Function $C$ is defined on positive integers as follows: \[C(n) = \begin{cases} \dfrac n 2 & \text{if $n$ is even}, \\ 3n+1 & \text{if $n$ is odd}. \end{cases}\]Find the smallest positive integer $m$ such that $C^{m}(9) = 1$. What does this notation mean?
