Let $\mathbb{S} =\{a_1,\ a_2,\ \cdots,\ a_n\}$ be a permutation of $\{1,\ 2,\ \cdots,\ n\}$ which satisfies the condition that for every $a_i$, $(i=1$, $2$, $\cdots$, $n)$, there exists an $a_j$ where $i< j \le n$ such that $a_j=a_i+1$ or $a_j=a_i-1$. Find the number of such $\mathbb{S}$.