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 Python (3.4.3) (judge verdict: Time Limit Exceeded)

from collections import deque
H, W = list(map(int, input().split()))
dx = [-1, 1, 0, 0]
dy = [0, 0, -1, 1]
used = [[False for i in range(W)] for j in range(H)]
S = []
for i in range(H):
        S.append(input())
b = 0
w = 0
ans = 0
for i in range(H):
    for j in range(W):
        q = deque()
        used[i][j] = True
        q.append([i, j])
        b = 0
        w = 0
        while len(q) != 0:
            tmp = q.pop()
            if S[tmp[0]][tmp[1]] == '#':
                b += 1
            else:
                w += 1
            for k in range(4):
                if tmp[0] + dx[k] > H - 1 or tmp[1] + dy[k] > W - 1 or tmp[0] + dx[k] < 0 or tmp[1] + dy[k] < 0:
                    continue
                if S[tmp[0] + dx[k]][tmp[1] + dy[k]] == S[tmp[0]][tmp[1]]:
                    continue
                if used[tmp[0] + dx[k]][tmp[1] + dy[k]]:
                    continue
                used[tmp[0] + dx[k]][tmp[1] + dy[k]] = True
                q.append([tmp[0] + dx[k], tmp[1] + dy[k]])
        ans += b * w
print(ans)