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())
a = [list("*"*(w+2))]
for i in range(h):
  a.append(['*'] + list(input()) + ['*'])
a.append(list("*"*(w+2)))

b = [[0]*(w+2) for _ in range(h+2)]
direction = [(1, 0), (-1, 0), (0, 1), (0, -1)]
ans=0
for i in range(1,h+1):
  for j in range(1,w+1):
    if a[i][j]=='#' and b[i][j]==0:
      countw = countb = 0
      stackb = [(i, j)]
      stackw = []
      while stackb:
        xb, yb = stackb.pop(-1)
        if b[xb][yb] != 0: continue
        countb+=1
        b[xb][yb]=1
        for d in direction:
          p, q = xb + d[0], yb + d[1]
          if a[p][q]=='.' and b[p][q]==0:
            stackw.append((p, q))
        while stackw:
          xw, yw = stackw.pop(-1)
          if b[xw][yw] != 0: continue
          countw+=1
          b[xw][yw]=1
          for d in direction:
            p, q = xw + d[0], yw + d[1]
            if a[p][q]=='#' and b[p][q]==0:
              stackb.append((p, q))
      ans += countb*countw
print(ans)