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())
S = [input() for _ in range(H)]
visited = [[False] * W for _ in range(H)]
ans = 0
for si in range(H):
    for sj in range(W):
        if visited[si][sj]:
            continue
        visited[si][sj] = True
        queue = deque()
        queue.append((si, sj))
        black = 0
        white = 0
        while queue:
            i, j = queue.popleft()
            if S[i][j] == '#':
                black += 1
            else:
                white += 1
            for di, dj in [(1, 0), (0, 1), (-1, 0), (0, -1)]:
                ni, nj = i+di, j+dj
                if 0 <= ni < H and 0 <= nj < W and not visited[ni][nj] and S[i][j] != S[ni][nj]:
                    visited[ni][nj] = True
                    queue.append((ni, nj))
        ans += black * white
print(ans)