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* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
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-----------------------------------------------------------------------------
Statistic identifier: St000170
-----------------------------------------------------------------------------
Collection: Semistandard tableaux
-----------------------------------------------------------------------------
Description: The trace of a semistandard tableau.
This is the sum of the entries on the diagonal.
-----------------------------------------------------------------------------
References: [1] Stanley, R. P. The conjugate trace and trace of a plane partition [[MathSciNet:0309748]]
[2] Gansner, E. R. The Hillman-Grassl correspondence and the enumeration of reverse plane partitions [[MathSciNet:0607040]]
[3] Gansner, E. R. The enumeration of plane partitions via the Burge correspondence [[MathSciNet:0630832]]
[4] Krattenthaler, C. Generating functions for plane partitions of a given shape [[MathSciNet:1072987]]
-----------------------------------------------------------------------------
Code:
def statistic(T):
m = 0
for i, row in enumerate(T):
try:
m += row[i]
except IndexError:
break
return m
-----------------------------------------------------------------------------
Statistic values:
[[1]] => 1
[[2]] => 2
[[3]] => 3
[[4]] => 4
[[5]] => 5
[[6]] => 6
[[1,1]] => 1
[[1,2]] => 1
[[2,2]] => 2
[[1],[2]] => 1
[[1,3]] => 1
[[2,3]] => 2
[[3,3]] => 3
[[1],[3]] => 1
[[2],[3]] => 2
[[1,4]] => 1
[[2,4]] => 2
[[3,4]] => 3
[[4,4]] => 4
[[1],[4]] => 1
[[2],[4]] => 2
[[3],[4]] => 3
[[1,5]] => 1
[[2,5]] => 2
[[3,5]] => 3
[[4,5]] => 4
[[5,5]] => 5
[[1],[5]] => 1
[[2],[5]] => 2
[[3],[5]] => 3
[[4],[5]] => 4
[[1,6]] => 1
[[2,6]] => 2
[[3,6]] => 3
[[4,6]] => 4
[[5,6]] => 5
[[6,6]] => 6
[[1],[6]] => 1
[[2],[6]] => 2
[[3],[6]] => 3
[[4],[6]] => 4
[[5],[6]] => 5
[[1,1,1]] => 1
[[1,1,2]] => 1
[[1,2,2]] => 1
[[2,2,2]] => 2
[[1,1],[2]] => 1
[[1,2],[2]] => 1
[[1,1,3]] => 1
[[1,2,3]] => 1
[[1,3,3]] => 1
[[2,2,3]] => 2
[[2,3,3]] => 2
[[3,3,3]] => 3
[[1,1],[3]] => 1
[[1,2],[3]] => 1
[[1,3],[2]] => 1
[[1,3],[3]] => 1
[[2,2],[3]] => 2
[[2,3],[3]] => 2
[[1],[2],[3]] => 1
[[1,1,4]] => 1
[[1,2,4]] => 1
[[1,3,4]] => 1
[[1,4,4]] => 1
[[2,2,4]] => 2
[[2,3,4]] => 2
[[2,4,4]] => 2
[[3,3,4]] => 3
[[3,4,4]] => 3
[[4,4,4]] => 4
[[1,1],[4]] => 1
[[1,2],[4]] => 1
[[1,4],[2]] => 1
[[1,3],[4]] => 1
[[1,4],[3]] => 1
[[1,4],[4]] => 1
[[2,2],[4]] => 2
[[2,3],[4]] => 2
[[2,4],[3]] => 2
[[2,4],[4]] => 2
[[3,3],[4]] => 3
[[3,4],[4]] => 3
[[1],[2],[4]] => 1
[[1],[3],[4]] => 1
[[2],[3],[4]] => 2
[[1,1,5]] => 1
[[1,2,5]] => 1
[[1,3,5]] => 1
[[1,4,5]] => 1
[[1,5,5]] => 1
[[2,2,5]] => 2
[[2,3,5]] => 2
[[2,4,5]] => 2
[[2,5,5]] => 2
[[3,3,5]] => 3
[[3,4,5]] => 3
[[3,5,5]] => 3
[[4,4,5]] => 4
[[4,5,5]] => 4
[[5,5,5]] => 5
[[1,1],[5]] => 1
[[1,2],[5]] => 1
[[1,5],[2]] => 1
[[1,3],[5]] => 1
[[1,5],[3]] => 1
[[1,4],[5]] => 1
[[1,5],[4]] => 1
[[1,5],[5]] => 1
[[2,2],[5]] => 2
[[2,3],[5]] => 2
[[2,5],[3]] => 2
[[2,4],[5]] => 2
[[2,5],[4]] => 2
[[2,5],[5]] => 2
[[3,3],[5]] => 3
[[3,4],[5]] => 3
[[3,5],[4]] => 3
[[3,5],[5]] => 3
[[4,4],[5]] => 4
[[4,5],[5]] => 4
[[1],[2],[5]] => 1
[[1],[3],[5]] => 1
[[1],[4],[5]] => 1
[[2],[3],[5]] => 2
[[2],[4],[5]] => 2
[[3],[4],[5]] => 3
[[1,1,1,1]] => 1
[[1,1,1,2]] => 1
[[1,1,2,2]] => 1
[[1,2,2,2]] => 1
[[2,2,2,2]] => 2
[[1,1,1],[2]] => 1
[[1,1,2],[2]] => 1
[[1,2,2],[2]] => 1
[[1,1],[2,2]] => 3
[[1,1,1,3]] => 1
[[1,1,2,3]] => 1
[[1,1,3,3]] => 1
[[1,2,2,3]] => 1
[[1,2,3,3]] => 1
[[1,3,3,3]] => 1
[[2,2,2,3]] => 2
[[2,2,3,3]] => 2
[[2,3,3,3]] => 2
[[3,3,3,3]] => 3
[[1,1,1],[3]] => 1
[[1,1,2],[3]] => 1
[[1,1,3],[2]] => 1
[[1,1,3],[3]] => 1
[[1,2,2],[3]] => 1
[[1,2,3],[2]] => 1
[[1,2,3],[3]] => 1
[[1,3,3],[2]] => 1
[[1,3,3],[3]] => 1
[[2,2,2],[3]] => 2
[[2,2,3],[3]] => 2
[[2,3,3],[3]] => 2
[[1,1],[2,3]] => 4
[[1,1],[3,3]] => 4
[[1,2],[2,3]] => 4
[[1,2],[3,3]] => 4
[[2,2],[3,3]] => 5
[[1,1],[2],[3]] => 1
[[1,2],[2],[3]] => 1
[[1,3],[2],[3]] => 1
[[1,1,1,4]] => 1
[[1,1,2,4]] => 1
[[1,1,3,4]] => 1
[[1,1,4,4]] => 1
[[1,2,2,4]] => 1
[[1,2,3,4]] => 1
[[1,2,4,4]] => 1
[[1,3,3,4]] => 1
[[1,3,4,4]] => 1
[[1,4,4,4]] => 1
[[2,2,2,4]] => 2
[[2,2,3,4]] => 2
[[2,2,4,4]] => 2
[[2,3,3,4]] => 2
[[2,3,4,4]] => 2
[[2,4,4,4]] => 2
[[3,3,3,4]] => 3
[[3,3,4,4]] => 3
[[3,4,4,4]] => 3
[[4,4,4,4]] => 4
[[1,1,1],[4]] => 1
[[1,1,2],[4]] => 1
[[1,1,4],[2]] => 1
[[1,1,3],[4]] => 1
[[1,1,4],[3]] => 1
[[1,1,4],[4]] => 1
[[1,2,2],[4]] => 1
[[1,2,4],[2]] => 1
[[1,2,3],[4]] => 1
[[1,2,4],[3]] => 1
[[1,3,4],[2]] => 1
[[1,2,4],[4]] => 1
