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 = (int(i) for i in input().split())
s = [input() for i in range(h)]
x,v,ans = [[] for i in range(h*w)],[1]*(h*w),0
for i in range(h):
    for j in range(w):
        if i!=h-1 and s[i][j]!=s[i+1][j]:
            x[i*w+j].append((i+1)*w+j)
            x[(i+1)*w+j].append(i*w+j)
        if j!=w-1 and s[i][j]!=s[i][j+1]:
            x[i*w+j].append(i*w+j+1)
            x[i*w+j+1].append(i*w+j)
for i in range(h*w):
    if v[i]:
        q,a,b,v[i] = [i],0,0,0
        while q:
            p = q.pop()
            if s[p//w][p%w]=="#": a+=1
            else: b+=1
            for j in x[p]:
                if v[j]:
                    q.append(j)
                    v[j] = 0
        ans+=a*b
print(ans)