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------------------------------------------------------------------------
Map identifier: Mp00207
------------------------------------------------------------------------
Map name: horizontal strip sizes
------------------------------------------------------------------------
Domain: Standard tableaux
------------------------------------------------------------------------
Codomain: Integer compositions
------------------------------------------------------------------------
Description: The composition of horizontal strip sizes.
We associate to a standard Young tableau $T$ the composition $(c_1,\dots,c_k)$, such that $k$ is minimal and the numbers $c_1+\dots+c_i + 1,\dots,c_1+\dots+c_{i+1}$ form a horizontal strip in $T$ for all $i$.
------------------------------------------------------------------------
References: [1] Karaali, G., Senturia, I., Taşkin, Müge A New Partial Order on SYT [[arXiv:2102.00116]]
------------------------------------------------------------------------
Code:
def mapping(T):
n = T.size()
d = {i: T.cells_containing(i)[0][1] for i in range(1, n+1)}
strips = []
strip = []
y = -1
for i in range(1, n+1):
if d[i] <= y:
strips.append(strip)
strip = []
y = 0
else:
y = d[i]
strip.append(i)
strips.append(strip)
return Composition([len(strip) for strip in strips])
------------------------------------------------------------------------
Map images:
[[1]] => [1]
[[1,2]] => [2]
[[1],[2]] => [1,1]
[[1,2,3]] => [3]
[[1,3],[2]] => [1,2]
[[1,2],[3]] => [2,1]
[[1],[2],[3]] => [1,1,1]
[[1,2,3,4]] => [4]
[[1,3,4],[2]] => [1,3]
[[1,2,4],[3]] => [2,2]
[[1,2,3],[4]] => [3,1]
[[1,3],[2,4]] => [1,2,1]
[[1,2],[3,4]] => [2,2]
[[1,4],[2],[3]] => [1,1,2]
[[1,3],[2],[4]] => [1,2,1]
[[1,2],[3],[4]] => [2,1,1]
[[1],[2],[3],[4]] => [1,1,1,1]
[[1,2,3,4,5]] => [5]
[[1,3,4,5],[2]] => [1,4]
[[1,2,4,5],[3]] => [2,3]
[[1,2,3,5],[4]] => [3,2]
[[1,2,3,4],[5]] => [4,1]
[[1,3,5],[2,4]] => [1,2,2]
[[1,2,5],[3,4]] => [2,3]
[[1,3,4],[2,5]] => [1,3,1]
[[1,2,4],[3,5]] => [2,2,1]
[[1,2,3],[4,5]] => [3,2]
[[1,4,5],[2],[3]] => [1,1,3]
[[1,3,5],[2],[4]] => [1,2,2]
[[1,2,5],[3],[4]] => [2,1,2]
[[1,3,4],[2],[5]] => [1,3,1]
[[1,2,4],[3],[5]] => [2,2,1]
[[1,2,3],[4],[5]] => [3,1,1]
[[1,4],[2,5],[3]] => [1,1,2,1]
[[1,3],[2,5],[4]] => [1,2,2]
[[1,2],[3,5],[4]] => [2,1,2]
[[1,3],[2,4],[5]] => [1,2,1,1]
[[1,2],[3,4],[5]] => [2,2,1]
[[1,5],[2],[3],[4]] => [1,1,1,2]
[[1,4],[2],[3],[5]] => [1,1,2,1]
[[1,3],[2],[4],[5]] => [1,2,1,1]
[[1,2],[3],[4],[5]] => [2,1,1,1]
[[1],[2],[3],[4],[5]] => [1,1,1,1,1]
[[1,2,3,4,5,6]] => [6]
[[1,3,4,5,6],[2]] => [1,5]
[[1,2,4,5,6],[3]] => [2,4]
[[1,2,3,5,6],[4]] => [3,3]
[[1,2,3,4,6],[5]] => [4,2]
[[1,2,3,4,5],[6]] => [5,1]
[[1,3,5,6],[2,4]] => [1,2,3]
[[1,2,5,6],[3,4]] => [2,4]
[[1,3,4,6],[2,5]] => [1,3,2]
[[1,2,4,6],[3,5]] => [2,2,2]
[[1,2,3,6],[4,5]] => [3,3]
[[1,3,4,5],[2,6]] => [1,4,1]
[[1,2,4,5],[3,6]] => [2,3,1]
[[1,2,3,5],[4,6]] => [3,2,1]
[[1,2,3,4],[5,6]] => [4,2]
[[1,4,5,6],[2],[3]] => [1,1,4]
[[1,3,5,6],[2],[4]] => [1,2,3]
[[1,2,5,6],[3],[4]] => [2,1,3]
[[1,3,4,6],[2],[5]] => [1,3,2]
[[1,2,4,6],[3],[5]] => [2,2,2]
[[1,2,3,6],[4],[5]] => [3,1,2]
[[1,3,4,5],[2],[6]] => [1,4,1]
[[1,2,4,5],[3],[6]] => [2,3,1]
[[1,2,3,5],[4],[6]] => [3,2,1]
[[1,2,3,4],[5],[6]] => [4,1,1]
[[1,3,5],[2,4,6]] => [1,2,2,1]
[[1,2,5],[3,4,6]] => [2,3,1]
[[1,3,4],[2,5,6]] => [1,3,2]
[[1,2,4],[3,5,6]] => [2,2,2]
[[1,2,3],[4,5,6]] => [3,3]
[[1,4,6],[2,5],[3]] => [1,1,2,2]
[[1,3,6],[2,5],[4]] => [1,2,3]
[[1,2,6],[3,5],[4]] => [2,1,3]
[[1,3,6],[2,4],[5]] => [1,2,1,2]
[[1,2,6],[3,4],[5]] => [2,2,2]
[[1,4,5],[2,6],[3]] => [1,1,3,1]
[[1,3,5],[2,6],[4]] => [1,2,2,1]
[[1,2,5],[3,6],[4]] => [2,1,2,1]
[[1,3,4],[2,6],[5]] => [1,3,2]
[[1,2,4],[3,6],[5]] => [2,2,2]
[[1,2,3],[4,6],[5]] => [3,1,2]
[[1,3,5],[2,4],[6]] => [1,2,2,1]
[[1,2,5],[3,4],[6]] => [2,3,1]
[[1,3,4],[2,5],[6]] => [1,3,1,1]
[[1,2,4],[3,5],[6]] => [2,2,1,1]
[[1,2,3],[4,5],[6]] => [3,2,1]
[[1,5,6],[2],[3],[4]] => [1,1,1,3]
[[1,4,6],[2],[3],[5]] => [1,1,2,2]
[[1,3,6],[2],[4],[5]] => [1,2,1,2]
[[1,2,6],[3],[4],[5]] => [2,1,1,2]
[[1,4,5],[2],[3],[6]] => [1,1,3,1]
[[1,3,5],[2],[4],[6]] => [1,2,2,1]
[[1,2,5],[3],[4],[6]] => [2,1,2,1]
[[1,3,4],[2],[5],[6]] => [1,3,1,1]
[[1,2,4],[3],[5],[6]] => [2,2,1,1]
[[1,2,3],[4],[5],[6]] => [3,1,1,1]
[[1,4],[2,5],[3,6]] => [1,1,2,2]
[[1,3],[2,5],[4,6]] => [1,2,2,1]
[[1,2],[3,5],[4,6]] => [2,1,2,1]
[[1,3],[2,4],[5,6]] => [1,2,1,2]
[[1,2],[3,4],[5,6]] => [2,2,2]
[[1,5],[2,6],[3],[4]] => [1,1,1,2,1]
[[1,4],[2,6],[3],[5]] => [1,1,2,2]
[[1,3],[2,6],[4],[5]] => [1,2,1,2]
[[1,2],[3,6],[4],[5]] => [2,1,1,2]
[[1,4],[2,5],[3],[6]] => [1,1,2,1,1]
[[1,3],[2,5],[4],[6]] => [1,2,2,1]
[[1,2],[3,5],[4],[6]] => [2,1,2,1]
[[1,3],[2,4],[5],[6]] => [1,2,1,1,1]
[[1,2],[3,4],[5],[6]] => [2,2,1,1]
[[1,6],[2],[3],[4],[5]] => [1,1,1,1,2]
[[1,5],[2],[3],[4],[6]] => [1,1,1,2,1]
[[1,4],[2],[3],[5],[6]] => [1,1,2,1,1]
[[1,3],[2],[4],[5],[6]] => [1,2,1,1,1]
[[1,2],[3],[4],[5],[6]] => [2,1,1,1,1]
[[1],[2],[3],[4],[5],[6]] => [1,1,1,1,1,1]
[[1,2,3,4,5,6,7]] => [7]
[[1,3,4,5,6,7],[2]] => [1,6]
[[1,2,4,5,6,7],[3]] => [2,5]
[[1,2,3,5,6,7],[4]] => [3,4]
[[1,2,3,4,6,7],[5]] => [4,3]
[[1,2,3,4,5,7],[6]] => [5,2]
[[1,2,3,4,5,6],[7]] => [6,1]
[[1,3,5,6,7],[2,4]] => [1,2,4]
[[1,2,5,6,7],[3,4]] => [2,5]
[[1,3,4,6,7],[2,5]] => [1,3,3]
[[1,2,4,6,7],[3,5]] => [2,2,3]
[[1,2,3,6,7],[4,5]] => [3,4]
[[1,3,4,5,7],[2,6]] => [1,4,2]
[[1,2,4,5,7],[3,6]] => [2,3,2]
[[1,2,3,5,7],[4,6]] => [3,2,2]
[[1,2,3,4,7],[5,6]] => [4,3]
[[1,3,4,5,6],[2,7]] => [1,5,1]
[[1,2,4,5,6],[3,7]] => [2,4,1]
[[1,2,3,5,6],[4,7]] => [3,3,1]
[[1,2,3,4,6],[5,7]] => [4,2,1]
[[1,2,3,4,5],[6,7]] => [5,2]
[[1,4,5,6,7],[2],[3]] => [1,1,5]
[[1,3,5,6,7],[2],[4]] => [1,2,4]
[[1,2,5,6,7],[3],[4]] => [2,1,4]
[[1,3,4,6,7],[2],[5]] => [1,3,3]
[[1,2,4,6,7],[3],[5]] => [2,2,3]
[[1,2,3,6,7],[4],[5]] => [3,1,3]
[[1,3,4,5,7],[2],[6]] => [1,4,2]
[[1,2,4,5,7],[3],[6]] => [2,3,2]
[[1,2,3,5,7],[4],[6]] => [3,2,2]
