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-----------------------------------------------------------------------------
Statistic identifier: St001406
-----------------------------------------------------------------------------
Collection: Gelfand-Tsetlin patterns
-----------------------------------------------------------------------------
Description: The number of nonzero entries in a Gelfand Tsetlin pattern.
-----------------------------------------------------------------------------
References:
-----------------------------------------------------------------------------
Code:
def statistic(P):
return sum(sum(1 for e in r if e != 0) for r in P)
-----------------------------------------------------------------------------
Statistic values:
[[1,0],[0]] => 1
[[1,0],[1]] => 2
[[2,0],[0]] => 1
[[2,0],[1]] => 2
[[2,0],[2]] => 2
[[1,1],[1]] => 3
[[3,0],[0]] => 1
[[3,0],[1]] => 2
[[3,0],[2]] => 2
[[3,0],[3]] => 2
[[2,1],[1]] => 3
[[2,1],[2]] => 3
[[5,0],[0]] => 1
[[5,0],[1]] => 2
[[5,0],[2]] => 2
[[5,0],[3]] => 2
[[5,0],[4]] => 2
[[5,0],[5]] => 2
[[4,1],[1]] => 3
[[4,1],[2]] => 3
[[4,1],[3]] => 3
[[4,1],[4]] => 3
[[3,2],[2]] => 3
[[3,2],[3]] => 3
[[6,0],[0]] => 1
[[6,0],[1]] => 2
[[6,0],[2]] => 2
[[6,0],[3]] => 2
[[6,0],[4]] => 2
[[6,0],[5]] => 2
[[6,0],[6]] => 2
[[5,1],[1]] => 3
[[5,1],[2]] => 3
[[5,1],[3]] => 3
[[5,1],[4]] => 3
[[5,1],[5]] => 3
[[4,2],[2]] => 3
[[4,2],[3]] => 3
[[4,2],[4]] => 3
[[3,3],[3]] => 3
[[2,0,0],[0,0],[0]] => 1
[[2,0,0],[1,0],[0]] => 2
[[2,0,0],[1,0],[1]] => 3
[[2,0,0],[2,0],[0]] => 2
[[2,0,0],[2,0],[1]] => 3
[[2,0,0],[2,0],[2]] => 3
[[1,1,0],[1,0],[0]] => 3
[[1,1,0],[1,0],[1]] => 4
[[1,1,0],[1,1],[1]] => 5
[[3,0,0],[0,0],[0]] => 1
[[3,0,0],[1,0],[0]] => 2
[[3,0,0],[1,0],[1]] => 3
[[3,0,0],[2,0],[0]] => 2
[[3,0,0],[2,0],[1]] => 3
[[3,0,0],[2,0],[2]] => 3
[[3,0,0],[3,0],[0]] => 2
[[3,0,0],[3,0],[1]] => 3
[[3,0,0],[3,0],[2]] => 3
[[3,0,0],[3,0],[3]] => 3
[[2,1,0],[1,0],[0]] => 3
[[2,1,0],[1,0],[1]] => 4
[[2,1,0],[1,1],[1]] => 5
[[2,1,0],[2,0],[0]] => 3
[[2,1,0],[2,0],[1]] => 4
[[2,1,0],[2,0],[2]] => 4
[[2,1,0],[2,1],[1]] => 5
[[2,1,0],[2,1],[2]] => 5
[[1,1,1],[1,1],[1]] => 6
[[5,0,0],[0,0],[0]] => 1
[[5,0,0],[1,0],[0]] => 2
[[5,0,0],[1,0],[1]] => 3
[[5,0,0],[2,0],[0]] => 2
[[5,0,0],[2,0],[1]] => 3
[[5,0,0],[2,0],[2]] => 3
[[6,0,0],[0,0],[0]] => 1
[[6,0,0],[1,0],[0]] => 2
[[6,0,0],[1,0],[1]] => 3
[[6,0,0],[2,0],[0]] => 2
[[6,0,0],[2,0],[1]] => 3
[[6,0,0],[2,0],[2]] => 3
[[6,0,0],[3,0],[0]] => 2
[[6,0,0],[3,0],[1]] => 3
[[6,0,0],[3,0],[2]] => 3
[[6,0,0],[3,0],[3]] => 3
[[6,0,0],[4,0],[0]] => 2
[[6,0,0],[4,0],[1]] => 3
[[6,0,0],[4,0],[2]] => 3
[[6,0,0],[4,0],[3]] => 3
[[6,0,0],[4,0],[4]] => 3
[[6,0,0],[5,0],[0]] => 2
[[6,0,0],[5,0],[1]] => 3
[[6,0,0],[5,0],[2]] => 3
[[6,0,0],[5,0],[3]] => 3
[[6,0,0],[5,0],[4]] => 3
[[6,0,0],[5,0],[5]] => 3
[[6,0,0],[6,0],[0]] => 2
[[6,0,0],[6,0],[1]] => 3
[[6,0,0],[6,0],[2]] => 3
[[6,0,0],[6,0],[3]] => 3
[[6,0,0],[6,0],[4]] => 3
[[6,0,0],[6,0],[5]] => 3
[[6,0,0],[6,0],[6]] => 3
[[5,1,0],[1,0],[0]] => 3
[[5,1,0],[1,0],[1]] => 4
[[5,1,0],[1,1],[1]] => 5
[[5,1,0],[2,0],[0]] => 3
[[5,1,0],[2,0],[1]] => 4
[[5,1,0],[2,0],[2]] => 4
[[5,1,0],[2,1],[1]] => 5
[[5,1,0],[2,1],[2]] => 5
[[5,1,0],[3,0],[0]] => 3
[[5,1,0],[3,0],[1]] => 4
[[5,1,0],[3,0],[2]] => 4
[[5,1,0],[3,0],[3]] => 4
[[5,1,0],[3,1],[1]] => 5
[[5,1,0],[3,1],[2]] => 5
[[5,1,0],[3,1],[3]] => 5
[[5,1,0],[4,0],[0]] => 3
[[5,1,0],[4,0],[1]] => 4
[[5,1,0],[4,0],[2]] => 4
[[5,1,0],[4,0],[3]] => 4
[[5,1,0],[4,0],[4]] => 4
[[5,1,0],[4,1],[1]] => 5
[[5,1,0],[4,1],[2]] => 5
[[5,1,0],[4,1],[3]] => 5
[[5,1,0],[4,1],[4]] => 5
[[5,1,0],[5,0],[0]] => 3
[[5,1,0],[5,0],[1]] => 4
[[5,1,0],[5,0],[2]] => 4
[[5,1,0],[5,0],[3]] => 4
[[5,1,0],[5,0],[4]] => 4
[[5,1,0],[5,0],[5]] => 4
[[5,1,0],[5,1],[1]] => 5
[[5,1,0],[5,1],[2]] => 5
[[5,1,0],[5,1],[3]] => 5
[[5,1,0],[5,1],[4]] => 5
[[5,1,0],[5,1],[5]] => 5
[[4,2,0],[2,0],[0]] => 3
[[4,2,0],[2,0],[1]] => 4
[[4,2,0],[2,0],[2]] => 4
[[4,2,0],[2,1],[1]] => 5
[[4,2,0],[2,1],[2]] => 5
[[4,2,0],[2,2],[2]] => 5
[[4,2,0],[3,0],[0]] => 3
[[4,2,0],[3,0],[1]] => 4
[[4,2,0],[3,0],[2]] => 4
[[4,2,0],[3,0],[3]] => 4
[[4,2,0],[3,1],[1]] => 5
[[4,2,0],[3,1],[2]] => 5
[[4,2,0],[3,1],[3]] => 5
[[4,2,0],[3,2],[2]] => 5
[[4,2,0],[3,2],[3]] => 5
[[4,2,0],[4,0],[0]] => 3
[[4,2,0],[4,0],[1]] => 4
[[4,2,0],[4,0],[2]] => 4
[[4,2,0],[4,0],[3]] => 4
[[4,2,0],[4,0],[4]] => 4
[[4,2,0],[4,1],[1]] => 5
[[4,2,0],[4,1],[2]] => 5
[[4,2,0],[4,1],[3]] => 5
[[4,2,0],[4,1],[4]] => 5
[[4,2,0],[4,2],[2]] => 5
[[4,2,0],[4,2],[3]] => 5
[[4,2,0],[4,2],[4]] => 5
[[4,1,1],[1,1],[1]] => 6
[[4,1,1],[2,1],[1]] => 6
[[4,1,1],[2,1],[2]] => 6
[[4,1,1],[3,1],[1]] => 6
[[4,1,1],[3,1],[2]] => 6
[[4,1,1],[3,1],[3]] => 6
[[4,1,1],[4,1],[1]] => 6
[[4,1,1],[4,1],[2]] => 6
[[4,1,1],[4,1],[3]] => 6
[[4,1,1],[4,1],[4]] => 6
[[3,3,0],[3,0],[0]] => 3
[[3,3,0],[3,0],[1]] => 4
[[3,3,0],[3,0],[2]] => 4
[[3,3,0],[3,0],[3]] => 4
[[3,3,0],[3,1],[1]] => 5
[[3,3,0],[3,1],[2]] => 5
[[3,3,0],[3,1],[3]] => 5
[[3,3,0],[3,2],[2]] => 5
[[3,3,0],[3,2],[3]] => 5
[[3,3,0],[3,3],[3]] => 5
[[3,2,1],[2,1],[1]] => 6
[[3,2,1],[2,1],[2]] => 6
[[3,2,1],[2,2],[2]] => 6
[[3,2,1],[3,1],[1]] => 6
[[3,2,1],[3,1],[2]] => 6
[[3,2,1],[3,1],[3]] => 6
[[3,2,1],[3,2],[2]] => 6
[[3,2,1],[3,2],[3]] => 6
[[2,2,2],[2,2],[2]] => 6
[[1,0,0,0],[0,0,0],[0,0],[0]] => 1
[[1,0,0,0],[1,0,0],[0,0],[0]] => 2
[[1,0,0,0],[1,0,0],[1,0],[0]] => 3
[[1,0,0,0],[1,0,0],[1,0],[1]] => 4
[[2,0,0,0],[0,0,0],[0,0],[0]] => 1
[[2,0,0,0],[1,0,0],[0,0],[0]] => 2
[[2,0,0,0],[1,0,0],[1,0],[0]] => 3
[[2,0,0,0],[1,0,0],[1,0],[1]] => 4
[[2,0,0,0],[2,0,0],[0,0],[0]] => 2
[[2,0,0,0],[2,0,0],[1,0],[0]] => 3
[[2,0,0,0],[2,0,0],[1,0],[1]] => 4
[[2,0,0,0],[2,0,0],[2,0],[0]] => 3
[[2,0,0,0],[2,0,0],[2,0],[1]] => 4
[[2,0,0,0],[2,0,0],[2,0],[2]] => 4
[[1,1,0,0],[1,0,0],[0,0],[0]] => 3
[[1,1,0,0],[1,0,0],[1,0],[0]] => 4
[[1,1,0,0],[1,0,0],[1,0],[1]] => 5
[[1,1,0,0],[1,1,0],[1,0],[0]] => 5
[[1,1,0,0],[1,1,0],[1,0],[1]] => 6
[[1,1,0,0],[1,1,0],[1,1],[1]] => 7
[[4,0,0,0],[0,0,0],[0,0],[0]] => 1
[[4,0,0,0],[1,0,0],[0,0],[0]] => 2
[[4,0,0,0],[1,0,0],[1,0],[0]] => 3
[[4,0,0,0],[1,0,0],[1,0],[1]] => 4
[[4,0,0,0],[2,0,0],[0,0],[0]] => 2
[[4,0,0,0],[2,0,0],[1,0],[0]] => 3
[[4,0,0,0],[2,0,0],[1,0],[1]] => 4
[[4,0,0,0],[2,0,0],[2,0],[0]] => 3
[[4,0,0,0],[2,0,0],[2,0],[1]] => 4
[[4,0,0,0],[2,0,0],[2,0],[2]] => 4
[[4,0,0,0],[3,0,0],[0,0],[0]] => 2
[[4,0,0,0],[3,0,0],[1,0],[0]] => 3
[[4,0,0,0],[3,0,0],[1,0],[1]] => 4
[[4,0,0,0],[3,0,0],[2,0],[0]] => 3
[[4,0,0,0],[3,0,0],[2,0],[1]] => 4
[[4,0,0,0],[3,0,0],[2,0],[2]] => 4
[[4,0,0,0],[3,0,0],[3,0],[0]] => 3
[[4,0,0,0],[3,0,0],[3,0],[1]] => 4
[[4,0,0,0],[3,0,0],[3,0],[2]] => 4
[[4,0,0,0],[3,0,0],[3,0],[3]] => 4
[[4,0,0,0],[4,0,0],[0,0],[0]] => 2
[[4,0,0,0],[4,0,0],[1,0],[0]] => 3
[[4,0,0,0],[4,0,0],[1,0],[1]] => 4
[[4,0,0,0],[4,0,0],[2,0],[0]] => 3
[[4,0,0,0],[4,0,0],[2,0],[1]] => 4
[[4,0,0,0],[4,0,0],[2,0],[2]] => 4
[[4,0,0,0],[4,0,0],[3,0],[0]] => 3
[[4,0,0,0],[4,0,0],[3,0],[1]] => 4
[[4,0,0,0],[4,0,0],[3,0],[2]] => 4
[[4,0,0,0],[4,0,0],[3,0],[3]] => 4
[[4,0,0,0],[4,0,0],[4,0],[0]] => 3
[[4,0,0,0],[4,0,0],[4,0],[1]] => 4
[[4,0,0,0],[4,0,0],[4,0],[2]] => 4
[[4,0,0,0],[4,0,0],[4,0],[3]] => 4
