Problem: 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.

Examples

Input

3 3
.#.
..#
#..


Output

10


Input

3 3
.#.
..#
..


Output

10


Input

2 4
....
....


Output

0


Input

4 3


...


Output

6

Solution (in PYTHON3):

Solution:
from collections import deque

H, W = map(int, input().split())
seen = [[False]*W for _ in range(H)]
dx,dy = [1, 0, -1, 0], [0, 1, 0, -1]
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] == '.') or (S[px][py]=='.' and S[nx][ny] == '#'):
						d.append((nx, ny))
						seen[nx][ny] = 1
						if S[px][py] == '#':
							w += 1
						else:
							b += 1
			c += b*w

print(c)