Each cell of a $n \times m$ board either contains a turret or is empty. When a turret is activated, it instantly shoots in each of the four directions, north, east, south and west. If a turret is hit by another turret, it is activated and then destroyed. Turrets have infinitely long range.

You are given a board with some turrets in it. How many existing turrets can you destroy by placing a new turret in an empty cell and activating it?

Input

The first line of the input contains two integers, $n$ and $m$, the height and width of the board. Each of the next $n$ lines contain $m$ characters. + denotes that the cell is occupied by a turret and . denotes that the cell is empty.

There is at least one empty cell.

Output

Output one integer, the maximum number of existing turrets you can destroy.

Constraints

• $1 \le n, m \le 1000$

Examples

Input:

3 4
++..
+...
..++

Output:

5

Input:

4 5
++...
..+..
....+
...++

Output:

5