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)]

check = [[0] * W for _ in range(H)]

ans = 0

move = [[1, 0], [-1, 0], [0, 1], [0, -1]]

for h in range(H):
    for w in range(W):
        if check[h][w] == 1:
            continue
        black = 0
        white = 0

        stack = [[h, w]]
        check[h][w] = 1
        if S[h][w] == '#':
            black += 1
        elif S[h][w] == '.':
            white += 1

        while len(stack) != 0:
            x, y = stack.pop()
            tmp = S[x][y]
            for dx, dy in move:
                nx = x + dx
                ny = y + dy
                if 0 <= nx < H and 0 <= ny < W and tmp != S[nx][ny] and check[nx][ny] == 0:
                    check[nx][ny] = 1
                    stack.append([nx, ny])
                    if S[nx][ny] == '#':
                        black += 1
                    elif S[nx][ny] == '.':
                        white += 1
        
        ans += black * white

print (ans)