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:
from itertools import product
H, W = map(int, input().split())
s = [input() for _ in range(H)]
visited = [[0]*W for _ in range(H)]
ans = 0

for y, x in product(range(H), range(W)):
    if visited[y][x]:
        continue
    visited[y][x] = 1
    w, b = 0, 0
    if s[y][x] == '#':
        b += 1
    else:
        w += 1
    stack = [(y, x)]

    while stack:
        cy, cx = stack.pop()
        for dy, dx in ((cy+1, cx), (cy-1, cx), (cy, cx+1), (cy, cx-1)):
            if not (0 <= dy < H and 0 <= dx < W) or visited[dy][dx] or s[cy][cx] == s[dy][dx]:
                continue
            visited[dy][dx] = 1
            if s[dy][dx] == '#':
                b += 1
            else:
                w += 1
            stack.append((dy, dx))

    ans += w * b

print(ans)