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
sys.setrecursionlimit(1000000)

h,w=map(int,input().split())
s=[input() for _ in range(h)]
t=[[None]*w for _ in range(h)]

def dfs(i,j,color):

  if not (0<=i<h and 0<=j<w):return 0,0
  if s[i][j]==color: return 0,0
  if t[i][j]:return 0,0

  t[i][j]=True
  wh,bl=0,0
  if s[i][j]=="#":
    bl+=1
  else:
    wh+=1

  tmp1,tmp2=dfs(i+1,j,s[i][j])
  wh,bl=wh+tmp1,bl+tmp2

  tmp1,tmp2=dfs(i-1,j,s[i][j])
  wh,bl=wh+tmp1,bl+tmp2
        
  tmp1,tmp2=dfs(i,j-1,s[i][j])
  wh,bl=wh+tmp1,bl+tmp2

  tmp1,tmp2=dfs(i,j+1,s[i][j])
  wh,bl=wh+tmp1,bl+tmp2

  return wh,bl

ans=0
for i in range(h):
  for j in range(w):
    a,b=dfs(i,j,"!")
    ans+=a*b

print(ans)