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)

class UnionFind(object):
 
    def __init__(self, size):
        self.table = [-1 for _ in range(size)]
 
    def find(self, x):
        if self.table[x] < 0:
            return x
        self.table[x] = self.find(self.table[x])
        return self.table[x]
 
    def same(self, x, y):
        return self.find(x) == self.find(y)
 
    def union(self, x, y):
        s1 = self.find(x)
        s2 = self.find(y)
        if s1 == s2:
            return False
        if self.table[s1] > self.table[s2]:
            s1, s2 = s2, s1
        self.table[s1] += self.table[s2]
        self.table[s2] = s1
        return True

H, W = list(map(int, input().split()))
S = list(input() for _ in range(H))
uf = UnionFind(H*W)

def get(h, w):
    return h * W + w

for h in range(H):
    for w in range(W):        
        for dh, dw in zip((0, 1), (1, 0)):
            if (h + dh) >= H or (w + dw) >= W:
                continue
            if S[h][w] != S[h+dh][w+dw]:
                uf.union(get(h, w), get(h+dh, w+dw))


from itertools import product

C1 = []
C2 = []

for h in range(H):
    for w in range(W):
        if S[h][w] == ".":
            C1.append((h, w))
        else:
            C2.append((h, w))

white = [0] * (H * W)
black = [0] * (H * W)

for h in range(H):
    for w in range(W):
        n = get(h, w)
        par = uf.find(n)
        # print(h, w, n, par)
        if par < 0:
            par = n
        if S[h][w] == ".":
            white[par] += 1
        else:
            black[par] += 1
            
ans = 0
# print(white)
# print(black)
for h in range(H):
    for w in range(W):
        n = get(h, w)
        ans += white[n] * black[n]
print(ans)