[[1,2,3,4,7],[5],[6]] => [4,1,2]
[[1,3,4,5,6],[2],[7]] => [1,5,1]
[[1,2,4,5,6],[3],[7]] => [2,4,1]
[[1,2,3,5,6],[4],[7]] => [3,3,1]
[[1,2,3,4,6],[5],[7]] => [4,2,1]
[[1,2,3,4,5],[6],[7]] => [5,1,1]
[[1,3,5,7],[2,4,6]] => [1,2,2,2]
[[1,2,5,7],[3,4,6]] => [2,3,2]
[[1,3,4,7],[2,5,6]] => [1,3,3]
[[1,2,4,7],[3,5,6]] => [2,2,3]
[[1,2,3,7],[4,5,6]] => [3,4]
[[1,3,5,6],[2,4,7]] => [1,2,3,1]
[[1,2,5,6],[3,4,7]] => [2,4,1]
[[1,3,4,6],[2,5,7]] => [1,3,2,1]
[[1,2,4,6],[3,5,7]] => [2,2,2,1]
[[1,2,3,6],[4,5,7]] => [3,3,1]
[[1,3,4,5],[2,6,7]] => [1,4,2]
[[1,2,4,5],[3,6,7]] => [2,3,2]
[[1,2,3,5],[4,6,7]] => [3,2,2]
[[1,2,3,4],[5,6,7]] => [4,3]
[[1,4,6,7],[2,5],[3]] => [1,1,2,3]
[[1,3,6,7],[2,5],[4]] => [1,2,4]
[[1,2,6,7],[3,5],[4]] => [2,1,4]
[[1,3,6,7],[2,4],[5]] => [1,2,1,3]
[[1,2,6,7],[3,4],[5]] => [2,2,3]
[[1,4,5,7],[2,6],[3]] => [1,1,3,2]
[[1,3,5,7],[2,6],[4]] => [1,2,2,2]
[[1,2,5,7],[3,6],[4]] => [2,1,2,2]
[[1,3,4,7],[2,6],[5]] => [1,3,3]
[[1,2,4,7],[3,6],[5]] => [2,2,3]
[[1,2,3,7],[4,6],[5]] => [3,1,3]
[[1,3,5,7],[2,4],[6]] => [1,2,2,2]
[[1,2,5,7],[3,4],[6]] => [2,3,2]
[[1,3,4,7],[2,5],[6]] => [1,3,1,2]
[[1,2,4,7],[3,5],[6]] => [2,2,1,2]
[[1,2,3,7],[4,5],[6]] => [3,2,2]
[[1,4,5,6],[2,7],[3]] => [1,1,4,1]
[[1,3,5,6],[2,7],[4]] => [1,2,3,1]
[[1,2,5,6],[3,7],[4]] => [2,1,3,1]
[[1,3,4,6],[2,7],[5]] => [1,3,2,1]
[[1,2,4,6],[3,7],[5]] => [2,2,2,1]
[[1,2,3,6],[4,7],[5]] => [3,1,2,1]
[[1,3,4,5],[2,7],[6]] => [1,4,2]
[[1,2,4,5],[3,7],[6]] => [2,3,2]
[[1,2,3,5],[4,7],[6]] => [3,2,2]
[[1,2,3,4],[5,7],[6]] => [4,1,2]
[[1,3,5,6],[2,4],[7]] => [1,2,3,1]
[[1,2,5,6],[3,4],[7]] => [2,4,1]
[[1,3,4,6],[2,5],[7]] => [1,3,2,1]
[[1,2,4,6],[3,5],[7]] => [2,2,2,1]
[[1,2,3,6],[4,5],[7]] => [3,3,1]
[[1,3,4,5],[2,6],[7]] => [1,4,1,1]
[[1,2,4,5],[3,6],[7]] => [2,3,1,1]
[[1,2,3,5],[4,6],[7]] => [3,2,1,1]
[[1,2,3,4],[5,6],[7]] => [4,2,1]
[[1,5,6,7],[2],[3],[4]] => [1,1,1,4]
[[1,4,6,7],[2],[3],[5]] => [1,1,2,3]
[[1,3,6,7],[2],[4],[5]] => [1,2,1,3]
[[1,2,6,7],[3],[4],[5]] => [2,1,1,3]
[[1,4,5,7],[2],[3],[6]] => [1,1,3,2]
[[1,3,5,7],[2],[4],[6]] => [1,2,2,2]
[[1,2,5,7],[3],[4],[6]] => [2,1,2,2]
[[1,3,4,7],[2],[5],[6]] => [1,3,1,2]
[[1,2,4,7],[3],[5],[6]] => [2,2,1,2]
[[1,2,3,7],[4],[5],[6]] => [3,1,1,2]
[[1,4,5,6],[2],[3],[7]] => [1,1,4,1]
[[1,3,5,6],[2],[4],[7]] => [1,2,3,1]
[[1,2,5,6],[3],[4],[7]] => [2,1,3,1]
[[1,3,4,6],[2],[5],[7]] => [1,3,2,1]
[[1,2,4,6],[3],[5],[7]] => [2,2,2,1]
[[1,2,3,6],[4],[5],[7]] => [3,1,2,1]
[[1,3,4,5],[2],[6],[7]] => [1,4,1,1]
[[1,2,4,5],[3],[6],[7]] => [2,3,1,1]
[[1,2,3,5],[4],[6],[7]] => [3,2,1,1]
[[1,2,3,4],[5],[6],[7]] => [4,1,1,1]
[[1,4,6],[2,5,7],[3]] => [1,1,2,2,1]
[[1,3,6],[2,5,7],[4]] => [1,2,3,1]
[[1,2,6],[3,5,7],[4]] => [2,1,3,1]
[[1,3,6],[2,4,7],[5]] => [1,2,1,2,1]
[[1,2,6],[3,4,7],[5]] => [2,2,2,1]
[[1,4,5],[2,6,7],[3]] => [1,1,3,2]
[[1,3,5],[2,6,7],[4]] => [1,2,2,2]
[[1,2,5],[3,6,7],[4]] => [2,1,2,2]
[[1,3,4],[2,6,7],[5]] => [1,3,3]
[[1,2,4],[3,6,7],[5]] => [2,2,3]
[[1,2,3],[4,6,7],[5]] => [3,1,3]
[[1,3,5],[2,4,7],[6]] => [1,2,2,2]
[[1,2,5],[3,4,7],[6]] => [2,3,2]
[[1,3,4],[2,5,7],[6]] => [1,3,1,2]
[[1,2,4],[3,5,7],[6]] => [2,2,1,2]
[[1,2,3],[4,5,7],[6]] => [3,2,2]
[[1,3,5],[2,4,6],[7]] => [1,2,2,1,1]
[[1,2,5],[3,4,6],[7]] => [2,3,1,1]
[[1,3,4],[2,5,6],[7]] => [1,3,2,1]
[[1,2,4],[3,5,6],[7]] => [2,2,2,1]
[[1,2,3],[4,5,6],[7]] => [3,3,1]
[[1,4,7],[2,5],[3,6]] => [1,1,2,3]
[[1,3,7],[2,5],[4,6]] => [1,2,2,2]
[[1,2,7],[3,5],[4,6]] => [2,1,2,2]
[[1,3,7],[2,4],[5,6]] => [1,2,1,3]
[[1,2,7],[3,4],[5,6]] => [2,2,3]
[[1,4,6],[2,5],[3,7]] => [1,1,2,2,1]
[[1,3,6],[2,5],[4,7]] => [1,2,3,1]
[[1,2,6],[3,5],[4,7]] => [2,1,3,1]
[[1,3,6],[2,4],[5,7]] => [1,2,1,2,1]
[[1,2,6],[3,4],[5,7]] => [2,2,2,1]
[[1,4,5],[2,6],[3,7]] => [1,1,3,2]
[[1,3,5],[2,6],[4,7]] => [1,2,2,2]
[[1,2,5],[3,6],[4,7]] => [2,1,2,2]
[[1,3,4],[2,6],[5,7]] => [1,3,2,1]
[[1,2,4],[3,6],[5,7]] => [2,2,2,1]
[[1,2,3],[4,6],[5,7]] => [3,1,2,1]
[[1,3,5],[2,4],[6,7]] => [1,2,2,2]
[[1,2,5],[3,4],[6,7]] => [2,3,2]
[[1,3,4],[2,5],[6,7]] => [1,3,1,2]
[[1,2,4],[3,5],[6,7]] => [2,2,1,2]
[[1,2,3],[4,5],[6,7]] => [3,2,2]
[[1,5,7],[2,6],[3],[4]] => [1,1,1,2,2]
[[1,4,7],[2,6],[3],[5]] => [1,1,2,3]
[[1,3,7],[2,6],[4],[5]] => [1,2,1,3]
[[1,2,7],[3,6],[4],[5]] => [2,1,1,3]
[[1,4,7],[2,5],[3],[6]] => [1,1,2,1,2]
[[1,3,7],[2,5],[4],[6]] => [1,2,2,2]
[[1,2,7],[3,5],[4],[6]] => [2,1,2,2]
[[1,3,7],[2,4],[5],[6]] => [1,2,1,1,2]
[[1,2,7],[3,4],[5],[6]] => [2,2,1,2]
[[1,5,6],[2,7],[3],[4]] => [1,1,1,3,1]
[[1,4,6],[2,7],[3],[5]] => [1,1,2,2,1]
[[1,3,6],[2,7],[4],[5]] => [1,2,1,2,1]
[[1,2,6],[3,7],[4],[5]] => [2,1,1,2,1]
[[1,4,5],[2,7],[3],[6]] => [1,1,3,2]
[[1,3,5],[2,7],[4],[6]] => [1,2,2,2]
[[1,2,5],[3,7],[4],[6]] => [2,1,2,2]
[[1,3,4],[2,7],[5],[6]] => [1,3,1,2]
[[1,2,4],[3,7],[5],[6]] => [2,2,1,2]
[[1,2,3],[4,7],[5],[6]] => [3,1,1,2]
[[1,4,6],[2,5],[3],[7]] => [1,1,2,2,1]
[[1,3,6],[2,5],[4],[7]] => [1,2,3,1]
[[1,2,6],[3,5],[4],[7]] => [2,1,3,1]
[[1,3,6],[2,4],[5],[7]] => [1,2,1,2,1]
[[1,2,6],[3,4],[5],[7]] => [2,2,2,1]
[[1,4,5],[2,6],[3],[7]] => [1,1,3,1,1]
[[1,3,5],[2,6],[4],[7]] => [1,2,2,1,1]
[[1,2,5],[3,6],[4],[7]] => [2,1,2,1,1]
[[1,3,4],[2,6],[5],[7]] => [1,3,2,1]
[[1,2,4],[3,6],[5],[7]] => [2,2,2,1]
[[1,2,3],[4,6],[5],[7]] => [3,1,2,1]
[[1,3,5],[2,4],[6],[7]] => [1,2,2,1,1]
[[1,2,5],[3,4],[6],[7]] => [2,3,1,1]
[[1,3,4],[2,5],[6],[7]] => [1,3,1,1,1]
[[1,2,4],[3,5],[6],[7]] => [2,2,1,1,1]
[[1,2,3],[4,5],[6],[7]] => [3,2,1,1]
[[1,6,7],[2],[3],[4],[5]] => [1,1,1,1,3]
[[1,5,7],[2],[3],[4],[6]] => [1,1,1,2,2]
[[1,4,7],[2],[3],[5],[6]] => [1,1,2,1,2]
[[1,3,7],[2],[4],[5],[6]] => [1,2,1,1,2]
[[1,2,7],[3],[4],[5],[6]] => [2,1,1,1,2]
[[1,5,6],[2],[3],[4],[7]] => [1,1,1,3,1]
[[1,4,6],[2],[3],[5],[7]] => [1,1,2,2,1]
[[1,3,6],[2],[4],[5],[7]] => [1,2,1,2,1]
[[1,2,6],[3],[4],[5],[7]] => [2,1,1,2,1]
[[1,4,5],[2],[3],[6],[7]] => [1,1,3,1,1]
[[1,3,5],[2],[4],[6],[7]] => [1,2,2,1,1]
[[1,2,5],[3],[4],[6],[7]] => [2,1,2,1,1]
[[1,3,4],[2],[5],[6],[7]] => [1,3,1,1,1]
[[1,2,4],[3],[5],[6],[7]] => [2,2,1,1,1]
