Question 12
Let $A,$ $M,$ and $C$ be nonnegative integers such that $A + M + C = 12.$ What is the maximum value of $$
\begin{aligned} &A \cdot M \cdot C + A \cdot M \\ &\quad {}+ M \cdot C + C \cdot A? \end{aligned}
$$
\begin{aligned} &A \cdot M \cdot C + A \cdot M \\ &\quad {}+ M \cdot C + C \cdot A? \end{aligned}
$$