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
readline = sys.stdin.readline

H,W = map(int,readline().split())

grid = [readline().rstrip() for i in range(H)]

visited = set()
ans = 0
from collections import deque
cases = ((0,1),(0,-1),(1,0),(-1,0))
for i in range(H):
  for j in range(W):
    if (i,j) in visited:
      continue
    if grid[i][j] == ".":
      continue
    q = deque()
    black = 0
    white = 0
    q.append([i,j,1])
    aim = ".#"
    while q:
      y,x,isblack = q.popleft()
      if (y,x) in visited:
        continue
      if aim[isblack] != grid[y][x]:
        continue
      visited.add((y,x))
      if isblack:
        black += 1
      else:
        white += 1
      isblack ^= 1
      for c in cases:
        if 0 <= y + c[0] < H and 0 <= x + c[1] < W:
          q.append([y + c[0],x + c[1],isblack])
    ans += black * white
print(ans)