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())
m = [input() for _ in range(h)]
seen = [[0]*w for _ in range(h)]
dxy =[(1,0),(0,1),(-1,0),(0,-1)]
cnt = 0
for i in range(h):
  for j in range(w):
    if not seen[i][j]:
      bcnt,wcnt = 0,0
      q = [(i,j)]
      while q:
        y,x = q.pop()
        if seen[y][x]:
          continue
        if m[y][x] == "#":
          bcnt += 1
        else:
          wcnt += 1
        seen[y][x] = 1
        for dx,dy in dxy:
          if 0<=x+dx<w and 0<=y+dy<h and not seen[y+dy][x+dx] and m[y+dy][x+dx] != m[y][x]:
            q.append((y+dy,x+dx))
      cnt += bcnt*wcnt
print(cnt)