At summer camp, there are $20$ campers in each of the swimming class, the archery class, and the rock climbing class. Each camper is in at least one of these classes. If $4$ campers are in all three classes, and $24$ campers are in exactly one of the classes, find the number of campers who are in exactly two classes.

Let's think step by step and output the final answer within \boxed{}.
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