2014 Pascal Problem 22

A rectangular flag is divided into four triangles, labelled Left, Right, Top, and Bottom, as shown. Each triangle is to be coloured one of red, white, blue, green, and purple so that no two triangles that share an edge are the same colour. How many different flags can be made?

\textbf{(A)}\ 180\quad \textbf{(B)}\ 200\quad \textbf{(C)}\ 220\quad \textbf{(D)}\ 240\quad \textbf{(E)}\ 260

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.