[[1,4,4],[2]] => 1
[[1,3,3],[4]] => 1
[[1,3,4],[3]] => 1
[[1,3,4],[4]] => 1
[[1,4,4],[3]] => 1
[[1,4,4],[4]] => 1
[[2,2,2],[4]] => 2
[[2,2,3],[4]] => 2
[[2,2,4],[3]] => 2
[[2,2,4],[4]] => 2
[[2,3,3],[4]] => 2
[[2,3,4],[3]] => 2
[[2,3,4],[4]] => 2
[[2,4,4],[3]] => 2
[[2,4,4],[4]] => 2
[[3,3,3],[4]] => 3
[[3,3,4],[4]] => 3
[[3,4,4],[4]] => 3
[[1,1],[2,4]] => 5
[[1,1],[3,4]] => 5
[[1,1],[4,4]] => 5
[[1,2],[2,4]] => 5
[[1,2],[3,4]] => 5
[[1,3],[2,4]] => 5
[[1,2],[4,4]] => 5
[[1,3],[3,4]] => 5
[[1,3],[4,4]] => 5
[[2,2],[3,4]] => 6
[[2,2],[4,4]] => 6
[[2,3],[3,4]] => 6
[[2,3],[4,4]] => 6
[[3,3],[4,4]] => 7
[[1,1],[2],[4]] => 1
[[1,1],[3],[4]] => 1
[[1,2],[2],[4]] => 1
[[1,2],[3],[4]] => 1
[[1,3],[2],[4]] => 1
[[1,4],[2],[3]] => 1
[[1,4],[2],[4]] => 1
[[1,3],[3],[4]] => 1
[[1,4],[3],[4]] => 1
[[2,2],[3],[4]] => 2
[[2,3],[3],[4]] => 2
[[2,4],[3],[4]] => 2
[[1],[2],[3],[4]] => 1
[[1,1,1,1,1]] => 1
[[1,1,1,1,2]] => 1
[[1,1,1,2,2]] => 1
[[1,1,2,2,2]] => 1
[[1,2,2,2,2]] => 1
[[2,2,2,2,2]] => 2
[[1,1,1,1],[2]] => 1
[[1,1,1,2],[2]] => 1
[[1,1,2,2],[2]] => 1
[[1,2,2,2],[2]] => 1
[[1,1,1],[2,2]] => 3
[[1,1,2],[2,2]] => 3
[[1,1,1,1,3]] => 1
[[1,1,1,2,3]] => 1
[[1,1,1,3,3]] => 1
[[1,1,2,2,3]] => 1
[[1,1,2,3,3]] => 1
[[1,1,3,3,3]] => 1
[[1,2,2,2,3]] => 1
[[1,2,2,3,3]] => 1
[[1,2,3,3,3]] => 1
[[1,3,3,3,3]] => 1
[[2,2,2,2,3]] => 2
[[2,2,2,3,3]] => 2
[[2,2,3,3,3]] => 2
[[2,3,3,3,3]] => 2
[[3,3,3,3,3]] => 3
[[1,1,1,1],[3]] => 1
[[1,1,1,2],[3]] => 1
[[1,1,1,3],[2]] => 1
[[1,1,1,3],[3]] => 1
[[1,1,2,2],[3]] => 1
[[1,1,2,3],[2]] => 1
[[1,1,2,3],[3]] => 1
[[1,1,3,3],[2]] => 1
[[1,1,3,3],[3]] => 1
[[1,2,2,2],[3]] => 1
[[1,2,2,3],[2]] => 1
[[1,2,2,3],[3]] => 1
[[1,2,3,3],[2]] => 1
[[1,2,3,3],[3]] => 1
[[1,3,3,3],[2]] => 1
[[1,3,3,3],[3]] => 1
[[2,2,2,2],[3]] => 2
[[2,2,2,3],[3]] => 2
[[2,2,3,3],[3]] => 2
[[2,3,3,3],[3]] => 2
[[1,1,1],[2,3]] => 4
[[1,1,1],[3,3]] => 4
[[1,1,2],[2,3]] => 4
[[1,1,3],[2,2]] => 3
[[1,1,2],[3,3]] => 4
[[1,1,3],[2,3]] => 4
[[1,1,3],[3,3]] => 4
[[1,2,2],[2,3]] => 4
[[1,2,2],[3,3]] => 4
[[1,2,3],[2,3]] => 4
[[1,2,3],[3,3]] => 4
[[2,2,2],[3,3]] => 5
[[2,2,3],[3,3]] => 5
[[1,1,1],[2],[3]] => 1
[[1,1,2],[2],[3]] => 1
[[1,1,3],[2],[3]] => 1
[[1,2,2],[2],[3]] => 1
[[1,2,3],[2],[3]] => 1
[[1,3,3],[2],[3]] => 1
[[1,1],[2,2],[3]] => 3
[[1,1],[2,3],[3]] => 4
[[1,2],[2,3],[3]] => 4
[[1,2,3,4,5]] => 1
[[1,2,3,4],[5]] => 1
[[1,2,3,5],[4]] => 1
[[1,2,4,5],[3]] => 1
[[1,3,4,5],[2]] => 1
[[1,2,3],[4,5]] => 6
[[1,2,4],[3,5]] => 6
[[1,2,5],[3,4]] => 5
[[1,3,4],[2,5]] => 6
[[1,3,5],[2,4]] => 5
[[1,2,3],[4],[5]] => 1
[[1,2,4],[3],[5]] => 1
[[1,2,5],[3],[4]] => 1
[[1,3,4],[2],[5]] => 1
[[1,3,5],[2],[4]] => 1
[[1,4,5],[2],[3]] => 1
[[1,2],[3,4],[5]] => 5
[[1,2],[3,5],[4]] => 6
[[1,3],[2,4],[5]] => 5
[[1,3],[2,5],[4]] => 6
[[1,4],[2,5],[3]] => 6
[[1,2],[3],[4],[5]] => 1
[[1,3],[2],[4],[5]] => 1
[[1,4],[2],[3],[5]] => 1
[[1,5],[2],[3],[4]] => 1
[[1],[2],[3],[4],[5]] => 1
[[1,1,1,1,1,2]] => 1
[[1,1,1,1,2,2]] => 1
[[1,1,1,2,2,2]] => 1
[[1,1,2,2,2,2]] => 1
[[1,2,2,2,2,2]] => 1
[[2,2,2,2,2,2]] => 2
[[1,1,1,1,1],[2]] => 1
[[1,1,1,1,2],[2]] => 1
[[1,1,1,2,2],[2]] => 1
[[1,1,2,2,2],[2]] => 1
[[1,2,2,2,2],[2]] => 1
[[1,1,1,1],[2,2]] => 3
[[1,1,1,2],[2,2]] => 3
[[1,1,2,2],[2,2]] => 3
[[1,1,1],[2,2,2]] => 3
[[1,1,1,2,2],[3]] => 1
[[1,1,1,2,3],[3]] => 1
[[1,1,2,2,2],[3]] => 1
[[1,1,2,2,3],[3]] => 1
[[1,1,2,3,3],[3]] => 1
[[1,2,2,2,3],[3]] => 1
[[1,2,2,3,3],[3]] => 1
[[1,1,1],[2,2],[3]] => 3
[[1,1,1],[2,3],[3]] => 4
[[1,1,2],[2,2],[3]] => 3
[[1,1,2],[2,3],[3]] => 4
[[1,1,3],[2,3],[3]] => 4
[[1,2,2],[2,3],[3]] => 4
[[1,2,3],[2,3],[3]] => 4
[[1,2,3,4,5,6]] => 1
[[1,2,3,4,5],[6]] => 1
[[1,2,3,4,6],[5]] => 1
[[1,2,3,4],[5],[6]] => 1
[[1,2,3,5,6],[4]] => 1
[[1,2,3,5],[4,6]] => 7
[[1,2,3,5],[4],[6]] => 1
[[1,2,3,4],[5,6]] => 7
[[1,2,3,6],[4],[5]] => 1
[[1,2,3],[4],[5],[6]] => 1
[[1,2,4,5,6],[3]] => 1
[[1,2,4,5],[3,6]] => 7
[[1,2,4,6],[3,5]] => 6
[[1,2,4],[3,5],[6]] => 6
[[1,2,4,5],[3],[6]] => 1
[[1,2,4,6],[3],[5]] => 1
[[1,2,4],[3],[5],[6]] => 1
[[1,2,3,6],[4,5]] => 6
[[1,2,3],[4,5],[6]] => 6
[[1,2,5,6],[3],[4]] => 1
[[1,2,5],[3,6],[4]] => 7
[[1,2,5],[3],[4],[6]] => 1
[[1,2,3],[4,6],[5]] => 7
[[1,2,4],[3,6],[5]] => 7
[[1,2,6],[3],[4],[5]] => 1
[[1,2],[3],[4],[5],[6]] => 1
[[1,3,4,5,6],[2]] => 1
[[1,3,4,5],[2,6]] => 7
[[1,3,4,6],[2,5]] => 6
[[1,3,4],[2,5],[6]] => 6
[[1,3,5,6],[2,4]] => 5
[[1,3,5],[2,4,6]] => 5
[[1,3,5],[2,4],[6]] => 5
[[1,3,4],[2,5,6]] => 6
[[1,3,6],[2,4],[5]] => 5
[[1,3],[2,4],[5],[6]] => 5
[[1,3,4,5],[2],[6]] => 1
[[1,3,4,6],[2],[5]] => 1
[[1,3,4],[2],[5],[6]] => 1
[[1,3,5,6],[2],[4]] => 1
[[1,3,5],[2,6],[4]] => 7
[[1,3,5],[2],[4],[6]] => 1
[[1,3,4],[2,6],[5]] => 7