[[4,0,0,0],[4,0,0],[4,0],[4]] => 4
[[3,1,0,0],[1,0,0],[0,0],[0]] => 3
[[3,1,0,0],[1,0,0],[1,0],[0]] => 4
[[3,1,0,0],[1,0,0],[1,0],[1]] => 5
[[3,1,0,0],[1,1,0],[1,0],[0]] => 5
[[3,1,0,0],[1,1,0],[1,0],[1]] => 6
[[3,1,0,0],[1,1,0],[1,1],[1]] => 7
[[3,1,0,0],[2,0,0],[0,0],[0]] => 3
[[3,1,0,0],[2,0,0],[1,0],[0]] => 4
[[3,1,0,0],[2,0,0],[1,0],[1]] => 5
[[3,1,0,0],[2,0,0],[2,0],[0]] => 4
[[3,1,0,0],[2,0,0],[2,0],[1]] => 5
[[3,1,0,0],[2,0,0],[2,0],[2]] => 5
[[3,1,0,0],[2,1,0],[1,0],[0]] => 5
[[3,1,0,0],[2,1,0],[1,0],[1]] => 6
[[3,1,0,0],[2,1,0],[1,1],[1]] => 7
[[3,1,0,0],[2,1,0],[2,0],[0]] => 5
[[3,1,0,0],[2,1,0],[2,0],[1]] => 6
[[3,1,0,0],[2,1,0],[2,0],[2]] => 6
[[3,1,0,0],[2,1,0],[2,1],[1]] => 7
[[3,1,0,0],[2,1,0],[2,1],[2]] => 7
[[3,1,0,0],[3,0,0],[0,0],[0]] => 3
[[3,1,0,0],[3,0,0],[1,0],[0]] => 4
[[3,1,0,0],[3,0,0],[1,0],[1]] => 5
[[3,1,0,0],[3,0,0],[2,0],[0]] => 4
[[3,1,0,0],[3,0,0],[2,0],[1]] => 5
[[3,1,0,0],[3,0,0],[2,0],[2]] => 5
[[3,1,0,0],[3,0,0],[3,0],[0]] => 4
[[3,1,0,0],[3,0,0],[3,0],[1]] => 5
[[3,1,0,0],[3,0,0],[3,0],[2]] => 5
[[3,1,0,0],[3,0,0],[3,0],[3]] => 5
[[3,1,0,0],[3,1,0],[1,0],[0]] => 5
[[3,1,0,0],[3,1,0],[1,0],[1]] => 6
[[3,1,0,0],[3,1,0],[1,1],[1]] => 7
[[3,1,0,0],[3,1,0],[2,0],[0]] => 5
[[3,1,0,0],[3,1,0],[2,0],[1]] => 6
[[3,1,0,0],[3,1,0],[2,0],[2]] => 6
[[3,1,0,0],[3,1,0],[2,1],[1]] => 7
[[3,1,0,0],[3,1,0],[2,1],[2]] => 7
[[3,1,0,0],[3,1,0],[3,0],[0]] => 5
[[3,1,0,0],[3,1,0],[3,0],[1]] => 6
[[3,1,0,0],[3,1,0],[3,0],[2]] => 6
[[3,1,0,0],[3,1,0],[3,0],[3]] => 6
[[3,1,0,0],[3,1,0],[3,1],[1]] => 7
[[3,1,0,0],[3,1,0],[3,1],[2]] => 7
[[3,1,0,0],[3,1,0],[3,1],[3]] => 7
[[2,2,0,0],[2,0,0],[0,0],[0]] => 3
[[2,2,0,0],[2,0,0],[1,0],[0]] => 4
[[2,2,0,0],[2,0,0],[1,0],[1]] => 5
[[2,2,0,0],[2,0,0],[2,0],[0]] => 4
[[2,2,0,0],[2,0,0],[2,0],[1]] => 5
[[2,2,0,0],[2,0,0],[2,0],[2]] => 5
[[2,2,0,0],[2,1,0],[1,0],[0]] => 5
[[2,2,0,0],[2,1,0],[1,0],[1]] => 6
[[2,2,0,0],[2,1,0],[1,1],[1]] => 7
[[2,2,0,0],[2,1,0],[2,0],[0]] => 5
[[2,2,0,0],[2,1,0],[2,0],[1]] => 6
[[2,2,0,0],[2,1,0],[2,0],[2]] => 6
[[2,2,0,0],[2,1,0],[2,1],[1]] => 7
[[2,2,0,0],[2,1,0],[2,1],[2]] => 7
[[2,2,0,0],[2,2,0],[2,0],[0]] => 5
[[2,2,0,0],[2,2,0],[2,0],[1]] => 6
[[2,2,0,0],[2,2,0],[2,0],[2]] => 6
[[2,2,0,0],[2,2,0],[2,1],[1]] => 7
[[2,2,0,0],[2,2,0],[2,1],[2]] => 7
[[2,2,0,0],[2,2,0],[2,2],[2]] => 7
[[2,1,1,0],[1,1,0],[1,0],[0]] => 6
[[2,1,1,0],[1,1,0],[1,0],[1]] => 7
[[2,1,1,0],[1,1,0],[1,1],[1]] => 8
[[2,1,1,0],[1,1,1],[1,1],[1]] => 9
[[2,1,1,0],[2,1,0],[1,0],[0]] => 6
[[2,1,1,0],[2,1,0],[1,0],[1]] => 7
[[2,1,1,0],[2,1,0],[1,1],[1]] => 8
[[2,1,1,0],[2,1,0],[2,0],[0]] => 6
[[2,1,1,0],[2,1,0],[2,0],[1]] => 7
[[2,1,1,0],[2,1,0],[2,0],[2]] => 7
[[2,1,1,0],[2,1,0],[2,1],[1]] => 8
[[2,1,1,0],[2,1,0],[2,1],[2]] => 8
[[2,1,1,0],[2,1,1],[1,1],[1]] => 9
[[2,1,1,0],[2,1,1],[2,1],[1]] => 9
[[2,1,1,0],[2,1,1],[2,1],[2]] => 9
[[1,1,1,1],[1,1,1],[1,1],[1]] => 10
[[5,0,0,0],[0,0,0],[0,0],[0]] => 1
[[5,0,0,0],[1,0,0],[0,0],[0]] => 2
[[5,0,0,0],[1,0,0],[1,0],[0]] => 3
[[5,0,0,0],[1,0,0],[1,0],[1]] => 4
[[5,0,0,0],[2,0,0],[0,0],[0]] => 2
[[5,0,0,0],[2,0,0],[1,0],[0]] => 3
[[5,0,0,0],[2,0,0],[1,0],[1]] => 4
[[5,0,0,0],[2,0,0],[2,0],[0]] => 3
[[5,0,0,0],[2,0,0],[2,0],[1]] => 4
[[5,0,0,0],[2,0,0],[2,0],[2]] => 4
[[5,0,0,0],[3,0,0],[0,0],[0]] => 2
[[5,0,0,0],[3,0,0],[1,0],[0]] => 3
[[5,0,0,0],[3,0,0],[1,0],[1]] => 4
[[5,0,0,0],[3,0,0],[2,0],[0]] => 3
[[5,0,0,0],[3,0,0],[2,0],[1]] => 4
[[5,0,0,0],[3,0,0],[2,0],[2]] => 4
[[5,0,0,0],[3,0,0],[3,0],[0]] => 3
[[5,0,0,0],[3,0,0],[3,0],[1]] => 4
[[5,0,0,0],[3,0,0],[3,0],[2]] => 4
[[5,0,0,0],[3,0,0],[3,0],[3]] => 4
[[5,0,0,0],[4,0,0],[0,0],[0]] => 2
[[5,0,0,0],[4,0,0],[1,0],[0]] => 3
[[5,0,0,0],[4,0,0],[1,0],[1]] => 4
[[5,0,0,0],[4,0,0],[2,0],[0]] => 3
[[5,0,0,0],[4,0,0],[2,0],[1]] => 4
[[5,0,0,0],[4,0,0],[2,0],[2]] => 4
[[5,0,0,0],[4,0,0],[3,0],[0]] => 3
[[5,0,0,0],[4,0,0],[3,0],[1]] => 4
[[5,0,0,0],[4,0,0],[3,0],[2]] => 4
[[5,0,0,0],[4,0,0],[3,0],[3]] => 4
[[5,0,0,0],[4,0,0],[4,0],[0]] => 3
[[5,0,0,0],[4,0,0],[4,0],[1]] => 4
[[5,0,0,0],[4,0,0],[4,0],[2]] => 4
[[5,0,0,0],[4,0,0],[4,0],[3]] => 4
[[5,0,0,0],[4,0,0],[4,0],[4]] => 4
[[5,0,0,0],[5,0,0],[0,0],[0]] => 2
[[5,0,0,0],[5,0,0],[1,0],[0]] => 3
[[5,0,0,0],[5,0,0],[1,0],[1]] => 4
[[5,0,0,0],[5,0,0],[2,0],[0]] => 3
[[5,0,0,0],[5,0,0],[2,0],[1]] => 4
[[5,0,0,0],[5,0,0],[2,0],[2]] => 4
[[5,0,0,0],[5,0,0],[3,0],[0]] => 3
[[5,0,0,0],[5,0,0],[3,0],[1]] => 4
[[5,0,0,0],[5,0,0],[3,0],[2]] => 4
[[5,0,0,0],[5,0,0],[3,0],[3]] => 4
[[5,0,0,0],[5,0,0],[4,0],[0]] => 3
[[5,0,0,0],[5,0,0],[4,0],[1]] => 4
[[5,0,0,0],[5,0,0],[4,0],[2]] => 4
[[5,0,0,0],[5,0,0],[4,0],[3]] => 4
[[5,0,0,0],[5,0,0],[4,0],[4]] => 4
[[5,0,0,0],[5,0,0],[5,0],[0]] => 3
[[5,0,0,0],[5,0,0],[5,0],[1]] => 4
[[5,0,0,0],[5,0,0],[5,0],[2]] => 4
[[5,0,0,0],[5,0,0],[5,0],[3]] => 4
[[5,0,0,0],[5,0,0],[5,0],[4]] => 4
[[5,0,0,0],[5,0,0],[5,0],[5]] => 4
[[4,1,0,0],[1,0,0],[0,0],[0]] => 3
[[4,1,0,0],[1,0,0],[1,0],[0]] => 4
[[4,1,0,0],[1,0,0],[1,0],[1]] => 5
[[4,1,0,0],[1,1,0],[1,0],[0]] => 5
[[4,1,0,0],[1,1,0],[1,0],[1]] => 6
[[4,1,0,0],[1,1,0],[1,1],[1]] => 7
[[4,1,0,0],[2,0,0],[0,0],[0]] => 3
[[4,1,0,0],[2,0,0],[1,0],[0]] => 4
[[4,1,0,0],[2,0,0],[1,0],[1]] => 5
[[4,1,0,0],[2,0,0],[2,0],[0]] => 4
[[4,1,0,0],[2,0,0],[2,0],[1]] => 5
[[4,1,0,0],[2,0,0],[2,0],[2]] => 5
[[4,1,0,0],[2,1,0],[1,0],[0]] => 5
[[4,1,0,0],[2,1,0],[1,0],[1]] => 6
[[4,1,0,0],[2,1,0],[1,1],[1]] => 7
[[4,1,0,0],[2,1,0],[2,0],[0]] => 5
[[4,1,0,0],[2,1,0],[2,0],[1]] => 6
[[4,1,0,0],[2,1,0],[2,0],[2]] => 6
[[4,1,0,0],[2,1,0],[2,1],[1]] => 7
[[4,1,0,0],[2,1,0],[2,1],[2]] => 7
[[4,1,0,0],[3,0,0],[0,0],[0]] => 3
[[4,1,0,0],[3,0,0],[1,0],[0]] => 4
[[4,1,0,0],[3,0,0],[1,0],[1]] => 5
[[4,1,0,0],[3,0,0],[2,0],[0]] => 4
[[4,1,0,0],[3,0,0],[2,0],[1]] => 5
[[4,1,0,0],[3,0,0],[2,0],[2]] => 5
[[4,1,0,0],[3,0,0],[3,0],[0]] => 4
[[4,1,0,0],[3,0,0],[3,0],[1]] => 5
[[4,1,0,0],[3,0,0],[3,0],[2]] => 5
[[4,1,0,0],[3,0,0],[3,0],[3]] => 5
[[4,1,0,0],[3,1,0],[1,0],[0]] => 5
[[4,1,0,0],[3,1,0],[1,0],[1]] => 6
[[4,1,0,0],[3,1,0],[1,1],[1]] => 7
[[4,1,0,0],[3,1,0],[2,0],[0]] => 5
[[4,1,0,0],[3,1,0],[2,0],[1]] => 6
[[4,1,0,0],[3,1,0],[2,0],[2]] => 6
[[4,1,0,0],[3,1,0],[2,1],[1]] => 7
[[4,1,0,0],[3,1,0],[2,1],[2]] => 7
[[4,1,0,0],[3,1,0],[3,0],[0]] => 5
[[4,1,0,0],[3,1,0],[3,0],[1]] => 6
[[4,1,0,0],[3,1,0],[3,0],[2]] => 6
[[4,1,0,0],[3,1,0],[3,0],[3]] => 6
[[4,1,0,0],[3,1,0],[3,1],[1]] => 7
[[4,1,0,0],[3,1,0],[3,1],[2]] => 7
[[4,1,0,0],[3,1,0],[3,1],[3]] => 7
[[4,1,0,0],[4,0,0],[0,0],[0]] => 3
[[4,1,0,0],[4,0,0],[1,0],[0]] => 4
[[4,1,0,0],[4,0,0],[1,0],[1]] => 5
[[4,1,0,0],[4,0,0],[2,0],[0]] => 4
[[4,1,0,0],[4,0,0],[2,0],[1]] => 5
[[4,1,0,0],[4,0,0],[2,0],[2]] => 5
[[4,1,0,0],[4,0,0],[3,0],[0]] => 4
[[4,1,0,0],[4,0,0],[3,0],[1]] => 5
[[4,1,0,0],[4,0,0],[3,0],[2]] => 5
[[4,1,0,0],[4,0,0],[3,0],[3]] => 5
[[4,1,0,0],[4,0,0],[4,0],[0]] => 4
[[4,1,0,0],[4,0,0],[4,0],[1]] => 5
[[4,1,0,0],[4,0,0],[4,0],[2]] => 5
[[4,1,0,0],[4,0,0],[4,0],[3]] => 5
[[4,1,0,0],[4,0,0],[4,0],[4]] => 5
[[4,1,0,0],[4,1,0],[1,0],[0]] => 5
[[4,1,0,0],[4,1,0],[1,0],[1]] => 6
[[4,1,0,0],[4,1,0],[1,1],[1]] => 7
[[4,1,0,0],[4,1,0],[2,0],[0]] => 5
[[4,1,0,0],[4,1,0],[2,0],[1]] => 6
[[4,1,0,0],[4,1,0],[2,0],[2]] => 6
