Let $m$ be a positive integer, and suppose that $9$ is its own inverse $\pmod m$, but $3$ is $\textbf{not}$ its own inverse $\pmod m$.

How many possible values for $m$ are there?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $m$ be a positive integer, and suppose that $9$ is its own inverse $\pmod m$, but $3$ is $\textbf{not}$ its own inverse $\pmod m$.

How many possible values for $m$ are there?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
6
Let $m$ be a positive integer, and suppose that $9$ is its own inverse $\pmod m$, but $3$ is $\textbf{not}$ its own inverse $\pmod m$.

How many possible values for $m$ are there?
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