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-----------------------------------------------------------------------------
Statistic identifier: St001805
-----------------------------------------------------------------------------
Collection: Semistandard tableaux
-----------------------------------------------------------------------------
Description: The maximal overlap of a cylindrical tableau associated with a semistandard tableau.
A cylindrical tableau associated with a semistandard Young tableau $T$ is the skew semistandard tableau obtained by gluing two copies of $T$ such that the inner shape is a rectangle.
The overlap, recorded in this statistic, equals $\max_C\big(2\ell(T) - \ell(C)\big)$, where $\ell$ denotes the number of rows of a tableau and the maximum is taken over all cylindrical tableaux.
-----------------------------------------------------------------------------
References:
-----------------------------------------------------------------------------
Code:
def statistic(T):
if not T:
return 0
w = len(T[0])
l = len(T)
d = 0
while d < l and len(T[d]) == w and T[0][w-1] <= T[l-1-d][0]:
d += 1
return d
-----------------------------------------------------------------------------
Statistic values:
[[1,2]] => 0
[[2,2]] => 1
[[1],[2]] => 2
[[1,3]] => 0
[[2,3]] => 0
[[3,3]] => 1
[[1],[3]] => 2
[[2],[3]] => 2
[[1,4]] => 0
[[2,4]] => 0
[[3,4]] => 0
[[4,4]] => 1
[[1],[4]] => 2
[[2],[4]] => 2
[[3],[4]] => 2
[[1,5]] => 0
[[2,5]] => 0
[[3,5]] => 0
[[4,5]] => 0
[[5,5]] => 1
[[1],[5]] => 2
[[2],[5]] => 2
[[3],[5]] => 2
[[4],[5]] => 2
[[1,6]] => 0
[[2,6]] => 0
[[3,6]] => 0
[[4,6]] => 0
[[5,6]] => 0
[[6,6]] => 1
[[1],[6]] => 2
[[2],[6]] => 2
[[3],[6]] => 2
[[4],[6]] => 2
[[5],[6]] => 2
[[1,7]] => 0
[[2,7]] => 0
[[3,7]] => 0
[[4,7]] => 0
[[5,7]] => 0
[[6,7]] => 0
[[7,7]] => 1
[[1],[7]] => 2
[[2],[7]] => 2
[[3],[7]] => 2
[[4],[7]] => 2
[[5],[7]] => 2
[[6],[7]] => 2
[[1,8]] => 0
[[2,8]] => 0
[[3,8]] => 0
[[4,8]] => 0
[[5,8]] => 0
[[6,8]] => 0
[[7,8]] => 0
[[8,8]] => 1
[[1],[8]] => 2
[[2],[8]] => 2
[[3],[8]] => 2
[[4],[8]] => 2
[[5],[8]] => 2
[[6],[8]] => 2
[[7],[8]] => 2
[[1,1,2]] => 0
[[1,2,2]] => 0
[[2,2,2]] => 1
[[1,1],[2]] => 1
[[1,2],[2]] => 1
[[1,1,3]] => 0
[[1,2,3]] => 0
[[1,3,3]] => 0
[[2,2,3]] => 0
[[2,3,3]] => 0
[[3,3,3]] => 1
[[1,1],[3]] => 1
[[1,2],[3]] => 1
[[1,3],[2]] => 0
[[1,3],[3]] => 1
[[2,2],[3]] => 1
[[2,3],[3]] => 1
[[1],[2],[3]] => 3
[[1,1,4]] => 0
[[1,2,4]] => 0
[[1,3,4]] => 0
[[1,4,4]] => 0
[[2,2,4]] => 0
[[2,3,4]] => 0
[[2,4,4]] => 0
[[3,3,4]] => 0
[[3,4,4]] => 0
[[4,4,4]] => 1
[[1,1],[4]] => 1
[[1,2],[4]] => 1
[[1,4],[2]] => 0
[[1,3],[4]] => 1
[[1,4],[3]] => 0
[[1,4],[4]] => 1
[[2,2],[4]] => 1
[[2,3],[4]] => 1
[[2,4],[3]] => 0
[[2,4],[4]] => 1
[[3,3],[4]] => 1
[[3,4],[4]] => 1
[[1],[2],[4]] => 3
[[1],[3],[4]] => 3
[[2],[3],[4]] => 3
[[1,1,5]] => 0
[[1,2,5]] => 0
[[1,3,5]] => 0
[[1,4,5]] => 0
[[1,5,5]] => 0
[[2,2,5]] => 0
[[2,3,5]] => 0
[[2,4,5]] => 0
[[2,5,5]] => 0
[[3,3,5]] => 0
[[3,4,5]] => 0
[[3,5,5]] => 0
