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:
import sys
sys.setrecursionlimit(10 ** 9)
input = sys.stdin.readline

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

seen = [[False for _ in range(W)] for _ in range(H)]
dx = [1,-1,0,0]
dy = [0,0,1,-1]
numb = 0
numw = 0

def dfs(y,x):
  global numb
  global numw
  seen[y][x] = True
  if S[y][x] == '#':
    numb += 1
  if S[y][x] == '.':
    numw += 1
  for i in range(4):
    if not(0<=y+dy[i]<H) or not(0<=x+dx[i]<W):
      continue
    if seen[y+dy[i]][x+dx[i]]:
      continue
    if S[y][x] == S[y+dy[i]][x+dx[i]]:
      continue
    dfs(y+dy[i],x+dx[i])

ans = 0
for i in range(H):
  for j in range(W):
    numb = 0
    numw = 0
    if S[i][j] == '#' and not seen[i][j]:
      dfs(i,j)
      ans += numb * numw
print(ans)