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:
H,W=map(int,input().split())
h=range(H)
w=range(W)
S=[input() for _ in h]
M=[[-1]*W for _ in h]
k=0
for y in h:
 for x in w:
  if M[y][x]!=-1:continue
  M[y][x]=k;Q=[(y,x)]
  while len(Q)>0:
   i,j=Q.pop();s=S[i][j];p=i+1;q=i-1;r=j+1;t=j-1
   if p<H and M[p][j]==-1 and s!=S[p][j]:M[p][j]=k;Q+=[(p,j)]
   if i>0 and M[q][j]==-1 and s!=S[q][j]:M[q][j]=k;Q+=[(q,j)]
   if r<W and M[i][r]==-1 and s!=S[i][r]:M[i][r]=k;Q+=[(i,r)]
   if j>0 and M[i][t]==-1 and s!=S[i][t]:M[i][t]=k;Q+=[(i,t)]
  k+=1
s={}
d={}
for i in h:
 for j in w:
  m=M[i][j]
  if S[i][j]=='#':s[m]=s.get(m,0)+1
  else:d[m]=d.get(m,0)+1
print(sum(s.get(i,0)*d.get(i,0)for i in range(k)))