[[4,4,5]] => 0
[[4,5,5]] => 0
[[5,5,5]] => 1
[[1,1],[5]] => 1
[[1,2],[5]] => 1
[[1,5],[2]] => 0
[[1,3],[5]] => 1
[[1,5],[3]] => 0
[[1,4],[5]] => 1
[[1,5],[4]] => 0
[[1,5],[5]] => 1
[[2,2],[5]] => 1
[[2,3],[5]] => 1
[[2,5],[3]] => 0
[[2,4],[5]] => 1
[[2,5],[4]] => 0
[[2,5],[5]] => 1
[[3,3],[5]] => 1
[[3,4],[5]] => 1
[[3,5],[4]] => 0
[[3,5],[5]] => 1
[[4,4],[5]] => 1
[[4,5],[5]] => 1
[[1],[2],[5]] => 3
[[1],[3],[5]] => 3
[[1],[4],[5]] => 3
[[2],[3],[5]] => 3
[[2],[4],[5]] => 3
[[3],[4],[5]] => 3
[[1,1,6]] => 0
[[1,2,6]] => 0
[[1,3,6]] => 0
[[1,4,6]] => 0
[[1,5,6]] => 0
[[1,6,6]] => 0
[[2,2,6]] => 0
[[2,3,6]] => 0
[[2,4,6]] => 0
[[2,5,6]] => 0
[[2,6,6]] => 0
[[3,3,6]] => 0
[[3,4,6]] => 0
[[3,5,6]] => 0
[[3,6,6]] => 0
[[4,4,6]] => 0
[[4,5,6]] => 0
[[4,6,6]] => 0
[[5,5,6]] => 0
[[5,6,6]] => 0
[[6,6,6]] => 1
[[1,1],[6]] => 1
[[1,2],[6]] => 1
[[1,6],[2]] => 0
[[1,3],[6]] => 1
[[1,6],[3]] => 0
[[1,4],[6]] => 1
[[1,6],[4]] => 0
[[1,5],[6]] => 1
[[1,6],[5]] => 0
[[1,6],[6]] => 1
[[2,2],[6]] => 1
[[2,3],[6]] => 1
[[2,6],[3]] => 0
[[2,4],[6]] => 1
[[2,6],[4]] => 0
[[2,5],[6]] => 1
[[2,6],[5]] => 0
[[2,6],[6]] => 1
[[3,3],[6]] => 1
[[3,4],[6]] => 1
[[3,6],[4]] => 0
[[3,5],[6]] => 1
[[3,6],[5]] => 0
[[3,6],[6]] => 1
[[4,4],[6]] => 1
[[4,5],[6]] => 1
[[4,6],[5]] => 0
[[4,6],[6]] => 1
[[5,5],[6]] => 1
[[5,6],[6]] => 1
[[1],[2],[6]] => 3
[[1],[3],[6]] => 3
[[1],[4],[6]] => 3
[[1],[5],[6]] => 3
[[2],[3],[6]] => 3
[[2],[4],[6]] => 3
[[2],[5],[6]] => 3
[[3],[4],[6]] => 3
[[3],[5],[6]] => 3
[[4],[5],[6]] => 3
[[1,1,7]] => 0
[[1,2,7]] => 0
[[1,3,7]] => 0
[[1,4,7]] => 0
[[1,5,7]] => 0
[[1,6,7]] => 0
[[1,7,7]] => 0
[[2,2,7]] => 0
[[2,3,7]] => 0
[[2,4,7]] => 0
[[2,5,7]] => 0
[[2,6,7]] => 0
[[2,7,7]] => 0
[[3,3,7]] => 0
[[3,4,7]] => 0
[[3,5,7]] => 0
[[3,6,7]] => 0
[[3,7,7]] => 0
[[4,4,7]] => 0
[[4,5,7]] => 0
[[4,6,7]] => 0
[[4,7,7]] => 0
[[5,5,7]] => 0
[[5,6,7]] => 0
[[5,7,7]] => 0
[[6,6,7]] => 0
[[6,7,7]] => 0
[[7,7,7]] => 1
[[1,1],[7]] => 1
[[1,2],[7]] => 1
[[1,7],[2]] => 0
[[1,3],[7]] => 1
[[1,7],[3]] => 0
[[1,4],[7]] => 1
[[1,7],[4]] => 0
[[1,5],[7]] => 1
[[1,7],[5]] => 0
[[1,6],[7]] => 1
[[1,7],[6]] => 0
[[1,7],[7]] => 1
[[2,2],[7]] => 1
[[2,3],[7]] => 1
[[2,7],[3]] => 0
[[2,4],[7]] => 1
[[2,7],[4]] => 0
[[2,5],[7]] => 1
[[2,7],[5]] => 0
[[2,6],[7]] => 1
[[2,7],[6]] => 0
[[2,7],[7]] => 1
[[3,3],[7]] => 1
[[3,4],[7]] => 1
[[3,7],[4]] => 0
[[3,5],[7]] => 1
[[3,7],[5]] => 0
[[3,6],[7]] => 1
[[3,7],[6]] => 0
[[3,7],[7]] => 1
[[4,4],[7]] => 1
[[4,5],[7]] => 1
[[4,7],[5]] => 0
[[4,6],[7]] => 1
[[4,7],[6]] => 0
[[4,7],[7]] => 1
[[5,5],[7]] => 1
[[5,6],[7]] => 1
[[5,7],[6]] => 0
[[5,7],[7]] => 1
[[6,6],[7]] => 1
[[6,7],[7]] => 1
[[1],[2],[7]] => 3
[[1],[3],[7]] => 3
[[1],[4],[7]] => 3
[[1],[5],[7]] => 3
[[1],[6],[7]] => 3
[[2],[3],[7]] => 3
[[2],[4],[7]] => 3
[[2],[5],[7]] => 3
[[2],[6],[7]] => 3
[[3],[4],[7]] => 3
[[3],[5],[7]] => 3
[[3],[6],[7]] => 3
[[4],[5],[7]] => 3
[[4],[6],[7]] => 3
[[5],[6],[7]] => 3
[[1,1,1,2]] => 0
[[1,1,2,2]] => 0
[[1,2,2,2]] => 0
[[2,2,2,2]] => 1
