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* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
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* This information is distributed in the hope that it will be useful, *
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-----------------------------------------------------------------------------
Statistic identifier: St001921
-----------------------------------------------------------------------------
Collection: Plane partitions
-----------------------------------------------------------------------------
Description: The number of boxes that can be added such that the result is a plane partition.
-----------------------------------------------------------------------------
References:
-----------------------------------------------------------------------------
Code:
def statistic(p):
c = 0
for i, row in enumerate(list(p) + [(0,)]):
for j, entry in enumerate(row + (0,)):
h = None if not j else row[j-1]
v = None if not i or len(p[i-1]) == j else p[i-1][j]
if (h is None or entry < h) and (v is None or entry < v):
c += 1
return c
-----------------------------------------------------------------------------
Statistic values:
[[1]] => 3
[[1],[1]] => 4
[[2]] => 3
[[1,1]] => 3
[[1],[1],[1]] => 5
[[2],[1]] => 5
[[1,1],[1]] => 4
[[3]] => 3
[[2,1]] => 4
[[1,1,1]] => 3
[[1],[1],[1],[1]] => 6
[[2],[1],[1]] => 6
[[2],[2]] => 4
[[1,1],[1],[1]] => 5
[[1,1],[1,1]] => 4
[[3],[1]] => 5
[[2,1],[1]] => 6
[[1,1,1],[1]] => 4
[[4]] => 3
[[3,1]] => 4
[[2,2]] => 3
[[2,1,1]] => 4
[[1,1,1,1]] => 3
[[1],[1],[1],[1],[1]] => 7
[[2],[1],[1],[1]] => 7
[[2],[2],[1]] => 6
[[1,1],[1],[1],[1]] => 6
[[1,1],[1,1],[1]] => 5
[[3],[1],[1]] => 6
[[3],[2]] => 5
[[2,1],[1],[1]] => 7
[[2,1],[2]] => 5
[[2,1],[1,1]] => 6
[[1,1,1],[1],[1]] => 5
[[1,1,1],[1,1]] => 4
[[4],[1]] => 5
[[3,1],[1]] => 6
[[2,2],[1]] => 5
[[2,1,1],[1]] => 6
[[1,1,1,1],[1]] => 4
[[5]] => 3
[[4,1]] => 4
[[3,2]] => 4
[[3,1,1]] => 4
[[2,2,1]] => 4
[[2,1,1,1]] => 4
[[1,1,1,1,1]] => 3
[[1],[1],[1],[1],[1],[1]] => 8
[[2],[1],[1],[1],[1]] => 8
[[2],[2],[1],[1]] => 7
[[2],[2],[2]] => 5
[[1,1],[1],[1],[1],[1]] => 7
[[1,1],[1,1],[1],[1]] => 6
[[1,1],[1,1],[1,1]] => 5
[[3],[1],[1],[1]] => 7
[[3],[2],[1]] => 7
[[3],[3]] => 4
[[2,1],[1],[1],[1]] => 8
[[2,1],[2],[1]] => 7
[[2,1],[1,1],[1]] => 7
[[2,1],[2,1]] => 5
[[1,1,1],[1],[1],[1]] => 6
[[1,1,1],[1,1],[1]] => 5
[[1,1,1],[1,1,1]] => 4
[[4],[1],[1]] => 6
[[4],[2]] => 5
[[3,1],[1],[1]] => 7
[[3,1],[2]] => 6
[[3,1],[1,1]] => 6
[[2,2],[1],[1]] => 6
[[2,2],[2]] => 4
[[2,2],[1,1]] => 5
[[2,1,1],[1],[1]] => 7
[[2,1,1],[2]] => 5
[[2,1,1],[1,1]] => 6
[[1,1,1,1],[1],[1]] => 5
[[1,1,1,1],[1,1]] => 4
[[5],[1]] => 5
[[4,1],[1]] => 6
[[3,2],[1]] => 6
[[3,1,1],[1]] => 6
[[2,2,1],[1]] => 6
[[2,1,1,1],[1]] => 6
[[1,1,1,1,1],[1]] => 4
[[6]] => 3
[[5,1]] => 4
[[4,2]] => 4
[[4,1,1]] => 4
[[3,3]] => 3
[[3,2,1]] => 5
[[3,1,1,1]] => 4
[[2,2,2]] => 3
[[2,2,1,1]] => 4
[[2,1,1,1,1]] => 4
[[1,1,1,1,1,1]] => 3
[[1],[1],[1],[1],[1],[1],[1]] => 9
[[2],[1],[1],[1],[1],[1]] => 9
[[2],[2],[1],[1],[1]] => 8
[[2],[2],[2],[1]] => 7
[[1,1],[1],[1],[1],[1],[1]] => 8
[[1,1],[1,1],[1],[1],[1]] => 7
[[1,1],[1,1],[1,1],[1]] => 6
[[3],[1],[1],[1],[1]] => 8
[[3],[2],[1],[1]] => 8
[[3],[2],[2]] => 6
[[3],[3],[1]] => 6
[[2,1],[1],[1],[1],[1]] => 9
[[2,1],[2],[1],[1]] => 8
[[2,1],[2],[2]] => 6
[[2,1],[1,1],[1],[1]] => 8
[[2,1],[1,1],[1,1]] => 7
[[2,1],[2,1],[1]] => 7
[[1,1,1],[1],[1],[1],[1]] => 7
[[1,1,1],[1,1],[1],[1]] => 6
[[1,1,1],[1,1],[1,1]] => 5
[[1,1,1],[1,1,1],[1]] => 5
[[4],[1],[1],[1]] => 7
[[4],[2],[1]] => 7
[[4],[3]] => 5
