2009 Cayley Problem 21

A *lattice point* is a point with integer coordinates. (For example, (1,4) is a lattice point but (\frac{3}{2},4) is not.) The line y = 3x - 5 passes through square PQRS as shown in the diagram. If the coordinates of R are (2009, 2009), then the number of lattice points on the line which are inside the square is

\textbf{(A)}\ 666\quad \textbf{(B)}\ 667\quad \textbf{(C)}\ 668\quad \textbf{(D)}\ 669\quad \textbf{(E)}\ 670

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 Cayley contests here.