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())
s = [[''] * (w + 2)]
s += [[''] + list(input()) + [''] for _ in range(h)]
s += [[''] * (w + 2)]
m = [[1] * (w + 2)]
m += [[1] + [0] * w + [1] for _ in range(h)]
m += [[1] * (w + 2) for _ in range(h + 2)]
ans = 0
for i in range(1, h + 1):
    for j in range(1, w + 1):
        if m[i][j] == 1:
            continue
        m[i][j] = 1
        qs = [[i, j]]
        white = 0
        black = 0
        while len(qs) != 0:
            q = qs.pop(0)
            if s[q[0]][q[1]] == '.':
                white += 1
            else:
                black += 1
            m[q[0]][q[1]] = 1
            for k in [[1, 0], [-1, 0], [0, 1], [0, -1]]:
                if m[q[0] + k[0]][q[1] + k[1]] == 0 and s[q[0]][q[1]] != s[q[0] + k[0]][q[1] + k[1]]:
                    m[q[0] + k[0]][q[1] + k[1]] = 1
                    qs.append([q[0] + k[0], q[1] + k[1]])
        ans += black * white
print(ans)