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: Accepted)

from collections import deque

DIRECTIONS = [(0, 1), (1, 0), (0, -1), (-1, 0)]


def count(start, S, H, W, tested):
    if tested[start[0]][start[1]]:
        return 0
    q = deque()
    q.append((start[0], start[1], "#"))
    white = 0
    black = 0
    while(len(q)):
        i, j, color = q.popleft()
        if tested[i][j]:
            continue
        tested[i][j] = True
        if color == ".":
            white += 1
            ncolor = "#"
        else:  # color == "#":
            black += 1
            ncolor = "."
        for d in DIRECTIONS:
            ni = i + d[0]
            nj = j + d[1]
            if 0 <= ni and ni < H and 0 <= nj and nj < W and S[ni][nj] == ncolor:
                q.append((ni, nj, ncolor))
    return black * white


def main():
    H, W = map(int, input().split())
    S = [input() for _ in range(H)]
    tested = [[False] * W for _ in range(H)]
    retval = 0
    for i in range(H):
        for j in range(W):
            if(S[i][j] == "#"):
                retval += count((i, j), S, H, W, tested)
    print(retval)


if __name__ == "__main__":
    main()