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())

board=[]
check=[[None]*W for i in range(H)]
answer=0

for i in range(H):
  S=list(input())
  board.append(S)
  
def dfs(i,j,color):
  if not (0<=i<H and 0<=j<W):
    return 0,0
  if board[i][j]==color:
    return 0,0
  if check[i][j]:
    return 0,0
  
  check[i][j]=True
  black,white=0,0
  
  if board[i][j]=='#':
  	black+=1
  else:
    white+=1
 
  tempblack,tempwhite=dfs(i+1,j,board[i][j])
  black+=tempblack
  white+=tempwhite
  
  tempblack,tempwhite=dfs(i-1,j,board[i][j])
  black+=tempblack
  white+=tempwhite
  
  tempblack,tempwhite=dfs(i,j+1,board[i][j])
  black+=tempblack
  white+=tempwhite

  tempblack,tempwhite=dfs(i,j-1,board[i][j])
  black+=tempblack
  white+=tempwhite
  return black,white

for i in range(H):
  for j in range(W):
    black,white=dfs(i,j,"!")
    answer+=black*white
print(answer)