[[1,1,1],[2]] => 1
[[1,1,2],[2]] => 1
[[1,2,2],[2]] => 1
[[1,1],[2,2]] => 2
[[1,1,1,3]] => 0
[[1,1,2,3]] => 0
[[1,1,3,3]] => 0
[[1,2,2,3]] => 0
[[1,2,3,3]] => 0
[[1,3,3,3]] => 0
[[2,2,2,3]] => 0
[[2,2,3,3]] => 0
[[2,3,3,3]] => 0
[[3,3,3,3]] => 1
[[1,1,1],[3]] => 1
[[1,1,2],[3]] => 1
[[1,1,3],[2]] => 0
[[1,1,3],[3]] => 1
[[1,2,2],[3]] => 1
[[1,2,3],[2]] => 0
[[1,2,3],[3]] => 1
[[1,3,3],[2]] => 0
[[1,3,3],[3]] => 1
[[2,2,2],[3]] => 1
[[2,2,3],[3]] => 1
[[2,3,3],[3]] => 1
[[1,1],[2,3]] => 2
[[1,1],[3,3]] => 2
[[1,2],[2,3]] => 1
[[1,2],[3,3]] => 1
[[2,2],[3,3]] => 2
[[1,1],[2],[3]] => 1
[[1,2],[2],[3]] => 1
[[1,3],[2],[3]] => 1
[[1,1,1,4]] => 0
[[1,1,2,4]] => 0
[[1,1,3,4]] => 0
[[1,1,4,4]] => 0
[[1,2,2,4]] => 0
[[1,2,3,4]] => 0
[[1,2,4,4]] => 0
[[1,3,3,4]] => 0
[[1,3,4,4]] => 0
[[1,4,4,4]] => 0
[[2,2,2,4]] => 0
[[2,2,3,4]] => 0
[[2,2,4,4]] => 0
[[2,3,3,4]] => 0
[[2,3,4,4]] => 0
[[2,4,4,4]] => 0
[[3,3,3,4]] => 0
[[3,3,4,4]] => 0
[[3,4,4,4]] => 0
[[4,4,4,4]] => 1
[[1,1,1],[4]] => 1
[[1,1,2],[4]] => 1
[[1,1,4],[2]] => 0
[[1,1,3],[4]] => 1
[[1,1,4],[3]] => 0
[[1,1,4],[4]] => 1
[[1,2,2],[4]] => 1
[[1,2,4],[2]] => 0
[[1,2,3],[4]] => 1
[[1,2,4],[3]] => 0
[[1,3,4],[2]] => 0
[[1,2,4],[4]] => 1
[[1,4,4],[2]] => 0
[[1,3,3],[4]] => 1
[[1,3,4],[3]] => 0
[[1,3,4],[4]] => 1
[[1,4,4],[3]] => 0
[[1,4,4],[4]] => 1
[[2,2,2],[4]] => 1
[[2,2,3],[4]] => 1
[[2,2,4],[3]] => 0
[[2,2,4],[4]] => 1
[[2,3,3],[4]] => 1
[[2,3,4],[3]] => 0
[[2,3,4],[4]] => 1
[[2,4,4],[3]] => 0
[[2,4,4],[4]] => 1
[[3,3,3],[4]] => 1
[[3,3,4],[4]] => 1
[[3,4,4],[4]] => 1
[[1,1],[2,4]] => 2
[[1,1],[3,4]] => 2
[[1,1],[4,4]] => 2
[[1,2],[2,4]] => 1
[[1,2],[3,4]] => 1
[[1,3],[2,4]] => 0
[[1,2],[4,4]] => 1
[[1,3],[3,4]] => 1
[[1,3],[4,4]] => 1
[[2,2],[3,4]] => 2
[[2,2],[4,4]] => 2
[[2,3],[3,4]] => 1
[[2,3],[4,4]] => 1
[[3,3],[4,4]] => 2
[[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]] => 0
[[1,4],[2],[4]] => 1
[[1,3],[3],[4]] => 1
[[1,4],[3],[4]] => 1
[[2,2],[3],[4]] => 1
[[2,3],[3],[4]] => 1
[[2,4],[3],[4]] => 1
[[1],[2],[3],[4]] => 4
[[1,1,1,5]] => 0
[[1,1,2,5]] => 0
[[1,1,3,5]] => 0
[[1,1,4,5]] => 0
[[1,1,5,5]] => 0
[[1,2,2,5]] => 0
[[1,2,3,5]] => 0
[[1,2,4,5]] => 0
[[1,2,5,5]] => 0
[[1,3,3,5]] => 0
[[1,3,4,5]] => 0
[[1,3,5,5]] => 0
[[1,4,4,5]] => 0
[[1,4,5,5]] => 0
[[1,5,5,5]] => 0
[[2,2,2,5]] => 0
[[2,2,3,5]] => 0
[[2,2,4,5]] => 0
[[2,2,5,5]] => 0
[[2,3,3,5]] => 0
[[2,3,4,5]] => 0
[[2,3,5,5]] => 0
[[2,4,4,5]] => 0
[[2,4,5,5]] => 0
[[2,5,5,5]] => 0
[[3,3,3,5]] => 0
[[3,3,4,5]] => 0
[[3,3,5,5]] => 0
[[3,4,4,5]] => 0
[[3,4,5,5]] => 0
[[3,5,5,5]] => 0
[[4,4,4,5]] => 0
[[4,4,5,5]] => 0
[[4,5,5,5]] => 0
[[5,5,5,5]] => 1
[[1,1,1],[5]] => 1
[[1,1,2],[5]] => 1
[[1,1,5],[2]] => 0
[[1,1,3],[5]] => 1
[[1,1,5],[3]] => 0
[[1,1,4],[5]] => 1
[[1,1,5],[4]] => 0
[[1,1,5],[5]] => 1
[[1,2,2],[5]] => 1
[[1,2,5],[2]] => 0
[[1,2,3],[5]] => 1
[[1,2,5],[3]] => 0
[[1,3,5],[2]] => 0
[[1,2,4],[5]] => 1
[[1,2,5],[4]] => 0
[[1,4,5],[2]] => 0
[[1,2,5],[5]] => 1
[[1,5,5],[2]] => 0
[[1,3,3],[5]] => 1
[[1,3,5],[3]] => 0
