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:
from collections import deque
h,w = map(int,input().split())
sq = [list(input()) for i in range(h)]
prt = [[0 for i in range(w)] for j in range(h)]
for i in range(h):
  for j in range(w):
    c = i + j
    if sq[i][j] == "#":
      c += 1
    prt[i][j] = c%2
que = deque([])
ans = 0
visited = [[0 for i in range(w)] for j in range(h)]
for i in range(h):
  for j in range(w):
    if visited[i][j] != 1:
      que.append((i,j))
      cnt = 0
      cntb = 0
      while que:
        x,y = que.popleft()
        if visited[x][y] != 1:
          cnt += 1
          if sq[x][y] == "#":
            cntb += 1
          visited[x][y] = 1
          for n_x,n_y in ((x+1,y),(x-1,y),(x,y+1),(x,y-1)):
            if 0<=n_x<h and 0<=n_y<w:
              if visited[n_x][n_y] != 1 and prt[n_x][n_y] == prt[x][y]:
                que.append((n_x,n_y))
      ans += cntb*(cnt-cntb)

print(ans)