Question 22Let $(a_1,a_2,\ldots,a_{10})$ be a list of the first $10$ positive integers such that for each $2\le i\le10$ either $a_i + 1$ or $a_i-1$ or both appear somewhere before $a_i$ in the list. How many such lists are there?$ \ 120 $$ 512 $$ \ 1024 $$181{,}440$$362{,}880$