For a finite set M we define the power set of M to be the set of all subsets of M, and we denote the power set of M by P(M). For a set M with 4 elements, determine the number of functions f: P(M) \rightarrow P(M) that satisfy the relation
f(A) \cup f(B)=f(A \cup B)
for any sets A, B \in P(M).