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 (7.3.0) (judge verdict: Accepted)

from collections import deque

dx,dy = [1, 0, -1, 0], [0, 1, 0, -1]

H, W = map(int, input().split())
seen = [[False]*W for _ in range(H)]
c,S = 0,[]
for _ in range(H):
	S.append(input())

for i in range(H):
	for j in range(W):
		if (S[i][j]=='#') and (not seen[i][j]):
			d = deque()
			d.append((i, j))
			seen[i][j],b,w = True,1,0
			while d:
				px,py = d.popleft()
				for x,y in zip(dx,dy):
					nx, ny = px+x, py+y
					if nx < 0 or ny < 0 or nx >= H or ny >= W or seen[nx][ny]:
						continue
					if S[px][py]=='#' and S[nx][ny] == '.':
						d.append((nx, ny))
						seen[nx][ny] = 1
						w += 1
					elif S[px][py]=='.' and S[nx][ny] == '#':
						d.append((nx, ny))
						seen[nx][ny] = 1
						b += 1
			c += b*w

print(c)