2010 Pascal Problem 9

The nine interior intersection points on a 4 by 4 grid of squares are shown. How many interior intersection points are there on a 12 by 12 grid of squares?

\textbf{(A)}\ 100\quad \textbf{(B)}\ 121\quad \textbf{(C)}\ 132\quad \textbf{(D)}\ 144\quad \textbf{(E)}\ 169

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 Pascal contests here.