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 = [list(input()) for _ in range(h)]
check = [[0] * w for _ in range(h)]
move = [[1, 0], [-1, 0], [0, 1], [0, -1]]
ans = 0

for i in range(h):
    for j in range(w):
        if check[i][j] == 1:
            continue
        black, white = 0, 0 

        stack = [[i, j]]
        check[i][j] = 1
        if s[i][j] == '#':
            black += 1
        else:
            white += 1

        while len(stack) > 0:
            x, y = stack.pop()
            tmp = s[x][y]
            for dx, dy in move:
                nx, ny = x + dx, y + dy
                if 0 <= nx < h and 0 <= ny < w and tmp != s[nx][ny] and check[nx][ny] == 0:
                    stack.append([nx, ny])
                    check[nx][ny] = 1
                    if s[nx][ny] == '#':
                        black += 1
                    else:
                        white += 1

        ans += black * white

print(ans)

# %%