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 = (int(i) for i in input().split())
maze = [input() for _ in range(h)]
visited = [[False]*w for _ in range(h)]
  
def solve2(i,j):
  d = [(1,0),(0,1),(-1,0),(0,-1)]
  queue = deque([(i,j)])
  b,c = 0,0
  while queue:
    (x,y) = queue.popleft()
    if maze[x][y] =='#':b+=1
    else:c += 1
    visited[x][y] = True
    
    for dx,dy in d:
      nx,ny = x+dx,y+dy
      #print(nx,ny)
      if nx <= -1 or nx >= h or ny <= -1 or ny >= w:
        continue
      if visited[nx][ny]:
        continue
      #print(maze[nx][ny],maze[x][y])
      if maze[nx][ny] != maze[x][y]:
       visited[nx][ny] = True
       queue.append([nx,ny])
        
 # print(b,c)
  return b*c

ans = 0
for i in range(h):
  for j in range(w):
    if not visited[i][j]:
     ans += solve2(i,j)
print(ans)