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:
H, W = map(int, input().split())
S = [0]*(H+2)
S[0] = '*'*(W+2)
S[H+1] = '*'*(W+2)
for h in range(1,H+1):
  S[h] = '*' + input() + '*'

import sys
sys.setrecursionlimit(10**8)

bw = ['#','.']

visited = [[False]*(W+2) for h in range(H+2)]
ans = 0
dh = [0,1,0,-1]
dw = [1,0,-1,0]

def dfs(h,w,c):
  #print(h,w,c, bw_count)
  for i in range(4):
    h0 = h+dh[i]
    w0 = w+dw[i]
    if S[h0][w0]==bw[c^1] and visited[h0][w0]==False:
      visited[h0][w0]=True
      bw_count[c^1]+=1
      dfs(h0,w0,c^1)
  
for h in range(H+2):
  for w in range(W+2):
    if S[h][w]=='#' and visited[h][w]==False:
      bw_count = [1,0]
      visited[h][w]=True
      dfs(h,w,0)
      ans += bw_count[0]*bw_count[1]

print(ans)   

#print(*ans, sep='\n')