[[1,3,6],[2],[4],[5]] => 1
[[1,3],[2],[4],[5],[6]] => 1
[[1,2,5,6],[3,4]] => 5
[[1,2,5],[3,4,6]] => 5
[[1,2,5],[3,4],[6]] => 5
[[1,2,4],[3,5,6]] => 6
[[1,2,6],[3,4],[5]] => 5
[[1,2],[3,4],[5],[6]] => 5
[[1,4,5,6],[2],[3]] => 1
[[1,4,5],[2,6],[3]] => 7
[[1,4,6],[2,5],[3]] => 6
[[1,4],[2,5],[3,6]] => 6
[[1,4],[2,5],[3],[6]] => 6
[[1,4,5],[2],[3],[6]] => 1
[[1,4,6],[2],[3],[5]] => 1
[[1,4],[2],[3],[5],[6]] => 1
[[1,2,3],[4,5,6]] => 6
[[1,2,6],[3,5],[4]] => 6
[[1,2],[3,5],[4],[6]] => 6
[[1,3,6],[2,5],[4]] => 6
[[1,3],[2,5],[4,6]] => 6
[[1,3],[2,5],[4],[6]] => 6
[[1,2],[3,5],[4,6]] => 6
[[1,5,6],[2],[3],[4]] => 1
[[1,5],[2,6],[3],[4]] => 7
[[1,5],[2],[3],[4],[6]] => 1
[[1,2],[3,6],[4],[5]] => 7
[[1,3],[2,4],[5,6]] => 5
[[1,3],[2,6],[4],[5]] => 7
[[1,2],[3,4],[5,6]] => 5
[[1,4],[2,6],[3],[5]] => 7
[[1,6],[2],[3],[4],[5]] => 1
[[1],[2],[3],[4],[5],[6]] => 1
[[1,1,1,1],[2,2,2],[3,3],[4]] => 3
[[1,1,1,2],[2,2,2],[3,3],[4]] => 3
[[1,1,1,1],[2,2,3],[3,3],[4]] => 3
[[1,1,1,2],[2,2,3],[3,3],[4]] => 3
[[1,1,1,3],[2,2,3],[3,3],[4]] => 3
[[1,1,2,2],[2,2,3],[3,3],[4]] => 3
[[1,1,2,3],[2,2,3],[3,3],[4]] => 3
[[1,1,1,1],[2,2,2],[3,4],[4]] => 3
[[1,1,1,2],[2,2,2],[3,4],[4]] => 3
[[1,1,1,1],[2,2,3],[3,4],[4]] => 3
[[1,1,1,2],[2,2,3],[3,4],[4]] => 3
[[1,1,1,3],[2,2,3],[3,4],[4]] => 3
[[1,1,2,2],[2,2,3],[3,4],[4]] => 3
[[1,1,2,3],[2,2,3],[3,4],[4]] => 3
[[1,1,1,1],[2,2,4],[3,4],[4]] => 3
[[1,1,1,2],[2,2,4],[3,4],[4]] => 3
[[1,1,1,3],[2,2,4],[3,4],[4]] => 3
[[1,1,1,4],[2,2,4],[3,4],[4]] => 3
[[1,1,2,2],[2,2,4],[3,4],[4]] => 3
[[1,1,2,3],[2,2,4],[3,4],[4]] => 3
[[1,1,2,4],[2,2,4],[3,4],[4]] => 3
[[1,1,1,1],[2,3,3],[3,4],[4]] => 4
[[1,1,1,2],[2,3,3],[3,4],[4]] => 4
[[1,1,1,3],[2,3,3],[3,4],[4]] => 4
[[1,1,2,2],[2,3,3],[3,4],[4]] => 4
[[1,1,2,3],[2,3,3],[3,4],[4]] => 4
[[1,1,1,1],[2,3,4],[3,4],[4]] => 4
[[1,1,1,2],[2,3,4],[3,4],[4]] => 4
[[1,1,1,3],[2,3,4],[3,4],[4]] => 4
[[1,1,1,4],[2,3,4],[3,4],[4]] => 4
[[1,1,2,2],[2,3,4],[3,4],[4]] => 4
[[1,1,2,3],[2,3,4],[3,4],[4]] => 4
[[1,1,2,4],[2,3,4],[3,4],[4]] => 4
[[1,1,3,3],[2,3,4],[3,4],[4]] => 4
[[1,1,3,4],[2,3,4],[3,4],[4]] => 4
[[1,2,2,2],[2,3,3],[3,4],[4]] => 4
[[1,2,2,3],[2,3,3],[3,4],[4]] => 4
[[1,2,2,2],[2,3,4],[3,4],[4]] => 4
[[1,2,2,3],[2,3,4],[3,4],[4]] => 4
[[1,2,2,4],[2,3,4],[3,4],[4]] => 4
[[1,2,3,3],[2,3,4],[3,4],[4]] => 4
[[1,2,3,4],[2,3,4],[3,4],[4]] => 4
[[1,1,1,1,2,2,2],[3,3],[4]] => 4
[[1,1,1,2,2,2,2],[3,3],[4]] => 4
[[1,1,1,1,2,2,3],[3,3],[4]] => 4
[[1,1,1,2,2,2,3],[3,3],[4]] => 4
[[1,1,1,2,2,3,3],[3,3],[4]] => 4
[[1,1,2,2,2,2,3],[3,3],[4]] => 4
[[1,1,2,2,2,3,3],[3,3],[4]] => 4
[[1,1,1,1,2,2,2],[3,4],[4]] => 5
[[1,1,1,2,2,2,2],[3,4],[4]] => 5
[[1,1,1,1,2,2,3],[3,4],[4]] => 5
[[1,1,1,2,2,2,3],[3,4],[4]] => 5
[[1,1,1,2,2,3],[3,3,4],[4]] => 4
[[1,1,2,2,2,2,3],[3,4],[4]] => 5
[[1,1,2,2,2,3],[3,3,4],[4]] => 4
[[1,1,1,1,2,2,4],[3,4],[4]] => 5
[[1,1,1,2,2,2,4],[3,4],[4]] => 5
[[1,1,1,2,2,4,4],[3,3],[4]] => 4
[[1,1,1,2,2,4,4],[3,4],[4]] => 5
[[1,1,2,2,2,2,4],[3,4],[4]] => 5
[[1,1,2,2,2,4,4],[3,3],[4]] => 4
[[1,1,2,2,2,4,4],[3,4],[4]] => 5
[[1,1,1,1,2,3,3],[3,4],[4]] => 5
[[1,1,1,2,2,3,3],[3,4],[4]] => 5
[[1,1,1,2,3,3,3],[3,4],[4]] => 5
[[1,1,2,2,2,3,3],[3,4],[4]] => 5
[[1,1,2,2,3,3,3],[3,4],[4]] => 5
[[1,1,1,1,2,3,4],[3,4],[4]] => 5
[[1,1,1,2,2,3,4],[3,4],[4]] => 5
[[1,1,1,2,3,3,4],[3,4],[4]] => 5
[[1,1,1,2,3,4,4],[3,4],[4]] => 5
[[1,1,2,2,2,3,4],[3,4],[4]] => 5
[[1,1,2,2,3,3,4],[3,4],[4]] => 5
[[1,1,2,2,3,4,4],[3,4],[4]] => 5
[[1,1,2,3,3,3,4],[3,4],[4]] => 5
[[1,1,2,3,3,4,4],[3,4],[4]] => 5
[[1,2,2,2,2,3,3],[3,4],[4]] => 5
[[1,2,2,2,3,3,3],[3,4],[4]] => 5
[[1,2,2,2,2,3,4],[3,4],[4]] => 5
[[1,2,2,2,3,3,4],[3,4],[4]] => 5
[[1,2,2,2,3,4,4],[3,4],[4]] => 5
[[1,2,2,3,3,3,4],[3,4],[4]] => 5
[[1,2,2,3,3,4,4],[3,4],[4]] => 5
[[1,1,1,1,1],[2,2,2,2],[3,3,3],[4,4],[5]] => 6
[[1,1,1,1,2],[2,2,2,2],[3,3,3],[4,4],[5]] => 6
[[1,1,1,1,1],[2,2,2,3],[3,3,3],[4,4],[5]] => 6
[[1,1,1,1,2],[2,2,2,3],[3,3,3],[4,4],[5]] => 6
[[1,1,1,1,3],[2,2,2,3],[3,3,3],[4,4],[5]] => 6
[[1,1,1,2,2],[2,2,2,3],[3,3,3],[4,4],[5]] => 6
[[1,1,1,2,3],[2,2,2,3],[3,3,3],[4,4],[5]] => 6
[[1,1,1,1,1],[2,2,2,2],[3,3,4],[4,4],[5]] => 7
[[1,1,1,1,2],[2,2,2,2],[3,3,4],[4,4],[5]] => 7
[[1,1,1,1,1],[2,2,2,3],[3,3,4],[4,4],[5]] => 7
[[1,1,1,1,2],[2,2,2,3],[3,3,4],[4,4],[5]] => 7
[[1,1,1,1,3],[2,2,2,3],[3,3,4],[4,4],[5]] => 7
[[1,1,1,2,3],[2,2,2,3],[3,3,4],[4,4],[5]] => 7
[[1,1,1,1,1],[2,2,2,4],[3,3,4],[4,4],[5]] => 7
[[1,1,1,1,2],[2,2,2,4],[3,3,4],[4,4],[5]] => 7
[[1,1,1,1,3],[2,2,2,4],[3,3,4],[4,4],[5]] => 7
[[1,1,1,1,4],[2,2,2,4],[3,3,4],[4,4],[5]] => 7
[[1,1,1,2,2],[2,2,2,4],[3,3,4],[4,4],[5]] => 7
[[1,1,1,2,4],[2,2,2,4],[3,3,4],[4,4],[5]] => 7
