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
from collections import deque as dq
input = sys.stdin.readline
H, W = map(int, input().split())
S = [list(input()) for _ in range(H)]
d = [-1, 0, 1, 0]
vis = [[0] * W for _ in range(H)]
Q = dq([])
res = 0
for i in range(H):
  for j in range(W):
    if vis[i][j] == 1: continue
    Q.append((i, j))
    w = 0
    b = 0
    while len(Q):
      p = Q.popleft()
      if S[p[0]][p[1]] == "#": b += 1
      elif S[p[0]][p[1]] == ".": w += 1
      vis[p[0]][p[1]] = 1
      for way in range(4):
        x = p[1] + d[way]
        y = p[0] + d[-1 - way]
        if 0 <= y < H and (0 <= x < W):
          if S[p[0]][p[1]] == S[y][x]:
            continue
          if vis[y][x] == 1: continue
          Q.append((y, x))
          vis[y][x] = 1
    res += b * w
print(res)