[[1,2,3],[4],[5],[6],[7]] => [3,1,1,1,1]
[[1,5],[2,6],[3,7],[4]] => [1,1,1,2,2]
[[1,4],[2,6],[3,7],[5]] => [1,1,2,2,1]
[[1,3],[2,6],[4,7],[5]] => [1,2,1,2,1]
[[1,2],[3,6],[4,7],[5]] => [2,1,1,2,1]
[[1,4],[2,5],[3,7],[6]] => [1,1,2,1,2]
[[1,3],[2,5],[4,7],[6]] => [1,2,2,2]
[[1,2],[3,5],[4,7],[6]] => [2,1,2,2]
[[1,3],[2,4],[5,7],[6]] => [1,2,1,1,2]
[[1,2],[3,4],[5,7],[6]] => [2,2,1,2]
[[1,4],[2,5],[3,6],[7]] => [1,1,2,2,1]
[[1,3],[2,5],[4,6],[7]] => [1,2,2,1,1]
[[1,2],[3,5],[4,6],[7]] => [2,1,2,1,1]
[[1,3],[2,4],[5,6],[7]] => [1,2,1,2,1]
[[1,2],[3,4],[5,6],[7]] => [2,2,2,1]
[[1,6],[2,7],[3],[4],[5]] => [1,1,1,1,2,1]
[[1,5],[2,7],[3],[4],[6]] => [1,1,1,2,2]
[[1,4],[2,7],[3],[5],[6]] => [1,1,2,1,2]
[[1,3],[2,7],[4],[5],[6]] => [1,2,1,1,2]
[[1,2],[3,7],[4],[5],[6]] => [2,1,1,1,2]
[[1,5],[2,6],[3],[4],[7]] => [1,1,1,2,1,1]
[[1,4],[2,6],[3],[5],[7]] => [1,1,2,2,1]
[[1,3],[2,6],[4],[5],[7]] => [1,2,1,2,1]
[[1,2],[3,6],[4],[5],[7]] => [2,1,1,2,1]
[[1,4],[2,5],[3],[6],[7]] => [1,1,2,1,1,1]
[[1,3],[2,5],[4],[6],[7]] => [1,2,2,1,1]
[[1,2],[3,5],[4],[6],[7]] => [2,1,2,1,1]
[[1,3],[2,4],[5],[6],[7]] => [1,2,1,1,1,1]
[[1,2],[3,4],[5],[6],[7]] => [2,2,1,1,1]
[[1,7],[2],[3],[4],[5],[6]] => [1,1,1,1,1,2]
[[1,6],[2],[3],[4],[5],[7]] => [1,1,1,1,2,1]
[[1,5],[2],[3],[4],[6],[7]] => [1,1,1,2,1,1]
[[1,4],[2],[3],[5],[6],[7]] => [1,1,2,1,1,1]
[[1,3],[2],[4],[5],[6],[7]] => [1,2,1,1,1,1]
[[1,2],[3],[4],[5],[6],[7]] => [2,1,1,1,1,1]
[[1],[2],[3],[4],[5],[6],[7]] => [1,1,1,1,1,1,1]
[[1,2,3,4,5,6,7,8]] => [8]
[[1,3,4,5,6,7,8],[2]] => [1,7]
[[1,2,4,5,6,7,8],[3]] => [2,6]
[[1,2,3,5,6,7,8],[4]] => [3,5]
[[1,2,3,4,6,7,8],[5]] => [4,4]
[[1,2,3,4,5,7,8],[6]] => [5,3]
[[1,2,3,4,5,6,8],[7]] => [6,2]
[[1,2,3,4,5,6,7],[8]] => [7,1]
[[1,3,5,6,7,8],[2,4]] => [1,2,5]
[[1,2,5,6,7,8],[3,4]] => [2,6]
[[1,3,4,6,7,8],[2,5]] => [1,3,4]
[[1,2,4,6,7,8],[3,5]] => [2,2,4]
[[1,2,3,6,7,8],[4,5]] => [3,5]
[[1,3,4,5,7,8],[2,6]] => [1,4,3]
[[1,2,4,5,7,8],[3,6]] => [2,3,3]
[[1,2,3,5,7,8],[4,6]] => [3,2,3]
[[1,2,3,4,7,8],[5,6]] => [4,4]
[[1,3,4,5,6,8],[2,7]] => [1,5,2]
[[1,2,4,5,6,8],[3,7]] => [2,4,2]
[[1,2,3,5,6,8],[4,7]] => [3,3,2]
[[1,2,3,4,6,8],[5,7]] => [4,2,2]
[[1,2,3,4,5,8],[6,7]] => [5,3]
[[1,3,4,5,6,7],[2,8]] => [1,6,1]
[[1,2,4,5,6,7],[3,8]] => [2,5,1]
[[1,2,3,5,6,7],[4,8]] => [3,4,1]
[[1,2,3,4,6,7],[5,8]] => [4,3,1]
[[1,2,3,4,5,7],[6,8]] => [5,2,1]
[[1,2,3,4,5,6],[7,8]] => [6,2]
[[1,4,5,6,7,8],[2],[3]] => [1,1,6]
[[1,3,5,6,7,8],[2],[4]] => [1,2,5]
[[1,2,5,6,7,8],[3],[4]] => [2,1,5]
[[1,3,4,6,7,8],[2],[5]] => [1,3,4]
[[1,2,4,6,7,8],[3],[5]] => [2,2,4]
[[1,2,3,6,7,8],[4],[5]] => [3,1,4]
[[1,3,4,5,7,8],[2],[6]] => [1,4,3]
[[1,2,4,5,7,8],[3],[6]] => [2,3,3]
[[1,2,3,5,7,8],[4],[6]] => [3,2,3]
[[1,2,3,4,7,8],[5],[6]] => [4,1,3]
[[1,3,4,5,6,8],[2],[7]] => [1,5,2]
[[1,2,4,5,6,8],[3],[7]] => [2,4,2]
[[1,2,3,5,6,8],[4],[7]] => [3,3,2]
[[1,2,3,4,6,8],[5],[7]] => [4,2,2]
[[1,2,3,4,5,8],[6],[7]] => [5,1,2]
[[1,3,4,5,6,7],[2],[8]] => [1,6,1]
[[1,2,4,5,6,7],[3],[8]] => [2,5,1]
[[1,2,3,5,6,7],[4],[8]] => [3,4,1]
[[1,2,3,4,6,7],[5],[8]] => [4,3,1]
[[1,2,3,4,5,7],[6],[8]] => [5,2,1]
[[1,2,3,4,5,6],[7],[8]] => [6,1,1]
[[1,3,5,7,8],[2,4,6]] => [1,2,2,3]
[[1,2,5,7,8],[3,4,6]] => [2,3,3]
[[1,3,4,7,8],[2,5,6]] => [1,3,4]
[[1,2,4,7,8],[3,5,6]] => [2,2,4]
[[1,2,3,7,8],[4,5,6]] => [3,5]
[[1,3,5,6,8],[2,4,7]] => [1,2,3,2]
[[1,2,5,6,8],[3,4,7]] => [2,4,2]
[[1,3,4,6,8],[2,5,7]] => [1,3,2,2]
[[1,2,4,6,8],[3,5,7]] => [2,2,2,2]
[[1,2,3,6,8],[4,5,7]] => [3,3,2]
[[1,3,4,5,8],[2,6,7]] => [1,4,3]
[[1,2,4,5,8],[3,6,7]] => [2,3,3]
[[1,2,3,5,8],[4,6,7]] => [3,2,3]
[[1,2,3,4,8],[5,6,7]] => [4,4]
[[1,3,5,6,7],[2,4,8]] => [1,2,4,1]
[[1,2,5,6,7],[3,4,8]] => [2,5,1]
[[1,3,4,6,7],[2,5,8]] => [1,3,3,1]
[[1,2,4,6,7],[3,5,8]] => [2,2,3,1]
[[1,2,3,6,7],[4,5,8]] => [3,4,1]
[[1,3,4,5,7],[2,6,8]] => [1,4,2,1]
[[1,2,4,5,7],[3,6,8]] => [2,3,2,1]
[[1,2,3,5,7],[4,6,8]] => [3,2,2,1]
[[1,2,3,4,7],[5,6,8]] => [4,3,1]
[[1,3,4,5,6],[2,7,8]] => [1,5,2]
[[1,2,4,5,6],[3,7,8]] => [2,4,2]
[[1,2,3,5,6],[4,7,8]] => [3,3,2]
[[1,2,3,4,6],[5,7,8]] => [4,2,2]
[[1,2,3,4,5],[6,7,8]] => [5,3]
[[1,4,6,7,8],[2,5],[3]] => [1,1,2,4]
[[1,3,6,7,8],[2,5],[4]] => [1,2,5]
[[1,2,6,7,8],[3,5],[4]] => [2,1,5]
[[1,3,6,7,8],[2,4],[5]] => [1,2,1,4]
[[1,2,6,7,8],[3,4],[5]] => [2,2,4]
[[1,4,5,7,8],[2,6],[3]] => [1,1,3,3]
[[1,3,5,7,8],[2,6],[4]] => [1,2,2,3]
[[1,2,5,7,8],[3,6],[4]] => [2,1,2,3]
[[1,3,4,7,8],[2,6],[5]] => [1,3,4]
[[1,2,4,7,8],[3,6],[5]] => [2,2,4]
[[1,2,3,7,8],[4,6],[5]] => [3,1,4]
[[1,3,5,7,8],[2,4],[6]] => [1,2,2,3]
[[1,2,5,7,8],[3,4],[6]] => [2,3,3]
[[1,3,4,7,8],[2,5],[6]] => [1,3,1,3]
[[1,2,4,7,8],[3,5],[6]] => [2,2,1,3]
[[1,2,3,7,8],[4,5],[6]] => [3,2,3]
[[1,4,5,6,8],[2,7],[3]] => [1,1,4,2]
[[1,3,5,6,8],[2,7],[4]] => [1,2,3,2]
[[1,2,5,6,8],[3,7],[4]] => [2,1,3,2]
[[1,3,4,6,8],[2,7],[5]] => [1,3,2,2]
[[1,2,4,6,8],[3,7],[5]] => [2,2,2,2]
[[1,2,3,6,8],[4,7],[5]] => [3,1,2,2]
[[1,3,4,5,8],[2,7],[6]] => [1,4,3]
[[1,2,4,5,8],[3,7],[6]] => [2,3,3]
[[1,2,3,5,8],[4,7],[6]] => [3,2,3]
[[1,2,3,4,8],[5,7],[6]] => [4,1,3]
[[1,3,5,6,8],[2,4],[7]] => [1,2,3,2]
[[1,2,5,6,8],[3,4],[7]] => [2,4,2]
[[1,3,4,6,8],[2,5],[7]] => [1,3,2,2]
[[1,2,4,6,8],[3,5],[7]] => [2,2,2,2]
[[1,2,3,6,8],[4,5],[7]] => [3,3,2]
[[1,3,4,5,8],[2,6],[7]] => [1,4,1,2]
[[1,2,4,5,8],[3,6],[7]] => [2,3,1,2]
[[1,2,3,5,8],[4,6],[7]] => [3,2,1,2]
[[1,2,3,4,8],[5,6],[7]] => [4,2,2]
[[1,4,5,6,7],[2,8],[3]] => [1,1,5,1]
[[1,3,5,6,7],[2,8],[4]] => [1,2,4,1]
[[1,2,5,6,7],[3,8],[4]] => [2,1,4,1]
[[1,3,4,6,7],[2,8],[5]] => [1,3,3,1]
[[1,2,4,6,7],[3,8],[5]] => [2,2,3,1]
[[1,2,3,6,7],[4,8],[5]] => [3,1,3,1]
[[1,3,4,5,7],[2,8],[6]] => [1,4,2,1]
[[1,2,4,5,7],[3,8],[6]] => [2,3,2,1]
[[1,2,3,5,7],[4,8],[6]] => [3,2,2,1]
[[1,2,3,4,7],[5,8],[6]] => [4,1,2,1]
[[1,3,4,5,6],[2,8],[7]] => [1,5,2]
[[1,2,4,5,6],[3,8],[7]] => [2,4,2]
[[1,2,3,5,6],[4,8],[7]] => [3,3,2]
[[1,2,3,4,6],[5,8],[7]] => [4,2,2]
[[1,2,3,4,5],[6,8],[7]] => [5,1,2]
[[1,3,5,6,7],[2,4],[8]] => [1,2,4,1]
[[1,2,5,6,7],[3,4],[8]] => [2,5,1]