[[1,1,1,1,1],[2,2,3,3],[3,3,4],[4,4],[5]] => 7
[[1,1,1,1,3],[2,2,3,3],[3,3,4],[4,4],[5]] => 7
[[1,1,1,1,1],[2,2,3,4],[3,3,4],[4,4],[5]] => 7
[[1,1,1,1,2],[2,2,3,4],[3,3,4],[4,4],[5]] => 7
[[1,1,1,1,4],[2,2,3,4],[3,3,4],[4,4],[5]] => 7
[[1,1,1,2,3],[2,2,3,4],[3,3,4],[4,4],[5]] => 7
[[1,1,1,3,3],[2,2,3,4],[3,3,4],[4,4],[5]] => 7
[[1,1,1,3,4],[2,2,3,4],[3,3,4],[4,4],[5]] => 7
[[1,1,2,2,2],[2,2,3,3],[3,3,4],[4,4],[5]] => 7
[[1,1,2,2,3],[2,2,3,3],[3,3,4],[4,4],[5]] => 7
[[1,1,2,2,2],[2,2,3,4],[3,3,4],[4,4],[5]] => 7
[[1,1,2,2,4],[2,2,3,4],[3,3,4],[4,4],[5]] => 7
[[1,1,2,3,3],[2,2,3,4],[3,3,4],[4,4],[5]] => 7
[[1,1,2,3,4],[2,2,3,4],[3,3,4],[4,4],[5]] => 7
[[1,1,1,1,1],[2,2,2,2],[3,3,3],[4,5],[5]] => 6
[[1,1,1,1,2],[2,2,2,2],[3,3,3],[4,5],[5]] => 6
[[1,1,1,1,1],[2,2,2,3],[3,3,3],[4,5],[5]] => 6
[[1,1,1,1,2],[2,2,2,3],[3,3,3],[4,5],[5]] => 6
[[1,1,1,1,3],[2,2,2,3],[3,3,3],[4,5],[5]] => 6
[[1,1,1,2,2],[2,2,2,3],[3,3,3],[4,5],[5]] => 6
[[1,1,1,2,3],[2,2,2,3],[3,3,3],[4,5],[5]] => 6
[[1,1,1,1,1],[2,2,2,2],[3,3,4],[4,5],[5]] => 7
[[1,1,1,1,2],[2,2,2,2],[3,3,4],[4,5],[5]] => 7
[[1,1,1,1,1],[2,2,2,3],[3,3,4],[4,5],[5]] => 7
[[1,1,1,1,2],[2,2,2,3],[3,3,4],[4,5],[5]] => 7
[[1,1,1,1,3],[2,2,2,3],[3,3,4],[4,5],[5]] => 7
[[1,1,1,2,3],[2,2,2,3],[3,3,4],[4,5],[5]] => 7
[[1,1,1,1,1],[2,2,2,4],[3,3,4],[4,5],[5]] => 7
[[1,1,1,1,2],[2,2,2,4],[3,3,4],[4,5],[5]] => 7
[[1,1,1,1,3],[2,2,2,4],[3,3,4],[4,5],[5]] => 7
[[1,1,1,1,4],[2,2,2,4],[3,3,4],[4,5],[5]] => 7
[[1,1,1,1,1],[2,2,3,4],[3,3,4],[4,5],[5]] => 7
[[1,1,1,1,2],[2,2,3,4],[3,3,4],[4,5],[5]] => 7
[[1,1,1,2,3],[2,2,3,4],[3,3,4],[4,5],[5]] => 7
[[1,1,2,3,4],[2,2,3,4],[3,3,4],[4,5],[5]] => 7
[[1,1,1,1,1],[2,2,2,2],[3,3,5],[4,5],[5]] => 8
[[1,1,1,1,2],[2,2,2,2],[3,3,5],[4,5],[5]] => 8
[[1,1,1,1,1],[2,2,2,3],[3,3,5],[4,5],[5]] => 8
[[1,1,1,1,2],[2,2,2,3],[3,3,5],[4,5],[5]] => 8
[[1,1,1,1,3],[2,2,2,3],[3,3,5],[4,5],[5]] => 8
[[1,1,1,1,1],[2,2,2,4],[3,3,5],[4,5],[5]] => 8
[[1,1,1,1,2],[2,2,2,4],[3,3,5],[4,5],[5]] => 8
[[1,1,1,1,3],[2,2,2,4],[3,3,5],[4,5],[5]] => 8
[[1,1,1,1,4],[2,2,2,4],[3,3,5],[4,5],[5]] => 8
[[1,1,1,1,1],[2,2,2,5],[3,3,5],[4,5],[5]] => 8
[[1,1,1,1,2],[2,2,2,5],[3,3,5],[4,5],[5]] => 8
[[1,1,1,1,3],[2,2,2,5],[3,3,5],[4,5],[5]] => 8
[[1,1,1,1,4],[2,2,2,5],[3,3,5],[4,5],[5]] => 8
[[1,1,1,1,5],[2,2,2,5],[3,3,5],[4,5],[5]] => 8
[[1,1,1,2,2],[2,2,2,5],[3,3,5],[4,5],[5]] => 8
[[1,1,1,2,5],[2,2,2,5],[3,3,5],[4,5],[5]] => 8
[[1,1,1,1,1],[2,2,3,3],[3,3,5],[4,5],[5]] => 8
[[1,1,1,1,3],[2,2,3,3],[3,3,5],[4,5],[5]] => 8
[[1,1,1,1,1],[2,2,3,5],[3,3,5],[4,5],[5]] => 8
[[1,1,1,1,5],[2,2,3,5],[3,3,5],[4,5],[5]] => 8
[[1,1,1,3,3],[2,2,3,5],[3,3,5],[4,5],[5]] => 8
[[1,1,1,3,5],[2,2,3,5],[3,3,5],[4,5],[5]] => 8
[[1,1,2,2,2],[2,2,3,3],[3,3,5],[4,5],[5]] => 8
[[1,1,2,2,3],[2,2,3,3],[3,3,5],[4,5],[5]] => 8
[[1,1,2,2,2],[2,2,3,5],[3,3,5],[4,5],[5]] => 8
[[1,1,2,2,5],[2,2,3,5],[3,3,5],[4,5],[5]] => 8
[[1,1,2,3,3],[2,2,3,5],[3,3,5],[4,5],[5]] => 8
[[1,1,2,3,5],[2,2,3,5],[3,3,5],[4,5],[5]] => 8
[[1,1,1,1,1],[2,2,2,2],[3,4,4],[4,5],[5]] => 7
[[1,1,1,1,2],[2,2,2,2],[3,4,4],[4,5],[5]] => 7
[[1,1,1,1,1],[2,2,2,4],[3,4,4],[4,5],[5]] => 7
[[1,1,1,1,4],[2,2,2,4],[3,4,4],[4,5],[5]] => 7
[[1,1,1,2,2],[2,2,2,4],[3,4,4],[4,5],[5]] => 7
[[1,1,1,2,4],[2,2,2,4],[3,4,4],[4,5],[5]] => 7
[[1,1,1,1,1],[2,2,2,2],[3,4,5],[4,5],[5]] => 8
[[1,1,1,1,2],[2,2,2,2],[3,4,5],[4,5],[5]] => 8
[[1,1,1,1,1],[2,2,2,3],[3,4,5],[4,5],[5]] => 8
[[1,1,1,1,2],[2,2,2,3],[3,4,5],[4,5],[5]] => 8
[[1,1,1,2,3],[2,2,2,3],[3,4,5],[4,5],[5]] => 8
[[1,1,1,1,1],[2,2,2,5],[3,4,5],[4,5],[5]] => 8
[[1,1,1,1,5],[2,2,2,5],[3,4,5],[4,5],[5]] => 8
[[1,1,1,2,2],[2,2,2,5],[3,4,5],[4,5],[5]] => 8
[[1,1,1,2,5],[2,2,2,5],[3,4,5],[4,5],[5]] => 8
[[1,1,1,1,1],[2,2,3,4],[3,4,5],[4,5],[5]] => 8
[[1,1,1,1,2],[2,2,3,4],[3,4,5],[4,5],[5]] => 8
[[1,1,1,2,3],[2,2,3,4],[3,4,5],[4,5],[5]] => 8
[[1,1,2,3,4],[2,2,3,4],[3,4,5],[4,5],[5]] => 8
[[1,1,1,1,1],[2,2,4,4],[3,4,5],[4,5],[5]] => 8
[[1,1,1,1,4],[2,2,4,4],[3,4,5],[4,5],[5]] => 8
[[1,1,1,1,1],[2,2,4,5],[3,4,5],[4,5],[5]] => 8
[[1,1,1,1,5],[2,2,4,5],[3,4,5],[4,5],[5]] => 8
[[1,1,1,4,4],[2,2,4,5],[3,4,5],[4,5],[5]] => 8
[[1,1,1,4,5],[2,2,4,5],[3,4,5],[4,5],[5]] => 8
[[1,1,2,2,2],[2,2,4,4],[3,4,5],[4,5],[5]] => 8
[[1,1,2,2,4],[2,2,4,4],[3,4,5],[4,5],[5]] => 8
[[1,1,2,2,2],[2,2,4,5],[3,4,5],[4,5],[5]] => 8
[[1,1,2,2,5],[2,2,4,5],[3,4,5],[4,5],[5]] => 8
[[1,1,2,4,4],[2,2,4,5],[3,4,5],[4,5],[5]] => 8
[[1,1,2,4,5],[2,2,4,5],[3,4,5],[4,5],[5]] => 8
[[1,1,1,1,1],[2,3,3,3],[3,4,4],[4,5],[5]] => 8
[[1,1,1,1,3],[2,3,3,3],[3,4,4],[4,5],[5]] => 8
[[1,1,1,1,1],[2,3,3,4],[3,4,4],[4,5],[5]] => 8
[[1,1,1,1,4],[2,3,3,4],[3,4,4],[4,5],[5]] => 8
