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 = [input() for _ in range(h)]

d_i = [-1, 0, 1, 0]
d_j = [0, -1, 0, 1]

ans = 0
visited = [[False]*w for _ in range(h)]
for i in range(h):
    for j in range(w):
        if visited[i][j]:
            continue
        b = 0
        wh = 0
        q = deque()
        q.append((i,j))
        visited[i][j] = True
        while len(q) > 0:
            c_h, c_w = q.pop()
            if s[c_h][c_w] == '#':
                b += 1
            else:
                wh += 1
            for dir in range(4):
                n_h = c_h+d_i[dir]
                n_w = c_w+d_j[dir]
                if n_h < 0 or h-1 < n_h or n_w < 0 or w-1 < n_w:
                    continue
                if visited[n_h][n_w]:
                    continue
                if s[c_h][c_w] == s[n_h][n_w]:
                    continue
                q.append((n_h, n_w))
                visited[n_h][n_w] = True
        ans += b*wh
print(ans)