Circles Ringed Between Concentric Circles

Two concentric circles $C_1$ and $C_2$ have radii $3$ and $5$, respectively. Jerome draws $n$ circles of radius $1$ in the region inside $C_2$ but outside $C_1$ such that any two of the $n$ circles do not intersect, and each circle touches $C_1$ and $C_2$. For how many integers $n$ in the set $\{6, 8, 12\}$ is this possible?