AMC 12 2012b Problem 18

Let $(a_1,a_2, \dots ,a_{10})$ 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 \textbf{(B)}\ 512 \textbf{(C)}\ 1024 \textbf{(D)}\ 181,440 \textbf{(E)}\ 362,880