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:
H, W = map(int, input().split())
s = [input() for _ in range(H)]


def dfs(startx: int, starty: int) -> set:
    dxdy = [[1, 0], [-1, 0], [0, 1], [0, -1]]
    stack = [(startx, starty, s[starty][startx] == '#')]
    reached = set()
    reached.add((startx, starty))
    b, w = 0, 0
    while stack:
        d = stack.pop()
        if d[2]:
            b += 1
        else:
            w += 1
        for a in dxdy:
            x = d[0] + a[0]
            y = d[1] + a[1]
            if (x, y) not in reached and 0 <= x < W and 0 <= y < H and d[2] ^ (s[y][x] == '#'):
                stack.append((x, y, s[y][x] == '#'))
                reached.add((x, y))
    return (reached, b, w)


reach = set()
ans = 0
for i in range(H):
    for j in range(W):
        if (j, i) not in reach:
            res = dfs(j, i)
            reach |= res[0]
            ans += res[1] * res[2]
print(ans)