[[3,1],[1],[1],[1]] => 8
[[3,1],[2],[1]] => 8
[[3,1],[1,1],[1]] => 7
[[3,1],[3]] => 5
[[3,1],[2,1]] => 6
[[2,2],[1],[1],[1]] => 7
[[2,2],[2],[1]] => 6
[[2,2],[1,1],[1]] => 6
[[2,2],[2,1]] => 5
[[2,1,1],[1],[1],[1]] => 8
[[2,1,1],[2],[1]] => 7
[[2,1,1],[1,1],[1]] => 7
[[2,1,1],[2,1]] => 5
[[2,1,1],[1,1,1]] => 6
[[1,1,1,1],[1],[1],[1]] => 6
[[1,1,1,1],[1,1],[1]] => 5
[[1,1,1,1],[1,1,1]] => 4
[[5],[1],[1]] => 6
[[5],[2]] => 5
[[4,1],[1],[1]] => 7
[[4,1],[2]] => 6
[[4,1],[1,1]] => 6
[[3,2],[1],[1]] => 7
[[3,2],[2]] => 6
[[3,2],[1,1]] => 6
[[3,1,1],[1],[1]] => 7
[[3,1,1],[2]] => 6
[[3,1,1],[1,1]] => 6
[[2,2,1],[1],[1]] => 7
[[2,2,1],[2]] => 5
[[2,2,1],[1,1]] => 6
[[2,1,1,1],[1],[1]] => 7
[[2,1,1,1],[2]] => 5
[[2,1,1,1],[1,1]] => 6
[[1,1,1,1,1],[1],[1]] => 5
[[1,1,1,1,1],[1,1]] => 4
[[6],[1]] => 5
[[5,1],[1]] => 6
[[4,2],[1]] => 6
[[4,1,1],[1]] => 6
[[3,3],[1]] => 5
[[3,2,1],[1]] => 7
[[3,1,1,1],[1]] => 6
[[2,2,2],[1]] => 5
[[2,2,1,1],[1]] => 6
[[2,1,1,1,1],[1]] => 6
[[1,1,1,1,1,1],[1]] => 4
[[7]] => 3
[[6,1]] => 4
[[5,2]] => 4
[[5,1,1]] => 4
[[4,3]] => 4
[[4,2,1]] => 5
[[4,1,1,1]] => 4
[[3,3,1]] => 4
[[3,2,2]] => 4
[[3,2,1,1]] => 5
[[3,1,1,1,1]] => 4
[[2,2,2,1]] => 4
[[2,2,1,1,1]] => 4
[[2,1,1,1,1,1]] => 4
[[1,1,1,1,1,1,1]] => 3
[[1],[1],[1],[1],[1],[1],[1],[1]] => 10
[[2],[1],[1],[1],[1],[1],[1]] => 10
[[2],[2],[1],[1],[1],[1]] => 9
[[2],[2],[2],[1],[1]] => 8
[[2],[2],[2],[2]] => 6
[[1,1],[1],[1],[1],[1],[1],[1]] => 9
[[1,1],[1,1],[1],[1],[1],[1]] => 8
[[1,1],[1,1],[1,1],[1],[1]] => 7
[[1,1],[1,1],[1,1],[1,1]] => 6
[[3],[1],[1],[1],[1],[1]] => 9
[[3],[2],[1],[1],[1]] => 9
[[3],[2],[2],[1]] => 8
[[3],[3],[1],[1]] => 7
[[3],[3],[2]] => 6
[[2,1],[1],[1],[1],[1],[1]] => 10
[[2,1],[2],[1],[1],[1]] => 9
[[2,1],[2],[2],[1]] => 8
[[2,1],[1,1],[1],[1],[1]] => 9
[[2,1],[1,1],[1,1],[1]] => 8
[[2,1],[2,1],[1],[1]] => 8
[[2,1],[2,1],[2]] => 6
[[2,1],[2,1],[1,1]] => 7
[[1,1,1],[1],[1],[1],[1],[1]] => 8
[[1,1,1],[1,1],[1],[1],[1]] => 7
[[1,1,1],[1,1],[1,1],[1]] => 6
[[1,1,1],[1,1,1],[1],[1]] => 6
[[1,1,1],[1,1,1],[1,1]] => 5
[[4],[1],[1],[1],[1]] => 8
[[4],[2],[1],[1]] => 8
[[4],[2],[2]] => 6
[[4],[3],[1]] => 7
[[4],[4]] => 4
[[3,1],[1],[1],[1],[1]] => 9
[[3,1],[2],[1],[1]] => 9
[[3,1],[2],[2]] => 7
[[3,1],[1,1],[1],[1]] => 8
[[3,1],[1,1],[1,1]] => 7
[[3,1],[3],[1]] => 7
[[3,1],[2,1],[1]] => 8
[[3,1],[3,1]] => 5
[[2,2],[1],[1],[1],[1]] => 8
[[2,2],[2],[1],[1]] => 7
[[2,2],[2],[2]] => 5
[[2,2],[1,1],[1],[1]] => 7
[[2,2],[1,1],[1,1]] => 6
[[2,2],[2,1],[1]] => 7
[[2,2],[2,2]] => 4
[[2,1,1],[1],[1],[1],[1]] => 9
[[2,1,1],[2],[1],[1]] => 8
[[2,1,1],[2],[2]] => 6
[[2,1,1],[1,1],[1],[1]] => 8
[[2,1,1],[1,1],[1,1]] => 7
[[2,1,1],[2,1],[1]] => 7
[[2,1,1],[1,1,1],[1]] => 7
[[2,1,1],[2,1,1]] => 5
[[1,1,1,1],[1],[1],[1],[1]] => 7
[[1,1,1,1],[1,1],[1],[1]] => 6
[[1,1,1,1],[1,1],[1,1]] => 5
[[1,1,1,1],[1,1,1],[1]] => 5
[[1,1,1,1],[1,1,1,1]] => 4
[[5],[1],[1],[1]] => 7
[[5],[2],[1]] => 7
[[5],[3]] => 5
[[4,1],[1],[1],[1]] => 8
[[4,1],[2],[1]] => 8
[[4,1],[1,1],[1]] => 7
[[4,1],[3]] => 6
[[4,1],[2,1]] => 6
[[3,2],[1],[1],[1]] => 8
[[3,2],[2],[1]] => 8
[[3,2],[1,1],[1]] => 7
[[3,2],[3]] => 5
[[3,2],[2,1]] => 7
[[3,1,1],[1],[1],[1]] => 8
[[3,1,1],[2],[1]] => 8
[[3,1,1],[1,1],[1]] => 7
[[3,1,1],[3]] => 5
[[3,1,1],[2,1]] => 6
[[3,1,1],[1,1,1]] => 6
[[2,2,1],[1],[1],[1]] => 8
[[2,2,1],[2],[1]] => 7
[[2,2,1],[1,1],[1]] => 7
[[2,2,1],[2,1]] => 6
[[2,2,1],[1,1,1]] => 6
[[2,1,1,1],[1],[1],[1]] => 8
[[2,1,1,1],[2],[1]] => 7
[[2,1,1,1],[1,1],[1]] => 7
[[2,1,1,1],[2,1]] => 5
[[2,1,1,1],[1,1,1]] => 6
[[1,1,1,1,1],[1],[1],[1]] => 6
[[1,1,1,1,1],[1,1],[1]] => 5
