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: Accepted)

dy = (-1,0,1,0)
dx = (0,1,0,-1)

h,w = map(int,input().split())
grid = [input() for _ in range(h)]

ans = 0
dist = [[-1] * w for _ in range(h)]
for i in range(h):
    for j in range(w):
        if dist[i][j] < 0:
            odd = 0
            even = 1
            dist[i][j] = 0
            stack = [(i,j)]
            while stack:
                a,b = stack.pop()
                if grid[a][b] == '#':
                    for k in range(4):
                        y = a + dy[k]
                        x = b + dx[k]
                        if y < 0 or y >= h:
                            continue
                        if x < 0 or x >= w:
                            continue
                        if grid[y][x] == '.' and dist[y][x] < 0:
                            if dist[a][b] == 0:
                                dist[y][x] = 1
                                odd += 1
                            else:
                                dist[y][x] = 0
                                even += 1
                            stack.append((y,x))
                else:
                    for k in range(4):
                        y = a + dy[k]
                        x = b + dx[k]
                        if y < 0 or y >= h:
                            continue
                        if x < 0 or x >= w:
                            continue
                        if grid[y][x] == '#' and dist[y][x] < 0:
                            if dist[a][b] == 0:
                                dist[y][x] = 1
                                odd += 1
                            else:
                                dist[y][x] = 0
                                even += 1
                            stack.append((y,x))    
            ans += even * odd
print(ans)