[[1,1,1,3,3],[2,3,3,4],[3,4,4],[4,5],[5]] => 8
[[1,1,1,3,4],[2,3,3,4],[3,4,4],[4,5],[5]] => 8
[[1,1,1,1,1],[2,3,3,3],[3,4,5],[4,5],[5]] => 9
[[1,1,1,1,3],[2,3,3,3],[3,4,5],[4,5],[5]] => 9
[[1,1,1,1,1],[2,3,3,5],[3,4,5],[4,5],[5]] => 9
[[1,1,1,1,5],[2,3,3,5],[3,4,5],[4,5],[5]] => 9
[[1,1,1,3,3],[2,3,3,5],[3,4,5],[4,5],[5]] => 9
[[1,1,1,3,5],[2,3,3,5],[3,4,5],[4,5],[5]] => 9
[[1,1,1,1,1],[2,3,4,4],[3,4,5],[4,5],[5]] => 9
[[1,1,1,1,4],[2,3,4,4],[3,4,5],[4,5],[5]] => 9
[[1,1,1,1,1],[2,3,4,5],[3,4,5],[4,5],[5]] => 9
[[1,1,1,1,2],[2,3,4,5],[3,4,5],[4,5],[5]] => 9
[[1,1,1,1,5],[2,3,4,5],[3,4,5],[4,5],[5]] => 9
[[1,1,1,2,3],[2,3,4,5],[3,4,5],[4,5],[5]] => 9
[[1,1,1,4,4],[2,3,4,5],[3,4,5],[4,5],[5]] => 9
[[1,1,1,4,5],[2,3,4,5],[3,4,5],[4,5],[5]] => 9
[[1,1,2,3,4],[2,3,4,5],[3,4,5],[4,5],[5]] => 9
[[1,1,3,3,3],[2,3,4,4],[3,4,5],[4,5],[5]] => 9
[[1,1,3,3,4],[2,3,4,4],[3,4,5],[4,5],[5]] => 9
[[1,1,3,3,3],[2,3,4,5],[3,4,5],[4,5],[5]] => 9
[[1,1,3,3,5],[2,3,4,5],[3,4,5],[4,5],[5]] => 9
[[1,1,3,4,4],[2,3,4,5],[3,4,5],[4,5],[5]] => 9
[[1,1,3,4,5],[2,3,4,5],[3,4,5],[4,5],[5]] => 9
[[1,2,2,2,2],[2,3,3,3],[3,4,4],[4,5],[5]] => 8
[[1,2,2,2,3],[2,3,3,3],[3,4,4],[4,5],[5]] => 8
[[1,2,2,2,2],[2,3,3,4],[3,4,4],[4,5],[5]] => 8
[[1,2,2,2,4],[2,3,3,4],[3,4,4],[4,5],[5]] => 8
[[1,2,2,3,3],[2,3,3,4],[3,4,4],[4,5],[5]] => 8
[[1,2,2,3,4],[2,3,3,4],[3,4,4],[4,5],[5]] => 8
[[1,2,2,2,2],[2,3,3,3],[3,4,5],[4,5],[5]] => 9
[[1,2,2,2,3],[2,3,3,3],[3,4,5],[4,5],[5]] => 9
[[1,2,2,2,2],[2,3,3,5],[3,4,5],[4,5],[5]] => 9
[[1,2,2,2,5],[2,3,3,5],[3,4,5],[4,5],[5]] => 9
[[1,2,2,3,3],[2,3,3,5],[3,4,5],[4,5],[5]] => 9
[[1,2,2,3,5],[2,3,3,5],[3,4,5],[4,5],[5]] => 9
[[1,2,2,2,2],[2,3,4,4],[3,4,5],[4,5],[5]] => 9
[[1,2,2,2,4],[2,3,4,4],[3,4,5],[4,5],[5]] => 9
[[1,2,2,2,2],[2,3,4,5],[3,4,5],[4,5],[5]] => 9
[[1,2,2,2,5],[2,3,4,5],[3,4,5],[4,5],[5]] => 9
[[1,2,2,4,4],[2,3,4,5],[3,4,5],[4,5],[5]] => 9
[[1,2,2,4,5],[2,3,4,5],[3,4,5],[4,5],[5]] => 9
[[1,2,3,3,3],[2,3,4,4],[3,4,5],[4,5],[5]] => 9
[[1,2,3,3,4],[2,3,4,4],[3,4,5],[4,5],[5]] => 9
[[1,2,3,3,3],[2,3,4,5],[3,4,5],[4,5],[5]] => 9
[[1,2,3,3,5],[2,3,4,5],[3,4,5],[4,5],[5]] => 9
[[1,2,3,4,4],[2,3,4,5],[3,4,5],[4,5],[5]] => 9
[[1,2,3,4,5],[2,3,4,5],[3,4,5],[4,5],[5]] => 9
[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,4],[5,5],[6]] => 6
[[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,3],[4,4,4],[5,5],[6]] => 6
[[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,5],[6]] => 6
[[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,5],[6]] => 6
[[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,5],[6]] => 6
[[1,1,1,1,2,3],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,5],[6]] => 6
[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,4,4],[5,5],[6]] => 6
[[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,4],[4,4,4],[5,5],[6]] => 6
[[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,4],[4,4,4],[5,5],[6]] => 6
[[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,4],[4,4,4],[5,5],[6]] => 6
[[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,4],[4,4,4],[5,5],[6]] => 6
[[1,1,1,1,2,3],[2,2,2,2,3],[3,3,3,4],[4,4,4],[5,5],[6]] => 6
[[1,1,1,1,1,1],[2,2,2,2,4],[3,3,3,4],[4,4,4],[5,5],[6]] => 6
[[1,1,1,1,1,2],[2,2,2,2,4],[3,3,3,4],[4,4,4],[5,5],[6]] => 6
[[1,1,1,1,1,3],[2,2,2,2,4],[3,3,3,4],[4,4,4],[5,5],[6]] => 6
[[1,1,1,1,1,4],[2,2,2,2,4],[3,3,3,4],[4,4,4],[5,5],[6]] => 6
[[1,1,1,1,1,1],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,5],[6]] => 6
[[1,1,1,1,1,2],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,5],[6]] => 6
[[1,1,1,1,2,3],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,5],[6]] => 6
[[1,1,1,2,3,4],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,5],[6]] => 6
[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,5],[5,5],[6]] => 6
[[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,3],[4,4,5],[5,5],[6]] => 6
[[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,4,5],[5,5],[6]] => 6
[[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,3],[4,4,5],[5,5],[6]] => 6
[[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,3],[4,4,5],[5,5],[6]] => 6
[[1,1,1,1,2,3],[2,2,2,2,3],[3,3,3,3],[4,4,5],[5,5],[6]] => 6
[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,4,5],[5,5],[6]] => 6
[[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,4],[4,4,5],[5,5],[6]] => 6
[[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,4],[4,4,5],[5,5],[6]] => 6
[[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,4],[4,4,5],[5,5],[6]] => 6
[[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,4],[4,4,5],[5,5],[6]] => 6
[[1,1,1,1,2,3],[2,2,2,2,3],[3,3,3,4],[4,4,5],[5,5],[6]] => 6
