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(410000)

h,w = map(int,input().split())
F = []
for i in range(h):
  F.append(list(input()))
  
V = [[False]*w for _ in range(h)]

def dfs(y,x,c):      
  V[y][x] = True
  black = 0
  white = 0
  if c =='#':
    black+=1
  else:
    white+=1
  for dy,dx in [(-1,0),(0,1),(1,0),(0,-1)]:
    ny = y + dy
    nx = x + dx
    if 0<=ny<h and 0<=nx<w:      
      if F[ny][nx]!=c and V[ny][nx] == False:
        nc = '#'
        if c =='#':
          nc = '.'
        bn,wn = dfs(ny,nx,nc)
        black += bn
        white += wn  
  return black,white
        
ans = 0
for i in range(h):
  for j in range(w):
    if F[i][j] == '#':      
      black,white = dfs(i,j,'#')
      ans += black*white
      
print(ans)