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 defaultdict as dd
H, W = map(int, input().split())
S = [input() for _ in range(H)]

i = 0
color = []
edge = dd(lambda: dd(int))
for h in range(H):
  for w in range(W):
    color.append(S[h][w])
    if w != 0:
      j = i-1
      if S[h][w-1] != S[h][w]:
        edge[i][j] = 1
        edge[j][i] = 1
    if h != 0:
      j = i-W
      if S[h-1][w] != S[h][w]:
        edge[i][j] = 1
        edge[j][i] = 1
    i += 1

visited = [False] * i
ans = 0
for k in range(i):
  if not visited[k]:
    count = { '#': 0, '.': 0 }
    queue = set([k])
    while queue:
      j = queue.pop()
      count[color[j]] += 1
      visited[j] = True
      for dst in edge[j]:
        if not visited[dst]:
          queue.add(dst)
    ans += count['#'] * count['.']
print(ans)