1999 Gauss 8 Problem 9

André is hiking on the paths shown in the map. He is planning to visit sites A to M in alphabetical order. He can never retrace his steps and he must proceed directly from one site to the next. What is the largest number of labelled points he can visit before going out of alphabetical order?

\textbf{(A)}\ 6\quad \textbf{(B)}\ 7\quad \textbf{(C)}\ 8\quad \textbf{(D)}\ 10\quad \textbf{(E)}\ 13

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 Gauss contests here.