Not Easy to Cross Bridges!
In the following diagram, let \(A,B,C,D,E\) and \(F\) represent islands and the lines connecting them bridges. A man begins at \(A\) and walks from island to island. He stops for lunch when he cannot continue to walk without crossing the same bridge twice. If \(m\) denotes the number of ways he can take his walk and \(n\) denotes the possible location of his first lunch, what is the value of \(m\) and \(n\)?