[[1,1,1,1,1,1],[2,2,2,2,4],[3,3,3,4],[4,4,5],[5,5],[6]] => 6
[[1,1,1,1,1,2],[2,2,2,2,4],[3,3,3,4],[4,4,5],[5,5],[6]] => 6
[[1,1,1,1,1,3],[2,2,2,2,4],[3,3,3,4],[4,4,5],[5,5],[6]] => 6
[[1,1,1,1,1,4],[2,2,2,2,4],[3,3,3,4],[4,4,5],[5,5],[6]] => 6
[[1,1,1,1,1,1],[2,2,2,3,4],[3,3,3,4],[4,4,5],[5,5],[6]] => 6
[[1,1,1,1,1,2],[2,2,2,3,4],[3,3,3,4],[4,4,5],[5,5],[6]] => 6
[[1,1,1,1,2,3],[2,2,2,3,4],[3,3,3,4],[4,4,5],[5,5],[6]] => 6
[[1,1,1,2,3,4],[2,2,2,3,4],[3,3,3,4],[4,4,5],[5,5],[6]] => 6
[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,5],[4,4,5],[5,5],[6]] => 6
[[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,5],[4,4,5],[5,5],[6]] => 6
[[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,5],[4,4,5],[5,5],[6]] => 6
[[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,5],[4,4,5],[5,5],[6]] => 6
[[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,5],[4,4,5],[5,5],[6]] => 6
[[1,1,1,1,1,1],[2,2,2,2,4],[3,3,3,5],[4,4,5],[5,5],[6]] => 6
[[1,1,1,1,1,2],[2,2,2,2,4],[3,3,3,5],[4,4,5],[5,5],[6]] => 6
[[1,1,1,1,1,3],[2,2,2,2,4],[3,3,3,5],[4,4,5],[5,5],[6]] => 6
[[1,1,1,1,1,4],[2,2,2,2,4],[3,3,3,5],[4,4,5],[5,5],[6]] => 6
[[1,1,1,1,1,1],[2,2,2,2,5],[3,3,3,5],[4,4,5],[5,5],[6]] => 6
[[1,1,1,1,1,2],[2,2,2,2,5],[3,3,3,5],[4,4,5],[5,5],[6]] => 6
[[1,1,1,1,1,3],[2,2,2,2,5],[3,3,3,5],[4,4,5],[5,5],[6]] => 6
[[1,1,1,1,1,4],[2,2,2,2,5],[3,3,3,5],[4,4,5],[5,5],[6]] => 6
[[1,1,1,1,1,5],[2,2,2,2,5],[3,3,3,5],[4,4,5],[5,5],[6]] => 6
[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,4,5],[4,4,5],[5,5],[6]] => 7
[[1,1,1,1,1,2],[2,2,2,2,2],[3,3,4,5],[4,4,5],[5,5],[6]] => 7
[[1,1,1,1,1,1],[2,2,2,2,3],[3,3,4,5],[4,4,5],[5,5],[6]] => 7
[[1,1,1,1,1,2],[2,2,2,2,3],[3,3,4,5],[4,4,5],[5,5],[6]] => 7
[[1,1,1,1,2,3],[2,2,2,2,3],[3,3,4,5],[4,4,5],[5,5],[6]] => 7
[[1,1,1,1,1,1],[2,2,2,3,4],[3,3,4,5],[4,4,5],[5,5],[6]] => 7
[[1,1,1,1,1,2],[2,2,2,3,4],[3,3,4,5],[4,4,5],[5,5],[6]] => 7
[[1,1,1,1,2,3],[2,2,2,3,4],[3,3,4,5],[4,4,5],[5,5],[6]] => 7
[[1,1,1,2,3,4],[2,2,2,3,4],[3,3,4,5],[4,4,5],[5,5],[6]] => 7
[[1,1,1,1,1,1],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,5],[6]] => 7
[[1,1,1,1,1,2],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,5],[6]] => 7
[[1,1,1,1,2,3],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,5],[6]] => 7
[[1,1,1,2,3,4],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,5],[6]] => 7
[[1,1,2,3,4,5],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,5],[6]] => 7
[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,4],[5,6],[6]] => 6
[[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,3],[4,4,4],[5,6],[6]] => 6
[[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,6],[6]] => 6
[[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,6],[6]] => 6
[[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,6],[6]] => 6
[[1,1,1,1,2,3],[2,2,2,2,3],[3,3,3,3],[4,4,4],[5,6],[6]] => 6
[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,4,4],[5,6],[6]] => 6
[[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,4],[4,4,4],[5,6],[6]] => 6
[[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,4],[4,4,4],[5,6],[6]] => 6
[[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,4],[4,4,4],[5,6],[6]] => 6
[[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,4],[4,4,4],[5,6],[6]] => 6
[[1,1,1,1,2,3],[2,2,2,2,3],[3,3,3,4],[4,4,4],[5,6],[6]] => 6
[[1,1,1,1,1,1],[2,2,2,2,4],[3,3,3,4],[4,4,4],[5,6],[6]] => 6
[[1,1,1,1,1,2],[2,2,2,2,4],[3,3,3,4],[4,4,4],[5,6],[6]] => 6
[[1,1,1,1,1,3],[2,2,2,2,4],[3,3,3,4],[4,4,4],[5,6],[6]] => 6
[[1,1,1,1,1,4],[2,2,2,2,4],[3,3,3,4],[4,4,4],[5,6],[6]] => 6
[[1,1,1,1,1,1],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,6],[6]] => 6
[[1,1,1,1,1,2],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,6],[6]] => 6
[[1,1,1,1,2,3],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,6],[6]] => 6
[[1,1,1,2,3,4],[2,2,2,3,4],[3,3,3,4],[4,4,4],[5,6],[6]] => 6
[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,5],[5,6],[6]] => 6
[[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,3],[4,4,5],[5,6],[6]] => 6
[[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,4,5],[5,6],[6]] => 6
[[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,3],[4,4,5],[5,6],[6]] => 6
[[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,3],[4,4,5],[5,6],[6]] => 6
[[1,1,1,1,2,3],[2,2,2,2,3],[3,3,3,3],[4,4,5],[5,6],[6]] => 6
[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,4,5],[5,6],[6]] => 6
[[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,4],[4,4,5],[5,6],[6]] => 6
[[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,4],[4,4,5],[5,6],[6]] => 6
