Given an *n*×*n*×*n* cube divided into
*n*^{3} unit cubes if A and B are oppposite vertices,
a legal path from A to B must be on the surface of the cube and be
along line segments. One must always be getting closer to B (in other
words, one can move up, but not down, right, but not left, and toward
the viewer, but not away from the viewer).

A sample legal path is shown when *n* = 3. How many legal paths
are there for an *n*×*n*×*n* cube?

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