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: Wrong Answer)

class UnionFind(object):
    def __init__(self, size):
        self.parent = [i for i in range(size)]
        self.rank = [0 for _ in range(size)]


    def find(self, x):
        if self.parent[x] == x:
            return x
        else:
            return self.find(self.parent[x])


    def unite(self, x, y):
        x = self.find(x)
        y = self.find(y)
        if x == y:
            return

        if self.rank[x] < self.rank[y]:
            self.parent[x] = y
        else:
            self.parent[y] = x
            if self.rank[x] == self.rank[y]:
                self.rank[x] += 1

    def same(self, x, y):
        return self.find(x) == self.find(y)

H, W = map(int, input().split())
#P = list(map(int, input().split()))
S = [input() for _ in range(H)]

def kake(i, j):
    return i * W + j

u = UnionFind(H*W)

for i in range(H):
    for j in range(W):
        if H != 1:
            if i != 0:
                if S[i][j] != S[i - 1][j]:
                    u.unite(kake(i, j), kake(i - 1, j))
            if i != H - 1:
                if S[i][j] != S[i + 1][j]:
                    u.unite(kake(i, j), kake(i + 1, j))
        if W != 1:
            if j != 0:
                if S[i][j] != S[i][j - 1]:
                    u.unite(kake(i, j), kake(i, j - 1))
            if j != W - 1:
                if S[i][j] != S[i][j + 1]:
                    u.unite(kake(i, j), kake(i, j + 1))


ans = [[0, 0] for _ in range(H*W)]

for i in range(H):
    for j in range(W):
        if (i+j)%2 == 0:
            ans[u.parent[kake(i, j)]][0] += 1
        else:
            ans[u.parent[kake(i, j)]][1] += 1

pri = 0

for i in range(H):
    for j in range(W):
        pri += ans[kake(i, j)][0] * ans[kake(i, j)][1]

print(pri)