Matt is asked to write the numbers from 1 to 10 in order, but he forgets how to count.  He writes a permutation of the numbers $\{1, 2, 3\ldots , 10\}$ across his paper such that:
[list]
[*]The leftmost number is 1.
[*]The rightmost number is 10.
[*]Exactly one number (not including 1 or 10) is less than both the number to its immediate left and the number to its immediate right.[/list]
How many such permutations are there?

Let's think step by step and output the final answer within \boxed{}.
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