Let $n\in \mathbb{Z}_{> 0}$. The  set $S$ contains all positive integers written in decimal form that simultaneously satisfy the following conditions:
[list=1][*] each element of $S$ has exactly $n$ digits;
[*] each element of $S$ is divisible by $3$;
[*] each element of $S$ has all its digits from the set $\{3,5,7,9\}$ [/list]
Find $\mid S\mid$