Triangles

You packed plenty of puzzle books for the trip to Beijing, and many of them ask questions like this one: how many triangles can you find in Figure 1?

Figure 1: the picture drawn by the second example input.

After a few of them you get bored and start working out how to solve the puzzle with a program instead. Today that program is exactly what you need.

The first line contains two integers r and c ($1 \le r \le 3000$, $1 \le c \le 6000$), the size of the picture, where r is the number of rows of vertices and c is the number of columns of vertices.

The next $2r-1$ lines hold the picture, each with at most $2c-1$ characters. Odd lines contain grid vertices, written as the lowercase letter x, together with zero or more horizontal edges. Even lines contain zero or more diagonal edges. Picture lines numbered $4k+1$ have vertices in positions 1, 5, 9, 13, and so on, while lines numbered $4k+3$ have vertices in positions 3, 7, 11, 15, and so on. A vertex can therefore sit only in one of the c positions 1, 3, 5, ..., $2c-1$. Every possible vertex appears in the input.

A horizontal edge between two neighboring vertices is drawn as three hyphens ---. A diagonal edge is drawn as a single forward slash / or a single backslash \. An edge character sits exactly between the two vertices it joins. Every other position holds a space. Trailing whitespace on a line may be omitted.

Print the number of triangles of any size formed by the drawn edges. All three sides of a triangle must lie on drawn edges, and one side is a run of consecutive edges in the same direction.