[[1,3,4],[5]] => 1
[[1,3,5],[4]] => 0
[[1,4,5],[3]] => 0
[[1,3,5],[5]] => 1
[[1,5,5],[3]] => 0
[[1,4,4],[5]] => 1
[[1,4,5],[4]] => 0
[[1,4,5],[5]] => 1
[[1,5,5],[4]] => 0
[[1,5,5],[5]] => 1
[[2,2,2],[5]] => 1
[[2,2,3],[5]] => 1
[[2,2,5],[3]] => 0
[[2,2,4],[5]] => 1
[[2,2,5],[4]] => 0
[[2,2,5],[5]] => 1
[[2,3,3],[5]] => 1
[[2,3,5],[3]] => 0
[[2,3,4],[5]] => 1
[[2,3,5],[4]] => 0
[[2,4,5],[3]] => 0
[[2,3,5],[5]] => 1
[[2,5,5],[3]] => 0
[[2,4,4],[5]] => 1
[[2,4,5],[4]] => 0
[[2,4,5],[5]] => 1
[[2,5,5],[4]] => 0
[[2,5,5],[5]] => 1
[[3,3,3],[5]] => 1
[[3,3,4],[5]] => 1
[[3,3,5],[4]] => 0
[[3,3,5],[5]] => 1
[[3,4,4],[5]] => 1
[[3,4,5],[4]] => 0
[[3,4,5],[5]] => 1
[[3,5,5],[4]] => 0
[[3,5,5],[5]] => 1
[[4,4,4],[5]] => 1
[[4,4,5],[5]] => 1
[[4,5,5],[5]] => 1
[[1,1],[2,5]] => 2
[[1,1],[3,5]] => 2
[[1,1],[4,5]] => 2
[[1,1],[5,5]] => 2
[[1,2],[2,5]] => 1
[[1,2],[3,5]] => 1
[[1,3],[2,5]] => 0
[[1,2],[4,5]] => 1
[[1,4],[2,5]] => 0
[[1,2],[5,5]] => 1
[[1,3],[3,5]] => 1
[[1,3],[4,5]] => 1
[[1,4],[3,5]] => 0
[[1,3],[5,5]] => 1
[[1,4],[4,5]] => 1
[[1,4],[5,5]] => 1
[[2,2],[3,5]] => 2
[[2,2],[4,5]] => 2
[[2,2],[5,5]] => 2
[[2,3],[3,5]] => 1
[[2,3],[4,5]] => 1
[[2,4],[3,5]] => 0
[[2,3],[5,5]] => 1
[[2,4],[4,5]] => 1
[[2,4],[5,5]] => 1
[[3,3],[4,5]] => 2
[[3,3],[5,5]] => 2
[[3,4],[4,5]] => 1
[[3,4],[5,5]] => 1
[[4,4],[5,5]] => 2
[[1,1],[2],[5]] => 1
[[1,1],[3],[5]] => 1
[[1,1],[4],[5]] => 1
[[1,2],[2],[5]] => 1
[[1,2],[3],[5]] => 1
[[1,3],[2],[5]] => 1
[[1,5],[2],[3]] => 0
[[1,2],[4],[5]] => 1
[[1,4],[2],[5]] => 1
[[1,5],[2],[4]] => 0
[[1,5],[2],[5]] => 1
[[1,3],[3],[5]] => 1
[[1,3],[4],[5]] => 1
[[1,4],[3],[5]] => 1
[[1,5],[3],[4]] => 0
[[1,5],[3],[5]] => 1
[[1,4],[4],[5]] => 1
[[1,5],[4],[5]] => 1
[[2,2],[3],[5]] => 1
[[2,2],[4],[5]] => 1
[[2,3],[3],[5]] => 1
[[2,3],[4],[5]] => 1
[[2,4],[3],[5]] => 1
[[2,5],[3],[4]] => 0
[[2,5],[3],[5]] => 1
[[2,4],[4],[5]] => 1
[[2,5],[4],[5]] => 1
[[3,3],[4],[5]] => 1
[[3,4],[4],[5]] => 1
[[3,5],[4],[5]] => 1
[[1],[2],[3],[5]] => 4
[[1],[2],[4],[5]] => 4
[[1],[3],[4],[5]] => 4
[[2],[3],[4],[5]] => 4
[[1,1,1,6]] => 0
[[1,1,2,6]] => 0
[[1,1,3,6]] => 0
[[1,1,4,6]] => 0
[[1,1,5,6]] => 0
[[1,1,6,6]] => 0
[[1,2,2,6]] => 0
[[1,2,3,6]] => 0
[[1,2,4,6]] => 0
[[1,2,5,6]] => 0
[[1,2,6,6]] => 0
[[1,3,3,6]] => 0
[[1,3,4,6]] => 0
[[1,3,5,6]] => 0
[[1,3,6,6]] => 0
[[1,4,4,6]] => 0
[[1,4,5,6]] => 0
[[1,4,6,6]] => 0
[[1,5,5,6]] => 0
[[1,5,6,6]] => 0
[[1,6,6,6]] => 0
[[2,2,2,6]] => 0
[[2,2,3,6]] => 0
[[2,2,4,6]] => 0
[[2,2,5,6]] => 0
[[2,2,6,6]] => 0
[[2,3,3,6]] => 0
[[2,3,4,6]] => 0
[[2,3,5,6]] => 0
[[2,3,6,6]] => 0
[[2,4,4,6]] => 0
[[2,4,5,6]] => 0
[[2,4,6,6]] => 0
[[2,5,5,6]] => 0
[[2,5,6,6]] => 0
[[2,6,6,6]] => 0
[[3,3,3,6]] => 0
[[3,3,4,6]] => 0
[[3,3,5,6]] => 0
[[3,3,6,6]] => 0
[[3,4,4,6]] => 0
[[3,4,5,6]] => 0
[[3,4,6,6]] => 0
[[3,5,5,6]] => 0
[[3,5,6,6]] => 0
[[3,6,6,6]] => 0
[[4,4,4,6]] => 0
[[4,4,5,6]] => 0
[[4,4,6,6]] => 0
[[4,5,5,6]] => 0
[[4,5,6,6]] => 0
[[4,6,6,6]] => 0
[[5,5,5,6]] => 0
[[5,5,6,6]] => 0
[[5,6,6,6]] => 0
[[6,6,6,6]] => 1
