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 collections import deque

H, W = map(int, input().split())
Ss = []
for _ in range(H):
  Ss.append(input())

mp = [[0]*W for _ in range(H)]
dxy = [[-1,0],[1,0],[0,-1],[0,1]]
lst = []

q = deque([])
num = 1
for i in range(H):
  for j in range(W):
    if mp[i][j] == 0:
      q.append((i,j))
      mp[i][j] = num
      dic = {'#':0, '.':0}
      while q:
        t = q.popleft()
        dic[Ss[t[0]][t[1]]] += 1
        for k in range(4):
          if t[0] + dxy[k][0] >= 0 and t[0] + dxy[k][0] < H \
             and t[1] + dxy[k][1] >= 0 and t[1] + dxy[k][1] < W \
             and Ss[t[0]][t[1]] != Ss[t[0]+dxy[k][0]][t[1]+dxy[k][1]]\
             and mp[t[0]+dxy[k][0]][t[1]+dxy[k][1]] == 0:
            
            mp[t[0]+dxy[k][0]][t[1]+dxy[k][1]] = num
            q.append((t[0]+dxy[k][0],t[1]+dxy[k][1]))
      lst.append(dic)
      num += 1

rlt = 0
for d in lst:
  rlt += d['#']*d['.']

print(rlt)