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 itertools import chain, product
H,W = map(int,input().split())
grid = list(chain(
    ([None,]*(W+2),),
    (list(chain(
      (None,),
      map(lambda x: x=='#', input()),
      (None,),
      )) for _ in range(H)),
    ([None,]*(W+2),),
    ))

neighbors = ((1,0),(0,1),(-1,0),(0,-1))

res = 0

stack = []

for y,x in product(range(1,H+1),range(1,W+1)):
  if grid[y][x] is None:
    continue
  stack.append((y,x))
  black,white = 0,0

  while stack:
    y,x = stack.pop()
    v = grid[y][x]
    if v is None:
      continue
    grid[y][x] = None

    if v:
      black += 1
    else:
      white += 1
    v = not v

    for dy,dx in neighbors:
      w = grid[y+dy][x+dx]
      if w == v:
        stack.append((y+dy,x+dx))

  res += black*white

print(res)