RO-NMO 2006 Problem 101

Let $M$ be a set composed of $n$ elements and let $\mathcal P (M)$ be its power set. Find all functions $f : \mathcal P (M) \to \{ 0,1,2,\ldots,n \}$ that have the properties

(a) $f(A) \neq 0$ , for $A \neq \phi$ ;

(b) $f \left( A \cup B \right) = f \left( A \cap B \right) + f \left( A \Delta B \right)$ , for all $A,B \in \mathcal P (M)$ , where $A \Delta B = \left( A \cup B \right) \backslash \left( A \cap B \right)$ .