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(200000)
def dfs(x,y):
  vis[x][y]=1
  now=s[x][y]
  b=now=='#'
  w=now=='.'
  for i in range(4):
    nx=x+dx[i]
    ny=y+dy[i]
    if not(0<=nx<r and 0<=ny<c) or vis[nx][ny] or s[nx][ny]==now:continue
    black,white=dfs(nx,ny)
    b+=black
    w+=white
  return b,w
r,c=map(int,input().split())
s=[input() for _ in range(r)]
vis=[[0]*c for _ in range(r)]
ans=0
dx=(-1,0,1,0)
dy=(0,-1,0,1)
for i in range(r):
  for j in range(c):
    if vis[i][j]:continue
    b,w=dfs(i,j)
    ans+=b*w
print(ans)