Given a finite set S \subset \mathbb{R}^{3}, define f(S) to be the mininum integer k such that there exist k planes that divide \mathbb{R}^{3} into a set of regions, where no region contains more than one point in S. Suppose that
M(n)=\max \{f(S):|S|=n\} \text { and } m(n)=\min \{f(S):|S|=n\}
Evaluate M(200) \cdot m(200).