[[1,1,1,1,1],[1,1,1]] => 4
[[6],[1],[1]] => 6
[[6],[2]] => 5
[[5,1],[1],[1]] => 7
[[5,1],[2]] => 6
[[5,1],[1,1]] => 6
[[4,2],[1],[1]] => 7
[[4,2],[2]] => 6
[[4,2],[1,1]] => 6
[[4,1,1],[1],[1]] => 7
[[4,1,1],[2]] => 6
[[4,1,1],[1,1]] => 6
[[3,3],[1],[1]] => 6
[[3,3],[2]] => 5
[[3,3],[1,1]] => 5
[[3,2,1],[1],[1]] => 8
[[3,2,1],[2]] => 7
[[3,2,1],[1,1]] => 7
[[3,1,1,1],[1],[1]] => 7
[[3,1,1,1],[2]] => 6
[[3,1,1,1],[1,1]] => 6
[[2,2,2],[1],[1]] => 6
[[2,2,2],[2]] => 4
[[2,2,2],[1,1]] => 5
[[2,2,1,1],[1],[1]] => 7
[[2,2,1,1],[2]] => 5
[[2,2,1,1],[1,1]] => 6
[[2,1,1,1,1],[1],[1]] => 7
[[2,1,1,1,1],[2]] => 5
[[2,1,1,1,1],[1,1]] => 6
[[1,1,1,1,1,1],[1],[1]] => 5
[[1,1,1,1,1,1],[1,1]] => 4
[[7],[1]] => 5
[[6,1],[1]] => 6
[[5,2],[1]] => 6
[[5,1,1],[1]] => 6
[[4,3],[1]] => 6
[[4,2,1],[1]] => 7
[[4,1,1,1],[1]] => 6
[[3,3,1],[1]] => 6
[[3,2,2],[1]] => 6
[[3,2,1,1],[1]] => 7
[[3,1,1,1,1],[1]] => 6
[[2,2,2,1],[1]] => 6
[[2,2,1,1,1],[1]] => 6
[[2,1,1,1,1,1],[1]] => 6
[[1,1,1,1,1,1,1],[1]] => 4
[[8]] => 3
[[7,1]] => 4
[[6,2]] => 4
[[6,1,1]] => 4
[[5,3]] => 4
[[5,2,1]] => 5
[[5,1,1,1]] => 4
[[4,4]] => 3
[[4,3,1]] => 5
[[4,2,2]] => 4
[[4,2,1,1]] => 5
[[4,1,1,1,1]] => 4
[[3,3,2]] => 4
[[3,3,1,1]] => 4
[[3,2,2,1]] => 5
[[3,2,1,1,1]] => 5
[[3,1,1,1,1,1]] => 4
[[2,2,2,2]] => 3
[[2,2,2,1,1]] => 4
[[2,2,1,1,1,1]] => 4
[[2,1,1,1,1,1,1]] => 4
[[1,1,1,1,1,1,1,1]] => 3
[[1],[1],[1],[1],[1],[1],[1],[1],[1]] => 11
[[2],[1],[1],[1],[1],[1],[1],[1]] => 11
[[2],[2],[1],[1],[1],[1],[1]] => 10
[[2],[2],[2],[1],[1],[1]] => 9
[[2],[2],[2],[2],[1]] => 8
[[1,1],[1],[1],[1],[1],[1],[1],[1]] => 10
[[1,1],[1,1],[1],[1],[1],[1],[1]] => 9
[[1,1],[1,1],[1,1],[1],[1],[1]] => 8
[[1,1],[1,1],[1,1],[1,1],[1]] => 7
[[3],[1],[1],[1],[1],[1],[1]] => 10
[[3],[2],[1],[1],[1],[1]] => 10
[[3],[2],[2],[1],[1]] => 9
[[3],[2],[2],[2]] => 7
[[3],[3],[1],[1],[1]] => 8
[[3],[3],[2],[1]] => 8
[[3],[3],[3]] => 5
[[2,1],[1],[1],[1],[1],[1],[1]] => 11
[[2,1],[2],[1],[1],[1],[1]] => 10
[[2,1],[2],[2],[1],[1]] => 9
[[2,1],[2],[2],[2]] => 7
[[2,1],[1,1],[1],[1],[1],[1]] => 10
[[2,1],[1,1],[1,1],[1],[1]] => 9
[[2,1],[1,1],[1,1],[1,1]] => 8
[[2,1],[2,1],[1],[1],[1]] => 9
[[2,1],[2,1],[2],[1]] => 8
[[2,1],[2,1],[1,1],[1]] => 8
[[2,1],[2,1],[2,1]] => 6
[[1,1,1],[1],[1],[1],[1],[1],[1]] => 9
[[1,1,1],[1,1],[1],[1],[1],[1]] => 8
[[1,1,1],[1,1],[1,1],[1],[1]] => 7
[[1,1,1],[1,1],[1,1],[1,1]] => 6
[[1,1,1],[1,1,1],[1],[1],[1]] => 7
[[1,1,1],[1,1,1],[1,1],[1]] => 6
[[1,1,1],[1,1,1],[1,1,1]] => 5
[[4],[1],[1],[1],[1],[1]] => 9
[[4],[2],[1],[1],[1]] => 9
[[4],[2],[2],[1]] => 8
[[4],[3],[1],[1]] => 8
[[4],[3],[2]] => 7
[[4],[4],[1]] => 6
[[3,1],[1],[1],[1],[1],[1]] => 10
[[3,1],[2],[1],[1],[1]] => 10
[[3,1],[2],[2],[1]] => 9
[[3,1],[1,1],[1],[1],[1]] => 9
[[3,1],[1,1],[1,1],[1]] => 8
[[3,1],[3],[1],[1]] => 8
[[3,1],[3],[2]] => 7
[[3,1],[2,1],[1],[1]] => 9
[[3,1],[2,1],[2]] => 7
[[3,1],[2,1],[1,1]] => 8
[[3,1],[3,1],[1]] => 7
[[2,2],[1],[1],[1],[1],[1]] => 9
[[2,2],[2],[1],[1],[1]] => 8
[[2,2],[2],[2],[1]] => 7
[[2,2],[1,1],[1],[1],[1]] => 8
[[2,2],[1,1],[1,1],[1]] => 7
[[2,2],[2,1],[1],[1]] => 8
[[2,2],[2,1],[2]] => 6
[[2,2],[2,1],[1,1]] => 7
[[2,2],[2,2],[1]] => 6
[[2,1,1],[1],[1],[1],[1],[1]] => 10
[[2,1,1],[2],[1],[1],[1]] => 9
[[2,1,1],[2],[2],[1]] => 8
[[2,1,1],[1,1],[1],[1],[1]] => 9
[[2,1,1],[1,1],[1,1],[1]] => 8
[[2,1,1],[2,1],[1],[1]] => 8
[[2,1,1],[2,1],[2]] => 6
[[2,1,1],[2,1],[1,1]] => 7
[[2,1,1],[1,1,1],[1],[1]] => 8
[[2,1,1],[1,1,1],[1,1]] => 7
[[2,1,1],[2,1,1],[1]] => 7
[[1,1,1,1],[1],[1],[1],[1],[1]] => 8
[[1,1,1,1],[1,1],[1],[1],[1]] => 7
[[1,1,1,1],[1,1],[1,1],[1]] => 6
[[1,1,1,1],[1,1,1],[1],[1]] => 6