[[1,3,4,6,7],[2,5],[8]] => [1,3,3,1]
[[1,2,4,6,7],[3,5],[8]] => [2,2,3,1]
[[1,2,3,6,7],[4,5],[8]] => [3,4,1]
[[1,3,4,5,7],[2,6],[8]] => [1,4,2,1]
[[1,2,4,5,7],[3,6],[8]] => [2,3,2,1]
[[1,2,3,5,7],[4,6],[8]] => [3,2,2,1]
[[1,2,3,4,7],[5,6],[8]] => [4,3,1]
[[1,3,4,5,6],[2,7],[8]] => [1,5,1,1]
[[1,2,4,5,6],[3,7],[8]] => [2,4,1,1]
[[1,2,3,5,6],[4,7],[8]] => [3,3,1,1]
[[1,2,3,4,6],[5,7],[8]] => [4,2,1,1]
[[1,2,3,4,5],[6,7],[8]] => [5,2,1]
[[1,5,6,7,8],[2],[3],[4]] => [1,1,1,5]
[[1,4,6,7,8],[2],[3],[5]] => [1,1,2,4]
[[1,3,6,7,8],[2],[4],[5]] => [1,2,1,4]
[[1,2,6,7,8],[3],[4],[5]] => [2,1,1,4]
[[1,4,5,7,8],[2],[3],[6]] => [1,1,3,3]
[[1,3,5,7,8],[2],[4],[6]] => [1,2,2,3]
[[1,2,5,7,8],[3],[4],[6]] => [2,1,2,3]
[[1,3,4,7,8],[2],[5],[6]] => [1,3,1,3]
[[1,2,4,7,8],[3],[5],[6]] => [2,2,1,3]
[[1,2,3,7,8],[4],[5],[6]] => [3,1,1,3]
[[1,4,5,6,8],[2],[3],[7]] => [1,1,4,2]
[[1,3,5,6,8],[2],[4],[7]] => [1,2,3,2]
[[1,2,5,6,8],[3],[4],[7]] => [2,1,3,2]
[[1,3,4,6,8],[2],[5],[7]] => [1,3,2,2]
[[1,2,4,6,8],[3],[5],[7]] => [2,2,2,2]
[[1,2,3,6,8],[4],[5],[7]] => [3,1,2,2]
[[1,3,4,5,8],[2],[6],[7]] => [1,4,1,2]
[[1,2,4,5,8],[3],[6],[7]] => [2,3,1,2]
[[1,2,3,5,8],[4],[6],[7]] => [3,2,1,2]
[[1,2,3,4,8],[5],[6],[7]] => [4,1,1,2]
[[1,4,5,6,7],[2],[3],[8]] => [1,1,5,1]
[[1,3,5,6,7],[2],[4],[8]] => [1,2,4,1]
[[1,2,5,6,7],[3],[4],[8]] => [2,1,4,1]
[[1,3,4,6,7],[2],[5],[8]] => [1,3,3,1]
[[1,2,4,6,7],[3],[5],[8]] => [2,2,3,1]
[[1,2,3,6,7],[4],[5],[8]] => [3,1,3,1]
[[1,3,4,5,7],[2],[6],[8]] => [1,4,2,1]
[[1,2,4,5,7],[3],[6],[8]] => [2,3,2,1]
[[1,2,3,5,7],[4],[6],[8]] => [3,2,2,1]
[[1,2,3,4,7],[5],[6],[8]] => [4,1,2,1]
[[1,3,4,5,6],[2],[7],[8]] => [1,5,1,1]
[[1,2,4,5,6],[3],[7],[8]] => [2,4,1,1]
[[1,2,3,5,6],[4],[7],[8]] => [3,3,1,1]
[[1,2,3,4,6],[5],[7],[8]] => [4,2,1,1]
[[1,2,3,4,5],[6],[7],[8]] => [5,1,1,1]
[[1,3,5,7],[2,4,6,8]] => [1,2,2,2,1]
[[1,2,5,7],[3,4,6,8]] => [2,3,2,1]
[[1,3,4,7],[2,5,6,8]] => [1,3,3,1]
[[1,2,4,7],[3,5,6,8]] => [2,2,3,1]
[[1,2,3,7],[4,5,6,8]] => [3,4,1]
[[1,3,5,6],[2,4,7,8]] => [1,2,3,2]
[[1,2,5,6],[3,4,7,8]] => [2,4,2]
[[1,3,4,6],[2,5,7,8]] => [1,3,2,2]
[[1,2,4,6],[3,5,7,8]] => [2,2,2,2]
[[1,2,3,6],[4,5,7,8]] => [3,3,2]
[[1,3,4,5],[2,6,7,8]] => [1,4,3]
[[1,2,4,5],[3,6,7,8]] => [2,3,3]
[[1,2,3,5],[4,6,7,8]] => [3,2,3]
[[1,2,3,4],[5,6,7,8]] => [4,4]
[[1,4,6,8],[2,5,7],[3]] => [1,1,2,2,2]
[[1,3,6,8],[2,5,7],[4]] => [1,2,3,2]
[[1,2,6,8],[3,5,7],[4]] => [2,1,3,2]
[[1,3,6,8],[2,4,7],[5]] => [1,2,1,2,2]
[[1,2,6,8],[3,4,7],[5]] => [2,2,2,2]
[[1,4,5,8],[2,6,7],[3]] => [1,1,3,3]
[[1,3,5,8],[2,6,7],[4]] => [1,2,2,3]
[[1,2,5,8],[3,6,7],[4]] => [2,1,2,3]
[[1,3,4,8],[2,6,7],[5]] => [1,3,4]
[[1,2,4,8],[3,6,7],[5]] => [2,2,4]
[[1,2,3,8],[4,6,7],[5]] => [3,1,4]
[[1,3,5,8],[2,4,7],[6]] => [1,2,2,3]
[[1,2,5,8],[3,4,7],[6]] => [2,3,3]
[[1,3,4,8],[2,5,7],[6]] => [1,3,1,3]
[[1,2,4,8],[3,5,7],[6]] => [2,2,1,3]
[[1,2,3,8],[4,5,7],[6]] => [3,2,3]
[[1,3,5,8],[2,4,6],[7]] => [1,2,2,1,2]
[[1,2,5,8],[3,4,6],[7]] => [2,3,1,2]
[[1,3,4,8],[2,5,6],[7]] => [1,3,2,2]
[[1,2,4,8],[3,5,6],[7]] => [2,2,2,2]
[[1,2,3,8],[4,5,6],[7]] => [3,3,2]
[[1,4,6,7],[2,5,8],[3]] => [1,1,2,3,1]
[[1,3,6,7],[2,5,8],[4]] => [1,2,4,1]
[[1,2,6,7],[3,5,8],[4]] => [2,1,4,1]
[[1,3,6,7],[2,4,8],[5]] => [1,2,1,3,1]
[[1,2,6,7],[3,4,8],[5]] => [2,2,3,1]
[[1,4,5,7],[2,6,8],[3]] => [1,1,3,2,1]
[[1,3,5,7],[2,6,8],[4]] => [1,2,2,2,1]
[[1,2,5,7],[3,6,8],[4]] => [2,1,2,2,1]
[[1,3,4,7],[2,6,8],[5]] => [1,3,3,1]
[[1,2,4,7],[3,6,8],[5]] => [2,2,3,1]
[[1,2,3,7],[4,6,8],[5]] => [3,1,3,1]
[[1,3,5,7],[2,4,8],[6]] => [1,2,2,2,1]
[[1,2,5,7],[3,4,8],[6]] => [2,3,2,1]
[[1,3,4,7],[2,5,8],[6]] => [1,3,1,2,1]
[[1,2,4,7],[3,5,8],[6]] => [2,2,1,2,1]
[[1,2,3,7],[4,5,8],[6]] => [3,2,2,1]
[[1,4,5,6],[2,7,8],[3]] => [1,1,4,2]
[[1,3,5,6],[2,7,8],[4]] => [1,2,3,2]
[[1,2,5,6],[3,7,8],[4]] => [2,1,3,2]
[[1,3,4,6],[2,7,8],[5]] => [1,3,2,2]
[[1,2,4,6],[3,7,8],[5]] => [2,2,2,2]
[[1,2,3,6],[4,7,8],[5]] => [3,1,2,2]
[[1,3,4,5],[2,7,8],[6]] => [1,4,3]
[[1,2,4,5],[3,7,8],[6]] => [2,3,3]
[[1,2,3,5],[4,7,8],[6]] => [3,2,3]
[[1,2,3,4],[5,7,8],[6]] => [4,1,3]
[[1,3,5,6],[2,4,8],[7]] => [1,2,3,2]
[[1,2,5,6],[3,4,8],[7]] => [2,4,2]
[[1,3,4,6],[2,5,8],[7]] => [1,3,2,2]
[[1,2,4,6],[3,5,8],[7]] => [2,2,2,2]
[[1,2,3,6],[4,5,8],[7]] => [3,3,2]
[[1,3,4,5],[2,6,8],[7]] => [1,4,1,2]
[[1,2,4,5],[3,6,8],[7]] => [2,3,1,2]
[[1,2,3,5],[4,6,8],[7]] => [3,2,1,2]
[[1,2,3,4],[5,6,8],[7]] => [4,2,2]
[[1,3,5,7],[2,4,6],[8]] => [1,2,2,2,1]
[[1,2,5,7],[3,4,6],[8]] => [2,3,2,1]
[[1,3,4,7],[2,5,6],[8]] => [1,3,3,1]
[[1,2,4,7],[3,5,6],[8]] => [2,2,3,1]
[[1,2,3,7],[4,5,6],[8]] => [3,4,1]
[[1,3,5,6],[2,4,7],[8]] => [1,2,3,1,1]
[[1,2,5,6],[3,4,7],[8]] => [2,4,1,1]
[[1,3,4,6],[2,5,7],[8]] => [1,3,2,1,1]
[[1,2,4,6],[3,5,7],[8]] => [2,2,2,1,1]
[[1,2,3,6],[4,5,7],[8]] => [3,3,1,1]
[[1,3,4,5],[2,6,7],[8]] => [1,4,2,1]
[[1,2,4,5],[3,6,7],[8]] => [2,3,2,1]
[[1,2,3,5],[4,6,7],[8]] => [3,2,2,1]
[[1,2,3,4],[5,6,7],[8]] => [4,3,1]
[[1,4,7,8],[2,5],[3,6]] => [1,1,2,4]
[[1,3,7,8],[2,5],[4,6]] => [1,2,2,3]
[[1,2,7,8],[3,5],[4,6]] => [2,1,2,3]
[[1,3,7,8],[2,4],[5,6]] => [1,2,1,4]
[[1,2,7,8],[3,4],[5,6]] => [2,2,4]
[[1,4,6,8],[2,5],[3,7]] => [1,1,2,2,2]
[[1,3,6,8],[2,5],[4,7]] => [1,2,3,2]
[[1,2,6,8],[3,5],[4,7]] => [2,1,3,2]
[[1,3,6,8],[2,4],[5,7]] => [1,2,1,2,2]
[[1,2,6,8],[3,4],[5,7]] => [2,2,2,2]
[[1,4,5,8],[2,6],[3,7]] => [1,1,3,3]
[[1,3,5,8],[2,6],[4,7]] => [1,2,2,3]
[[1,2,5,8],[3,6],[4,7]] => [2,1,2,3]
[[1,3,4,8],[2,6],[5,7]] => [1,3,2,2]
[[1,2,4,8],[3,6],[5,7]] => [2,2,2,2]
[[1,2,3,8],[4,6],[5,7]] => [3,1,2,2]
[[1,3,5,8],[2,4],[6,7]] => [1,2,2,3]
[[1,2,5,8],[3,4],[6,7]] => [2,3,3]
[[1,3,4,8],[2,5],[6,7]] => [1,3,1,3]
[[1,2,4,8],[3,5],[6,7]] => [2,2,1,3]
[[1,2,3,8],[4,5],[6,7]] => [3,2,3]
[[1,4,6,7],[2,5],[3,8]] => [1,1,2,3,1]
[[1,3,6,7],[2,5],[4,8]] => [1,2,4,1]
[[1,2,6,7],[3,5],[4,8]] => [2,1,4,1]
[[1,3,6,7],[2,4],[5,8]] => [1,2,1,3,1]
[[1,2,6,7],[3,4],[5,8]] => [2,2,3,1]
[[1,4,5,7],[2,6],[3,8]] => [1,1,3,2,1]
[[1,3,5,7],[2,6],[4,8]] => [1,2,2,2,1]
[[1,2,5,7],[3,6],[4,8]] => [2,1,2,2,1]
