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 defaultdict
import sys
sys.setrecursionlimit(10**6)
H,W=map(int,input().split())
Map=[input() for i in range(H)]
G=[[[] for i in range(W)] for i in range(H)]
for i in range(H):
  for j in range(W):
    if i>=1:
      if Map[i-1][j]!=Map[i][j]:
        G[i][j].append((i-1,j))
    if j>=1:
      if Map[i][j-1]!=Map[i][j]:
        G[i][j].append((i,j-1))
    if i<=H-2:
      if Map[i+1][j]!=Map[i][j]:
        G[i][j].append((i+1,j))
    if j<=W-2:
      if Map[i][j+1]!=Map[i][j]:
        G[i][j].append((i,j+1))
Visited=[[False]*W for i in range(H)]
def dfs(x,y):
  w,b=0,0
  if Visited[x][y]:
    return (0,0)
  Visited[x][y]=True
  if Map[x][y]==".":
    w+=1
  else:
    b+=1
  for p,q in G[x][y]:
    if not Visited[p][q]:
      w_,b_=dfs(p,q)
      w+=w_
      b+=b_
  return (w,b)
ans=0
for i in range(H):
  for j in range(W):
    p,q=dfs(i,j)
    ans+=p*q
print(ans)