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:
def main():
	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, grid[y][x])]
			d = {"#": 0, ".": 0}
			while q:
				cy, cx, cc = 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 cc == grid[ny][nx]:
						continue
					nc = grid[ny][nx]
					d[nc] += 1
					vis[ny][nx] = True
					q.append((ny, nx, nc))
			ans += d["#"] * d["."]
	print(ans)

if __name__=="__main__":
	main()