[[1,1,1],[6]] => 1
[[1,1,2],[6]] => 1
[[1,1,6],[2]] => 0
[[1,1,3],[6]] => 1
[[1,1,6],[3]] => 0
[[1,1,4],[6]] => 1
[[1,1,6],[4]] => 0
[[1,1,5],[6]] => 1
[[1,1,6],[5]] => 0
[[1,1,6],[6]] => 1
[[1,2,2],[6]] => 1
[[1,2,6],[2]] => 0
[[1,2,3],[6]] => 1
[[1,2,6],[3]] => 0
[[1,3,6],[2]] => 0
[[1,2,4],[6]] => 1
[[1,2,6],[4]] => 0
[[1,4,6],[2]] => 0
[[1,2,5],[6]] => 1
[[1,2,6],[5]] => 0
[[1,5,6],[2]] => 0
[[1,2,6],[6]] => 1
[[1,6,6],[2]] => 0
[[1,3,3],[6]] => 1
[[1,3,6],[3]] => 0
[[1,3,4],[6]] => 1
[[1,3,6],[4]] => 0
[[1,4,6],[3]] => 0
[[1,3,5],[6]] => 1
[[1,3,6],[5]] => 0
[[1,5,6],[3]] => 0
[[1,3,6],[6]] => 1
[[1,6,6],[3]] => 0
[[1,4,4],[6]] => 1
[[1,4,6],[4]] => 0
[[1,4,5],[6]] => 1
[[1,4,6],[5]] => 0
[[1,5,6],[4]] => 0
[[1,4,6],[6]] => 1
[[1,6,6],[4]] => 0
[[1,5,5],[6]] => 1
[[1,5,6],[5]] => 0
[[1,5,6],[6]] => 1
[[1,6,6],[5]] => 0
[[1,6,6],[6]] => 1
[[2,2,2],[6]] => 1
[[2,2,3],[6]] => 1
[[2,2,6],[3]] => 0
[[2,2,4],[6]] => 1
[[2,2,6],[4]] => 0
[[2,2,5],[6]] => 1
[[2,2,6],[5]] => 0
[[2,2,6],[6]] => 1
[[2,3,3],[6]] => 1
[[2,3,6],[3]] => 0
[[2,3,4],[6]] => 1
[[2,3,6],[4]] => 0
[[2,4,6],[3]] => 0
[[2,3,5],[6]] => 1
[[2,3,6],[5]] => 0
[[2,5,6],[3]] => 0
[[2,3,6],[6]] => 1
[[2,6,6],[3]] => 0
[[2,4,4],[6]] => 1
[[2,4,6],[4]] => 0
[[2,4,5],[6]] => 1
[[2,4,6],[5]] => 0
[[2,5,6],[4]] => 0
[[2,4,6],[6]] => 1
[[2,6,6],[4]] => 0
[[2,5,5],[6]] => 1
[[2,5,6],[5]] => 0
[[2,5,6],[6]] => 1
[[2,6,6],[5]] => 0
[[2,6,6],[6]] => 1
[[3,3,3],[6]] => 1
[[3,3,4],[6]] => 1
[[3,3,6],[4]] => 0
[[3,3,5],[6]] => 1
[[3,3,6],[5]] => 0
[[3,3,6],[6]] => 1
[[3,4,4],[6]] => 1
[[3,4,6],[4]] => 0
[[3,4,5],[6]] => 1
[[3,4,6],[5]] => 0
[[3,5,6],[4]] => 0
[[3,4,6],[6]] => 1
[[3,6,6],[4]] => 0
[[3,5,5],[6]] => 1
[[3,5,6],[5]] => 0
[[3,5,6],[6]] => 1
[[3,6,6],[5]] => 0
[[3,6,6],[6]] => 1
[[4,4,4],[6]] => 1
[[4,4,5],[6]] => 1
[[4,4,6],[5]] => 0
[[4,4,6],[6]] => 1
[[4,5,5],[6]] => 1
[[4,5,6],[5]] => 0
[[4,5,6],[6]] => 1
[[4,6,6],[5]] => 0
[[4,6,6],[6]] => 1
[[5,5,5],[6]] => 1
[[5,5,6],[6]] => 1
[[5,6,6],[6]] => 1
[[1,1],[2,6]] => 2
[[1,1],[3,6]] => 2
[[1,1],[4,6]] => 2
[[1,1],[5,6]] => 2
[[1,1],[6,6]] => 2
[[1,2],[2,6]] => 1
[[1,2],[3,6]] => 1
[[1,3],[2,6]] => 0
[[1,2],[4,6]] => 1
[[1,4],[2,6]] => 0
[[1,2],[5,6]] => 1
[[1,5],[2,6]] => 0
[[1,2],[6,6]] => 1
[[1,3],[3,6]] => 1
[[1,3],[4,6]] => 1
[[1,4],[3,6]] => 0
[[1,3],[5,6]] => 1
[[1,5],[3,6]] => 0
[[1,3],[6,6]] => 1
[[1,4],[4,6]] => 1
[[1,4],[5,6]] => 1
[[1,5],[4,6]] => 0
[[1,4],[6,6]] => 1
[[1,5],[5,6]] => 1
[[1,5],[6,6]] => 1
[[2,2],[3,6]] => 2
[[2,2],[4,6]] => 2
[[2,2],[5,6]] => 2
[[2,2],[6,6]] => 2
[[2,3],[3,6]] => 1
[[2,3],[4,6]] => 1
[[2,4],[3,6]] => 0
[[2,3],[5,6]] => 1
[[2,5],[3,6]] => 0
[[2,3],[6,6]] => 1
[[2,4],[4,6]] => 1
[[2,4],[5,6]] => 1
[[2,5],[4,6]] => 0
[[2,4],[6,6]] => 1
[[2,5],[5,6]] => 1
[[2,5],[6,6]] => 1
[[3,3],[4,6]] => 2
[[3,3],[5,6]] => 2
[[3,3],[6,6]] => 2
[[3,4],[4,6]] => 1
[[3,4],[5,6]] => 1
[[3,5],[4,6]] => 0
[[3,4],[6,6]] => 1
[[3,5],[5,6]] => 1
[[3,5],[6,6]] => 1
[[4,4],[5,6]] => 2
[[4,4],[6,6]] => 2
[[4,5],[5,6]] => 1