[[4,1,0,0],[4,1,0],[2,1],[1]] => 7
[[4,1,0,0],[4,1,0],[2,1],[2]] => 7
[[4,1,0,0],[4,1,0],[3,0],[0]] => 5
[[4,1,0,0],[4,1,0],[3,0],[1]] => 6
[[4,1,0,0],[4,1,0],[3,0],[2]] => 6
[[4,1,0,0],[4,1,0],[3,0],[3]] => 6
[[4,1,0,0],[4,1,0],[3,1],[1]] => 7
[[4,1,0,0],[4,1,0],[3,1],[2]] => 7
[[4,1,0,0],[4,1,0],[3,1],[3]] => 7
[[4,1,0,0],[4,1,0],[4,0],[0]] => 5
[[4,1,0,0],[4,1,0],[4,0],[1]] => 6
[[4,1,0,0],[4,1,0],[4,0],[2]] => 6
[[4,1,0,0],[4,1,0],[4,0],[3]] => 6
[[4,1,0,0],[4,1,0],[4,0],[4]] => 6
[[4,1,0,0],[4,1,0],[4,1],[1]] => 7
[[4,1,0,0],[4,1,0],[4,1],[2]] => 7
[[4,1,0,0],[4,1,0],[4,1],[3]] => 7
[[4,1,0,0],[4,1,0],[4,1],[4]] => 7
[[3,2,0,0],[2,0,0],[0,0],[0]] => 3
[[3,2,0,0],[2,0,0],[1,0],[0]] => 4
[[3,2,0,0],[2,0,0],[1,0],[1]] => 5
[[3,2,0,0],[2,0,0],[2,0],[0]] => 4
[[3,2,0,0],[2,0,0],[2,0],[1]] => 5
[[3,2,0,0],[2,0,0],[2,0],[2]] => 5
[[3,2,0,0],[2,1,0],[1,0],[0]] => 5
[[3,2,0,0],[2,1,0],[1,0],[1]] => 6
[[3,2,0,0],[2,1,0],[1,1],[1]] => 7
[[3,2,0,0],[2,1,0],[2,0],[0]] => 5
[[3,2,0,0],[2,1,0],[2,0],[1]] => 6
[[3,2,0,0],[2,1,0],[2,0],[2]] => 6
[[3,2,0,0],[2,1,0],[2,1],[1]] => 7
[[3,2,0,0],[2,1,0],[2,1],[2]] => 7
[[3,2,0,0],[2,2,0],[2,0],[0]] => 5
[[3,2,0,0],[2,2,0],[2,0],[1]] => 6
[[3,2,0,0],[2,2,0],[2,0],[2]] => 6
[[3,2,0,0],[2,2,0],[2,1],[1]] => 7
[[3,2,0,0],[2,2,0],[2,1],[2]] => 7
[[3,2,0,0],[2,2,0],[2,2],[2]] => 7
[[3,2,0,0],[3,0,0],[0,0],[0]] => 3
[[3,2,0,0],[3,0,0],[1,0],[0]] => 4
[[3,2,0,0],[3,0,0],[1,0],[1]] => 5
[[3,2,0,0],[3,0,0],[2,0],[0]] => 4
[[3,2,0,0],[3,0,0],[2,0],[1]] => 5
[[3,2,0,0],[3,0,0],[2,0],[2]] => 5
[[3,2,0,0],[3,0,0],[3,0],[0]] => 4
[[3,2,0,0],[3,0,0],[3,0],[1]] => 5
[[3,2,0,0],[3,0,0],[3,0],[2]] => 5
[[3,2,0,0],[3,0,0],[3,0],[3]] => 5
[[3,2,0,0],[3,1,0],[1,0],[0]] => 5
[[3,2,0,0],[3,1,0],[1,0],[1]] => 6
[[3,2,0,0],[3,1,0],[1,1],[1]] => 7
[[3,2,0,0],[3,1,0],[2,0],[0]] => 5
[[3,2,0,0],[3,1,0],[2,0],[1]] => 6
[[3,2,0,0],[3,1,0],[2,0],[2]] => 6
[[3,2,0,0],[3,1,0],[2,1],[1]] => 7
[[3,2,0,0],[3,1,0],[2,1],[2]] => 7
[[3,2,0,0],[3,1,0],[3,0],[0]] => 5
[[3,2,0,0],[3,1,0],[3,0],[1]] => 6
[[3,2,0,0],[3,1,0],[3,0],[2]] => 6
[[3,2,0,0],[3,1,0],[3,0],[3]] => 6
[[3,2,0,0],[3,1,0],[3,1],[1]] => 7
[[3,2,0,0],[3,1,0],[3,1],[2]] => 7
[[3,2,0,0],[3,1,0],[3,1],[3]] => 7
[[3,2,0,0],[3,2,0],[2,0],[0]] => 5
[[3,2,0,0],[3,2,0],[2,0],[1]] => 6
[[3,2,0,0],[3,2,0],[2,0],[2]] => 6
[[3,2,0,0],[3,2,0],[2,1],[1]] => 7
[[3,2,0,0],[3,2,0],[2,1],[2]] => 7
[[3,2,0,0],[3,2,0],[2,2],[2]] => 7
[[3,2,0,0],[3,2,0],[3,0],[0]] => 5
[[3,2,0,0],[3,2,0],[3,0],[1]] => 6
[[3,2,0,0],[3,2,0],[3,0],[2]] => 6
[[3,2,0,0],[3,2,0],[3,0],[3]] => 6
[[3,2,0,0],[3,2,0],[3,1],[1]] => 7
[[3,2,0,0],[3,2,0],[3,1],[2]] => 7
[[3,2,0,0],[3,2,0],[3,1],[3]] => 7
[[3,2,0,0],[3,2,0],[3,2],[2]] => 7
[[3,2,0,0],[3,2,0],[3,2],[3]] => 7
[[3,1,1,0],[1,1,0],[1,0],[0]] => 6
[[3,1,1,0],[1,1,0],[1,0],[1]] => 7
[[3,1,1,0],[1,1,0],[1,1],[1]] => 8
[[3,1,1,0],[1,1,1],[1,1],[1]] => 9
[[3,1,1,0],[2,1,0],[1,0],[0]] => 6
[[3,1,1,0],[2,1,0],[1,0],[1]] => 7
[[3,1,1,0],[2,1,0],[1,1],[1]] => 8
[[3,1,1,0],[2,1,0],[2,0],[0]] => 6
[[3,1,1,0],[2,1,0],[2,0],[1]] => 7
[[3,1,1,0],[2,1,0],[2,0],[2]] => 7
[[3,1,1,0],[2,1,0],[2,1],[1]] => 8
[[3,1,1,0],[2,1,0],[2,1],[2]] => 8
[[3,1,1,0],[2,1,1],[1,1],[1]] => 9
[[3,1,1,0],[2,1,1],[2,1],[1]] => 9
[[3,1,1,0],[2,1,1],[2,1],[2]] => 9
[[3,1,1,0],[3,1,0],[1,0],[0]] => 6
[[3,1,1,0],[3,1,0],[1,0],[1]] => 7
[[3,1,1,0],[3,1,0],[1,1],[1]] => 8
[[3,1,1,0],[3,1,0],[2,0],[0]] => 6
[[3,1,1,0],[3,1,0],[2,0],[1]] => 7
[[3,1,1,0],[3,1,0],[2,0],[2]] => 7
[[3,1,1,0],[3,1,0],[2,1],[1]] => 8
[[3,1,1,0],[3,1,0],[2,1],[2]] => 8
[[3,1,1,0],[3,1,0],[3,0],[0]] => 6
[[3,1,1,0],[3,1,0],[3,0],[1]] => 7
[[3,1,1,0],[3,1,0],[3,0],[2]] => 7
[[3,1,1,0],[3,1,0],[3,0],[3]] => 7
[[3,1,1,0],[3,1,0],[3,1],[1]] => 8
[[3,1,1,0],[3,1,0],[3,1],[2]] => 8
[[3,1,1,0],[3,1,0],[3,1],[3]] => 8
[[3,1,1,0],[3,1,1],[1,1],[1]] => 9
[[3,1,1,0],[3,1,1],[2,1],[1]] => 9
[[3,1,1,0],[3,1,1],[2,1],[2]] => 9
[[3,1,1,0],[3,1,1],[3,1],[1]] => 9
[[3,1,1,0],[3,1,1],[3,1],[2]] => 9
[[3,1,1,0],[3,1,1],[3,1],[3]] => 9
[[2,2,1,0],[2,1,0],[1,0],[0]] => 6
[[2,2,1,0],[2,1,0],[1,0],[1]] => 7
[[2,2,1,0],[2,1,0],[1,1],[1]] => 8
[[2,2,1,0],[2,1,0],[2,0],[0]] => 6
[[2,2,1,0],[2,1,0],[2,0],[1]] => 7
[[2,2,1,0],[2,1,0],[2,0],[2]] => 7
[[2,2,1,0],[2,1,0],[2,1],[1]] => 8
[[2,2,1,0],[2,1,0],[2,1],[2]] => 8
[[2,2,1,0],[2,1,1],[1,1],[1]] => 9
[[2,2,1,0],[2,1,1],[2,1],[1]] => 9
[[2,2,1,0],[2,1,1],[2,1],[2]] => 9
[[2,2,1,0],[2,2,0],[2,0],[0]] => 6
[[2,2,1,0],[2,2,0],[2,0],[1]] => 7
[[2,2,1,0],[2,2,0],[2,0],[2]] => 7
[[2,2,1,0],[2,2,0],[2,1],[1]] => 8
[[2,2,1,0],[2,2,0],[2,1],[2]] => 8
[[2,2,1,0],[2,2,0],[2,2],[2]] => 8
[[2,2,1,0],[2,2,1],[2,1],[1]] => 9
[[2,2,1,0],[2,2,1],[2,1],[2]] => 9
[[2,2,1,0],[2,2,1],[2,2],[2]] => 9
[[2,1,1,1],[1,1,1],[1,1],[1]] => 10
[[2,1,1,1],[2,1,1],[1,1],[1]] => 10
[[2,1,1,1],[2,1,1],[2,1],[1]] => 10
[[2,1,1,1],[2,1,1],[2,1],[2]] => 10
[[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => 1
[[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => 2
[[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => 3
[[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => 4
[[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => 5
[[3,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => 1
[[3,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => 2
[[3,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => 3
[[3,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => 4
[[3,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => 5
[[3,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => 2
[[3,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => 3
[[3,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => 4
[[3,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => 5
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => 3
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => 4
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => 5
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => 4
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => 5
[[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => 5
[[3,0,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]] => 2
[[3,0,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]] => 3
[[3,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]] => 4
[[3,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[1]] => 5
[[3,0,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]] => 3
[[3,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]] => 4
[[3,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[1]] => 5
[[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]] => 4
[[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[1]] => 5
[[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[2]] => 5
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]] => 3
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]] => 4
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]] => 5
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]] => 4
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]] => 5
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]] => 5
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]] => 4
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]] => 5
