2022 Pascal Problem 10

On the map shown, there are a number of routes from Mathville to Algebratown.

Each route must travel along the roads in the direction marked by the arrows. The total number of routes from Mathville to Algebratown is

\textbf{(A)}\ 3\quad \textbf{(B)}\ 4\quad \textbf{(C)}\ 8\quad \textbf{(D)}\ 6\quad \textbf{(E)}\ 10

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.