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, *s = open(0).read().split()
h = int(h)
w = int(w)

q = deque()
used = [False] * (h * w)

ans = 0
for i in range(h):
    for j in range(w):
        if not used[i * w + j]:
            bcnt = 0
            cnt = 0

            q.append((i, j))
            used[i * w + j] = True
            cnt += 1
            bcnt += s[i][j] == '#'

            while len(q):
                y, x = q.popleft()
                for dy, dx in [(0, 1), (1, 0), (0, -1), (-1, 0)]:
                    ny = y + dy
                    nx = x + dx
                    if 0 <= nx < w and 0 <= ny < h and s[y][x] != s[ny][nx] and not used[ny * w + nx]:
                        q.append((ny, nx))
                        used[ny * w + nx] = True
                        cnt += 1
                        bcnt += s[ny][nx] == '#'
            ans += bcnt * (cnt - bcnt)
print(ans)