AMC 12 2012a Problem 21

Let $a$, $b$, and $c$ be positive integers with $a\ge$ $b\ge$ $c$ such that $$\begin{align*}a^{2}-b^{2}-c^{2}+ab&=2011\text{ and}\\ a^{2}+3b^{2}+3c^{2}-3ab-2ac-2bc&=-1997 \end{align*}$$ What is $a$?

\textbf{(A)}\ 249 \textbf{(B)}\ 250 \textbf{(C)}\ 251 \textbf{(D)}\ 252 \textbf{(E)}\ 253