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:
belong=list()
group=list()
C=list()

def init(X):
  global belong,group,C
  belong=list(range(X))
  group=[[i] for i in range(X)]
  C=[[S[i//W][i%W]=='#',S[i//W][i%W]=='.'] for i in range(X)]

def unite(x,y):
  if len(group[belong[x]])<len(group[belong[y]]):
    x,y=y,x
  if belong[x]==belong[y]:
    return True
  z=belong[y]
  for i in range(len(group[z])):
    belong[group[z][-1]]=belong[x]
    group[belong[x]].append(group[z][-1])
    del group[z][-1]
  for i in range(2):
    C[belong[x]][i]+=C[z][i]
    C[z][i]=0
  return False

H,W=map(int,input().split())
S=[input() for i in range(H)]
init(H*W)
for i in range(H):
  for j in range(W):
    if i:
      if S[i][j]!=S[i-1][j]:
        unite(i*W+j,i*W+j-W)
    if j:
      if S[i][j]!=S[i][j-1]:
        unite(i*W+j,i*W+j-1)
    if i+1<H:
      if S[i][j]!=S[i+1][j]:
        unite(i*W+j,i*W+j+W)
    if j+1<W:
      if S[i][j]!=S[i][j+1]:
        unite(i*W+j,i*W+j+1)
P=0
for i in range(H*W):
  P+=C[i][0]*C[i][1]
print(P)