2016 AMC 10A Problem 14

How many ways are there to write 2016 as the sum of twos and threes, ignoring order? (For example, 1008\cdot 2 + 0\cdot 3 and 402\cdot 2 + 404\cdot 3 are two such ways.)

\textbf{(A)}\ 236\qquad\textbf{(B)}\ 336\qquad\textbf{(C)}\ 337\qquad\textbf{(D)}\ 403\qquad\textbf{(E)}\ 672

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.