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]] => 5
[[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]] => 5
[[2,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => 3
[[2,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => 4
[[2,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => 5
[[2,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => 6
[[2,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => 5
[[2,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => 6
[[2,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => 7
[[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => 7
[[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => 8
[[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => 9
[[2,1,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => 3
[[2,1,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => 4
[[2,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => 5
[[2,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => 6
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => 4
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => 5
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => 6
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => 5
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => 6
[[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => 6
[[2,1,0,0,0],[2,1,0,0],[1,0,0],[0,0],[0]] => 5
[[2,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[0]] => 6
[[2,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[1]] => 7
[[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[0]] => 7
[[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[1]] => 8
[[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,1],[1]] => 9
[[2,1,0,0,0],[2,1,0,0],[2,0,0],[0,0],[0]] => 5
[[2,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[0]] => 6
[[2,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[1]] => 7
[[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[0]] => 6
[[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[1]] => 7
[[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[2]] => 7
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[0]] => 7
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[1]] => 8
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,1],[1]] => 9
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[0]] => 7
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[1]] => 8
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[2]] => 8
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[1]] => 9
[[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[2]] => 9
[[1,1,1,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => 6
[[1,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => 7
[[1,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => 8
[[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => 8
[[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => 9
[[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => 10
[[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[0]] => 9
[[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[1]] => 10
[[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,1],[1]] => 11
[[1,1,1,0,0],[1,1,1,0],[1,1,1],[1,1],[1]] => 12
[[4,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => 1
[[4,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => 2
[[4,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => 3
[[4,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => 4
[[4,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => 5
[[4,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => 2
[[4,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => 3
[[4,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => 4
[[4,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => 5
[[4,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => 3
[[4,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => 4
[[4,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => 5
[[4,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => 4
[[4,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => 5
[[4,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => 5
[[4,0,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]] => 2
[[4,0,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]] => 3
[[4,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]] => 4
[[4,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[1]] => 5
[[4,0,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]] => 3
[[4,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]] => 4
[[4,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[1]] => 5
[[4,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]] => 4
[[4,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[1]] => 5
[[4,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[2]] => 5
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]] => 3
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]] => 4
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]] => 5
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]] => 4
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]] => 5
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]] => 5
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]] => 4
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]] => 5
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]] => 5
[[4,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]] => 5
[[4,0,0,0,0],[4,0,0,0],[0,0,0],[0,0],[0]] => 2
[[4,0,0,0,0],[4,0,0,0],[1,0,0],[0,0],[0]] => 3
[[4,0,0,0,0],[4,0,0,0],[1,0,0],[1,0],[0]] => 4
[[4,0,0,0,0],[4,0,0,0],[1,0,0],[1,0],[1]] => 5
[[4,0,0,0,0],[4,0,0,0],[2,0,0],[0,0],[0]] => 3
[[4,0,0,0,0],[4,0,0,0],[2,0,0],[1,0],[0]] => 4
[[4,0,0,0,0],[4,0,0,0],[2,0,0],[1,0],[1]] => 5
[[4,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[0]] => 4
[[4,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[1]] => 5
[[4,0,0,0,0],[4,0,0,0],[2,0,0],[2,0],[2]] => 5
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[0,0],[0]] => 3
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[1,0],[0]] => 4
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[1,0],[1]] => 5
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[0]] => 4
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[1]] => 5
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[2,0],[2]] => 5
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[0]] => 4
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[1]] => 5
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[2]] => 5
[[4,0,0,0,0],[4,0,0,0],[3,0,0],[3,0],[3]] => 5
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[0,0],[0]] => 3
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[1,0],[0]] => 4
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[1,0],[1]] => 5
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[2,0],[0]] => 4
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[2,0],[1]] => 5
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[2,0],[2]] => 5
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[0]] => 4
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[1]] => 5