[[1,3,4,7],[2,6],[5,8]] => [1,3,3,1]
[[1,2,4,7],[3,6],[5,8]] => [2,2,3,1]
[[1,2,3,7],[4,6],[5,8]] => [3,1,3,1]
[[1,3,5,7],[2,4],[6,8]] => [1,2,2,2,1]
[[1,2,5,7],[3,4],[6,8]] => [2,3,2,1]
[[1,3,4,7],[2,5],[6,8]] => [1,3,1,2,1]
[[1,2,4,7],[3,5],[6,8]] => [2,2,1,2,1]
[[1,2,3,7],[4,5],[6,8]] => [3,2,2,1]
[[1,4,5,6],[2,7],[3,8]] => [1,1,4,2]
[[1,3,5,6],[2,7],[4,8]] => [1,2,3,2]
[[1,2,5,6],[3,7],[4,8]] => [2,1,3,2]
[[1,3,4,6],[2,7],[5,8]] => [1,3,2,2]
[[1,2,4,6],[3,7],[5,8]] => [2,2,2,2]
[[1,2,3,6],[4,7],[5,8]] => [3,1,2,2]
[[1,3,4,5],[2,7],[6,8]] => [1,4,2,1]
[[1,2,4,5],[3,7],[6,8]] => [2,3,2,1]
[[1,2,3,5],[4,7],[6,8]] => [3,2,2,1]
[[1,2,3,4],[5,7],[6,8]] => [4,1,2,1]
[[1,3,5,6],[2,4],[7,8]] => [1,2,3,2]
[[1,2,5,6],[3,4],[7,8]] => [2,4,2]
[[1,3,4,6],[2,5],[7,8]] => [1,3,2,2]
[[1,2,4,6],[3,5],[7,8]] => [2,2,2,2]
[[1,2,3,6],[4,5],[7,8]] => [3,3,2]
[[1,3,4,5],[2,6],[7,8]] => [1,4,1,2]
[[1,2,4,5],[3,6],[7,8]] => [2,3,1,2]
[[1,2,3,5],[4,6],[7,8]] => [3,2,1,2]
[[1,2,3,4],[5,6],[7,8]] => [4,2,2]
[[1,5,7,8],[2,6],[3],[4]] => [1,1,1,2,3]
[[1,4,7,8],[2,6],[3],[5]] => [1,1,2,4]
[[1,3,7,8],[2,6],[4],[5]] => [1,2,1,4]
[[1,2,7,8],[3,6],[4],[5]] => [2,1,1,4]
[[1,4,7,8],[2,5],[3],[6]] => [1,1,2,1,3]
[[1,3,7,8],[2,5],[4],[6]] => [1,2,2,3]
[[1,2,7,8],[3,5],[4],[6]] => [2,1,2,3]
[[1,3,7,8],[2,4],[5],[6]] => [1,2,1,1,3]
[[1,2,7,8],[3,4],[5],[6]] => [2,2,1,3]
[[1,5,6,8],[2,7],[3],[4]] => [1,1,1,3,2]
[[1,4,6,8],[2,7],[3],[5]] => [1,1,2,2,2]
[[1,3,6,8],[2,7],[4],[5]] => [1,2,1,2,2]
[[1,2,6,8],[3,7],[4],[5]] => [2,1,1,2,2]
[[1,4,5,8],[2,7],[3],[6]] => [1,1,3,3]
[[1,3,5,8],[2,7],[4],[6]] => [1,2,2,3]
[[1,2,5,8],[3,7],[4],[6]] => [2,1,2,3]
[[1,3,4,8],[2,7],[5],[6]] => [1,3,1,3]
[[1,2,4,8],[3,7],[5],[6]] => [2,2,1,3]
[[1,2,3,8],[4,7],[5],[6]] => [3,1,1,3]
[[1,4,6,8],[2,5],[3],[7]] => [1,1,2,2,2]
[[1,3,6,8],[2,5],[4],[7]] => [1,2,3,2]
[[1,2,6,8],[3,5],[4],[7]] => [2,1,3,2]
[[1,3,6,8],[2,4],[5],[7]] => [1,2,1,2,2]
[[1,2,6,8],[3,4],[5],[7]] => [2,2,2,2]
[[1,4,5,8],[2,6],[3],[7]] => [1,1,3,1,2]
[[1,3,5,8],[2,6],[4],[7]] => [1,2,2,1,2]
[[1,2,5,8],[3,6],[4],[7]] => [2,1,2,1,2]
[[1,3,4,8],[2,6],[5],[7]] => [1,3,2,2]
[[1,2,4,8],[3,6],[5],[7]] => [2,2,2,2]
[[1,2,3,8],[4,6],[5],[7]] => [3,1,2,2]
[[1,3,5,8],[2,4],[6],[7]] => [1,2,2,1,2]
[[1,2,5,8],[3,4],[6],[7]] => [2,3,1,2]
[[1,3,4,8],[2,5],[6],[7]] => [1,3,1,1,2]
[[1,2,4,8],[3,5],[6],[7]] => [2,2,1,1,2]
[[1,2,3,8],[4,5],[6],[7]] => [3,2,1,2]
[[1,5,6,7],[2,8],[3],[4]] => [1,1,1,4,1]
[[1,4,6,7],[2,8],[3],[5]] => [1,1,2,3,1]
[[1,3,6,7],[2,8],[4],[5]] => [1,2,1,3,1]
[[1,2,6,7],[3,8],[4],[5]] => [2,1,1,3,1]
[[1,4,5,7],[2,8],[3],[6]] => [1,1,3,2,1]
[[1,3,5,7],[2,8],[4],[6]] => [1,2,2,2,1]
[[1,2,5,7],[3,8],[4],[6]] => [2,1,2,2,1]
[[1,3,4,7],[2,8],[5],[6]] => [1,3,1,2,1]
[[1,2,4,7],[3,8],[5],[6]] => [2,2,1,2,1]
[[1,2,3,7],[4,8],[5],[6]] => [3,1,1,2,1]
[[1,4,5,6],[2,8],[3],[7]] => [1,1,4,2]
[[1,3,5,6],[2,8],[4],[7]] => [1,2,3,2]
[[1,2,5,6],[3,8],[4],[7]] => [2,1,3,2]
[[1,3,4,6],[2,8],[5],[7]] => [1,3,2,2]
[[1,2,4,6],[3,8],[5],[7]] => [2,2,2,2]
[[1,2,3,6],[4,8],[5],[7]] => [3,1,2,2]
[[1,3,4,5],[2,8],[6],[7]] => [1,4,1,2]
[[1,2,4,5],[3,8],[6],[7]] => [2,3,1,2]
[[1,2,3,5],[4,8],[6],[7]] => [3,2,1,2]
[[1,2,3,4],[5,8],[6],[7]] => [4,1,1,2]
[[1,4,6,7],[2,5],[3],[8]] => [1,1,2,3,1]
[[1,3,6,7],[2,5],[4],[8]] => [1,2,4,1]
[[1,2,6,7],[3,5],[4],[8]] => [2,1,4,1]
[[1,3,6,7],[2,4],[5],[8]] => [1,2,1,3,1]
[[1,2,6,7],[3,4],[5],[8]] => [2,2,3,1]
[[1,4,5,7],[2,6],[3],[8]] => [1,1,3,2,1]
[[1,3,5,7],[2,6],[4],[8]] => [1,2,2,2,1]
[[1,2,5,7],[3,6],[4],[8]] => [2,1,2,2,1]
[[1,3,4,7],[2,6],[5],[8]] => [1,3,3,1]
[[1,2,4,7],[3,6],[5],[8]] => [2,2,3,1]
[[1,2,3,7],[4,6],[5],[8]] => [3,1,3,1]
[[1,3,5,7],[2,4],[6],[8]] => [1,2,2,2,1]
[[1,2,5,7],[3,4],[6],[8]] => [2,3,2,1]
[[1,3,4,7],[2,5],[6],[8]] => [1,3,1,2,1]
[[1,2,4,7],[3,5],[6],[8]] => [2,2,1,2,1]
[[1,2,3,7],[4,5],[6],[8]] => [3,2,2,1]
[[1,4,5,6],[2,7],[3],[8]] => [1,1,4,1,1]
[[1,3,5,6],[2,7],[4],[8]] => [1,2,3,1,1]
[[1,2,5,6],[3,7],[4],[8]] => [2,1,3,1,1]
[[1,3,4,6],[2,7],[5],[8]] => [1,3,2,1,1]
[[1,2,4,6],[3,7],[5],[8]] => [2,2,2,1,1]
[[1,2,3,6],[4,7],[5],[8]] => [3,1,2,1,1]
[[1,3,4,5],[2,7],[6],[8]] => [1,4,2,1]
[[1,2,4,5],[3,7],[6],[8]] => [2,3,2,1]
[[1,2,3,5],[4,7],[6],[8]] => [3,2,2,1]
[[1,2,3,4],[5,7],[6],[8]] => [4,1,2,1]
[[1,3,5,6],[2,4],[7],[8]] => [1,2,3,1,1]
[[1,2,5,6],[3,4],[7],[8]] => [2,4,1,1]
[[1,3,4,6],[2,5],[7],[8]] => [1,3,2,1,1]
[[1,2,4,6],[3,5],[7],[8]] => [2,2,2,1,1]
[[1,2,3,6],[4,5],[7],[8]] => [3,3,1,1]
[[1,3,4,5],[2,6],[7],[8]] => [1,4,1,1,1]
[[1,2,4,5],[3,6],[7],[8]] => [2,3,1,1,1]
[[1,2,3,5],[4,6],[7],[8]] => [3,2,1,1,1]
[[1,2,3,4],[5,6],[7],[8]] => [4,2,1,1]
[[1,6,7,8],[2],[3],[4],[5]] => [1,1,1,1,4]
[[1,5,7,8],[2],[3],[4],[6]] => [1,1,1,2,3]
[[1,4,7,8],[2],[3],[5],[6]] => [1,1,2,1,3]
[[1,3,7,8],[2],[4],[5],[6]] => [1,2,1,1,3]
[[1,2,7,8],[3],[4],[5],[6]] => [2,1,1,1,3]
[[1,5,6,8],[2],[3],[4],[7]] => [1,1,1,3,2]
[[1,4,6,8],[2],[3],[5],[7]] => [1,1,2,2,2]
[[1,3,6,8],[2],[4],[5],[7]] => [1,2,1,2,2]
[[1,2,6,8],[3],[4],[5],[7]] => [2,1,1,2,2]
[[1,4,5,8],[2],[3],[6],[7]] => [1,1,3,1,2]
[[1,3,5,8],[2],[4],[6],[7]] => [1,2,2,1,2]
[[1,2,5,8],[3],[4],[6],[7]] => [2,1,2,1,2]
[[1,3,4,8],[2],[5],[6],[7]] => [1,3,1,1,2]
[[1,2,4,8],[3],[5],[6],[7]] => [2,2,1,1,2]
[[1,2,3,8],[4],[5],[6],[7]] => [3,1,1,1,2]
[[1,5,6,7],[2],[3],[4],[8]] => [1,1,1,4,1]
[[1,4,6,7],[2],[3],[5],[8]] => [1,1,2,3,1]
[[1,3,6,7],[2],[4],[5],[8]] => [1,2,1,3,1]
[[1,2,6,7],[3],[4],[5],[8]] => [2,1,1,3,1]
[[1,4,5,7],[2],[3],[6],[8]] => [1,1,3,2,1]
[[1,3,5,7],[2],[4],[6],[8]] => [1,2,2,2,1]
[[1,2,5,7],[3],[4],[6],[8]] => [2,1,2,2,1]
[[1,3,4,7],[2],[5],[6],[8]] => [1,3,1,2,1]
[[1,2,4,7],[3],[5],[6],[8]] => [2,2,1,2,1]
[[1,2,3,7],[4],[5],[6],[8]] => [3,1,1,2,1]
[[1,4,5,6],[2],[3],[7],[8]] => [1,1,4,1,1]
[[1,3,5,6],[2],[4],[7],[8]] => [1,2,3,1,1]
[[1,2,5,6],[3],[4],[7],[8]] => [2,1,3,1,1]
[[1,3,4,6],[2],[5],[7],[8]] => [1,3,2,1,1]
[[1,2,4,6],[3],[5],[7],[8]] => [2,2,2,1,1]
[[1,2,3,6],[4],[5],[7],[8]] => [3,1,2,1,1]
