For your trip to Beijing, you have brought plenty of puzzle books, many of them containing challenges like the following: how many triangles can be found in Figure 1?

While these puzzles keep your interest for a while, you quickly get bored with them and instead start thinking about how you might solve them algorithmically. Who knows, maybe a problem like that will actually be used in this year’s contest. Well, guess what? Today is your lucky day!

The first line of input contains two integers $r$ and $c$ ($1
\leq r \le 3\, 000$, $1
\le c \leq 6\, 000$), specifying the picture size, where
$r$ is the number of rows
of vertices and $c$ is the
number of columns. Following this are $2r-1$ lines, each of them having at
most $2c-1$ characters.
Odd lines contain grid vertices (represented as lowercase
`x` characters) and zero or more
horizontal edges, while even lines contain zero or more
diagonal edges. Specifically, picture lines with numbers
$4k+1$ have vertices in
positions $1, 5, 9, 13, \ldots
$ while lines with numbers $4k+3$ have vertices in positions
$3, 7, 11, 15, \ldots
$ . All possible vertices are represented in the
input (for example, see how Figure 1 is represented in
Sample Input 2). Horizontal edges connecting neighboring
vertices are represented by three dashes. Diagonal edges are
represented by a single forward slash (‘`/`’) or backslash (‘`\`’) character. The
edge characters will be placed exactly between the
corresponding vertices. All other characters will be space
characters. Note that if any input line could contain trailing
whitespace, that whitespace may be omitted.

Display the number of triangles (of any size) formed by grid edges in the input picture.

Sample Input 1 | Sample Output 1 |
---|---|

3 3 x---x \ / x / \ x x |
1 |

Sample Input 2 | Sample Output 2 |
---|---|

4 10 x x---x---x x \ / / \ x x---x x x / \ / \ \ x x---x---x---x / / \ \ / \ x---x---x---x---x |
12 |