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:
from sys import stdin
nii=lambda:map(int,stdin.readline().split())
lnii=lambda:list(map(int,stdin.readline().split()))
from collections import deque

h,w=nii()
s=[list(input()) for i in range(h)]

def BFS(sy,sx,ans):
  s[sy][sx]='B'

  que=deque()
  que.append((sy,sx))

  b_cnt=1
  w_cnt=0

  while que:
    y,x=que.popleft()
    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 s[y][x]=='B' and s[ny][nx]=='.':
          w_cnt+=1
          s[ny][nx]='W'
          que.append((ny,nx))
        if s[y][x]=='W' and s[ny][nx]=='#':
          b_cnt+=1
          s[ny][nx]='B'
          que.append((ny,nx))

  ans+=b_cnt*w_cnt
  return ans

ans=0
for i in range(h):
  for j in range(w):
    if s[i][j]=='#':
      ans=BFS(i,j,ans)

print(ans)