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 PyPy3 (2.4.0) (judge verdict: Accepted)

# coding:utf-8

import sys
from collections import Counter, defaultdict, deque

INF = float('inf')
MOD = 10 ** 9 + 7

def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def I(): return int(sys.stdin.readline())
def S(): return input()


H, W = LI()
B = [[1 if s == '#' else 0 for s in S()] for _ in range(H)]


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

def BFS(i, j):
    ans = 0
    queue = deque([(i, j)])
    visited = set()
    visited_b = set()
    while queue:
        y, x = queue.pop()
        color = B[y][x]
        if color == 0 and (y, x) not in visited:
            # print(y, x)
            ans += 1
        if color == 1:
            visited_b.add((y, x))
        visited.add((y, x))
        for k in range(4):
            ny = y + dy[k]
            nx = x + dx[k]
            if (ny, nx) in visited:
                continue

            if ny < 0 or ny >= H or nx < 0 or nx >= W:
                continue

            if B[ny][nx] == color:
                continue

            queue.append((ny, nx))

    return ans, visited_b


ans = 0
visited_b = set()
for h in range(H):
    for w in range(W):
        if B[h][w] == 1 and (h, w) not in visited_b:
            tmp, v = BFS(h, w)
            ans += tmp * len(v)
            visited_b |= v
            # print(ans, v)

print(ans)