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[2]] => 5
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[3,0],[3]] => 5
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[0]] => 4
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[1]] => 5
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[2]] => 5
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[3]] => 5
[[4,0,0,0,0],[4,0,0,0],[4,0,0],[4,0],[4]] => 5
[[3,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => 3
[[3,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => 4
[[3,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => 5
[[3,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => 6
[[3,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => 5
[[3,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => 6
[[3,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => 7
[[3,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => 7
[[3,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => 8
[[3,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => 9
[[3,1,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => 3
[[3,1,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => 4
[[3,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => 5
[[3,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => 6
[[3,1,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => 4
[[3,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => 5
[[3,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => 6
[[3,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => 5
[[3,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => 6
[[3,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => 6
[[3,1,0,0,0],[2,1,0,0],[1,0,0],[0,0],[0]] => 5
[[3,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[0]] => 6
[[3,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[1]] => 7
[[3,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[0]] => 7
[[3,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[1]] => 8
[[3,1,0,0,0],[2,1,0,0],[1,1,0],[1,1],[1]] => 9
[[3,1,0,0,0],[2,1,0,0],[2,0,0],[0,0],[0]] => 5
[[3,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[0]] => 6
[[3,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[1]] => 7
[[3,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[0]] => 6
[[3,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[1]] => 7
[[3,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[2]] => 7
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[0]] => 7
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[1]] => 8
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[1,1],[1]] => 9
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[0]] => 7
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[1]] => 8
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[2]] => 8
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[1]] => 9
[[3,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[2]] => 9
[[3,1,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]] => 3
[[3,1,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]] => 4
[[3,1,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]] => 5
[[3,1,0,0,0],[3,0,0,0],[1,0,0],[1,0],[1]] => 6
[[3,1,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]] => 4
[[3,1,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]] => 5
[[3,1,0,0,0],[3,0,0,0],[2,0,0],[1,0],[1]] => 6
[[3,1,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]] => 5
[[3,1,0,0,0],[3,0,0,0],[2,0,0],[2,0],[1]] => 6
[[3,1,0,0,0],[3,0,0,0],[2,0,0],[2,0],[2]] => 6
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]] => 4
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]] => 5
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]] => 6
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]] => 5
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]] => 6
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]] => 6
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]] => 5
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]] => 6
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]] => 6
[[3,1,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]] => 6
[[3,1,0,0,0],[3,1,0,0],[1,0,0],[0,0],[0]] => 5
[[3,1,0,0,0],[3,1,0,0],[1,0,0],[1,0],[0]] => 6
[[3,1,0,0,0],[3,1,0,0],[1,0,0],[1,0],[1]] => 7
[[3,1,0,0,0],[3,1,0,0],[1,1,0],[1,0],[0]] => 7
[[3,1,0,0,0],[3,1,0,0],[1,1,0],[1,0],[1]] => 8
[[3,1,0,0,0],[3,1,0,0],[1,1,0],[1,1],[1]] => 9
[[3,1,0,0,0],[3,1,0,0],[2,0,0],[0,0],[0]] => 5
[[3,1,0,0,0],[3,1,0,0],[2,0,0],[1,0],[0]] => 6
[[3,1,0,0,0],[3,1,0,0],[2,0,0],[1,0],[1]] => 7
[[3,1,0,0,0],[3,1,0,0],[2,0,0],[2,0],[0]] => 6
[[3,1,0,0,0],[3,1,0,0],[2,0,0],[2,0],[1]] => 7
[[3,1,0,0,0],[3,1,0,0],[2,0,0],[2,0],[2]] => 7
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[1,0],[0]] => 7
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[1,0],[1]] => 8
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[1,1],[1]] => 9
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[0]] => 7
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[1]] => 8
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,0],[2]] => 8
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,1],[1]] => 9
[[3,1,0,0,0],[3,1,0,0],[2,1,0],[2,1],[2]] => 9
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[0,0],[0]] => 5
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[1,0],[0]] => 6
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[1,0],[1]] => 7
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[0]] => 6
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[1]] => 7
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[2,0],[2]] => 7
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[0]] => 6
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[1]] => 7
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[2]] => 7
[[3,1,0,0,0],[3,1,0,0],[3,0,0],[3,0],[3]] => 7
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[1,0],[0]] => 7
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[1,0],[1]] => 8
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[1,1],[1]] => 9
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,0],[0]] => 7
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,0],[1]] => 8
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,0],[2]] => 8
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,1],[1]] => 9
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[2,1],[2]] => 9
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[0]] => 7
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[1]] => 8
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[2]] => 8
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,0],[3]] => 8
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,1],[1]] => 9
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,1],[2]] => 9
[[3,1,0,0,0],[3,1,0,0],[3,1,0],[3,1],[3]] => 9
[[2,2,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => 3
[[2,2,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => 4
[[2,2,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => 5
[[2,2,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => 6
[[2,2,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => 4
