Suppose that $*(n) = \left\{ n-2, n+2, 2n, \frac{n}{2} \right\}$. For example, $*(6) = \{4, 8, 12, 3\}$. For how many distinct integers $n$ does $*(n)$ have exactly three distinct elements?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Suppose that $*(n) = \left\{ n-2, n+2, 2n, \frac{n}{2} \right\}$. For example, $*(6) = \{4, 8, 12, 3\}$. For how many distinct integers $n$ does $*(n)$ have exactly three distinct elements?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
5
Suppose that $*(n) = \left\{ n-2, n+2, 2n, \frac{n}{2} \right\}$. For example, $*(6) = \{4, 8, 12, 3\}$. For how many distinct integers $n$ does $*(n)$ have exactly three distinct elements?
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