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())
S = []
for _ in [0]*H:
	S.append(list(input().rstrip()))

visited = []
for _ in [0]*H:
	visited.append([False] * W)

delta = [[1, 0], [0, 1], [-1, 0], [0, -1]]

ans = 0
for x in range(H):
	for y in range(W):
		if visited[x][y]: continue
		b = 0
		w = 0
		queue = deque()
		queue.append([x, y])
		visited[x][y] = True
		while len(queue) is not 0:
			px, py = queue[0]
			queue.popleft()
			if S[px][py] == '#' : b += 1
			else: w += 1
			found = False
			for dx, dy in delta:
				nx = px + dx
				ny = py + dy
				if 0 <= nx < H and 0 <= ny < W and not visited[nx][ny]:
					if S[px][py] != S[nx][ny]:
						found = True
						visited[nx][ny] = True
						queue.append([nx, ny])

		ans += b * w

print(ans)