HELP FOR 25 POINTS!
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?