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 collections import deque

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


di = (1, 0, -1, 0)
dj = (0, 1, 0, -1)
visited = [[False] * W for _ in range(H)]

result = 0
for i in range(H):
    for j in range(W):

        if visited[i][j]:
            continue
        visited[i][j] = True

        b, w = 0, 0

        que = deque([(i, j)])
        while que:
            (ci, cj) = que.pop()
            if S[ci][cj] == '#':
                b += 1
            else:
                w += 1

            for d in range(4):

                ni, nj = ci + di[d], cj + dj[d]
                if not (0 <= ni < H and 0 <= nj < W):
                    continue

                if S[ci][cj] == S[ni][nj]:
                    continue

                if visited[ni][nj]:
                    continue
                visited[ni][nj] = True

                que.append((ni, nj))

        result += b * w


print(result)