2000 Gauss 7 Problem 15

In the diagram, all rows, columns and diagonals have the sum 12. What is the sum of the four corner numbers?

\begin{array}{|c|c|c|}\hline \phantom{4} & \phantom{4} & 4 \\ \hline \phantom{4} & 4 & \phantom{4} \\ \hline \phantom{4} & 3 & \phantom{4} \\ \hline \end{array}

\textbf{(A)}\ 14\quad \textbf{(B)}\ 15\quad \textbf{(C)}\ 16\quad \textbf{(D)}\ 17\quad \textbf{(E)}\ 12

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Gauss contests here.