[[2,2,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => 5
[[2,2,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => 6
[[2,2,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => 5
[[2,2,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => 6
[[2,2,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => 6
[[2,2,0,0,0],[2,1,0,0],[1,0,0],[0,0],[0]] => 5
[[2,2,0,0,0],[2,1,0,0],[1,0,0],[1,0],[0]] => 6
[[2,2,0,0,0],[2,1,0,0],[1,0,0],[1,0],[1]] => 7
[[2,2,0,0,0],[2,1,0,0],[1,1,0],[1,0],[0]] => 7
[[2,2,0,0,0],[2,1,0,0],[1,1,0],[1,0],[1]] => 8
[[2,2,0,0,0],[2,1,0,0],[1,1,0],[1,1],[1]] => 9
[[2,2,0,0,0],[2,1,0,0],[2,0,0],[0,0],[0]] => 5
[[2,2,0,0,0],[2,1,0,0],[2,0,0],[1,0],[0]] => 6
[[2,2,0,0,0],[2,1,0,0],[2,0,0],[1,0],[1]] => 7
[[2,2,0,0,0],[2,1,0,0],[2,0,0],[2,0],[0]] => 6
[[2,2,0,0,0],[2,1,0,0],[2,0,0],[2,0],[1]] => 7
[[2,2,0,0,0],[2,1,0,0],[2,0,0],[2,0],[2]] => 7
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[1,0],[0]] => 7
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[1,0],[1]] => 8
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[1,1],[1]] => 9
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,0],[0]] => 7
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,0],[1]] => 8
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,0],[2]] => 8
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,1],[1]] => 9
[[2,2,0,0,0],[2,1,0,0],[2,1,0],[2,1],[2]] => 9
[[2,2,0,0,0],[2,2,0,0],[2,0,0],[0,0],[0]] => 5
[[2,2,0,0,0],[2,2,0,0],[2,0,0],[1,0],[0]] => 6
[[2,2,0,0,0],[2,2,0,0],[2,0,0],[1,0],[1]] => 7
[[2,2,0,0,0],[2,2,0,0],[2,0,0],[2,0],[0]] => 6
[[2,2,0,0,0],[2,2,0,0],[2,0,0],[2,0],[1]] => 7
[[2,2,0,0,0],[2,2,0,0],[2,0,0],[2,0],[2]] => 7
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[1,0],[0]] => 7
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[1,0],[1]] => 8
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[1,1],[1]] => 9
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[0]] => 7
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[1]] => 8
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,0],[2]] => 8
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,1],[1]] => 9
[[2,2,0,0,0],[2,2,0,0],[2,1,0],[2,1],[2]] => 9
[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,0],[0]] => 7
[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,0],[1]] => 8
[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,0],[2]] => 8
[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,1],[1]] => 9
[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,1],[2]] => 9
[[2,2,0,0,0],[2,2,0,0],[2,2,0],[2,2],[2]] => 9
[[2,1,1,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => 6
[[2,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => 7
[[2,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => 8
[[2,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => 8
[[2,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => 9
[[2,1,1,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => 10
[[2,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[0]] => 9
[[2,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[1]] => 10
[[2,1,1,0,0],[1,1,1,0],[1,1,0],[1,1],[1]] => 11
[[2,1,1,0,0],[1,1,1,0],[1,1,1],[1,1],[1]] => 12
[[2,1,1,0,0],[2,1,0,0],[1,0,0],[0,0],[0]] => 6
[[2,1,1,0,0],[2,1,0,0],[1,0,0],[1,0],[0]] => 7
[[2,1,1,0,0],[2,1,0,0],[1,0,0],[1,0],[1]] => 8
[[2,1,1,0,0],[2,1,0,0],[1,1,0],[1,0],[0]] => 8
[[2,1,1,0,0],[2,1,0,0],[1,1,0],[1,0],[1]] => 9
[[2,1,1,0,0],[2,1,0,0],[1,1,0],[1,1],[1]] => 10
[[2,1,1,0,0],[2,1,0,0],[2,0,0],[0,0],[0]] => 6
[[2,1,1,0,0],[2,1,0,0],[2,0,0],[1,0],[0]] => 7
[[2,1,1,0,0],[2,1,0,0],[2,0,0],[1,0],[1]] => 8
[[2,1,1,0,0],[2,1,0,0],[2,0,0],[2,0],[0]] => 7
[[2,1,1,0,0],[2,1,0,0],[2,0,0],[2,0],[1]] => 8
[[2,1,1,0,0],[2,1,0,0],[2,0,0],[2,0],[2]] => 8
[[2,1,1,0,0],[2,1,0,0],[2,1,0],[1,0],[0]] => 8
[[2,1,1,0,0],[2,1,0,0],[2,1,0],[1,0],[1]] => 9
[[2,1,1,0,0],[2,1,0,0],[2,1,0],[1,1],[1]] => 10
[[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,0],[0]] => 8
[[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,0],[1]] => 9
[[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,0],[2]] => 9
[[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,1],[1]] => 10
[[2,1,1,0,0],[2,1,0,0],[2,1,0],[2,1],[2]] => 10
[[2,1,1,0,0],[2,1,1,0],[1,1,0],[1,0],[0]] => 9
[[2,1,1,0,0],[2,1,1,0],[1,1,0],[1,0],[1]] => 10
[[2,1,1,0,0],[2,1,1,0],[1,1,0],[1,1],[1]] => 11
[[2,1,1,0,0],[2,1,1,0],[1,1,1],[1,1],[1]] => 12
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[1,0],[0]] => 9
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[1,0],[1]] => 10
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[1,1],[1]] => 11
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[0]] => 9
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[1]] => 10
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,0],[2]] => 10
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,1],[1]] => 11
[[2,1,1,0,0],[2,1,1,0],[2,1,0],[2,1],[2]] => 11
[[2,1,1,0,0],[2,1,1,0],[2,1,1],[1,1],[1]] => 12
[[2,1,1,0,0],[2,1,1,0],[2,1,1],[2,1],[1]] => 12
[[2,1,1,0,0],[2,1,1,0],[2,1,1],[2,1],[2]] => 12
[[1,1,1,1,0],[1,1,1,0],[1,1,0],[1,0],[0]] => 10
[[1,1,1,1,0],[1,1,1,0],[1,1,0],[1,0],[1]] => 11
[[1,1,1,1,0],[1,1,1,0],[1,1,0],[1,1],[1]] => 12
[[1,1,1,1,0],[1,1,1,0],[1,1,1],[1,1],[1]] => 13
[[1,1,1,1,0],[1,1,1,1],[1,1,1],[1,1],[1]] => 14
[[2,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => 1
[[2,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => 2
[[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => 3
[[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => 4
[[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => 5
[[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => 6
[[2,0,0,0,0,0],[2,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => 2
[[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => 3
[[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => 4
[[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => 5
[[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => 6
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => 3
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => 4
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => 5
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => 6
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => 4
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => 5
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => 6
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => 5
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => 6
[[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => 6
[[1,1,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => 3
[[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => 4
[[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => 5
[[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => 6
[[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => 7
[[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => 5
[[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => 6
[[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => 7
[[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => 8
