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())
index = ".#".index
S = [list(map(index, input())) for i in range(H)]

dd = ((-1, 0), (0, -1), (1, 0), (0, 1))

used = [[0]*W for i in range(H)]
ans = 0
for i in range(H):
    for j in range(W):
        if used[i][j]:
            continue
        que = deque([(i, j)])
        used[i][j] = 1
        C = [0, 0]
        C[S[i][j]] += 1
        f = ((i + j) & 1) ^ S[i][j]
        while que:
            x, y = que.popleft()
            s = ((x + y) & 1) ^ 1
            for dx, dy in dd:
                nx = x + dx; ny = y + dy
                if not 0 <= nx < H or not 0 <= ny < W or used[nx][ny] or (s ^ S[nx][ny]) != f:
                    continue
                que.append((nx, ny))
                used[nx][ny] = 1
                C[S[nx][ny]] += 1
        ans += C[0] * C[1]
print(ans)