In 2016, Jiayuan fell in love with a game called "Bomb Man." Simply put, the game involves placing several bombs on a map to see if you can hit your opponent or avoid their bombs. While playing, Xiao H thought of the following problem: given a map, what is the maximum number of bombs that can be placed such that no two bombs can hit each other? The range of a bomb covers the row and column it is placed in. The power of a bomb can penetrate soft stones but cannot penetrate hard stones.

Given an $n \times m$ grid map: `represents an empty space. The bomb's power can penetrate it, and a bomb can be placed here. *xrepresents a soft stone. The bomb's power can penetrate it, but a bomb cannot be placed here. *#` represents a hard stone. The bomb's power cannot penetrate it, and a bomb cannot be placed here.

For example, given a $1 \times 4$ grid map *xx*, at most one bomb can be placed on this map. Given another $1 \times 4$ grid map *x#*, at most two bombs can be placed on this map.

Now, given an arbitrary $n \times m$ grid map, find the maximum number of bombs that can be placed.

Input

The first line contains two positive integers $n$ and $m$, representing the number of rows and columns of the map, respectively. $1 \le n, m \le 50$.

The next $n$ lines each contain $m$ characters, representing the grid map.

Output

Output a single integer $a$, representing the maximum number of bombs that can be placed.

Constraints

For 20% of the data, the number of * does not exceed 20. For 100% of the data, the number of * does not exceed $n \times m$.

Examples

Input 1

4 4
#***
*#**
**#*
xxx#

Output 1

5