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
H,W =list(map(int, input().split()))
S = [list(input()) for i in range(H)]
sys.setrecursionlimit(1000000)

black_visited_flag = [[False] * W for _ in range(H)] 

other_color = {".": "#", "#":'.'}

def dfs(i,j, color):
    num = 0
    black_num = 0
    #import IPython;IPython.embed()
    if i != 0:
        if S[i-1][j] == other_color[color] and not visit_flag[i-1][j]:
            visit_flag[i-1][j] = True
            _num, _black_num = dfs(i-1, j, other_color[color])
            num += _num
            black_num += _black_num
            if other_color[color] == "#":
                black_num += 1
                black_visited_flag[i-1][j] = True
            else:
                num += 1
    if i != H-1:
        if S[i+1][j] == other_color[color] and not visit_flag[i+1][j]:
            visit_flag[i+1][j] = True
            _num, _black_num = dfs(i+1, j, other_color[color])
            num += _num
            black_num += _black_num
            if other_color[color] == "#":
                black_num += 1
                black_visited_flag[i+1][j] = True
            else:
                num += 1
    if j != 0:
        if S[i][j-1] == other_color[color] and not visit_flag[i][j-1]:
            visit_flag[i][j-1] = True
            _num, _black_num = dfs(i, j -1, other_color[color])
            num += _num
            black_num += _black_num
            if other_color[color] == "#":
                black_num += 1
                black_visited_flag[i][j-1] = True
            else:
                num += 1
    if j != W-1:
        if S[i][j+1] == other_color[color] and not visit_flag[i][j+1]:
            visit_flag[i][j+1] = True
            _num, _black_num = dfs(i, j+1, other_color[color])
            num += _num
            black_num += _black_num
            if other_color[color] == "#":
                black_num += 1
                black_visited_flag[i][j+1] = True
            else:
                num += 1
    return num, black_num



ans = 0
for i, row in enumerate(S):
    for j, val in enumerate(row):
        if black_visited_flag[i][j] or S[i][j] == ".":
            continue
        visit_flag = [[False] * W for _ in range(H)] 
        num, black_num = dfs(i,j, "#")
        ans += (num * black_num)

print(ans)