[[4,5],[6,6]] => 1
[[5,5],[6,6]] => 2
[[1,1],[2],[6]] => 1
[[1,1],[3],[6]] => 1
[[1,1],[4],[6]] => 1
[[1,1],[5],[6]] => 1
[[1,2],[2],[6]] => 1
[[1,2],[3],[6]] => 1
[[1,3],[2],[6]] => 1
[[1,6],[2],[3]] => 0
[[1,2],[4],[6]] => 1
[[1,4],[2],[6]] => 1
[[1,6],[2],[4]] => 0
[[1,2],[5],[6]] => 1
[[1,5],[2],[6]] => 1
[[1,6],[2],[5]] => 0
[[1,6],[2],[6]] => 1
[[1,3],[3],[6]] => 1
[[1,3],[4],[6]] => 1
[[1,4],[3],[6]] => 1
[[1,6],[3],[4]] => 0
[[1,3],[5],[6]] => 1
[[1,5],[3],[6]] => 1
[[1,1,1,1,2]] => 0
[[1,1,1,2,2]] => 0
[[1,1,2,2,2]] => 0
[[1,2,2,2,2]] => 0
[[2,2,2,2,2]] => 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
[[1,1,1],[2,2]] => 1
[[1,1,2],[2,2]] => 1
[[1,1,1,1,3]] => 0
[[1,1,1,2,3]] => 0
[[1,1,1,3,3]] => 0
[[1,1,2,2,3]] => 0
[[1,1,2,3,3]] => 0
[[1,1,3,3,3]] => 0
[[1,2,2,2,3]] => 0
[[1,2,2,3,3]] => 0
[[1,2,3,3,3]] => 0
[[1,3,3,3,3]] => 0
[[2,2,2,2,3]] => 0
[[2,2,2,3,3]] => 0
[[2,2,3,3,3]] => 0
[[2,3,3,3,3]] => 0
[[3,3,3,3,3]] => 1
[[1,1,1,1],[3]] => 1
[[1,1,1,2],[3]] => 1
[[1,1,1,3],[2]] => 0
[[1,1,1,3],[3]] => 1
[[1,1,2,2],[3]] => 1
[[1,1,2,3],[2]] => 0
[[1,1,2,3],[3]] => 1
[[1,1,3,3],[2]] => 0
[[1,1,3,3],[3]] => 1
[[1,2,2,2],[3]] => 1
[[1,2,2,3],[2]] => 0
[[1,2,2,3],[3]] => 1
[[1,2,3,3],[2]] => 0
[[1,2,3,3],[3]] => 1
[[1,3,3,3],[2]] => 0
[[1,3,3,3],[3]] => 1
[[2,2,2,2],[3]] => 1
[[2,2,2,3],[3]] => 1
[[2,2,3,3],[3]] => 1
[[2,3,3,3],[3]] => 1
[[1,1,1],[2,3]] => 1
[[1,1,1],[3,3]] => 1
[[1,1,2],[2,3]] => 1
[[1,1,3],[2,2]] => 0
[[1,1,2],[3,3]] => 1
[[1,1,3],[2,3]] => 0
[[1,1,3],[3,3]] => 1
[[1,2,2],[2,3]] => 1
[[1,2,2],[3,3]] => 1
[[1,2,3],[2,3]] => 0
[[1,2,3],[3,3]] => 1
[[2,2,2],[3,3]] => 1
[[2,2,3],[3,3]] => 1
[[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]] => 2
[[1,1],[2,3],[3]] => 2
[[1,2],[2,3],[3]] => 2
[[1,1,1,1,4]] => 0
[[1,1,1,2,4]] => 0
[[1,1,1,3,4]] => 0
[[1,1,1,4,4]] => 0
[[1,1,2,2,4]] => 0
[[1,1,2,3,4]] => 0
[[1,1,2,4,4]] => 0
[[1,1,3,3,4]] => 0
[[1,1,3,4,4]] => 0
[[1,1,4,4,4]] => 0
[[1,2,2,2,4]] => 0
[[1,2,2,3,4]] => 0
[[1,2,2,4,4]] => 0
[[1,2,3,3,4]] => 0
[[1,2,3,4,4]] => 0
[[1,2,4,4,4]] => 0
[[1,3,3,3,4]] => 0
[[1,3,3,4,4]] => 0
[[1,3,4,4,4]] => 0
[[1,4,4,4,4]] => 0
[[2,2,2,2,4]] => 0
[[2,2,2,3,4]] => 0
[[2,2,2,4,4]] => 0
[[2,2,3,3,4]] => 0
[[2,2,3,4,4]] => 0
[[2,2,4,4,4]] => 0
[[2,3,3,3,4]] => 0
[[2,3,3,4,4]] => 0
[[2,3,4,4,4]] => 0
[[2,4,4,4,4]] => 0
[[3,3,3,3,4]] => 0
[[3,3,3,4,4]] => 0
[[3,3,4,4,4]] => 0
[[3,4,4,4,4]] => 0
[[4,4,4,4,4]] => 1
[[1,1,1,1],[4]] => 1
[[1,1,1,2],[4]] => 1
[[1,1,1,4],[2]] => 0
[[1,1,1,3],[4]] => 1
[[1,1,1,4],[3]] => 0
[[1,1,1,4],[4]] => 1
[[1,1,2,2],[4]] => 1
[[1,1,2,4],[2]] => 0
[[1,1,2,3],[4]] => 1
[[1,1,2,4],[3]] => 0
[[1,1,3,4],[2]] => 0
[[1,1,2,4],[4]] => 1
[[1,1,4,4],[2]] => 0
[[1,1,3,3],[4]] => 1
[[1,1,3,4],[3]] => 0
[[1,1,3,4],[4]] => 1
[[1,1,4,4],[3]] => 0
[[1,1,4,4],[4]] => 1
[[1,2,2,2],[4]] => 1
[[1,2,2,4],[2]] => 0
[[1,2,2,3],[4]] => 1
[[1,2,2,4],[3]] => 0
[[1,2,3,4],[2]] => 0
[[1,2,2,4],[4]] => 1
[[1,2,4,4],[2]] => 0
[[1,2,3,3],[4]] => 1
[[1,2,3,4],[3]] => 0
[[1,3,3,4],[2]] => 0
