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 = [int(_) for _ in input().split()]
S = [input() for _ in range(H)]
is_searched = [[False for _ in range(W)] for _ in range(H)]


def dfs(p, q):
    if is_searched[p][q] == 1:
        return 0
    count = {'#': 0, '.': 0}
    stack = [[p, q]]
    while stack:
        x, y = stack.pop()
        if is_searched[x][y] != 1:
            is_searched[x][y] = 1
            count[S[x][y]] += 1
            dxy = [[-1, 0], [1, 0], [0, -1], [0, 1]]
            for dx, dy in dxy:
                nx, ny = x + dx, y + dy
                if 0 <= nx < H and 0 <= ny < W and S[x][y] != S[nx][ny]:
                    stack += [[nx, ny]]
    return count['#'] * count['.']


print(sum([dfs(i, j) for i, j in itertools.product(range(H), range(W))]))