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 = [input() for _i in range(h)]
visit = [[-1 for _i in range(w)] for _j in range(h)]
r = 0
from collections import deque
for i in range(h):
    for j in range(w):
        if (s[i][j]=="#") and (visit[i][j]<0):
            q = deque([[i, j]])
            black = 1
            white = 0
            visit[i][j] = 1
            while q:
                x, y = q.popleft()
                for n, m in [[1,0], [0, 1], [-1,0], [0,-1]]:
                    if (0<=x+n) and (0<=y+m) and (x+n<h) and (y+m<w):
                        if (visit[x+n][y+m]<0) and (s[x][y]!=s[x+n][y+m]):
                            visit[x+n][y+m]=1
                            if s[x][y] == "#":
                                white += 1
                            else:
                                black += 1
                            q.append([x+n, y+m])
            r += black*white

print(r)