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 = [list(input()) for _ in range(H)]

visited = [[False] * W for _ in range(H)]

def search(sx, sy) :
    q = [(sx, sy)]
    visited[sy][sx] = True
    
    b, w = 0, 0
    if S[sy][sx] == '#' :
        b += 1
    else :
        w += 1
        
    while q :
        cx, cy = q.pop()
        for dx, dy in ((1, 0), (-1, 0), (0, 1), (0, -1)) :
            nx, ny = cx + dx, cy + dy
            if 0 <= nx < W and 0 <= ny < H and not visited[ny][nx] and S[cy][cx] != S[ny][nx] :
                visited[ny][nx] = True
                q.append((nx, ny))
                if S[ny][nx] == '#' :
                    b += 1
                else :
                    w += 1           
    return b * w

ret = 0
for y in range(H) :
    for x in range(W) :
        if not visited[y][x] :
            ret += search(x, y)
            
print(ret)