[[1,1,1,1],[1,1,1],[1,1]] => 5
[[1,1,1,1],[1,1,1,1],[1]] => 5
[[5],[1],[1],[1],[1]] => 8
[[5],[2],[1],[1]] => 8
[[5],[2],[2]] => 6
[[5],[3],[1]] => 7
[[5],[4]] => 5
[[4,1],[1],[1],[1],[1]] => 9
[[4,1],[2],[1],[1]] => 9
[[4,1],[2],[2]] => 7
[[4,1],[1,1],[1],[1]] => 8
[[4,1],[1,1],[1,1]] => 7
[[4,1],[3],[1]] => 8
[[4,1],[2,1],[1]] => 8
[[4,1],[4]] => 5
[[4,1],[3,1]] => 6
[[3,2],[1],[1],[1],[1]] => 9
[[3,2],[2],[1],[1]] => 9
[[3,2],[2],[2]] => 7
[[3,2],[1,1],[1],[1]] => 8
[[3,2],[1,1],[1,1]] => 7
[[3,2],[3],[1]] => 7
[[3,2],[2,1],[1]] => 9
[[3,2],[3,1]] => 6
[[3,2],[2,2]] => 6
[[3,1,1],[1],[1],[1],[1]] => 9
[[3,1,1],[2],[1],[1]] => 9
[[3,1,1],[2],[2]] => 7
[[3,1,1],[1,1],[1],[1]] => 8
[[3,1,1],[1,1],[1,1]] => 7
[[3,1,1],[3],[1]] => 7
[[3,1,1],[2,1],[1]] => 8
[[3,1,1],[1,1,1],[1]] => 7
[[3,1,1],[3,1]] => 5
[[3,1,1],[2,1,1]] => 6
[[2,2,1],[1],[1],[1],[1]] => 9
[[2,2,1],[2],[1],[1]] => 8
[[2,2,1],[2],[2]] => 6
[[2,2,1],[1,1],[1],[1]] => 8
[[2,2,1],[1,1],[1,1]] => 7
[[2,2,1],[2,1],[1]] => 8
[[2,2,1],[1,1,1],[1]] => 7
[[2,2,1],[2,2]] => 5
[[2,2,1],[2,1,1]] => 6
[[2,1,1,1],[1],[1],[1],[1]] => 9
[[2,1,1,1],[2],[1],[1]] => 8
[[2,1,1,1],[2],[2]] => 6
[[2,1,1,1],[1,1],[1],[1]] => 8
[[2,1,1,1],[1,1],[1,1]] => 7
[[2,1,1,1],[2,1],[1]] => 7
[[2,1,1,1],[1,1,1],[1]] => 7
[[2,1,1,1],[2,1,1]] => 5
[[2,1,1,1],[1,1,1,1]] => 6
[[1,1,1,1,1],[1],[1],[1],[1]] => 7
[[1,1,1,1,1],[1,1],[1],[1]] => 6
[[1,1,1,1,1],[1,1],[1,1]] => 5
[[1,1,1,1,1],[1,1,1],[1]] => 5
[[1,1,1,1,1],[1,1,1,1]] => 4
[[6],[1],[1],[1]] => 7
[[6],[2],[1]] => 7
[[6],[3]] => 5
[[5,1],[1],[1],[1]] => 8
[[5,1],[2],[1]] => 8
[[5,1],[1,1],[1]] => 7
[[5,1],[3]] => 6
[[5,1],[2,1]] => 6
[[4,2],[1],[1],[1]] => 8
[[4,2],[2],[1]] => 8
[[4,2],[1,1],[1]] => 7
[[4,2],[3]] => 6
[[4,2],[2,1]] => 7
[[4,1,1],[1],[1],[1]] => 8
[[4,1,1],[2],[1]] => 8
[[4,1,1],[1,1],[1]] => 7
[[4,1,1],[3]] => 6
[[4,1,1],[2,1]] => 6
[[4,1,1],[1,1,1]] => 6
[[3,3],[1],[1],[1]] => 7
[[3,3],[2],[1]] => 7
[[3,3],[1,1],[1]] => 6
[[3,3],[3]] => 4
[[3,3],[2,1]] => 6
[[3,2,1],[1],[1],[1]] => 9
[[3,2,1],[2],[1]] => 9
[[3,2,1],[1,1],[1]] => 8
[[3,2,1],[3]] => 6
[[3,2,1],[2,1]] => 8
[[3,2,1],[1,1,1]] => 7
[[3,1,1,1],[1],[1],[1]] => 8
[[3,1,1,1],[2],[1]] => 8
[[3,1,1,1],[1,1],[1]] => 7
[[3,1,1,1],[3]] => 5
[[3,1,1,1],[2,1]] => 6
[[3,1,1,1],[1,1,1]] => 6
[[2,2,2],[1],[1],[1]] => 7
[[2,2,2],[2],[1]] => 6
[[2,2,2],[1,1],[1]] => 6
[[2,2,2],[2,1]] => 5
[[2,2,2],[1,1,1]] => 5
[[2,2,1,1],[1],[1],[1]] => 8
[[2,2,1,1],[2],[1]] => 7
[[2,2,1,1],[1,1],[1]] => 7
[[2,2,1,1],[2,1]] => 6
[[2,2,1,1],[1,1,1]] => 6
[[2,1,1,1,1],[1],[1],[1]] => 8
[[2,1,1,1,1],[2],[1]] => 7
[[2,1,1,1,1],[1,1],[1]] => 7
[[2,1,1,1,1],[2,1]] => 5
[[2,1,1,1,1],[1,1,1]] => 6
[[1,1,1,1,1,1],[1],[1],[1]] => 6
[[1,1,1,1,1,1],[1,1],[1]] => 5
[[1,1,1,1,1,1],[1,1,1]] => 4
[[7],[1],[1]] => 6
[[7],[2]] => 5
[[6,1],[1],[1]] => 7
[[6,1],[2]] => 6
[[6,1],[1,1]] => 6
[[5,2],[1],[1]] => 7
[[5,2],[2]] => 6
[[5,2],[1,1]] => 6
[[5,1,1],[1],[1]] => 7
[[5,1,1],[2]] => 6
[[5,1,1],[1,1]] => 6
[[4,3],[1],[1]] => 7
[[4,3],[2]] => 6
[[4,3],[1,1]] => 6
[[4,2,1],[1],[1]] => 8
[[4,2,1],[2]] => 7
[[4,2,1],[1,1]] => 7
[[4,1,1,1],[1],[1]] => 7
[[4,1,1,1],[2]] => 6
[[4,1,1,1],[1,1]] => 6
[[3,3,1],[1],[1]] => 7
[[3,3,1],[2]] => 6
[[3,3,1],[1,1]] => 6
[[3,2,2],[1],[1]] => 7
[[3,2,2],[2]] => 6
[[3,2,2],[1,1]] => 6
[[3,2,1,1],[1],[1]] => 8
[[3,2,1,1],[2]] => 7
[[3,2,1,1],[1,1]] => 7
[[3,1,1,1,1],[1],[1]] => 7
[[3,1,1,1,1],[2]] => 6
[[3,1,1,1,1],[1,1]] => 6
[[2,2,2,1],[1],[1]] => 7
[[2,2,2,1],[2]] => 5
[[2,2,2,1],[1,1]] => 6
[[2,2,1,1,1],[1],[1]] => 7
[[2,2,1,1,1],[2]] => 5
[[2,2,1,1,1],[1,1]] => 6
