An equilateral triangle ABC has sides of length n, a positive integer. Divide the triangle into equilateral triangles of length 1, drawing parallel lines (at distance 1) to all sides of the triangle. A path is a continuous path, starting at the triangle with vertex A and always crossing from one small triangle to another on the side that both triangles share, in such a way that it never passes through a small triangle twice. Find the maximum number of triangles that can be visited. combinatorial geometrycombinatorics