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)

import sys
sys.setrecursionlimit(1000000)

def main():
    h, w = map(int, input().split())
    mp = ["X" * (w + 2)] + ["X" + input() + "X" for _ in range(h)] + ["X" * (w + 2)]
    checked = [[False] * (w + 2) for _ in range(h + 2)]
    vec = ((1, 0), (0, -1), (-1, 0), (0, 1))


    def search(x, y):
        checked[y][x] = True
        if mp[y][x] == "#":
            b_cnt = 1
            w_cnt = 0
            another = "."
        else:
            b_cnt = 0
            w_cnt = 1
            another = "#"
        for dx, dy in vec:
            nx, ny = x + dx, y + dy
            if not checked[ny][nx] and mp[ny][nx] == another:
                w_add, b_add = search(nx, ny)
                w_cnt += w_add
                b_cnt += b_add
        return w_cnt, b_cnt

    ans = 0
    for y in range(1, h + 1):
        for x in range(1, w + 1):
            if not checked[y][x]:
                w_cnt, b_cnt = search(x, y)
                ans += w_cnt * b_cnt

    print(ans)

main()