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 (7.3.0) (judge verdict: Time Limit Exceeded)

from collections import deque

h, w = map(int, input().split())
s = [list(map(str, input().rstrip())) for _ in range(h)]


moves = ((1, 0), (-1, 0), (0, 1), (0, -1))

ans = 0

for i in range(h):
    for j in range(w):
        if s[i][j] == "#":
            grid = [[0] * w for _ in range(h)]
            q = deque([(i, j)])
            grid[i][j] = 1
            while q:
                curr = q.popleft()
                cx, cy = curr[0], curr[1]
                for (mx, my) in moves:
                    if 0 <= cx + mx < h and 0 <= cy + my < w and grid[cx + mx][cy + my] == 0:
                        if s[cx][cy] != s[cx + mx][cy + my]:
                            q.append((cx + mx, cy + my))
                            if s[cx + mx][cy + my] == ".":
                                grid[cx + mx][cy + my] = 2
            grid = sum(grid, [])
            ans += grid.count(2)
            continue

print(ans)