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())

field = [["@"] * (w + 2)] + [list("@"+input()+"@") for _ in range(h)] + [["@"] * (w + 2)]
direction = [(0, -1), (0, 1), (1, 0), (-1, 0)]

flip = {".": "#", "#": "."}

def count_up(i, j):
    que = [(i, j)]
    cnt = {".": 0, "#": 0}
    while que:
        i, j = que.pop()
        now = field[i][j]
        field[i][j] = "@"
        fliped_chip = flip.get(now)
        if fliped_chip is not None:
            cnt[now] += 1
        for d in direction:
            dx, dy = d
            nx, ny = j + dx, i + dy
            next_chip = field[ny][nx]
            if next_chip == fliped_chip:
                que.append((ny, nx))
    return cnt

cnt = [[0] * w for _ in range(h)]
result = 0
for i in range(1, h + 1):
    for j in range(1, w + 1):
        dot_sharp = count_up(i, j)
        result += (dot_sharp["."] * dot_sharp["#"])
print(result)
#
#
# print("\n".join(map("".join, field)))
#
#