[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => 7
[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => 8
[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => 9
[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => 9
[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => 10
[[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => 11
[[3,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => 1
[[3,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => 2
[[3,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => 3
[[3,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => 4
[[3,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => 5
[[3,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => 6
[[3,0,0,0,0,0],[2,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => 2
[[3,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => 3
[[3,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => 4
[[3,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => 5
[[3,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => 6
[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => 3
[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => 4
[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => 5
[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => 6
[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => 4
[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => 5
[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => 6
[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => 5
[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => 6
[[3,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => 6
[[3,0,0,0,0,0],[3,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => 2
[[3,0,0,0,0,0],[3,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => 3
[[3,0,0,0,0,0],[3,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => 4
[[3,0,0,0,0,0],[3,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => 5
[[3,0,0,0,0,0],[3,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => 6
[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => 3
[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => 4
[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => 5
[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => 6
[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => 4
[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => 5
[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => 6
[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => 5
[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => 6
[[3,0,0,0,0,0],[3,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => 6
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[0,0,0],[0,0],[0]] => 3
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[1,0,0],[0,0],[0]] => 4
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[0]] => 5
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[1,0,0],[1,0],[1]] => 6
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[2,0,0],[0,0],[0]] => 4
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[0]] => 5
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[2,0,0],[1,0],[1]] => 6
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[0]] => 5
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[1]] => 6
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[2,0,0],[2,0],[2]] => 6
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[0,0],[0]] => 4
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[0]] => 5
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[1,0],[1]] => 6
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[0]] => 5
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[1]] => 6
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[2,0],[2]] => 6
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[0]] => 5
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[1]] => 6
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[2]] => 6
[[3,0,0,0,0,0],[3,0,0,0,0],[3,0,0,0],[3,0,0],[3,0],[3]] => 6
[[2,1,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => 3
[[2,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => 4
[[2,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => 5
[[2,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => 6
[[2,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => 7
[[2,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => 5
[[2,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => 6
[[2,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => 7
[[2,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => 8
[[2,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => 7
[[2,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => 8
[[2,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => 9
[[2,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => 9
[[2,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => 10
[[2,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => 11
[[2,1,0,0,0,0],[2,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => 3
[[2,1,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => 4
[[2,1,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => 5
[[2,1,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => 6
[[2,1,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => 7
[[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => 4
[[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => 5
[[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => 6
[[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => 7
[[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => 5
[[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => 6
[[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => 7
[[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => 6
[[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => 7
[[2,1,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => 7
[[2,1,0,0,0,0],[2,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => 5
[[2,1,0,0,0,0],[2,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => 6
[[2,1,0,0,0,0],[2,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => 7
[[2,1,0,0,0,0],[2,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => 8
[[2,1,0,0,0,0],[2,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => 7
[[2,1,0,0,0,0],[2,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => 8
[[2,1,0,0,0,0],[2,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => 9
[[2,1,0,0,0,0],[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => 9
[[2,1,0,0,0,0],[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => 10
[[2,1,0,0,0,0],[2,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => 11
[[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => 5
[[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => 6
[[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => 7
[[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => 8
[[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => 6
[[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => 7
[[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => 8
[[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => 7
[[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => 8