[[1,2,3,4],[4]] => 1
[[1,2,4,4],[3]] => 0
[[1,3,4,4],[2]] => 0
[[1,2,4,4],[4]] => 1
[[1,4,4,4],[2]] => 0
[[1,3,3,3],[4]] => 1
[[1,3,3,4],[3]] => 0
[[1,3,3,4],[4]] => 1
[[1,3,4,4],[3]] => 0
[[1,3,4,4],[4]] => 1
[[1,4,4,4],[3]] => 0
[[1,4,4,4],[4]] => 1
[[2,2,2,2],[4]] => 1
[[2,2,2,3],[4]] => 1
[[2,2,2,4],[3]] => 0
[[2,2,2,4],[4]] => 1
[[2,2,3,3],[4]] => 1
[[2,2,3,4],[3]] => 0
[[2,2,3,4],[4]] => 1
[[2,2,4,4],[3]] => 0
[[2,2,4,4],[4]] => 1
[[2,3,3,3],[4]] => 1
[[2,3,3,4],[3]] => 0
[[2,3,3,4],[4]] => 1
[[2,3,4,4],[3]] => 0
[[2,3,4,4],[4]] => 1
[[2,4,4,4],[3]] => 0
[[2,4,4,4],[4]] => 1
[[3,3,3,3],[4]] => 1
[[3,3,3,4],[4]] => 1
[[3,3,4,4],[4]] => 1
[[3,4,4,4],[4]] => 1
[[1,1,1],[2,4]] => 1
[[1,1,1],[3,4]] => 1
[[1,1,1],[4,4]] => 1
[[1,1,2],[2,4]] => 1
[[1,1,4],[2,2]] => 0
[[1,1,2],[3,4]] => 1
[[1,1,3],[2,4]] => 0
[[1,1,4],[2,3]] => 0
[[1,1,2],[4,4]] => 1
[[1,1,4],[2,4]] => 0
[[1,1,3],[3,4]] => 1
[[1,1,4],[3,3]] => 0
[[1,1,3],[4,4]] => 1
[[1,1,4],[3,4]] => 0
[[1,1,4],[4,4]] => 1
[[1,2,2],[2,4]] => 1
[[1,2,2],[3,4]] => 1
[[1,2,3],[2,4]] => 0
[[1,2,4],[2,3]] => 0
[[1,2,2],[4,4]] => 1
[[1,2,4],[2,4]] => 0
[[1,2,3],[3,4]] => 1
[[1,2,4],[3,3]] => 0
[[1,3,3],[2,4]] => 0
[[1,2,3],[4,4]] => 1
[[1,2,4],[3,4]] => 0
[[1,3,4],[2,4]] => 0
[[1,2,4],[4,4]] => 1
[[1,3,3],[3,4]] => 1
[[1,3,3],[4,4]] => 1
[[1,3,4],[3,4]] => 0
[[1,3,4],[4,4]] => 1
[[2,2,2],[3,4]] => 1
[[2,2,2],[4,4]] => 1
[[2,2,3],[3,4]] => 1
[[2,2,4],[3,3]] => 0
[[2,2,3],[4,4]] => 1
[[2,2,4],[3,4]] => 0
[[2,2,4],[4,4]] => 1
[[2,3,3],[3,4]] => 1
[[2,3,3],[4,4]] => 1
[[2,3,4],[3,4]] => 0
[[2,3,4],[4,4]] => 1
[[3,3,3],[4,4]] => 1
[[3,3,4],[4,4]] => 1
[[1,1,1],[2],[4]] => 1
[[1,1,1],[3],[4]] => 1
[[1,1,2],[2],[4]] => 1
[[1,1,2],[3],[4]] => 1
[[1,1,3],[2],[4]] => 1
[[1,1,4],[2],[3]] => 0
[[1,1,4],[2],[4]] => 1
[[1,1,3],[3],[4]] => 1
[[1,1,4],[3],[4]] => 1
[[1,2,2],[2],[4]] => 1
[[1,2,2],[3],[4]] => 1
[[1,2,3],[2],[4]] => 1
[[1,2,4],[2],[3]] => 0
[[1,2,4],[2],[4]] => 1
[[1,2,3],[3],[4]] => 1
[[1,3,3],[2],[4]] => 1
[[1,3,4],[2],[3]] => 0
[[1,2,4],[3],[4]] => 1
[[1,3,4],[2],[4]] => 1
[[1,4,4],[2],[3]] => 0
[[1,4,4],[2],[4]] => 1
[[1,3,3],[3],[4]] => 1
[[1,3,4],[3],[4]] => 1
[[1,4,4],[3],[4]] => 1
[[2,2,2],[3],[4]] => 1
[[2,2,3],[3],[4]] => 1
[[2,2,4],[3],[4]] => 1
[[2,3,3],[3],[4]] => 1
[[2,3,4],[3],[4]] => 1
[[2,4,4],[3],[4]] => 1
[[1,1],[2,2],[4]] => 2
[[1,1],[2,3],[4]] => 2
[[1,1],[2,4],[3]] => 2
[[1,1],[2,4],[4]] => 2
[[1,1],[3,3],[4]] => 2
[[1,1],[3,4],[4]] => 2
[[1,2],[2,3],[4]] => 2
[[1,2],[2,4],[3]] => 2
[[1,2],[2,4],[4]] => 2
[[1,2],[3,3],[4]] => 2
[[1,3],[2,4],[3]] => 1
[[1,2],[3,4],[4]] => 2
[[1,3],[2,4],[4]] => 1
[[1,3],[3,4],[4]] => 2
[[2,2],[3,3],[4]] => 2
[[2,2],[3,4],[4]] => 2
[[2,3],[3,4],[4]] => 2
[[1,1],[2],[3],[4]] => 1
[[1,2],[2],[3],[4]] => 1
[[1,3],[2],[3],[4]] => 1
[[1,4],[2],[3],[4]] => 1
[[1,1,1,1,1,2]] => 0
[[1,1,1,1,2,2]] => 0
[[1,1,1,2,2,2]] => 0
[[1,1,2,2,2,2]] => 0
[[1,2,2,2,2,2]] => 0
[[2,2,2,2,2,2]] => 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
[[1,1,1,1],[2,2]] => 1
