AMC 12 2000 Problem 12

Let $A, M,$ and $C$ be nonnegative integers such that $A + M + C=12$. What is the maximum value of $A \cdot M \cdot C + A \cdot M + M \cdot C + A \cdot C$?

\textbf{(A)}\ 62 \textbf{(B)}\ 72 \textbf{(C)}\ 92 \textbf{(D)}\ 102 \textbf{(E)}\ 112