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)

H, W = map(int, input().split())

X = [[0] * W for i in range(H)]
G = [[0,0] for i in range(W*H)] 
L = [[-1] * W for i in range(H)] # Group ID

for i in range(H):
    s = input()
    for j in range(W):
        if (i+j) % 2 == 0:
            if s[j] == "#":
                X[i][j] = 1
        else:
            if s[j] != "#":
                X[i][j] = 1
            
g = -1
for i in range(H):
    for j in range(W):
        if L[i][j] < 0:
            g += 1
            L[i][j] = g
            GGG = [[i,j]]
            post = [[i,j]]
            G[g][(i+j)%2] += 1
            while post:
                pre = post
                post = []
                for ggg in pre:
                    i0, j0 = ggg
                    if i0>0 and L[i0-1][j0] < 0 and X[i0][j0] == X[i0-1][j0]:
                        if [i0-1,j0] not in GGG:
                            post.append([i0-1,j0])
                            GGG.append([i0-1,j0])
                            L[i0-1][j0] = g
                            G[g][(i0+j0+1)%2] += 1
                    if i0<H-1 and L[i0+1][j0] < 0 and X[i0][j0] == X[i0+1][j0]:
                        if [i0+1,j0] not in GGG:
                            post.append([i0+1,j0])
                            GGG.append([i0+1,j0])
                            L[i0+1][j0] = g
                            G[g][(i0+j0+1)%2] += 1
                    if j0>0 and L[i0][j0-1] < 0 and X[i0][j0] == X[i0][j0-1]:
                        if [i0,j0-1] not in GGG:
                            post.append([i0,j0-1])
                            GGG.append([i0,j0-1])
                            L[i0][j0-1] = g
                            G[g][(i0+j0+1)%2] += 1
                    if j0<W-1 and L[i0][j0+1] < 0 and X[i0][j0] == X[i0][j0+1]:
                        if [i0,j0+1] not in GGG:
                            post.append([i0,j0+1])
                            GGG.append([i0,j0+1])
                            L[i0][j0+1] = g
                            G[g][(i0+j0+1)%2] += 1
                        
            # print(GGG)
# print(G)
ans = 0
for t in G:
    aa, bb = t
    ans += aa * bb
    
print(ans)