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 itertools import product

direction = []
for i in range(4):
    dx = 5 % (i + 1) - 1
    dy = 5 % (i + 2) - 1
    direction.append((dx, dy))
H, W = map(int, input().split())
grid = [input() for _ in range(H)]
visited = [[False for _ in range(W)] for _ in range(H)]
ans = 0
for i, j in product(range(H), range(W)):
    if visited[i][j]: continue
    stack = [(i, j)]
    black = 0; white = 0;
    while stack:
        x, y = stack.pop()
        if visited[x][y]: continue
        visited[x][y] = True
        if grid[x][y] == '#': black += 1
        else: white += 1
        for dx, dy in direction:
            temp_x, temp_y = min(max(x + dx, 0), H-1), min(max(y + dy, 0), W-1)
            if visited[temp_x][temp_y]: continue
            if grid[x][y] != grid[temp_x][temp_y]: stack.append((temp_x, temp_y))
    ans += black * white
print(ans)