[[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,4],[4,4,5],[5,6],[6]] => 6
[[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,4],[4,4,5],[5,6],[6]] => 6
[[1,1,1,1,2,3],[2,2,2,2,3],[3,3,3,4],[4,4,5],[5,6],[6]] => 6
[[1,1,1,1,1,1],[2,2,2,2,4],[3,3,3,4],[4,4,5],[5,6],[6]] => 6
[[1,1,1,1,1,2],[2,2,2,2,4],[3,3,3,4],[4,4,5],[5,6],[6]] => 6
[[1,1,1,1,1,3],[2,2,2,2,4],[3,3,3,4],[4,4,5],[5,6],[6]] => 6
[[1,1,1,1,1,4],[2,2,2,2,4],[3,3,3,4],[4,4,5],[5,6],[6]] => 6
[[1,1,1,1,1,1],[2,2,2,3,4],[3,3,3,4],[4,4,5],[5,6],[6]] => 6
[[1,1,1,1,1,2],[2,2,2,3,4],[3,3,3,4],[4,4,5],[5,6],[6]] => 6
[[1,1,1,1,2,3],[2,2,2,3,4],[3,3,3,4],[4,4,5],[5,6],[6]] => 6
[[1,1,1,2,3,4],[2,2,2,3,4],[3,3,3,4],[4,4,5],[5,6],[6]] => 6
[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,5],[4,4,5],[5,6],[6]] => 6
[[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,5],[4,4,5],[5,6],[6]] => 6
[[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,5],[4,4,5],[5,6],[6]] => 6
[[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,5],[4,4,5],[5,6],[6]] => 6
[[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,5],[4,4,5],[5,6],[6]] => 6
[[1,1,1,1,1,1],[2,2,2,2,4],[3,3,3,5],[4,4,5],[5,6],[6]] => 6
[[1,1,1,1,1,2],[2,2,2,2,4],[3,3,3,5],[4,4,5],[5,6],[6]] => 6
[[1,1,1,1,1,3],[2,2,2,2,4],[3,3,3,5],[4,4,5],[5,6],[6]] => 6
[[1,1,1,1,1,4],[2,2,2,2,4],[3,3,3,5],[4,4,5],[5,6],[6]] => 6
[[1,1,1,1,1,1],[2,2,2,2,5],[3,3,3,5],[4,4,5],[5,6],[6]] => 6
[[1,1,1,1,1,2],[2,2,2,2,5],[3,3,3,5],[4,4,5],[5,6],[6]] => 6
[[1,1,1,1,1,3],[2,2,2,2,5],[3,3,3,5],[4,4,5],[5,6],[6]] => 6
[[1,1,1,1,1,4],[2,2,2,2,5],[3,3,3,5],[4,4,5],[5,6],[6]] => 6
[[1,1,1,1,1,5],[2,2,2,2,5],[3,3,3,5],[4,4,5],[5,6],[6]] => 6
[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,4,5],[4,4,5],[5,6],[6]] => 7
[[1,1,1,1,1,2],[2,2,2,2,2],[3,3,4,5],[4,4,5],[5,6],[6]] => 7
[[1,1,1,1,1,1],[2,2,2,2,3],[3,3,4,5],[4,4,5],[5,6],[6]] => 7
[[1,1,1,1,1,2],[2,2,2,2,3],[3,3,4,5],[4,4,5],[5,6],[6]] => 7
[[1,1,1,1,2,3],[2,2,2,2,3],[3,3,4,5],[4,4,5],[5,6],[6]] => 7
[[1,1,1,1,1,1],[2,2,2,3,4],[3,3,4,5],[4,4,5],[5,6],[6]] => 7
[[1,1,1,1,1,2],[2,2,2,3,4],[3,3,4,5],[4,4,5],[5,6],[6]] => 7
[[1,1,1,1,2,3],[2,2,2,3,4],[3,3,4,5],[4,4,5],[5,6],[6]] => 7
[[1,1,1,2,3,4],[2,2,2,3,4],[3,3,4,5],[4,4,5],[5,6],[6]] => 7
[[1,1,1,1,1,1],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,6],[6]] => 7
[[1,1,1,1,1,2],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,6],[6]] => 7
[[1,1,1,1,2,3],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,6],[6]] => 7
[[1,1,1,2,3,4],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,6],[6]] => 7
[[1,1,2,3,4,5],[2,2,3,4,5],[3,3,4,5],[4,4,5],[5,6],[6]] => 7
[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,4,6],[5,6],[6]] => 6
[[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,3],[4,4,6],[5,6],[6]] => 6
[[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,4,6],[5,6],[6]] => 6
[[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,3],[4,4,6],[5,6],[6]] => 6
[[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,3],[4,4,6],[5,6],[6]] => 6
[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,4,6],[5,6],[6]] => 6
[[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,4],[4,4,6],[5,6],[6]] => 6
[[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,4],[4,4,6],[5,6],[6]] => 6
[[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,4],[4,4,6],[5,6],[6]] => 6
[[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,4],[4,4,6],[5,6],[6]] => 6
[[1,1,1,1,1,1],[2,2,2,2,4],[3,3,3,4],[4,4,6],[5,6],[6]] => 6
[[1,1,1,1,1,2],[2,2,2,2,4],[3,3,3,4],[4,4,6],[5,6],[6]] => 6
[[1,1,1,1,1,3],[2,2,2,2,4],[3,3,3,4],[4,4,6],[5,6],[6]] => 6
[[1,1,1,1,1,4],[2,2,2,2,4],[3,3,3,4],[4,4,6],[5,6],[6]] => 6
[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,5],[4,4,6],[5,6],[6]] => 6
[[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,5],[4,4,6],[5,6],[6]] => 6
[[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,5],[4,4,6],[5,6],[6]] => 6
[[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,5],[4,4,6],[5,6],[6]] => 6
[[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,5],[4,4,6],[5,6],[6]] => 6
[[1,1,1,1,1,1],[2,2,2,2,4],[3,3,3,5],[4,4,6],[5,6],[6]] => 6
[[1,1,1,1,1,2],[2,2,2,2,4],[3,3,3,5],[4,4,6],[5,6],[6]] => 6
[[1,1,1,1,1,3],[2,2,2,2,4],[3,3,3,5],[4,4,6],[5,6],[6]] => 6
[[1,1,1,1,1,4],[2,2,2,2,4],[3,3,3,5],[4,4,6],[5,6],[6]] => 6
[[1,1,1,1,1,1],[2,2,2,2,5],[3,3,3,5],[4,4,6],[5,6],[6]] => 6
[[1,1,1,1,1,2],[2,2,2,2,5],[3,3,3,5],[4,4,6],[5,6],[6]] => 6
[[1,1,1,1,1,3],[2,2,2,2,5],[3,3,3,5],[4,4,6],[5,6],[6]] => 6
[[1,1,1,1,1,4],[2,2,2,2,5],[3,3,3,5],[4,4,6],[5,6],[6]] => 6
