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 = list(map(int, input().split()))
sss = ['x' * (w + 2)] + list('x' + input() + 'x' for _ in range(h)) + ['x' * (w + 2)]
checked = [[False] * (w + 2) for _ in range(h + 2)]
ans = 0
move = [(1, 0), (-1, 0), (0, 1), (0, -1)]


def dfs(i, j):
    w_cnt, b_cnt = 0, 0
    q = [(i, j, sss[i][j] == '.')]
    while q:
        y, x, is_white = q.pop()
        if checked[y][x]:
            continue
        checked[y][x] = True
        if is_white:
            w_cnt += 1
        else:
            b_cnt += 1

        for di, dj in move:
            ni = y + di
            nj = x + dj
            if checked[ni][nj]:
                continue
            nc = sss[ni][nj]
            if nc == 'x':
                continue
            elif (nc == '.') == is_white:
                continue
            else:
                q.append((ni, nj, nc == '.'))
    return w_cnt * b_cnt


for i in range(1, h + 1):
    for j in range(1, w + 1):
        if checked[i][j]:
            continue
        ans += dfs(i, j)
print(ans)