[[1,3,4,5],[2],[6],[7],[8]] => [1,4,1,1,1]
[[1,2,4,5],[3],[6],[7],[8]] => [2,3,1,1,1]
[[1,2,3,5],[4],[6],[7],[8]] => [3,2,1,1,1]
[[1,2,3,4],[5],[6],[7],[8]] => [4,1,1,1,1]
[[1,4,7],[2,5,8],[3,6]] => [1,1,2,3,1]
[[1,3,7],[2,5,8],[4,6]] => [1,2,2,2,1]
[[1,2,7],[3,5,8],[4,6]] => [2,1,2,2,1]
[[1,3,7],[2,4,8],[5,6]] => [1,2,1,3,1]
[[1,2,7],[3,4,8],[5,6]] => [2,2,3,1]
[[1,4,6],[2,5,8],[3,7]] => [1,1,2,2,2]
[[1,3,6],[2,5,8],[4,7]] => [1,2,3,2]
[[1,2,6],[3,5,8],[4,7]] => [2,1,3,2]
[[1,3,6],[2,4,8],[5,7]] => [1,2,1,2,2]
[[1,2,6],[3,4,8],[5,7]] => [2,2,2,2]
[[1,4,5],[2,6,8],[3,7]] => [1,1,3,3]
[[1,3,5],[2,6,8],[4,7]] => [1,2,2,3]
[[1,2,5],[3,6,8],[4,7]] => [2,1,2,3]
[[1,3,4],[2,6,8],[5,7]] => [1,3,2,2]
[[1,2,4],[3,6,8],[5,7]] => [2,2,2,2]
[[1,2,3],[4,6,8],[5,7]] => [3,1,2,2]
[[1,3,5],[2,4,8],[6,7]] => [1,2,2,3]
[[1,2,5],[3,4,8],[6,7]] => [2,3,3]
[[1,3,4],[2,5,8],[6,7]] => [1,3,1,3]
[[1,2,4],[3,5,8],[6,7]] => [2,2,1,3]
[[1,2,3],[4,5,8],[6,7]] => [3,2,3]
[[1,4,6],[2,5,7],[3,8]] => [1,1,2,2,2]
[[1,3,6],[2,5,7],[4,8]] => [1,2,3,2]
[[1,2,6],[3,5,7],[4,8]] => [2,1,3,2]
[[1,3,6],[2,4,7],[5,8]] => [1,2,1,2,2]
[[1,2,6],[3,4,7],[5,8]] => [2,2,2,2]
[[1,4,5],[2,6,7],[3,8]] => [1,1,3,2,1]
[[1,3,5],[2,6,7],[4,8]] => [1,2,2,2,1]
[[1,2,5],[3,6,7],[4,8]] => [2,1,2,2,1]
[[1,3,4],[2,6,7],[5,8]] => [1,3,3,1]
[[1,2,4],[3,6,7],[5,8]] => [2,2,3,1]
[[1,2,3],[4,6,7],[5,8]] => [3,1,3,1]
[[1,3,5],[2,4,7],[6,8]] => [1,2,2,2,1]
[[1,2,5],[3,4,7],[6,8]] => [2,3,2,1]
[[1,3,4],[2,5,7],[6,8]] => [1,3,1,2,1]
[[1,2,4],[3,5,7],[6,8]] => [2,2,1,2,1]
[[1,2,3],[4,5,7],[6,8]] => [3,2,2,1]
[[1,3,5],[2,4,6],[7,8]] => [1,2,2,1,2]
[[1,2,5],[3,4,6],[7,8]] => [2,3,1,2]
[[1,3,4],[2,5,6],[7,8]] => [1,3,2,2]
[[1,2,4],[3,5,6],[7,8]] => [2,2,2,2]
[[1,2,3],[4,5,6],[7,8]] => [3,3,2]
[[1,5,7],[2,6,8],[3],[4]] => [1,1,1,2,2,1]
[[1,4,7],[2,6,8],[3],[5]] => [1,1,2,3,1]
[[1,3,7],[2,6,8],[4],[5]] => [1,2,1,3,1]
[[1,2,7],[3,6,8],[4],[5]] => [2,1,1,3,1]
[[1,4,7],[2,5,8],[3],[6]] => [1,1,2,1,2,1]
[[1,3,7],[2,5,8],[4],[6]] => [1,2,2,2,1]
[[1,2,7],[3,5,8],[4],[6]] => [2,1,2,2,1]
[[1,3,7],[2,4,8],[5],[6]] => [1,2,1,1,2,1]
[[1,2,7],[3,4,8],[5],[6]] => [2,2,1,2,1]
[[1,5,6],[2,7,8],[3],[4]] => [1,1,1,3,2]
[[1,4,6],[2,7,8],[3],[5]] => [1,1,2,2,2]
[[1,3,6],[2,7,8],[4],[5]] => [1,2,1,2,2]
[[1,2,6],[3,7,8],[4],[5]] => [2,1,1,2,2]
[[1,4,5],[2,7,8],[3],[6]] => [1,1,3,3]
[[1,3,5],[2,7,8],[4],[6]] => [1,2,2,3]
[[1,2,5],[3,7,8],[4],[6]] => [2,1,2,3]
[[1,3,4],[2,7,8],[5],[6]] => [1,3,1,3]
[[1,2,4],[3,7,8],[5],[6]] => [2,2,1,3]
[[1,2,3],[4,7,8],[5],[6]] => [3,1,1,3]
[[1,4,6],[2,5,8],[3],[7]] => [1,1,2,2,2]
[[1,3,6],[2,5,8],[4],[7]] => [1,2,3,2]
[[1,2,6],[3,5,8],[4],[7]] => [2,1,3,2]
[[1,3,6],[2,4,8],[5],[7]] => [1,2,1,2,2]
[[1,2,6],[3,4,8],[5],[7]] => [2,2,2,2]
[[1,4,5],[2,6,8],[3],[7]] => [1,1,3,1,2]
[[1,3,5],[2,6,8],[4],[7]] => [1,2,2,1,2]
[[1,2,5],[3,6,8],[4],[7]] => [2,1,2,1,2]
[[1,3,4],[2,6,8],[5],[7]] => [1,3,2,2]
[[1,2,4],[3,6,8],[5],[7]] => [2,2,2,2]
[[1,2,3],[4,6,8],[5],[7]] => [3,1,2,2]
[[1,3,5],[2,4,8],[6],[7]] => [1,2,2,1,2]
[[1,2,5],[3,4,8],[6],[7]] => [2,3,1,2]
[[1,3,4],[2,5,8],[6],[7]] => [1,3,1,1,2]
[[1,2,4],[3,5,8],[6],[7]] => [2,2,1,1,2]
[[1,2,3],[4,5,8],[6],[7]] => [3,2,1,2]
[[1,4,6],[2,5,7],[3],[8]] => [1,1,2,2,1,1]
[[1,3,6],[2,5,7],[4],[8]] => [1,2,3,1,1]
[[1,2,6],[3,5,7],[4],[8]] => [2,1,3,1,1]
[[1,3,6],[2,4,7],[5],[8]] => [1,2,1,2,1,1]
[[1,2,6],[3,4,7],[5],[8]] => [2,2,2,1,1]
[[1,4,5],[2,6,7],[3],[8]] => [1,1,3,2,1]
[[1,3,5],[2,6,7],[4],[8]] => [1,2,2,2,1]
[[1,2,5],[3,6,7],[4],[8]] => [2,1,2,2,1]
[[1,3,4],[2,6,7],[5],[8]] => [1,3,3,1]
[[1,2,4],[3,6,7],[5],[8]] => [2,2,3,1]
[[1,2,3],[4,6,7],[5],[8]] => [3,1,3,1]
[[1,3,5],[2,4,7],[6],[8]] => [1,2,2,2,1]
[[1,2,5],[3,4,7],[6],[8]] => [2,3,2,1]
[[1,3,4],[2,5,7],[6],[8]] => [1,3,1,2,1]
[[1,2,4],[3,5,7],[6],[8]] => [2,2,1,2,1]
[[1,2,3],[4,5,7],[6],[8]] => [3,2,2,1]
[[1,3,5],[2,4,6],[7],[8]] => [1,2,2,1,1,1]
[[1,2,5],[3,4,6],[7],[8]] => [2,3,1,1,1]
[[1,3,4],[2,5,6],[7],[8]] => [1,3,2,1,1]
[[1,2,4],[3,5,6],[7],[8]] => [2,2,2,1,1]
[[1,2,3],[4,5,6],[7],[8]] => [3,3,1,1]
[[1,5,8],[2,6],[3,7],[4]] => [1,1,1,2,3]
[[1,4,8],[2,6],[3,7],[5]] => [1,1,2,2,2]
[[1,3,8],[2,6],[4,7],[5]] => [1,2,1,2,2]
[[1,2,8],[3,6],[4,7],[5]] => [2,1,1,2,2]
[[1,4,8],[2,5],[3,7],[6]] => [1,1,2,1,3]
[[1,3,8],[2,5],[4,7],[6]] => [1,2,2,3]
[[1,2,8],[3,5],[4,7],[6]] => [2,1,2,3]
[[1,3,8],[2,4],[5,7],[6]] => [1,2,1,1,3]
[[1,2,8],[3,4],[5,7],[6]] => [2,2,1,3]
[[1,4,8],[2,5],[3,6],[7]] => [1,1,2,2,2]
[[1,3,8],[2,5],[4,6],[7]] => [1,2,2,1,2]
[[1,2,8],[3,5],[4,6],[7]] => [2,1,2,1,2]
[[1,3,8],[2,4],[5,6],[7]] => [1,2,1,2,2]
[[1,2,8],[3,4],[5,6],[7]] => [2,2,2,2]
[[1,5,7],[2,6],[3,8],[4]] => [1,1,1,2,2,1]
[[1,4,7],[2,6],[3,8],[5]] => [1,1,2,3,1]
[[1,3,7],[2,6],[4,8],[5]] => [1,2,1,3,1]
[[1,2,7],[3,6],[4,8],[5]] => [2,1,1,3,1]
[[1,4,7],[2,5],[3,8],[6]] => [1,1,2,1,2,1]
[[1,3,7],[2,5],[4,8],[6]] => [1,2,2,2,1]
[[1,2,7],[3,5],[4,8],[6]] => [2,1,2,2,1]
[[1,3,7],[2,4],[5,8],[6]] => [1,2,1,1,2,1]
[[1,2,7],[3,4],[5,8],[6]] => [2,2,1,2,1]
[[1,5,6],[2,7],[3,8],[4]] => [1,1,1,3,2]
[[1,4,6],[2,7],[3,8],[5]] => [1,1,2,2,2]
[[1,3,6],[2,7],[4,8],[5]] => [1,2,1,2,2]
[[1,2,6],[3,7],[4,8],[5]] => [2,1,1,2,2]
[[1,4,5],[2,7],[3,8],[6]] => [1,1,3,2,1]
[[1,3,5],[2,7],[4,8],[6]] => [1,2,2,2,1]
[[1,2,5],[3,7],[4,8],[6]] => [2,1,2,2,1]
[[1,3,4],[2,7],[5,8],[6]] => [1,3,1,2,1]
[[1,2,4],[3,7],[5,8],[6]] => [2,2,1,2,1]
[[1,2,3],[4,7],[5,8],[6]] => [3,1,1,2,1]
[[1,4,6],[2,5],[3,8],[7]] => [1,1,2,2,2]
[[1,3,6],[2,5],[4,8],[7]] => [1,2,3,2]
[[1,2,6],[3,5],[4,8],[7]] => [2,1,3,2]
[[1,3,6],[2,4],[5,8],[7]] => [1,2,1,2,2]
[[1,2,6],[3,4],[5,8],[7]] => [2,2,2,2]
[[1,4,5],[2,6],[3,8],[7]] => [1,1,3,1,2]
[[1,3,5],[2,6],[4,8],[7]] => [1,2,2,1,2]
[[1,2,5],[3,6],[4,8],[7]] => [2,1,2,1,2]
[[1,3,4],[2,6],[5,8],[7]] => [1,3,2,2]
[[1,2,4],[3,6],[5,8],[7]] => [2,2,2,2]
[[1,2,3],[4,6],[5,8],[7]] => [3,1,2,2]
[[1,3,5],[2,4],[6,8],[7]] => [1,2,2,1,2]
[[1,2,5],[3,4],[6,8],[7]] => [2,3,1,2]
[[1,3,4],[2,5],[6,8],[7]] => [1,3,1,1,2]
