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())
G=[["@"]*(w+2) for i in range(h+2)]
for i in range(1,h+1):
  G[i]=["@"]+list(input())+["@"]
V=[[0]*(w+2) for i in range(h+2)]
X=deque([])
Y=deque([])
XX=[-1,0,0,1]
YY=[0,-1,1,0]
ans=0
for i in range(h+2):
  for j in range(w+2):
    if V[i][j]==0 and G[i][j]=="#":
      X.append(i)
      Y.append(j)
      V[i][j]=1
      C=[1,0]
      while len(X)>0:
        x=X[0]
        y=Y[0]
        X.popleft()
        Y.popleft()
        if G[x][y]=="#":
          for k in range(4):
            if V[x+XX[k]][y+YY[k]]==0 and G[x+XX[k]][y+YY[k]]==".":
              X.append(x+XX[k])
              Y.append(y+YY[k])
              V[x+XX[k]][y+YY[k]]=1
              C[1]+=1
        else:
          for k in range(4):
            if V[x+XX[k]][y+YY[k]]==0 and G[x+XX[k]][y+YY[k]]=="#":
              X.append(x+XX[k])
              Y.append(y+YY[k])
              V[x+XX[k]][y+YY[k]]=1
              C[0]+=1
      ans=ans+C[0]*C[1]
print(ans)