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:
H,W = map(int, input().split())
grid = [-1] * (W+4) * 2
black_ind = []
for _ in range(H):
	grid += [-1]*2
	I = input()
	for i in range(W):
		if I[i] == '#':
			grid.append(1)
			black_ind.append(len(grid)-1)
		else:
			grid.append(0)
	grid += [-1]*2

grid += [-1] * (W+4) * 2

move = [1,-1,W+4,-(W+4)]
ans = 0
for b in black_ind:
	if grid[b] == 2:
		continue
	cnt_b = 1
	cnt_w = 0
	q = [b]
	grid[b] = 2
	while q:
		cp = q.pop()
		if grid[cp] == 2:
			for d in move:
				if grid[cp+d] == 0:
					grid[cp+d] = 3
					cnt_w += 1
					q.append(cp+d)
		elif grid[cp] == 3:
			for d in move:
				if grid[cp+d] == 1:
					grid[cp+d] = 2
					cnt_b += 1
					q.append(cp+d)

	ans += cnt_b * cnt_w
print(ans)