[[1,2,4],[3,5],[6,8],[7]] => [2,2,1,1,2]
[[1,2,3],[4,5],[6,8],[7]] => [3,2,1,2]
[[1,4,7],[2,5],[3,6],[8]] => [1,1,2,3,1]
[[1,3,7],[2,5],[4,6],[8]] => [1,2,2,2,1]
[[1,2,7],[3,5],[4,6],[8]] => [2,1,2,2,1]
[[1,3,7],[2,4],[5,6],[8]] => [1,2,1,3,1]
[[1,2,7],[3,4],[5,6],[8]] => [2,2,3,1]
[[1,4,6],[2,5],[3,7],[8]] => [1,1,2,2,1,1]
[[1,3,6],[2,5],[4,7],[8]] => [1,2,3,1,1]
[[1,2,6],[3,5],[4,7],[8]] => [2,1,3,1,1]
[[1,3,6],[2,4],[5,7],[8]] => [1,2,1,2,1,1]
[[1,2,6],[3,4],[5,7],[8]] => [2,2,2,1,1]
[[1,4,5],[2,6],[3,7],[8]] => [1,1,3,2,1]
[[1,3,5],[2,6],[4,7],[8]] => [1,2,2,2,1]
[[1,2,5],[3,6],[4,7],[8]] => [2,1,2,2,1]
[[1,3,4],[2,6],[5,7],[8]] => [1,3,2,1,1]
[[1,2,4],[3,6],[5,7],[8]] => [2,2,2,1,1]
[[1,2,3],[4,6],[5,7],[8]] => [3,1,2,1,1]
[[1,3,5],[2,4],[6,7],[8]] => [1,2,2,2,1]
[[1,2,5],[3,4],[6,7],[8]] => [2,3,2,1]
[[1,3,4],[2,5],[6,7],[8]] => [1,3,1,2,1]
[[1,2,4],[3,5],[6,7],[8]] => [2,2,1,2,1]
[[1,2,3],[4,5],[6,7],[8]] => [3,2,2,1]
[[1,6,8],[2,7],[3],[4],[5]] => [1,1,1,1,2,2]
[[1,5,8],[2,7],[3],[4],[6]] => [1,1,1,2,3]
[[1,4,8],[2,7],[3],[5],[6]] => [1,1,2,1,3]
[[1,3,8],[2,7],[4],[5],[6]] => [1,2,1,1,3]
[[1,2,8],[3,7],[4],[5],[6]] => [2,1,1,1,3]
[[1,5,8],[2,6],[3],[4],[7]] => [1,1,1,2,1,2]
[[1,4,8],[2,6],[3],[5],[7]] => [1,1,2,2,2]
[[1,3,8],[2,6],[4],[5],[7]] => [1,2,1,2,2]
[[1,2,8],[3,6],[4],[5],[7]] => [2,1,1,2,2]
[[1,4,8],[2,5],[3],[6],[7]] => [1,1,2,1,1,2]
[[1,3,8],[2,5],[4],[6],[7]] => [1,2,2,1,2]
[[1,2,8],[3,5],[4],[6],[7]] => [2,1,2,1,2]
[[1,3,8],[2,4],[5],[6],[7]] => [1,2,1,1,1,2]
[[1,2,8],[3,4],[5],[6],[7]] => [2,2,1,1,2]
[[1,6,7],[2,8],[3],[4],[5]] => [1,1,1,1,3,1]
[[1,5,7],[2,8],[3],[4],[6]] => [1,1,1,2,2,1]
[[1,4,7],[2,8],[3],[5],[6]] => [1,1,2,1,2,1]
[[1,3,7],[2,8],[4],[5],[6]] => [1,2,1,1,2,1]
[[1,2,7],[3,8],[4],[5],[6]] => [2,1,1,1,2,1]
[[1,5,6],[2,8],[3],[4],[7]] => [1,1,1,3,2]
[[1,4,6],[2,8],[3],[5],[7]] => [1,1,2,2,2]
[[1,3,6],[2,8],[4],[5],[7]] => [1,2,1,2,2]
[[1,2,6],[3,8],[4],[5],[7]] => [2,1,1,2,2]
[[1,4,5],[2,8],[3],[6],[7]] => [1,1,3,1,2]
[[1,3,5],[2,8],[4],[6],[7]] => [1,2,2,1,2]
[[1,2,5],[3,8],[4],[6],[7]] => [2,1,2,1,2]
[[1,3,4],[2,8],[5],[6],[7]] => [1,3,1,1,2]
[[1,2,4],[3,8],[5],[6],[7]] => [2,2,1,1,2]
[[1,2,3],[4,8],[5],[6],[7]] => [3,1,1,1,2]
[[1,5,7],[2,6],[3],[4],[8]] => [1,1,1,2,2,1]
[[1,4,7],[2,6],[3],[5],[8]] => [1,1,2,3,1]
[[1,3,7],[2,6],[4],[5],[8]] => [1,2,1,3,1]
[[1,2,7],[3,6],[4],[5],[8]] => [2,1,1,3,1]
[[1,4,7],[2,5],[3],[6],[8]] => [1,1,2,1,2,1]
[[1,3,7],[2,5],[4],[6],[8]] => [1,2,2,2,1]
[[1,2,7],[3,5],[4],[6],[8]] => [2,1,2,2,1]
[[1,3,7],[2,4],[5],[6],[8]] => [1,2,1,1,2,1]
[[1,2,7],[3,4],[5],[6],[8]] => [2,2,1,2,1]
[[1,5,6],[2,7],[3],[4],[8]] => [1,1,1,3,1,1]
[[1,4,6],[2,7],[3],[5],[8]] => [1,1,2,2,1,1]
[[1,3,6],[2,7],[4],[5],[8]] => [1,2,1,2,1,1]
[[1,2,6],[3,7],[4],[5],[8]] => [2,1,1,2,1,1]
[[1,4,5],[2,7],[3],[6],[8]] => [1,1,3,2,1]
[[1,3,5],[2,7],[4],[6],[8]] => [1,2,2,2,1]
[[1,2,5],[3,7],[4],[6],[8]] => [2,1,2,2,1]
[[1,3,4],[2,7],[5],[6],[8]] => [1,3,1,2,1]
[[1,2,4],[3,7],[5],[6],[8]] => [2,2,1,2,1]
[[1,2,3],[4,7],[5],[6],[8]] => [3,1,1,2,1]
[[1,4,6],[2,5],[3],[7],[8]] => [1,1,2,2,1,1]
[[1,3,6],[2,5],[4],[7],[8]] => [1,2,3,1,1]
[[1,2,6],[3,5],[4],[7],[8]] => [2,1,3,1,1]
[[1,3,6],[2,4],[5],[7],[8]] => [1,2,1,2,1,1]
[[1,2,6],[3,4],[5],[7],[8]] => [2,2,2,1,1]
[[1,4,5],[2,6],[3],[7],[8]] => [1,1,3,1,1,1]
[[1,3,5],[2,6],[4],[7],[8]] => [1,2,2,1,1,1]
[[1,2,5],[3,6],[4],[7],[8]] => [2,1,2,1,1,1]
[[1,3,4],[2,6],[5],[7],[8]] => [1,3,2,1,1]
[[1,2,4],[3,6],[5],[7],[8]] => [2,2,2,1,1]
[[1,2,3],[4,6],[5],[7],[8]] => [3,1,2,1,1]
[[1,3,5],[2,4],[6],[7],[8]] => [1,2,2,1,1,1]
[[1,2,5],[3,4],[6],[7],[8]] => [2,3,1,1,1]
[[1,3,4],[2,5],[6],[7],[8]] => [1,3,1,1,1,1]
[[1,2,4],[3,5],[6],[7],[8]] => [2,2,1,1,1,1]
[[1,2,3],[4,5],[6],[7],[8]] => [3,2,1,1,1]
[[1,7,8],[2],[3],[4],[5],[6]] => [1,1,1,1,1,3]
[[1,6,8],[2],[3],[4],[5],[7]] => [1,1,1,1,2,2]
[[1,5,8],[2],[3],[4],[6],[7]] => [1,1,1,2,1,2]
[[1,4,8],[2],[3],[5],[6],[7]] => [1,1,2,1,1,2]
[[1,3,8],[2],[4],[5],[6],[7]] => [1,2,1,1,1,2]
[[1,2,8],[3],[4],[5],[6],[7]] => [2,1,1,1,1,2]
[[1,6,7],[2],[3],[4],[5],[8]] => [1,1,1,1,3,1]
[[1,5,7],[2],[3],[4],[6],[8]] => [1,1,1,2,2,1]
[[1,4,7],[2],[3],[5],[6],[8]] => [1,1,2,1,2,1]
[[1,3,7],[2],[4],[5],[6],[8]] => [1,2,1,1,2,1]
[[1,2,7],[3],[4],[5],[6],[8]] => [2,1,1,1,2,1]
[[1,5,6],[2],[3],[4],[7],[8]] => [1,1,1,3,1,1]
[[1,4,6],[2],[3],[5],[7],[8]] => [1,1,2,2,1,1]
[[1,3,6],[2],[4],[5],[7],[8]] => [1,2,1,2,1,1]
[[1,2,6],[3],[4],[5],[7],[8]] => [2,1,1,2,1,1]
[[1,4,5],[2],[3],[6],[7],[8]] => [1,1,3,1,1,1]
[[1,3,5],[2],[4],[6],[7],[8]] => [1,2,2,1,1,1]
[[1,2,5],[3],[4],[6],[7],[8]] => [2,1,2,1,1,1]
[[1,3,4],[2],[5],[6],[7],[8]] => [1,3,1,1,1,1]
[[1,2,4],[3],[5],[6],[7],[8]] => [2,2,1,1,1,1]
[[1,2,3],[4],[5],[6],[7],[8]] => [3,1,1,1,1,1]
[[1,5],[2,6],[3,7],[4,8]] => [1,1,1,2,2,1]
[[1,4],[2,6],[3,7],[5,8]] => [1,1,2,2,2]
[[1,3],[2,6],[4,7],[5,8]] => [1,2,1,2,2]
[[1,2],[3,6],[4,7],[5,8]] => [2,1,1,2,2]
[[1,4],[2,5],[3,7],[6,8]] => [1,1,2,1,2,1]
[[1,3],[2,5],[4,7],[6,8]] => [1,2,2,2,1]
[[1,2],[3,5],[4,7],[6,8]] => [2,1,2,2,1]
[[1,3],[2,4],[5,7],[6,8]] => [1,2,1,1,2,1]
[[1,2],[3,4],[5,7],[6,8]] => [2,2,1,2,1]
[[1,4],[2,5],[3,6],[7,8]] => [1,1,2,2,2]
[[1,3],[2,5],[4,6],[7,8]] => [1,2,2,1,2]
[[1,2],[3,5],[4,6],[7,8]] => [2,1,2,1,2]
[[1,3],[2,4],[5,6],[7,8]] => [1,2,1,2,2]
[[1,2],[3,4],[5,6],[7,8]] => [2,2,2,2]
[[1,6],[2,7],[3,8],[4],[5]] => [1,1,1,1,2,2]
[[1,5],[2,7],[3,8],[4],[6]] => [1,1,1,2,2,1]
[[1,4],[2,7],[3,8],[5],[6]] => [1,1,2,1,2,1]
[[1,3],[2,7],[4,8],[5],[6]] => [1,2,1,1,2,1]
[[1,2],[3,7],[4,8],[5],[6]] => [2,1,1,1,2,1]
[[1,5],[2,6],[3,8],[4],[7]] => [1,1,1,2,1,2]
[[1,4],[2,6],[3,8],[5],[7]] => [1,1,2,2,2]
[[1,3],[2,6],[4,8],[5],[7]] => [1,2,1,2,2]
[[1,2],[3,6],[4,8],[5],[7]] => [2,1,1,2,2]
[[1,4],[2,5],[3,8],[6],[7]] => [1,1,2,1,1,2]
[[1,3],[2,5],[4,8],[6],[7]] => [1,2,2,1,2]
[[1,2],[3,5],[4,8],[6],[7]] => [2,1,2,1,2]
[[1,3],[2,4],[5,8],[6],[7]] => [1,2,1,1,1,2]
[[1,2],[3,4],[5,8],[6],[7]] => [2,2,1,1,2]