[[2,1,0,0,0,0],[2,1,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => 8
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[1,0,0],[0,0],[0]] => 7
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[0]] => 8
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[1,0,0],[1,0],[1]] => 9
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[0]] => 9
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,0],[1]] => 10
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[1,1,0],[1,1],[1]] => 11
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,0,0],[0,0],[0]] => 7
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[0]] => 8
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,0,0],[1,0],[1]] => 9
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[0]] => 8
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[1]] => 9
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,0,0],[2,0],[2]] => 9
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[0]] => 9
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,0],[1]] => 10
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,1,0],[1,1],[1]] => 11
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[0]] => 9
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[1]] => 10
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,0],[2]] => 10
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[1]] => 11
[[2,1,0,0,0,0],[2,1,0,0,0],[2,1,0,0],[2,1,0],[2,1],[2]] => 11
[[1,1,1,0,0,0],[1,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => 6
[[1,1,1,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => 7
[[1,1,1,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => 8
[[1,1,1,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => 9
[[1,1,1,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => 8
[[1,1,1,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => 9
[[1,1,1,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => 10
[[1,1,1,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => 10
[[1,1,1,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => 11
[[1,1,1,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => 12
[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => 9
[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => 10
[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => 11
[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => 11
[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => 12
[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => 13
[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[0]] => 12
[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,0],[1]] => 13
[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,1,0],[1,1,0],[1,1],[1]] => 14
[[1,1,1,0,0,0],[1,1,1,0,0],[1,1,1,0],[1,1,1],[1,1],[1]] => 15
[[1,0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => 1
[[1,0,0,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => 2
[[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => 3
[[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => 4
[[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => 5
[[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => 6
[[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => 7
[[2,0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => 1
[[2,0,0,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => 2
[[2,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => 3
[[2,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => 4
[[2,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => 5
[[2,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => 6
[[2,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => 7
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => 2
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => 3
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => 4
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => 5
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => 6
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => 7
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => 3
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => 4
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => 5
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => 6
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => 7
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[0,0,0],[0,0],[0]] => 4
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[0,0],[0]] => 5
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[0]] => 6
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[1,0,0],[1,0],[1]] => 7
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[0,0],[0]] => 5
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[0]] => 6
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[1,0],[1]] => 7
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[0]] => 6
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[1]] => 7
[[2,0,0,0,0,0,0],[2,0,0,0,0,0],[2,0,0,0,0],[2,0,0,0],[2,0,0],[2,0],[2]] => 7
[[1,1,0,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => 3
[[1,1,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => 4
[[1,1,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => 5
[[1,1,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => 6
[[1,1,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => 7
[[1,1,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => 8
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => 5
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => 6
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => 7
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => 8
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => 9
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => 7
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => 8
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => 9
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => 10
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[0,0],[0]] => 9
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[0]] => 10
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,0,0],[1,0],[1]] => 11
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[0]] => 11
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,0],[1]] => 12
[[1,1,0,0,0,0,0],[1,1,0,0,0,0],[1,1,0,0,0],[1,1,0,0],[1,1,0],[1,1],[1]] => 13
[[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => 1
[[1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => 2
[[1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0],[1,0,0,0,0,0],[0,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => 3
[[1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[0,0,0,0],[0,0,0],[0,0],[0]] => 4
[[1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[0,0,0],[0,0],[0]] => 5
[[1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[0,0],[0]] => 6
[[1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[0]] => 7
[[1,0,0,0,0,0,0,0],[1,0,0,0,0,0,0],[1,0,0,0,0,0],[1,0,0,0,0],[1,0,0,0],[1,0,0],[1,0],[1]] => 8
-----------------------------------------------------------------------------
Created: Jun 01, 2019 at 00:10 by Martin Rubey
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Last Updated: Jun 01, 2019 at 00:10 by Martin Rubey