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:
dxdy = [(0, 1), (0, -1), (1, 0), (-1, 0)]
h, w = map(int, input().split())
s = [list(input()) for _ in range(h)]
for i in range(h):
    for j in range(w):
        if (i + j) % 2:
            if s[i][j] == '.':
                s[i][j] = '#'
            else:
                s[i][j] = '.'
d = [[True] * w for _ in range(h)]
ans = 0
for i in range(h):
    for j in range(w):
        if not d[i][j]:
            continue
        d[i][j] = False
        st = [(i, j)]
        b, wh = 0, 0
        while st:
            y, x = st.pop()
            if (x + y) % 2:
                b += 1
            else:
                wh += 1
            for dx, dy in dxdy:
                if 0 <= x + dx < w and 0 <= y + dy < h and d[y + dy][x + dx] and s[y][x] == s[y + dy][x + dx]:
                    st.append((y + dy, x + dx))
                    d[y + dy][x + dx] = False
        ans += b * wh
print(ans)