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:
import itertools

h, w = map(int, input().split())
s = [input() for _ in range(h)]

diffs = [(0, 1), (0, -1), (1, 0), (-1, 0)]
t = [[0] * w for _ in range(h)]
group = 1
for i, j in itertools.product(range(h), range(w)):
    if t[i][j] != 0:
        continue

    stack = [(i, j)]
    while stack:
        x, y = stack.pop()
        t[x][y] = group
        for dx, dy in diffs:
            nx = x + dx
            ny = y + dy
            if 0 <= nx < h and 0 <= ny < w and t[nx][ny] == 0 and s[x][y] != s[nx][ny]:
                stack.append((nx, ny))
    group += 1

d = [[0] * 2 for _ in range(group)]
for i, j in itertools.product(range(h), range(w)):
    d[t[i][j]][0 if s[i][j] == '.' else 1] += 1

ans = sum(d[i][0] * d[i][1] for i in range(len(d)))
print(ans)