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:
# aising2019C - Alternating Path
def dfs(sx: int, sy: int) -> None:
    color = [0] * 2
    s_col = S[sx][sy]
    color[s_col] += 1
    S[sx][sy] = 2  # make the grid visited
    stack = [(sx, sy, s_col)]
    while stack:
        x, y, col = stack.pop()
        for dx, dy in dxy:
            nx, ny = x + dx, y + dy
            if 0 <= nx < H and 0 <= ny < W and S[nx][ny] == col ^ 1:
                stack.append((nx, ny, S[nx][ny]))
                color[S[nx][ny]] += 1
                S[nx][ny] = 2
    return color[0] * color[1]


def main():
    # separate S to connected components
    global H, W, S, dxy, blk, wht
    H, W, *S = open(0).read().split()
    H, W = int(H), int(W)
    S = [[1 if i == "#" else 0 for i in s] for s in S]
    dxy = [(1, 0), (-1, 0), (0, 1), (0, -1)]
    ans = 0
    for i in range(H):
        for j in range(W):
            if S[i][j] != 2:
                ans += dfs(i, j)
    print(ans)


if __name__ == "__main__":
    main()