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)

import sys
input = sys.stdin.readline

def unite(node_a, node_b):
    root_a, depth_a = node_a.root()
    root_b, depth_b = node_b.root()
    if root_a == root_b:# すでに連結成分
        return
    elif depth_a >= depth_b:# aの方が深い
        root_b.is_root = False
        root_b.parent = root_a
        root_a.white += root_b.white
        root_a.black += root_b.black
    else:# bの方が深い
        root_a.is_root = False
        root_a.parent = root_b
        root_b.white += root_a.white
        root_b.black += root_a.black

class Node:
    def __init__(self, color):# color: 0:white, 1:black
        self.parent = None
        self.is_root = True
        self.white = 1 if color == 0 else 0
        self.black = 1 if color == 1 else 0
    
    def root(self):
        node = self
        depth = 0
        while not node.is_root:
            node = node.parent
            depth += 1
        return node, depth

def main():
    H, W = map(int, input().split())
    s = [input().strip() for i in range(H)]
    
    nodes = [[Node(0 if s[j][i] == "." else 1) for i in range(W)] for j in range(H)]

    for y in range(H):
        for x in range(W):
            now = s[y][x]
            for nx, ny in [(x, y-1), (x+1, y), (x, y+1), (x-1, y)]:
                if 0 <= nx and nx < W and 0 <= ny and ny < H:
                    if s[ny][nx] != now:
                        unite(nodes[y][x], nodes[ny][nx])
    
    ans = 0
    count_roots = 0
    for y in range(H):
        for x in range(W):
            if nodes[y][x].is_root:
                count_roots += 1
                node = nodes[y][x]
                ans += node.white * node.black
    print(ans)
    print(count_roots)


if __name__ == "__main__":
    main()