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)]
mx=[1, -1, 0, 0]
my=[0, 0, 1, -1]
vis=[[0]*w for i in range(h)]
import queue
q=queue.Queue()
ans=0
for i in range(h):
  for j in range(w):
    if vis[i][j]==0:
      white=0
      black=0
      q.put([i, j])
      vis[i][j]=1
      while not q.empty():
        y, x = q.get()
        if s[y][x]==".":
          white+=1
        else:
          black+=1
        #vis[y][x]=1
        for k in range(4):
          nx=x+mx[k]
          ny=y+my[k]
          if 0<=nx<=w-1 and 0<=ny<=h-1 and vis[ny][nx]==0:
            if s[y][x] != s[ny][nx]:
              q.put([ny, nx])
              vis[ny][nx]=1
      if white+black!=1:
        ans+=white*black
print(ans)