2012 AMC 12B Problem 18

Let (a_1,a_2, \ldots ,a_{10}) be a list of the first 10 positive integers such that for each 2 \le i \le 10 either a_i+1 or a_i-1 or both appear somewhere before a_i in the list. How many such lists are there?

\textbf{(A)}\ 120\qquad\textbf{(B)}\ 512\qquad\textbf{(C)}\ 1024\qquad\textbf{(D)}\ 181,440\qquad\textbf{(E)}\ 362,880

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.