Problem: There is a grid with H rows and W columns, where each square is painted black or white.

You are given H strings S_1, S_2, ..., S_H, each of length W. If the square at the i-th row from the top and the j-th column from the left is painted black, the j-th character in the string S_i is `#`; if that square is painted white, the j-th character in the string S_i is `.`.

Find the number of pairs of a black square c_1 and a white square c_2 that satisfy the following condition:

* There is a path from the square c_1 to the square c_2 where we repeatedly move to a vertically or horizontally adjacent square through an alternating sequence of black and white squares: black, white, black, white...

Constraints

* 1 \leq H, W \leq 400
* |S_i| = W (1 \leq i \leq H)
* For each i (1 \leq i \leq H), the string S_i consists of characters `#` and `.`.

Input

Input is given from Standard Input in the following format:


H W
S_1
S_2
:
S_H


Output

Print the answer.

Examples

Input

3 3
.#.
..#
#..


Output

10


Input

3 3
.#.
..#
..


Output

10


Input

2 4
....
....


Output

0


Input

4 3


...


Output

6

Solution (in PYTHON3):

Solution:
t,*grid=open(0)
h,w=map(int,t.split())
vis=[[False]*w for _ in range(h)]
ans=0
for y in range(h):
	for x in range(w):
		if vis[y][x]:
			continue
		q=[(y,x)]
		d={"#":0,".":0}
		while q:
			cy,cx=q.pop(0)
			for ny,nx in ((cy+1,cx),(cy-1,cx),(cy,cx+1),(cy,cx-1)):
				if not (0<=ny<h and 0<=nx<w) or vis[ny][nx] or grid[cy][cx]==grid[ny][nx]:
					continue
				d[grid[ny][nx]]+=1
				vis[ny][nx]=True
				q.append((ny,nx))
		ans+=d["#"]*d["."]
print(ans)