# Alternating Permutation

Level pending

How many permutation of the set $$\{1, 2, 3, ..., 18\}$$ is an alternating permutation with number $$9$$ as its first element?

Note that permutation $$(9, 10, 8, 11, 7, 12, 6, 13, 5, 14, 4, 15, 3, 16, 2, 17, 1, 18)$$ is an alternating permutation but $$(9, 8, 18, 7, 17, 6, 16, 5, 15, 4, 14, 3, 13, 2, 12, 1, 11, 10)$$ is not.

Write only the first $$3$$ digits of the answer!

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