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)

import queue
H, W = map(int, input().split())
S = [list(map(int, input().replace(".", "0").replace("#","1"))) for h in range(H)]

Search = [(-1, 0), (0, -1), (1, 0), (0, 1)]
Total = 0
Visited = [[False for w in range(W)] for h in range(H)]
for h in range(H):
    for w in range(W):
        if not Visited[h][w]:
            Visited[h][w] = True
            Color = ([1, 0] if S[h][w] == 0 else [0, 1])
            Q = queue.Queue()
            Q.put((h, w, S[h][w]))
            while not Q.empty():
                nh, nw, nc = Q.get()
                for s in Search:
                    nexth, nextw = nh + s[0], nw + s[1]
                    if 0 <= nexth < H and 0 <= nextw < W:
                        if not Visited[nexth][nextw] and S[nexth][nextw] != nc:
                            nextc = S[nexth][nextw]
                            Visited[nexth][nextw] = True
                            Q.put((nexth, nextw, nextc))
                            Color[nextc] += 1
            Total += Color[0] * Color[1]

print(Total)