[[2,1,1,1,1,1],[1],[1]] => 7
[[2,1,1,1,1,1],[2]] => 5
[[2,1,1,1,1,1],[1,1]] => 6
[[1,1,1,1,1,1,1],[1],[1]] => 5
[[1,1,1,1,1,1,1],[1,1]] => 4
[[8],[1]] => 5
[[7,1],[1]] => 6
[[6,2],[1]] => 6
[[6,1,1],[1]] => 6
[[5,3],[1]] => 6
[[5,2,1],[1]] => 7
[[5,1,1,1],[1]] => 6
[[4,4],[1]] => 5
[[4,3,1],[1]] => 7
[[4,2,2],[1]] => 6
[[4,2,1,1],[1]] => 7
[[4,1,1,1,1],[1]] => 6
[[3,3,2],[1]] => 6
[[3,3,1,1],[1]] => 6
[[3,2,2,1],[1]] => 7
[[3,2,1,1,1],[1]] => 7
[[3,1,1,1,1,1],[1]] => 6
[[2,2,2,2],[1]] => 5
[[2,2,2,1,1],[1]] => 6
[[2,2,1,1,1,1],[1]] => 6
[[2,1,1,1,1,1,1],[1]] => 6
[[1,1,1,1,1,1,1,1],[1]] => 4
[[9]] => 3
[[8,1]] => 4
[[7,2]] => 4
[[7,1,1]] => 4
[[6,3]] => 4
[[6,2,1]] => 5
[[6,1,1,1]] => 4
[[5,4]] => 4
[[5,3,1]] => 5
[[5,2,2]] => 4
[[5,2,1,1]] => 5
[[5,1,1,1,1]] => 4
[[4,4,1]] => 4
[[4,3,2]] => 5
[[4,3,1,1]] => 5
[[4,2,2,1]] => 5
[[4,2,1,1,1]] => 5
[[4,1,1,1,1,1]] => 4
[[3,3,3]] => 3
[[3,3,2,1]] => 5
[[3,3,1,1,1]] => 4
[[3,2,2,2]] => 4
[[3,2,2,1,1]] => 5
[[3,2,1,1,1,1]] => 5
[[3,1,1,1,1,1,1]] => 4
[[2,2,2,2,1]] => 4
[[2,2,2,1,1,1]] => 4
[[2,2,1,1,1,1,1]] => 4
[[2,1,1,1,1,1,1,1]] => 4
[[1,1,1,1,1,1,1,1,1]] => 3
[[1],[1],[1],[1],[1],[1],[1],[1],[1],[1]] => 12
[[2],[1],[1],[1],[1],[1],[1],[1],[1]] => 12
[[2],[2],[1],[1],[1],[1],[1],[1]] => 11
[[2],[2],[2],[1],[1],[1],[1]] => 10
[[2],[2],[2],[2],[1],[1]] => 9
[[2],[2],[2],[2],[2]] => 7
[[1,1],[1],[1],[1],[1],[1],[1],[1],[1]] => 11
[[1,1],[1,1],[1],[1],[1],[1],[1],[1]] => 10
[[1,1],[1,1],[1,1],[1],[1],[1],[1]] => 9
[[1,1],[1,1],[1,1],[1,1],[1],[1]] => 8
[[1,1],[1,1],[1,1],[1,1],[1,1]] => 7
[[3],[1],[1],[1],[1],[1],[1],[1]] => 11
[[3],[2],[1],[1],[1],[1],[1]] => 11
[[3],[2],[2],[1],[1],[1]] => 10
[[3],[2],[2],[2],[1]] => 9
[[3],[3],[1],[1],[1],[1]] => 9
[[3],[3],[2],[1],[1]] => 9
[[3],[3],[2],[2]] => 7
[[3],[3],[3],[1]] => 7
[[2,1],[1],[1],[1],[1],[1],[1],[1]] => 12
[[2,1],[2],[1],[1],[1],[1],[1]] => 11
[[2,1],[2],[2],[1],[1],[1]] => 10
[[2,1],[2],[2],[2],[1]] => 9
[[2,1],[1,1],[1],[1],[1],[1],[1]] => 11
[[2,1],[1,1],[1,1],[1],[1],[1]] => 10
[[2,1],[1,1],[1,1],[1,1],[1]] => 9
[[2,1],[2,1],[1],[1],[1],[1]] => 10
[[2,1],[2,1],[2],[1],[1]] => 9
[[2,1],[2,1],[2],[2]] => 7
[[2,1],[2,1],[1,1],[1],[1]] => 9
[[2,1],[2,1],[1,1],[1,1]] => 8
[[2,1],[2,1],[2,1],[1]] => 8
[[1,1,1],[1],[1],[1],[1],[1],[1],[1]] => 10
[[1,1,1],[1,1],[1],[1],[1],[1],[1]] => 9
[[1,1,1],[1,1],[1,1],[1],[1],[1]] => 8
[[1,1,1],[1,1],[1,1],[1,1],[1]] => 7
[[1,1,1],[1,1,1],[1],[1],[1],[1]] => 8
[[1,1,1],[1,1,1],[1,1],[1],[1]] => 7
[[1,1,1],[1,1,1],[1,1],[1,1]] => 6
[[1,1,1],[1,1,1],[1,1,1],[1]] => 6
[[4],[1],[1],[1],[1],[1],[1]] => 10
[[4],[2],[1],[1],[1],[1]] => 10
[[4],[2],[2],[1],[1]] => 9
[[4],[2],[2],[2]] => 7
[[4],[3],[1],[1],[1]] => 9
[[4],[3],[2],[1]] => 9
[[4],[3],[3]] => 6
[[4],[4],[1],[1]] => 7
[[4],[4],[2]] => 6
[[3,1],[1],[1],[1],[1],[1],[1]] => 11
[[3,1],[2],[1],[1],[1],[1]] => 11
[[3,1],[2],[2],[1],[1]] => 10
[[3,1],[2],[2],[2]] => 8
[[3,1],[1,1],[1],[1],[1],[1]] => 10
[[3,1],[1,1],[1,1],[1],[1]] => 9
[[3,1],[1,1],[1,1],[1,1]] => 8
[[3,1],[3],[1],[1],[1]] => 9
[[3,1],[3],[2],[1]] => 9
[[3,1],[3],[3]] => 6
[[3,1],[2,1],[1],[1],[1]] => 10
[[3,1],[2,1],[2],[1]] => 9
[[3,1],[2,1],[1,1],[1]] => 9
[[3,1],[2,1],[2,1]] => 7
[[3,1],[3,1],[1],[1]] => 8
[[3,1],[3,1],[2]] => 7
[[3,1],[3,1],[1,1]] => 7
[[2,2],[1],[1],[1],[1],[1],[1]] => 10
[[2,2],[2],[1],[1],[1],[1]] => 9
[[2,2],[2],[2],[1],[1]] => 8
[[2,2],[2],[2],[2]] => 6
[[2,2],[1,1],[1],[1],[1],[1]] => 9
[[2,2],[1,1],[1,1],[1],[1]] => 8
[[2,2],[1,1],[1,1],[1,1]] => 7
[[2,2],[2,1],[1],[1],[1]] => 9
[[2,2],[2,1],[2],[1]] => 8
[[2,2],[2,1],[1,1],[1]] => 8
[[2,2],[2,1],[2,1]] => 6
