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())
grid =[list(input()) for i in range(h)]
visited=[[False]*w for i in range(h)]
ans=0
for i in range(h):
  for j in range(w):
    if visited[i][j]:
      continue
    q=[(i,j)]
    d={'#':0,'.':0}
    while q:
      cy,cx=q.pop(0)
      for ny,nx in ((cy+1,cx),(cy-1,cx),(cy,cx+1),(cy,cx-1)):
        if not(0<=ny<h and 0<=nx<w) or grid[cy][cx]==grid[ny][nx] or visited[ny][nx]:
          continue
        d[grid[ny][nx]]+=1
        visited[ny][nx]=True
        q.append((ny,nx))
    ans+=d['.']*d['#']
print(ans)