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 deque
h,w = map(int, input().split())
s = [input() for i in range(h)]
root = [[0,1],[1,0],[0,-1],[-1,0]]
def bfs(x,y):
  v[x][y]=1
  cnt=1
  cnt1=0
  d = deque([[x,y]])
  while len(d):
    e,f = d.popleft()
    c = s[e][f]
    for a,b in root:
      x1 = e+a
      y1 = f+b
      if x1>=0 and x1<h and y1>=0 and y1 <w and v[x1][y1]==0:
        if c == '.' and s[x1][y1]=='#':
          v[x1][y1]=1
          d.append([x1,y1])
          cnt+=1
        if c == '#' and s[x1][y1]=='.':
          v[x1][y1]=1
          d.append([x1,y1])
          cnt1+=1
  return cnt*cnt1
v = [[0 for i in range(w)] for j in range(h)]
ans=0
for i in range(h):
  for j in range(w):
    if v[i][j]:
      continue
    if s[i][j]=='#':
      ans+= bfs(i,j)
print(ans)