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:
f=lambda x:x if p[x]<0else f(p[x])
def u(x,y):
  x,y=f(x),f(y)
  if x!=y:
    if p[x]>p[y]:x,y=y,x
    p[x]+=p[y]
    p[y]=x
h,*s=open(0)
h,w=map(int,h.split())
r=range(h*w)
p=[-1]*h*w
for i in r:
  j,k=i//w,i%w
  h>j+1and s[j][k]!=s[j+1][k]and u(i,i+w)or w>k+1and s[j][k]!=s[j][k+1]and u(i,i+1)
d=[[0,0]for _ in r]
for i in r:d[f(i)][s[i//w][i%w]<'.']+=1
print(sum(i*j for i,j in d))