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, defaultdict

H, W = map(int, input().split())
S = [input() for i in range(H)]

visited = [[False] * W for i in range(H)]
ans = 0
for i in range(H):
    for j in range(W):
        if visited[i][j]:
            continue
        q = deque()
        q.append((i, j))
        visited[i][j] = True
        n = defaultdict(int)
        while len(q) > 0:
            si, sj = q.popleft()
            n[S[si][sj]] += 1
            for di, dj in [(-1, 0), (1, 0), (0, 1), (0, -1)]:
                if 0 <= si + di < H and 0 <= sj + dj < W and S[si][sj] != S[si + di][sj + dj] and not visited[si + di][sj + dj]:
                    q.append((si + di, sj + dj))
                    visited[si + di][sj + dj] = True
        ans += n['#'] * n['.']

print(ans)