[[2,2],[2,2],[1],[1]] => 7
[[2,2],[2,2],[2]] => 5
[[2,2],[2,2],[1,1]] => 6
[[2,1,1],[1],[1],[1],[1],[1],[1]] => 11
[[2,1,1],[2],[1],[1],[1],[1]] => 10
[[2,1,1],[2],[2],[1],[1]] => 9
[[2,1,1],[2],[2],[2]] => 7
[[2,1,1],[1,1],[1],[1],[1],[1]] => 10
[[2,1,1],[1,1],[1,1],[1],[1]] => 9
[[2,1,1],[1,1],[1,1],[1,1]] => 8
[[2,1,1],[2,1],[1],[1],[1]] => 9
[[2,1,1],[2,1],[2],[1]] => 8
[[2,1,1],[2,1],[1,1],[1]] => 8
[[2,1,1],[2,1],[2,1]] => 6
[[2,1,1],[1,1,1],[1],[1],[1]] => 9
[[2,1,1],[1,1,1],[1,1],[1]] => 8
[[2,1,1],[1,1,1],[1,1,1]] => 7
[[2,1,1],[2,1,1],[1],[1]] => 8
[[2,1,1],[2,1,1],[2]] => 6
[[2,1,1],[2,1,1],[1,1]] => 7
[[1,1,1,1],[1],[1],[1],[1],[1],[1]] => 9
[[1,1,1,1],[1,1],[1],[1],[1],[1]] => 8
[[1,1,1,1],[1,1],[1,1],[1],[1]] => 7
[[1,1,1,1],[1,1],[1,1],[1,1]] => 6
[[1,1,1,1],[1,1,1],[1],[1],[1]] => 7
[[1,1,1,1],[1,1,1],[1,1],[1]] => 6
[[1,1,1,1],[1,1,1],[1,1,1]] => 5
[[1,1,1,1],[1,1,1,1],[1],[1]] => 6
[[1,1,1,1],[1,1,1,1],[1,1]] => 5
[[5],[1],[1],[1],[1],[1]] => 9
[[5],[2],[1],[1],[1]] => 9
[[5],[2],[2],[1]] => 8
[[5],[3],[1],[1]] => 8
[[5],[3],[2]] => 7
[[5],[4],[1]] => 7
[[5],[5]] => 4
[[4,1],[1],[1],[1],[1],[1]] => 10
[[4,1],[2],[1],[1],[1]] => 10
[[4,1],[2],[2],[1]] => 9
[[4,1],[1,1],[1],[1],[1]] => 9
[[4,1],[1,1],[1,1],[1]] => 8
[[4,1],[3],[1],[1]] => 9
[[4,1],[3],[2]] => 8
[[4,1],[2,1],[1],[1]] => 9
[[4,1],[2,1],[2]] => 7
[[4,1],[2,1],[1,1]] => 8
[[4,1],[4],[1]] => 7
[[4,1],[3,1],[1]] => 8
[[4,1],[4,1]] => 5
[[3,2],[1],[1],[1],[1],[1]] => 10
[[3,2],[2],[1],[1],[1]] => 10
[[3,2],[2],[2],[1]] => 9
[[3,2],[1,1],[1],[1],[1]] => 9
[[3,2],[1,1],[1,1],[1]] => 8
[[3,2],[3],[1],[1]] => 8
[[3,2],[3],[2]] => 7
[[3,2],[2,1],[1],[1]] => 10
[[3,2],[2,1],[2]] => 8
[[3,2],[2,1],[1,1]] => 9
[[3,2],[3,1],[1]] => 8
[[3,2],[2,2],[1]] => 8
[[3,2],[3,2]] => 5
[[3,1,1],[1],[1],[1],[1],[1]] => 10
[[3,1,1],[2],[1],[1],[1]] => 10
[[3,1,1],[2],[2],[1]] => 9
[[3,1,1],[1,1],[1],[1],[1]] => 9
[[3,1,1],[1,1],[1,1],[1]] => 8
[[3,1,1],[3],[1],[1]] => 8
[[3,1,1],[3],[2]] => 7
[[3,1,1],[2,1],[1],[1]] => 9
[[3,1,1],[2,1],[2]] => 7
[[3,1,1],[2,1],[1,1]] => 8
[[3,1,1],[1,1,1],[1],[1]] => 8
[[3,1,1],[1,1,1],[1,1]] => 7
[[3,1,1],[3,1],[1]] => 7
[[3,1,1],[2,1,1],[1]] => 8
[[3,1,1],[3,1,1]] => 5
[[2,2,1],[1],[1],[1],[1],[1]] => 10
[[2,2,1],[2],[1],[1],[1]] => 9
[[2,2,1],[2],[2],[1]] => 8
[[2,2,1],[1,1],[1],[1],[1]] => 9
[[2,2,1],[1,1],[1,1],[1]] => 8
[[2,2,1],[2,1],[1],[1]] => 9
[[2,2,1],[2,1],[2]] => 7
[[2,2,1],[2,1],[1,1]] => 8
[[2,2,1],[1,1,1],[1],[1]] => 8
[[2,2,1],[1,1,1],[1,1]] => 7
[[2,2,1],[2,2],[1]] => 7
[[2,2,1],[2,1,1],[1]] => 8
[[2,2,1],[2,2,1]] => 5
[[2,1,1,1],[1],[1],[1],[1],[1]] => 10
[[2,1,1,1],[2],[1],[1],[1]] => 9
[[2,1,1,1],[2],[2],[1]] => 8
[[2,1,1,1],[1,1],[1],[1],[1]] => 9
[[2,1,1,1],[1,1],[1,1],[1]] => 8
[[2,1,1,1],[2,1],[1],[1]] => 8
[[2,1,1,1],[2,1],[2]] => 6
[[2,1,1,1],[2,1],[1,1]] => 7
[[2,1,1,1],[1,1,1],[1],[1]] => 8
[[2,1,1,1],[1,1,1],[1,1]] => 7
[[2,1,1,1],[2,1,1],[1]] => 7
[[2,1,1,1],[1,1,1,1],[1]] => 7
[[2,1,1,1],[2,1,1,1]] => 5
[[1,1,1,1,1],[1],[1],[1],[1],[1]] => 8
[[1,1,1,1,1],[1,1],[1],[1],[1]] => 7
[[1,1,1,1,1],[1,1],[1,1],[1]] => 6
[[1,1,1,1,1],[1,1,1],[1],[1]] => 6
[[1,1,1,1,1],[1,1,1],[1,1]] => 5
[[1,1,1,1,1],[1,1,1,1],[1]] => 5
[[1,1,1,1,1],[1,1,1,1,1]] => 4
[[6],[1],[1],[1],[1]] => 8
[[6],[2],[1],[1]] => 8
[[6],[2],[2]] => 6
[[6],[3],[1]] => 7
[[6],[4]] => 5
[[5,1],[1],[1],[1],[1]] => 9
[[5,1],[2],[1],[1]] => 9
[[5,1],[2],[2]] => 7
[[5,1],[1,1],[1],[1]] => 8
[[5,1],[1,1],[1,1]] => 7
[[5,1],[3],[1]] => 8
[[5,1],[2,1],[1]] => 8
[[5,1],[4]] => 6
[[5,1],[3,1]] => 6
[[4,2],[1],[1],[1],[1]] => 9
[[4,2],[2],[1],[1]] => 9
