Problem:
Score : 300 points

Problem Statement

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.

Sample Input 1

3 3
.#.
..#
#..

Sample Output 1

10

Some of the pairs satisfying the condition are ((1, 2), (3, 3)) and ((3, 1), (3, 2)), where (i, j) denotes the square at the i-th row from the top and the j-th column from the left.

Sample Input 2

2 4
....
....

Sample Output 2

0

Sample Input 3

4 3
###
###
...
###

Sample Output 3

6

Solution in PyPy3 (2.4.0) (judge verdict: Time Limit Exceeded)

def c_alternating_path(H, W, Grid):
    from collections import deque
    ans = 0
    for h in range(H):
        for w in range(W):
            if Grid[h][w] == '#':
                is_visit = [[False] * W for _ in range(H)]
                q = deque([(h, w)])
                while q:
                    row, col = q.pop()
                    if is_visit[row][col]:
                        continue
                    is_visit[row][col] = True
                    if Grid[row][col] == '.':
                        ans += 1
                    for dr, dc in zip((1, 0, -1, 0), (0, 1, 0, -1)):
                        nr, nc = row + dr, col + dc
                        if (0 <= nr < H and 0 <= nc < W
                                and Grid[row][col] != Grid[nr][nc]
                                and not is_visit[nr][nc]):
                            q.appendleft((nr, nc))
    return ans

H, W = [int(i) for i in input().split()]
Grid = [input() for _ in range(H)]
print(c_alternating_path(H, W, Grid))