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())
grid = [input() for _ in range(h)]
visited = [[0]*w for _ in range(h)]
moves = ((1, 0), (-1, 0), (0, 1), (0, -1))

ans = 0
for i in range(h):
    for j in range(w):
        if not visited[i][j]:
            bcnt, wcnt = 0, 0
            q = deque([(i, j)])
            while q:
                cx, cy = q.popleft()
                if visited[cx][cy]:
                    continue
                if grid[cx][cy] == "#":
                    bcnt += 1
                else:
                    wcnt += 1
                visited[cx][cy] = 1
                for (dx, dy) in moves:
                    if 0 <= cx + dx < h and 0 <= cy + dy < w and not visited[cx + dx][cy + dy] and grid[cx + dx][cy + dy] != grid[cx][cy]:
                        q.append((cx + dx, cy + dy))
            ans += bcnt * wcnt
print(ans)