[[4,2],[2],[2]] => 7
[[4,2],[1,1],[1],[1]] => 8
[[4,2],[1,1],[1,1]] => 7
[[4,2],[3],[1]] => 8
[[4,2],[2,1],[1]] => 9
[[4,2],[4]] => 5
[[4,2],[3,1]] => 7
[[4,2],[2,2]] => 6
[[4,1,1],[1],[1],[1],[1]] => 9
[[4,1,1],[2],[1],[1]] => 9
[[4,1,1],[2],[2]] => 7
[[4,1,1],[1,1],[1],[1]] => 8
[[4,1,1],[1,1],[1,1]] => 7
[[4,1,1],[3],[1]] => 8
[[4,1,1],[2,1],[1]] => 8
[[4,1,1],[1,1,1],[1]] => 7
[[4,1,1],[4]] => 5
[[4,1,1],[3,1]] => 6
[[4,1,1],[2,1,1]] => 6
[[3,3],[1],[1],[1],[1]] => 8
[[3,3],[2],[1],[1]] => 8
[[3,3],[2],[2]] => 6
[[3,3],[1,1],[1],[1]] => 7
[[3,3],[1,1],[1,1]] => 6
[[3,3],[3],[1]] => 6
[[3,3],[2,1],[1]] => 8
[[3,3],[3,1]] => 5
[[3,3],[2,2]] => 5
[[3,2,1],[1],[1],[1],[1]] => 10
[[3,2,1],[2],[1],[1]] => 10
[[3,2,1],[2],[2]] => 8
[[3,2,1],[1,1],[1],[1]] => 9
[[3,2,1],[1,1],[1,1]] => 8
[[3,2,1],[3],[1]] => 8
[[3,2,1],[2,1],[1]] => 10
[[3,2,1],[1,1,1],[1]] => 8
[[3,2,1],[3,1]] => 7
[[3,2,1],[2,2]] => 7
[[3,2,1],[2,1,1]] => 8
[[3,1,1,1],[1],[1],[1],[1]] => 9
[[3,1,1,1],[2],[1],[1]] => 9
[[3,1,1,1],[2],[2]] => 7
[[3,1,1,1],[1,1],[1],[1]] => 8
[[3,1,1,1],[1,1],[1,1]] => 7
[[3,1,1,1],[3],[1]] => 7
[[3,1,1,1],[2,1],[1]] => 8
[[3,1,1,1],[1,1,1],[1]] => 7
[[3,1,1,1],[3,1]] => 5
[[3,1,1,1],[2,1,1]] => 6
[[3,1,1,1],[1,1,1,1]] => 6
[[2,2,2],[1],[1],[1],[1]] => 8
[[2,2,2],[2],[1],[1]] => 7
[[2,2,2],[2],[2]] => 5
[[2,2,2],[1,1],[1],[1]] => 7
[[2,2,2],[1,1],[1,1]] => 6
[[2,2,2],[2,1],[1]] => 7
[[2,2,2],[1,1,1],[1]] => 6
[[2,2,2],[2,2]] => 4
[[2,2,2],[2,1,1]] => 5
[[2,2,1,1],[1],[1],[1],[1]] => 9
[[2,2,1,1],[2],[1],[1]] => 8
[[2,2,1,1],[2],[2]] => 6
[[2,2,1,1],[1,1],[1],[1]] => 8
[[2,2,1,1],[1,1],[1,1]] => 7
[[2,2,1,1],[2,1],[1]] => 8
[[2,2,1,1],[1,1,1],[1]] => 7
[[2,2,1,1],[2,2]] => 5
[[2,2,1,1],[2,1,1]] => 6
[[2,2,1,1],[1,1,1,1]] => 6
[[2,1,1,1,1],[1],[1],[1],[1]] => 9
[[2,1,1,1,1],[2],[1],[1]] => 8
[[2,1,1,1,1],[2],[2]] => 6
[[2,1,1,1,1],[1,1],[1],[1]] => 8
[[2,1,1,1,1],[1,1],[1,1]] => 7
[[2,1,1,1,1],[2,1],[1]] => 7
[[2,1,1,1,1],[1,1,1],[1]] => 7
[[2,1,1,1,1],[2,1,1]] => 5
[[2,1,1,1,1],[1,1,1,1]] => 6
[[1,1,1,1,1,1],[1],[1],[1],[1]] => 7
[[1,1,1,1,1,1],[1,1],[1],[1]] => 6
[[1,1,1,1,1,1],[1,1],[1,1]] => 5
[[1,1,1,1,1,1],[1,1,1],[1]] => 5
[[1,1,1,1,1,1],[1,1,1,1]] => 4
[[7],[1],[1],[1]] => 7
[[7],[2],[1]] => 7
[[7],[3]] => 5
[[6,1],[1],[1],[1]] => 8
[[6,1],[2],[1]] => 8
[[6,1],[1,1],[1]] => 7
[[6,1],[3]] => 6
[[6,1],[2,1]] => 6
[[5,2],[1],[1],[1]] => 8
[[5,2],[2],[1]] => 8
[[5,2],[1,1],[1]] => 7
[[5,2],[3]] => 6
[[5,2],[2,1]] => 7
[[5,1,1],[1],[1],[1]] => 8
[[5,1,1],[2],[1]] => 8
[[5,1,1],[1,1],[1]] => 7
[[5,1,1],[3]] => 6
[[5,1,1],[2,1]] => 6
[[5,1,1],[1,1,1]] => 6
[[4,3],[1],[1],[1]] => 8
[[4,3],[2],[1]] => 8
[[4,3],[1,1],[1]] => 7
[[4,3],[3]] => 6
[[4,3],[2,1]] => 7
[[4,2,1],[1],[1],[1]] => 9
[[4,2,1],[2],[1]] => 9
[[4,2,1],[1,1],[1]] => 8
[[4,2,1],[3]] => 7
[[4,2,1],[2,1]] => 8
[[4,2,1],[1,1,1]] => 7
[[4,1,1,1],[1],[1],[1]] => 8
[[4,1,1,1],[2],[1]] => 8
[[4,1,1,1],[1,1],[1]] => 7
[[4,1,1,1],[3]] => 6
[[4,1,1,1],[2,1]] => 6
[[4,1,1,1],[1,1,1]] => 6
[[3,3,1],[1],[1],[1]] => 8
[[3,3,1],[2],[1]] => 8
[[3,3,1],[1,1],[1]] => 7
[[3,3,1],[3]] => 5
[[3,3,1],[2,1]] => 7
[[3,3,1],[1,1,1]] => 6
[[3,2,2],[1],[1],[1]] => 8
[[3,2,2],[2],[1]] => 8
[[3,2,2],[1,1],[1]] => 7
[[3,2,2],[3]] => 5
[[3,2,2],[2,1]] => 7
[[3,2,2],[1,1,1]] => 6
[[3,2,1,1],[1],[1],[1]] => 9
[[3,2,1,1],[2],[1]] => 9
[[3,2,1,1],[1,1],[1]] => 8
[[3,2,1,1],[3]] => 6
[[3,2,1,1],[2,1]] => 8
[[3,2,1,1],[1,1,1]] => 7
[[3,1,1,1,1],[1],[1],[1]] => 8
[[3,1,1,1,1],[2],[1]] => 8
[[3,1,1,1,1],[1,1],[1]] => 7
[[3,1,1,1,1],[3]] => 5
[[3,1,1,1,1],[2,1]] => 6
[[3,1,1,1,1],[1,1,1]] => 6
