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: Accepted)

import sys
input = sys.stdin.readline
from collections import deque

def main():
    h, w = map(int, input().split())
    tizu = [input().strip() for _ in range(h)]
    directions = [[-1, 0], [1, 0], [0, -1], [0, 1]]
    used = [[False for _ in range(w)] for _ in range(h)]
    
    ans = 0
    for i in range(h):
        for j in range(w):
            if used[i][j]:
                continue
            used[i][j] = True
            queue = deque()
            queue.append([i, j])
            queue.append(tizu[i][j])
            b_cnt = 0
            w_cnt = 0
            while queue:
                pos = queue.popleft()
                bw = queue.popleft()
                if bw == "#":
                    b_cnt += 1
                else:
                    w_cnt += 1
                for dy, dx in directions:
                    ny = dy + pos[0]
                    nx = dx + pos[1]
                    if ny == -1 or ny == h or nx == -1 or nx == w:
                        continue
                    if used[ny][nx]:
                        continue
                    bw2 = tizu[ny][nx]
                    if bw == bw2:
                        continue
                    used[ny][nx] = True
                    queue.append([ny, nx])
                    queue.append(bw2)
            ans += b_cnt * w_cnt
    print(ans)

main()