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 = [[1 if i=="#" else 0 for i in input()] for _ in range(h)]
dy = (1, 0, -1, 0)
dx = (0, 1, 0, -1)
seen = [[False]*w for _ in range(h)]

def dfs(y, x):
  white = 0
  black = 0
  stack = [(y, x)]
  seen[y][x] = True
  while stack:
    s, t = stack.pop()
    if S[s][t]:
      black += 1
    else:
      white += 1
    for di, dj in zip(dy, dx):
      ny, nx = s+di, t+dj
      if 0 <= ny < h and 0 <= nx < w:
        if seen[ny][nx]:
          continue
        if S[s][t] ^ S[ny][nx]:
          seen[ny][nx] = True
          stack.append((ny, nx))
  return black, white

ans = 0
for i in range(h):
  for j in range(w):
    if not seen[i][j]:
      black, white = dfs(i, j)
      ans += black * white
print(ans)