A software system tracks four types of user permissions: Read ($R$), Write ($W$), Execute ($X$), and Admin ($A$) over a universal set of 200 users. Every user has at least one permission. The sets $R, W, X,$ and $A$ each contain exactly 110 users. For any two of these sets, their intersection contains exactly 60 users. For any three of these sets, their intersection contains exactly 35 users. The intersection of all four sets contains exactly 20 users. How many users have exactly two permissions?