => 4
[[6,5,4,3,3],[5,4,3,2]] => 4
[[7,6,5,4,3],[6,5,4,3]] => 5
[[2,2,2,2,2,1],[1,1,1,1]] => 1
[[3,3,3,3,3,1],[2,2,2,2,1]] => 2
[[3,3,3,3,2,1],[2,2,2,2]] => 2
[[4,4,4,4,3,1],[3,3,3,3,1]] => 3
[[3,3,3,2,2,1],[2,2,2,1]] => 2
[[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]] => 4
[[3,3,2,2,2,1],[2,2,1,1]] => 2
[[4,4,3,3,3,1],[3,3,2,2,1]] => 3
[[4,4,3,3,2,1],[3,3,2,2]] => 3
[[5,5,4,4,3,1],[4,4,3,3,1]] => 4
[[4,4,3,2,2,1],[3,3,2,1]] => 3
[[5,5,4,3,3,1],[4,4,3,2,1]] => 4
[[5,5,4,3,2,1],[4,4,3,2]] => 4
[[6,6,5,4,3,1],[5,5,4,3,1]] => 5
[[3,2,2,2,2,1],[2,1,1,1]] => 2
[[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]] => 4
[[4,3,3,2,2,1],[3,2,2,1]] => 3
[[5,4,4,3,3,1],[4,3,3,2,1]] => 4
[[5,4,4,3,2,1],[4,3,3,2]] => 4
[[6,5,5,4,3,1],[5,4,4,3,1]] => 5
[[4,3,2,2,2,1],[3,2,1,1]] => 3
[[5,4,3,3,3,1],[4,3,2,2,1]] => 4
[[5,4,3,3,2,1],[4,3,2,2]] => 4
[[6,5,4,4,3,1],[5,4,3,3,1]] => 5
[[5,4,3,2,2,1],[4,3,2,1]] => 4
[[6,5,4,3,3,1],[5,4,3,2,1]] => 5
[[6,5,4,3,2,1],[5,4,3,2]] => 5
[[7,6,5,4,3,1],[6,5,4,3,1]] => 6
[[2,2,2,2,2,2],[1,1,1,1,1]] => 1
[[3,3,3,3,3,2],[2,2,2,2,2]] => 2
[[3,3,3,3,2,2],[2,2,2,2,1]] => 2
[[4,4,4,4,3,2],[3,3,3,3,2]] => 3
[[3,3,3,2,2,2],[2,2,2,1,1]] => 2
[[4,4,4,3,3,2],[3,3,3,2,2]] => 3
[[4,4,4,3,2,2],[3,3,3,2,1]] => 3
[[5,5,5,4,3,2],[4,4,4,3,2]] => 4
[[3,3,2,2,2,2],[2,2,1,1,1]] => 2
[[4,4,3,3,3,2],[3,3,2,2,2]] => 3
[[4,4,3,3,2,2],[3,3,2,2,1]] => 3
[[5,5,4,4,3,2],[4,4,3,3,2]] => 4
[[4,4,3,2,2,2],[3,3,2,1,1]] => 3
[[5,5,4,3,3,2],[4,4,3,2,2]] => 4
[[5,5,4,3,2,2],[4,4,3,2,1]] => 4
[[6,6,5,4,3,2],[5,5,4,3,2]] => 5
[[3,2,2,2,2,2],[2,1,1,1,1]] => 2
[[4,3,3,3,3,2],[3,2,2,2,2]] => 3
[[4,3,3,3,2,2],[3,2,2,2,1]] => 3
[[5,4,4,4,3,2],[4,3,3,3,2]] => 4
[[4,3,3,2,2,2],[3,2,2,1,1]] => 3
[[5,4,4,3,3,2],[4,3,3,2,2]] => 4
[[5,4,4,3,2,2],[4,3,3,2,1]] => 4
[[6,5,5,4,3,2],[5,4,4,3,2]] => 5
[[4,3,2,2,2,2],[3,2,1,1,1]] => 3
[[5,4,3,3,3,2],[4,3,2,2,2]] => 4
[[5,4,3,3,2,2],[4,3,2,2,1]] => 4
[[6,5,4,4,3,2],[5,4,3,3,2]] => 5
[[5,4,3,2,2,2],[4,3,2,1,1]] => 4
[[6,5,4,3,3,2],[5,4,3,2,2]] => 5
[[6,5,4,3,2,2],[5,4,3,2,1]] => 5
[[7,6,5,4,3,2],[6,5,4,3,2]] => 6
[[1,1,1,1,1,1,1],[]] => 1
[[2,2,2,2,2,2,1],[1,1,1,1,1,1]] => 2
[[2,2,2,2,2,1,1],[1,1,1,1,1]] => 2
[[3,3,3,3,3,2,1],[2,2,2,2,2,1]] => 3
[[2,2,2,2,1,1,1],[1,1,1,1]] => 2
[[3,3,3,3,2,2,1],[2,2,2,2,1,1]] => 3
[[3,3,3,3,2,1,1],[2,2,2,2,1]] => 3
[[4,4,4,4,3,2,1],[3,3,3,3,2,1]] => 4
[[2,2,2,1,1,1,1],[1,1,1]] => 2
[[3,3,3,2,2,2,1],[2,2,2,1,1,1]] => 3
[[3,3,3,2,2,1,1],[2,2,2,1,1]] => 3
[[4,4,4,3,3,2,1],[3,3,3,2,2,1]] => 4
[[3,3,3,2,1,1,1],[2,2,2,1]] => 3
[[4,4,4,3,2,2,1],[3,3,3,2,1,1]] => 4
-----------------------------------------------------------------------------
Created: Sep 23, 2020 at 23:29 by Martin Rubey
-----------------------------------------------------------------------------
Last Updated: Sep 23, 2020 at 23:29 by Martin Rubey