[[1,1,1,1,1,5],[2,2,2,2,5],[3,3,3,5],[4,4,6],[5,6],[6]] => 6
[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,6],[4,4,6],[5,6],[6]] => 6
[[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,6],[4,4,6],[5,6],[6]] => 6
[[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,6],[4,4,6],[5,6],[6]] => 6
[[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,6],[4,4,6],[5,6],[6]] => 6
[[1,1,1,1,1,3],[2,2,2,2,3],[3,3,3,6],[4,4,6],[5,6],[6]] => 6
[[1,1,1,1,1,1],[2,2,2,2,4],[3,3,3,6],[4,4,6],[5,6],[6]] => 6
[[1,1,1,1,1,2],[2,2,2,2,4],[3,3,3,6],[4,4,6],[5,6],[6]] => 6
[[1,1,1,1,1,3],[2,2,2,2,4],[3,3,3,6],[4,4,6],[5,6],[6]] => 6
[[1,1,1,1,1,4],[2,2,2,2,4],[3,3,3,6],[4,4,6],[5,6],[6]] => 6
[[1,1,1,1,1,1],[2,2,2,2,5],[3,3,3,6],[4,4,6],[5,6],[6]] => 6
[[1,1,1,1,1,2],[2,2,2,2,5],[3,3,3,6],[4,4,6],[5,6],[6]] => 6
[[1,1,1,1,1,3],[2,2,2,2,5],[3,3,3,6],[4,4,6],[5,6],[6]] => 6
[[1,1,1,1,1,4],[2,2,2,2,5],[3,3,3,6],[4,4,6],[5,6],[6]] => 6
[[1,1,1,1,1,5],[2,2,2,2,5],[3,3,3,6],[4,4,6],[5,6],[6]] => 6
[[1,1,1,1,1,1],[2,2,2,2,6],[3,3,3,6],[4,4,6],[5,6],[6]] => 6
[[1,1,1,1,1,2],[2,2,2,2,6],[3,3,3,6],[4,4,6],[5,6],[6]] => 6
[[1,1,1,1,1,3],[2,2,2,2,6],[3,3,3,6],[4,4,6],[5,6],[6]] => 6
[[1,1,1,1,1,4],[2,2,2,2,6],[3,3,3,6],[4,4,6],[5,6],[6]] => 6
[[1,1,1,1,1,5],[2,2,2,2,6],[3,3,3,6],[4,4,6],[5,6],[6]] => 6
[[1,1,1,1,1,6],[2,2,2,2,6],[3,3,3,6],[4,4,6],[5,6],[6]] => 6
[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,3],[4,5,6],[5,6],[6]] => 6
[[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,3],[4,5,6],[5,6],[6]] => 6
[[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,3],[4,5,6],[5,6],[6]] => 6
[[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,3],[4,5,6],[5,6],[6]] => 6
[[1,1,1,1,2,3],[2,2,2,2,3],[3,3,3,3],[4,5,6],[5,6],[6]] => 6
[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,3,4],[4,5,6],[5,6],[6]] => 6
[[1,1,1,1,1,2],[2,2,2,2,2],[3,3,3,4],[4,5,6],[5,6],[6]] => 6
[[1,1,1,1,1,1],[2,2,2,2,3],[3,3,3,4],[4,5,6],[5,6],[6]] => 6
[[1,1,1,1,1,2],[2,2,2,2,3],[3,3,3,4],[4,5,6],[5,6],[6]] => 6
[[1,1,1,1,2,3],[2,2,2,2,3],[3,3,3,4],[4,5,6],[5,6],[6]] => 6
[[1,1,1,1,1,1],[2,2,2,3,4],[3,3,3,4],[4,5,6],[5,6],[6]] => 6
[[1,1,1,1,1,2],[2,2,2,3,4],[3,3,3,4],[4,5,6],[5,6],[6]] => 6
[[1,1,1,1,2,3],[2,2,2,3,4],[3,3,3,4],[4,5,6],[5,6],[6]] => 6
[[1,1,1,2,3,4],[2,2,2,3,4],[3,3,3,4],[4,5,6],[5,6],[6]] => 6
[[1,1,1,1,1,1],[2,2,2,2,2],[3,3,4,5],[4,5,6],[5,6],[6]] => 7
[[1,1,1,1,1,2],[2,2,2,2,2],[3,3,4,5],[4,5,6],[5,6],[6]] => 7
[[1,1,1,1,1,1],[2,2,2,2,3],[3,3,4,5],[4,5,6],[5,6],[6]] => 7
[[1,1,1,1,1,2],[2,2,2,2,3],[3,3,4,5],[4,5,6],[5,6],[6]] => 7
[[1,1,1,1,2,3],[2,2,2,2,3],[3,3,4,5],[4,5,6],[5,6],[6]] => 7
[[1,1,1,1,1,1],[2,2,2,3,4],[3,3,4,5],[4,5,6],[5,6],[6]] => 7
[[1,1,1,1,1,2],[2,2,2,3,4],[3,3,4,5],[4,5,6],[5,6],[6]] => 7
[[1,1,1,1,2,3],[2,2,2,3,4],[3,3,4,5],[4,5,6],[5,6],[6]] => 7
[[1,1,1,2,3,4],[2,2,2,3,4],[3,3,4,5],[4,5,6],[5,6],[6]] => 7
[[1,1,1,1,1,1],[2,2,3,4,5],[3,3,4,5],[4,5,6],[5,6],[6]] => 7
[[1,1,1,1,1,2],[2,2,3,4,5],[3,3,4,5],[4,5,6],[5,6],[6]] => 7
[[1,1,1,1,2,3],[2,2,3,4,5],[3,3,4,5],[4,5,6],[5,6],[6]] => 7
[[1,1,1,2,3,4],[2,2,3,4,5],[3,3,4,5],[4,5,6],[5,6],[6]] => 7
[[1,1,2,3,4,5],[2,2,3,4,5],[3,3,4,5],[4,5,6],[5,6],[6]] => 7
[[1,1,1,1,1,1],[2,2,2,2,2],[3,4,5,6],[4,5,6],[5,6],[6]] => 8
[[1,1,1,1,1,2],[2,2,2,2,2],[3,4,5,6],[4,5,6],[5,6],[6]] => 8
[[1,1,1,1,1,1],[2,2,2,2,3],[3,4,5,6],[4,5,6],[5,6],[6]] => 8
[[1,1,1,1,1,2],[2,2,2,2,3],[3,4,5,6],[4,5,6],[5,6],[6]] => 8
[[1,1,1,1,2,3],[2,2,2,2,3],[3,4,5,6],[4,5,6],[5,6],[6]] => 8
[[1,1,1,1,1,1],[2,2,2,3,4],[3,4,5,6],[4,5,6],[5,6],[6]] => 8
[[1,1,1,1,1,2],[2,2,2,3,4],[3,4,5,6],[4,5,6],[5,6],[6]] => 8
[[1,1,1,1,2,3],[2,2,2,3,4],[3,4,5,6],[4,5,6],[5,6],[6]] => 8
[[1,1,1,2,3,4],[2,2,2,3,4],[3,4,5,6],[4,5,6],[5,6],[6]] => 8
[[1,1,1,1,1,1],[2,2,3,4,5],[3,4,5,6],[4,5,6],[5,6],[6]] => 8
[[1,1,1,1,1,2],[2,2,3,4,5],[3,4,5,6],[4,5,6],[5,6],[6]] => 8
[[1,1,1,1,2,3],[2,2,3,4,5],[3,4,5,6],[4,5,6],[5,6],[6]] => 8
[[1,1,1,2,3,4],[2,2,3,4,5],[3,4,5,6],[4,5,6],[5,6],[6]] => 8
[[1,1,2,3,4,5],[2,2,3,4,5],[3,4,5,6],[4,5,6],[5,6],[6]] => 8
[[1,1,1,1,1,1],[2,3,4,5,6],[3,4,5,6],[4,5,6],[5,6],[6]] => 9
[[1,1,1,1,1,2],[2,3,4,5,6],[3,4,5,6],[4,5,6],[5,6],[6]] => 9
[[1,1,1,1,2,3],[2,3,4,5,6],[3,4,5,6],[4,5,6],[5,6],[6]] => 9
[[1,1,1,2,3,4],[2,3,4,5,6],[3,4,5,6],[4,5,6],[5,6],[6]] => 9
[[1,1,2,3,4,5],[2,3,4,5,6],[3,4,5,6],[4,5,6],[5,6],[6]] => 9
[[1,2,3,4,5,6],[2,3,4,5,6],[3,4,5,6],[4,5,6],[5,6],[6]] => 9
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Created: Nov 29, 2013 at 23:28 by Christian Krattenthaler
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Last Updated: Aug 09, 2019 at 12:47 by Martin Rubey