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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