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)]

visited = [[0]*w for i in range(h)]
ans = 0
for i in range(h):
    for j in range(w):
        black = 0
        white = 0
        stack = [[i,j]]
        while stack:
            a,b = stack.pop()
            if visited[a][b]!=1:
                visited[a][b]+=1
                if s[a][b]=='#':
                    black+=1
                else:
                    white+=1
                for x,y in [[1,0],[-1,0],[0,1],[0,-1]]:
                    c = a+y
                    d = b+x
                    if 0<=c<h and 0<=d<w:
                        if s[a][b]!=s[c][d]:
                            stack.append([c,d])
        ans += black*white
print(ans)