[[1,1,1,2],[2,2]] => 1
[[1,1,2,2],[2,2]] => 1
[[1,1,1],[2,2,2]] => 2
[[1,1,1,1,1,3]] => 0
[[1,1,1,1,2,3]] => 0
[[1,1,1,1,3,3]] => 0
[[1,1,1,2,2,3]] => 0
[[1,1,1,2,3,3]] => 0
[[1,1,1,3,3,3]] => 0
[[1,1,2,2,2,3]] => 0
[[1,1,2,2,3,3]] => 0
[[1,1,2,3,3,3]] => 0
[[1,1,3,3,3,3]] => 0
[[1,2,2,2,2,3]] => 0
[[1,2,2,2,3,3]] => 0
[[1,2,2,3,3,3]] => 0
[[1,2,3,3,3,3]] => 0
[[1,3,3,3,3,3]] => 0
[[2,2,2,2,2,3]] => 0
[[2,2,2,2,3,3]] => 0
[[2,2,2,3,3,3]] => 0
[[2,2,3,3,3,3]] => 0
[[2,3,3,3,3,3]] => 0
[[3,3,3,3,3,3]] => 1
[[1,1,1,1,1],[3]] => 1
[[1,1,1,1,2],[3]] => 1
[[1,1,1,1,3],[2]] => 0
[[1,1,1,1,3],[3]] => 1
[[1,1,1,2,2],[3]] => 1
[[1,1,1,2,3],[2]] => 0
[[1,1,1,2,3],[3]] => 1
[[1,1,1,3,3],[2]] => 0
[[1,1,1,3,3],[3]] => 1
[[1,1,2,2,2],[3]] => 1
[[1,1,2,2,3],[2]] => 0
[[1,1,2,2,3],[3]] => 1
[[1,1,2,3,3],[2]] => 0
[[1,1,2,3,3],[3]] => 1
[[1,1,3,3,3],[2]] => 0
[[1,1,3,3,3],[3]] => 1
[[1,2,2,2,2],[3]] => 1
[[1,2,2,2,3],[2]] => 0
[[1,2,2,2,3],[3]] => 1
[[1,2,2,3,3],[2]] => 0
[[1,2,2,3,3],[3]] => 1
[[1,2,3,3,3],[2]] => 0
[[1,2,3,3,3],[3]] => 1
[[1,3,3,3,3],[2]] => 0
[[1,3,3,3,3],[3]] => 1
[[2,2,2,2,2],[3]] => 1
[[2,2,2,2,3],[3]] => 1
[[2,2,2,3,3],[3]] => 1
[[2,2,3,3,3],[3]] => 1
[[2,3,3,3,3],[3]] => 1
[[1,1,1,1],[2,3]] => 1
[[1,1,1,1],[3,3]] => 1
[[1,1,1,2],[2,3]] => 1
[[1,1,1,3],[2,2]] => 0
[[1,1,1,2],[3,3]] => 1
[[1,1,1,3],[2,3]] => 0
[[1,1,1,3],[3,3]] => 1
[[1,1,2,2],[2,3]] => 1
[[1,1,2,3],[2,2]] => 0
[[1,1,2,2],[3,3]] => 1
[[1,1,2,3],[2,3]] => 0
[[1,1,3,3],[2,2]] => 0
[[1,1,2,3],[3,3]] => 1
[[1,1,3,3],[2,3]] => 0
[[1,1,3,3],[3,3]] => 1
[[1,2,2,2],[2,3]] => 1
[[1,2,2,2],[3,3]] => 1
[[1,2,2,3],[2,3]] => 0
[[1,2,2,3],[3,3]] => 1
[[1,2,3,3],[2,3]] => 0
[[1,2,3,3],[3,3]] => 1
[[2,2,2,2],[3,3]] => 1
[[2,2,2,3],[3,3]] => 1
[[2,2,3,3],[3,3]] => 1
[[1,1,1,1],[2],[3]] => 1
[[1,1,1,2],[2],[3]] => 1
[[1,1,1,3],[2],[3]] => 1
[[1,1,2,2],[2],[3]] => 1
[[1,1,2,3],[2],[3]] => 1
[[1,1,3,3],[2],[3]] => 1
[[1,2,2,2],[2],[3]] => 1
[[1,2,2,3],[2],[3]] => 1
[[1,2,3,3],[2],[3]] => 1
[[1,3,3,3],[2],[3]] => 1
[[1,1,1],[2,2,3]] => 2
[[1,1,1],[2,3,3]] => 2
[[1,1,1],[3,3,3]] => 2
[[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
[[2,2,2],[3,3,3]] => 2
[[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
[[1,1,3],[2,2],[3]] => 1
[[1,1,3],[2,3],[3]] => 1
[[1,2,2],[2,3],[3]] => 1
[[1,2,3],[2,3],[3]] => 1
[[1,1],[2,2],[3,3]] => 3
[[1,1,1,1,1,1,2]] => 0
[[1,1,1,1,1,2,2]] => 0
[[1,1,1,1,2,2,2]] => 0
[[1,1,1,2,2,2,2]] => 0
[[1,1,2,2,2,2,2]] => 0
[[1,2,2,2,2,2,2]] => 0
[[2,2,2,2,2,2,2]] => 1
[[1,1,1,1,1,1],[2]] => 1
[[1,1,1,1,1,2],[2]] => 1
[[1,1,1,1,2,2],[2]] => 1
[[1,1,1,2,2,2],[2]] => 1
[[1,1,2,2,2,2],[2]] => 1
[[1,2,2,2,2,2],[2]] => 1
[[1,1,1,1,1],[2,2]] => 1
[[1,1,1,1,2],[2,2]] => 1
[[1,1,1,2,2],[2,2]] => 1
[[1,1,2,2,2],[2,2]] => 1
[[1,1,1,1],[2,2,2]] => 1
[[1,1,1,2],[2,2,2]] => 1
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Created: Jun 06, 2022 at 20:05 by Martin Rubey
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Last Updated: Jun 06, 2022 at 20:05 by Martin Rubey