[[1,5],[2,6],[3,7],[4],[8]] => [1,1,1,2,2,1]
[[1,4],[2,6],[3,7],[5],[8]] => [1,1,2,2,1,1]
[[1,3],[2,6],[4,7],[5],[8]] => [1,2,1,2,1,1]
[[1,2],[3,6],[4,7],[5],[8]] => [2,1,1,2,1,1]
[[1,4],[2,5],[3,7],[6],[8]] => [1,1,2,1,2,1]
[[1,3],[2,5],[4,7],[6],[8]] => [1,2,2,2,1]
[[1,2],[3,5],[4,7],[6],[8]] => [2,1,2,2,1]
[[1,3],[2,4],[5,7],[6],[8]] => [1,2,1,1,2,1]
[[1,2],[3,4],[5,7],[6],[8]] => [2,2,1,2,1]
[[1,4],[2,5],[3,6],[7],[8]] => [1,1,2,2,1,1]
[[1,3],[2,5],[4,6],[7],[8]] => [1,2,2,1,1,1]
[[1,2],[3,5],[4,6],[7],[8]] => [2,1,2,1,1,1]
[[1,3],[2,4],[5,6],[7],[8]] => [1,2,1,2,1,1]
[[1,2],[3,4],[5,6],[7],[8]] => [2,2,2,1,1]
[[1,7],[2,8],[3],[4],[5],[6]] => [1,1,1,1,1,2,1]
[[1,6],[2,8],[3],[4],[5],[7]] => [1,1,1,1,2,2]
[[1,5],[2,8],[3],[4],[6],[7]] => [1,1,1,2,1,2]
[[1,4],[2,8],[3],[5],[6],[7]] => [1,1,2,1,1,2]
[[1,3],[2,8],[4],[5],[6],[7]] => [1,2,1,1,1,2]
[[1,2],[3,8],[4],[5],[6],[7]] => [2,1,1,1,1,2]
[[1,6],[2,7],[3],[4],[5],[8]] => [1,1,1,1,2,1,1]
[[1,5],[2,7],[3],[4],[6],[8]] => [1,1,1,2,2,1]
[[1,4],[2,7],[3],[5],[6],[8]] => [1,1,2,1,2,1]
[[1,3],[2,7],[4],[5],[6],[8]] => [1,2,1,1,2,1]
[[1,2],[3,7],[4],[5],[6],[8]] => [2,1,1,1,2,1]
[[1,5],[2,6],[3],[4],[7],[8]] => [1,1,1,2,1,1,1]
[[1,4],[2,6],[3],[5],[7],[8]] => [1,1,2,2,1,1]
[[1,3],[2,6],[4],[5],[7],[8]] => [1,2,1,2,1,1]
[[1,2],[3,6],[4],[5],[7],[8]] => [2,1,1,2,1,1]
[[1,4],[2,5],[3],[6],[7],[8]] => [1,1,2,1,1,1,1]
[[1,3],[2,5],[4],[6],[7],[8]] => [1,2,2,1,1,1]
[[1,2],[3,5],[4],[6],[7],[8]] => [2,1,2,1,1,1]
[[1,3],[2,4],[5],[6],[7],[8]] => [1,2,1,1,1,1,1]
[[1,2],[3,4],[5],[6],[7],[8]] => [2,2,1,1,1,1]
[[1,8],[2],[3],[4],[5],[6],[7]] => [1,1,1,1,1,1,2]
[[1,7],[2],[3],[4],[5],[6],[8]] => [1,1,1,1,1,2,1]
[[1,6],[2],[3],[4],[5],[7],[8]] => [1,1,1,1,2,1,1]
[[1,5],[2],[3],[4],[6],[7],[8]] => [1,1,1,2,1,1,1]
[[1,4],[2],[3],[5],[6],[7],[8]] => [1,1,2,1,1,1,1]
[[1,3],[2],[4],[5],[6],[7],[8]] => [1,2,1,1,1,1,1]
[[1,2],[3],[4],[5],[6],[7],[8]] => [2,1,1,1,1,1,1]
[[1],[2],[3],[4],[5],[6],[7],[8]] => [1,1,1,1,1,1,1,1]
[[1,3,5,7,9],[2,4,6,8,10]] => [1,2,2,2,2,1]
[[1,3,5,7,8],[2,4,6,9,10]] => [1,2,2,3,2]
[[1,3,5,6,9],[2,4,7,8,10]] => [1,2,3,3,1]
[[1,3,5,6,8],[2,4,7,9,10]] => [1,2,3,2,2]
[[1,3,5,6,7],[2,4,8,9,10]] => [1,2,4,3]
[[1,3,4,7,9],[2,5,6,8,10]] => [1,3,3,2,1]
[[1,3,4,7,8],[2,5,6,9,10]] => [1,3,4,2]
[[1,3,4,6,9],[2,5,7,8,10]] => [1,3,2,3,1]
[[1,3,4,6,8],[2,5,7,9,10]] => [1,3,2,2,2]
[[1,3,4,6,7],[2,5,8,9,10]] => [1,3,3,3]
[[1,3,4,5,9],[2,6,7,8,10]] => [1,4,4,1]
[[1,3,4,5,8],[2,6,7,9,10]] => [1,4,3,2]
[[1,3,4,5,7],[2,6,8,9,10]] => [1,4,2,3]
[[1,3,4,5,6],[2,7,8,9,10]] => [1,5,4]
[[1,2,5,7,9],[3,4,6,8,10]] => [2,3,2,2,1]
[[1,2,5,7,8],[3,4,6,9,10]] => [2,3,3,2]
[[1,2,5,6,9],[3,4,7,8,10]] => [2,4,3,1]
[[1,2,5,6,8],[3,4,7,9,10]] => [2,4,2,2]
[[1,2,5,6,7],[3,4,8,9,10]] => [2,5,3]
[[1,2,4,7,9],[3,5,6,8,10]] => [2,2,3,2,1]
[[1,2,4,7,8],[3,5,6,9,10]] => [2,2,4,2]
[[1,2,4,6,9],[3,5,7,8,10]] => [2,2,2,3,1]
[[1,2,4,6,8],[3,5,7,9,10]] => [2,2,2,2,2]
[[1,2,4,6,7],[3,5,8,9,10]] => [2,2,3,3]
[[1,2,4,5,9],[3,6,7,8,10]] => [2,3,4,1]
[[1,2,4,5,8],[3,6,7,9,10]] => [2,3,3,2]
[[1,2,4,5,7],[3,6,8,9,10]] => [2,3,2,3]
[[1,2,4,5,6],[3,7,8,9,10]] => [2,4,4]
[[1,2,3,7,9],[4,5,6,8,10]] => [3,4,2,1]
[[1,2,3,7,8],[4,5,6,9,10]] => [3,5,2]
[[1,2,3,6,9],[4,5,7,8,10]] => [3,3,3,1]
[[1,2,3,6,8],[4,5,7,9,10]] => [3,3,2,2]
[[1,2,3,6,7],[4,5,8,9,10]] => [3,4,3]
[[1,2,3,5,9],[4,6,7,8,10]] => [3,2,4,1]
[[1,2,3,5,8],[4,6,7,9,10]] => [3,2,3,2]
[[1,2,3,5,7],[4,6,8,9,10]] => [3,2,2,3]
[[1,2,3,5,6],[4,7,8,9,10]] => [3,3,4]
[[1,2,3,4,9],[5,6,7,8,10]] => [4,5,1]
[[1,2,3,4,8],[5,6,7,9,10]] => [4,4,2]
[[1,2,3,4,7],[5,6,8,9,10]] => [4,3,3]
[[1,2,3,4,6],[5,7,8,9,10]] => [4,2,4]
[[1,2,3,4,5],[6,7,8,9,10]] => [5,5]
[[1,3,5,7,9,11],[2,4,6,8,10,12]] => [1,2,2,2,2,2,1]
[[1,3,5,7,9,10],[2,4,6,8,11,12]] => [1,2,2,2,3,2]
[[1,3,5,7,8,11],[2,4,6,9,10,12]] => [1,2,2,3,3,1]
[[1,3,5,7,8,10],[2,4,6,9,11,12]] => [1,2,2,3,2,2]
[[1,3,5,7,8,9],[2,4,6,10,11,12]] => [1,2,2,4,3]
[[1,3,5,6,9,11],[2,4,7,8,10,12]] => [1,2,3,3,2,1]
[[1,3,5,6,9,10],[2,4,7,8,11,12]] => [1,2,3,4,2]
[[1,3,5,6,8,11],[2,4,7,9,10,12]] => [1,2,3,2,3,1]
[[1,3,5,6,8,10],[2,4,7,9,11,12]] => [1,2,3,2,2,2]
[[1,3,5,6,8,9],[2,4,7,10,11,12]] => [1,2,3,3,3]
[[1,3,5,6,7,11],[2,4,8,9,10,12]] => [1,2,4,4,1]
[[1,3,5,6,7,10],[2,4,8,9,11,12]] => [1,2,4,3,2]
[[1,3,5,6,7,9],[2,4,8,10,11,12]] => [1,2,4,2,3]
[[1,3,5,6,7,8],[2,4,9,10,11,12]] => [1,2,5,4]
[[1,3,4,7,9,11],[2,5,6,8,10,12]] => [1,3,3,2,2,1]
[[1,3,4,7,9,10],[2,5,6,8,11,12]] => [1,3,3,3,2]
[[1,3,4,7,8,11],[2,5,6,9,10,12]] => [1,3,4,3,1]
[[1,3,4,7,8,10],[2,5,6,9,11,12]] => [1,3,4,2,2]
[[1,3,4,7,8,9],[2,5,6,10,11,12]] => [1,3,5,3]
[[1,3,4,6,9,11],[2,5,7,8,10,12]] => [1,3,2,3,2,1]
[[1,3,4,6,9,10],[2,5,7,8,11,12]] => [1,3,2,4,2]
[[1,3,4,6,8,11],[2,5,7,9,10,12]] => [1,3,2,2,3,1]
[[1,3,4,6,8,10],[2,5,7,9,11,12]] => [1,3,2,2,2,2]
[[1,3,4,6,8,9],[2,5,7,10,11,12]] => [1,3,2,3,3]
[[1,3,4,6,7,11],[2,5,8,9,10,12]] => [1,3,3,4,1]
[[1,3,4,6,7,10],[2,5,8,9,11,12]] => [1,3,3,3,2]
[[1,3,4,6,7,9],[2,5,8,10,11,12]] => [1,3,3,2,3]
[[1,3,4,6,7,8],[2,5,9,10,11,12]] => [1,3,4,4]
[[1,3,4,5,9,11],[2,6,7,8,10,12]] => [1,4,4,2,1]
[[1,3,4,5,9,10],[2,6,7,8,11,12]] => [1,4,5,2]
[[1,3,4,5,8,11],[2,6,7,9,10,12]] => [1,4,3,3,1]
[[1,3,4,5,8,10],[2,6,7,9,11,12]] => [1,4,3,2,2]
[[1,3,4,5,8,9],[2,6,7,10,11,12]] => [1,4,4,3]
[[1,3,4,5,7,11],[2,6,8,9,10,12]] => [1,4,2,4,1]
[[1,3,4,5,7,10],[2,6,8,9,11,12]] => [1,4,2,3,2]
[[1,3,4,5,7,9],[2,6,8,10,11,12]] => [1,4,2,2,3]
[[1,3,4,5,7,8],[2,6,9,10,11,12]] => [1,4,3,4]
[[1,3,4,5,6,11],[2,7,8,9,10,12]] => [1,5,5,1]
[[1,3,4,5,6,10],[2,7,8,9,11,12]] => [1,5,4,2]
[[1,3,4,5,6,9],[2,7,8,10,11,12]] => [1,5,3,3]
[[1,3,4,5,6,8],[2,7,9,10,11,12]] => [1,5,2,4]
[[1,3,4,5,6,7],[2,8,9,10,11,12]] => [1,6,5]
[[1,2,5,7,9,11],[3,4,6,8,10,12]] => [2,3,2,2,2,1]
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Created: Feb 02, 2021 at 19:10 by Martin Rubey
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Last Updated: Feb 03, 2021 at 14:56 by Martin Rubey