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:
import sys
sys.setrecursionlimit(10**9)

H, W = map(int, input().split())
S = [input() for i in range(H)]

visited = set()
def dfs(x, y, c, white, black):
  global visited
  for dx, dy in [[1, 0], [0, 1], [-1, 0], [0, -1]]:
    xx = x + dx; yy = y + dy
    if 0<=xx<H and 0<=yy<W and (xx, yy) not in visited and S[xx][yy]!=c:
      cc = S[xx][yy]
      if cc == '.':
        white.add((xx, yy))
      else:
        black.add((xx, yy))
      visited.add((xx, yy))
      white, black = dfs(xx, yy, cc, white, black)
  return white, black

ans = 0
for x in range(H):
  for y in range(W):
    if (x, y) not in visited:
      visited.add((x, y))
      c = S[x][y]
      if c == '.':
        white = set(((x, y), )); black = set()
      else:
        white = set(); black = set(((x, y), ))
      white, black = dfs(x, y, c, white, black)
      ans += len(white) * len(black)

print(ans)