[[2,2,2,1],[1],[1],[1]] => 8
[[2,2,2,1],[2],[1]] => 7
[[2,2,2,1],[1,1],[1]] => 7
[[2,2,2,1],[2,1]] => 6
[[2,2,2,1],[1,1,1]] => 6
[[2,2,1,1,1],[1],[1],[1]] => 8
[[2,2,1,1,1],[2],[1]] => 7
[[2,2,1,1,1],[1,1],[1]] => 7
[[2,2,1,1,1],[2,1]] => 6
[[2,2,1,1,1],[1,1,1]] => 6
[[2,1,1,1,1,1],[1],[1],[1]] => 8
[[2,1,1,1,1,1],[2],[1]] => 7
[[2,1,1,1,1,1],[1,1],[1]] => 7
[[2,1,1,1,1,1],[2,1]] => 5
[[2,1,1,1,1,1],[1,1,1]] => 6
[[1,1,1,1,1,1,1],[1],[1],[1]] => 6
[[1,1,1,1,1,1,1],[1,1],[1]] => 5
[[1,1,1,1,1,1,1],[1,1,1]] => 4
[[8],[1],[1]] => 6
[[8],[2]] => 5
[[7,1],[1],[1]] => 7
[[7,1],[2]] => 6
[[7,1],[1,1]] => 6
[[6,2],[1],[1]] => 7
[[6,2],[2]] => 6
[[6,2],[1,1]] => 6
[[6,1,1],[1],[1]] => 7
[[6,1,1],[2]] => 6
[[6,1,1],[1,1]] => 6
[[5,3],[1],[1]] => 7
[[5,3],[2]] => 6
[[5,3],[1,1]] => 6
[[5,2,1],[1],[1]] => 8
[[5,2,1],[2]] => 7
[[5,2,1],[1,1]] => 7
[[5,1,1,1],[1],[1]] => 7
[[5,1,1,1],[2]] => 6
[[5,1,1,1],[1,1]] => 6
[[4,4],[1],[1]] => 6
[[4,4],[2]] => 5
[[4,4],[1,1]] => 5
[[4,3,1],[1],[1]] => 8
[[4,3,1],[2]] => 7
[[4,3,1],[1,1]] => 7
[[4,2,2],[1],[1]] => 7
[[4,2,2],[2]] => 6
[[4,2,2],[1,1]] => 6
[[4,2,1,1],[1],[1]] => 8
[[4,2,1,1],[2]] => 7
[[4,2,1,1],[1,1]] => 7
[[4,1,1,1,1],[1],[1]] => 7
[[4,1,1,1,1],[2]] => 6
[[4,1,1,1,1],[1,1]] => 6
[[3,3,2],[1],[1]] => 7
[[3,3,2],[2]] => 6
[[3,3,2],[1,1]] => 6
[[3,3,1,1],[1],[1]] => 7
[[3,3,1,1],[2]] => 6
[[3,3,1,1],[1,1]] => 6
[[3,2,2,1],[1],[1]] => 8
[[3,2,2,1],[2]] => 7
[[3,2,2,1],[1,1]] => 7
[[3,2,1,1,1],[1],[1]] => 8
[[3,2,1,1,1],[2]] => 7
[[3,2,1,1,1],[1,1]] => 7
[[3,1,1,1,1,1],[1],[1]] => 7
[[3,1,1,1,1,1],[2]] => 6
[[3,1,1,1,1,1],[1,1]] => 6
[[2,2,2,2],[1],[1]] => 6
[[2,2,2,2],[2]] => 4
[[2,2,2,2],[1,1]] => 5
[[2,2,2,1,1],[1],[1]] => 7
[[2,2,2,1,1],[2]] => 5
[[2,2,2,1,1],[1,1]] => 6
[[2,2,1,1,1,1],[1],[1]] => 7
[[2,2,1,1,1,1],[2]] => 5
[[2,2,1,1,1,1],[1,1]] => 6
[[2,1,1,1,1,1,1],[1],[1]] => 7
[[2,1,1,1,1,1,1],[2]] => 5
[[2,1,1,1,1,1,1],[1,1]] => 6
[[1,1,1,1,1,1,1,1],[1],[1]] => 5
[[1,1,1,1,1,1,1,1],[1,1]] => 4
[[9],[1]] => 5
[[8,1],[1]] => 6
[[7,2],[1]] => 6
[[7,1,1],[1]] => 6
[[6,3],[1]] => 6
[[6,2,1],[1]] => 7
[[6,1,1,1],[1]] => 6
[[5,4],[1]] => 6
[[5,3,1],[1]] => 7
[[5,2,2],[1]] => 6
[[5,2,1,1],[1]] => 7
[[5,1,1,1,1],[1]] => 6
[[4,4,1],[1]] => 6
[[4,3,2],[1]] => 7
[[4,3,1,1],[1]] => 7
[[4,2,2,1],[1]] => 7
[[4,2,1,1,1],[1]] => 7
[[4,1,1,1,1,1],[1]] => 6
[[3,3,3],[1]] => 5
[[3,3,2,1],[1]] => 7
[[3,3,1,1,1],[1]] => 6
[[3,2,2,2],[1]] => 6
[[3,2,2,1,1],[1]] => 7
[[3,2,1,1,1,1],[1]] => 7
[[3,1,1,1,1,1,1],[1]] => 6
[[2,2,2,2,1],[1]] => 6
[[2,2,2,1,1,1],[1]] => 6
[[2,2,1,1,1,1,1],[1]] => 6
[[2,1,1,1,1,1,1,1],[1]] => 6
[[1,1,1,1,1,1,1,1,1],[1]] => 4
[[10]] => 3
[[9,1]] => 4
[[8,2]] => 4
[[8,1,1]] => 4
[[7,3]] => 4
[[7,2,1]] => 5
[[7,1,1,1]] => 4
[[6,4]] => 4
[[6,3,1]] => 5
[[6,2,2]] => 4
[[6,2,1,1]] => 5
[[6,1,1,1,1]] => 4
[[5,5]] => 3
[[5,4,1]] => 5
[[5,3,2]] => 5
[[5,3,1,1]] => 5
[[5,2,2,1]] => 5
[[5,2,1,1,1]] => 5
[[5,1,1,1,1,1]] => 4
[[4,4,2]] => 4
[[4,4,1,1]] => 4
[[4,3,3]] => 4
[[4,3,2,1]] => 6
[[4,3,1,1,1]] => 5
[[4,2,2,2]] => 4
[[4,2,2,1,1]] => 5
[[4,2,1,1,1,1]] => 5
[[4,1,1,1,1,1,1]] => 4
[[3,3,3,1]] => 4
[[3,3,2,2]] => 4
[[3,3,2,1,1]] => 5
[[3,3,1,1,1,1]] => 4
[[3,2,2,2,1]] => 5
[[3,2,2,1,1,1]] => 5
[[3,2,1,1,1,1,1]] => 5
[[3,1,1,1,1,1,1,1]] => 4
[[2,2,2,2,2]] => 3
[[2,2,2,2,1,1]] => 4
[[2,2,2,1,1,1,1]] => 4
[[2,2,1,1,1,1,1,1]] => 4
[[2,1,1,1,1,1,1,1,1]] => 4
[[1,1,1,1,1,1,1,1,1,1]] => 3
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Created: Aug 28, 2023 at 09:50 by Martin Rubey
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Last Updated: Aug 28, 2023 at 09:50 by Martin Rubey