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:
h,w=map(int,input().split())
P=[]
for i in range(h):
  C=[str(_) for _ in input()]
  P+=C
par=[[-1,0,0] for _ in range(h*w)]
def find(x):
  if par[x][0]<0:
    return x
  else:
    par[x][0]=find(par[x][0])
    return par[x][0]
def unite(x,y):
  x=find(x)
  y=find(y)
  if x==y:
    return False
  else:
    if par[x][0]>par[y][0]:
      x,y=y,x
    par[x][0]+=par[y][0]
    par[y][0]=x
    return True
def same(x,y):
  return find(x)==find(y)
def size(x):
  return -par[find(x)][0]
for i in range(h*w):
  if P[i]=="#":
    par[i][1]+=1
    if (i+1)%w!=0 and P[i+1]==".":
      unite(i,i+1)
    if (i+w)<(h*w) and P[i+w]==".":
      unite(i,i+w)
  else:
    par[i][2]+=1
    if (i+1)%w!=0 and P[i+1]=="#":
      unite(i,i+1)
    if (i+w)<(h*w) and P[i+w]=="#":
      unite(i,i+w)
ans=0
for p,x,y in par:
  if p>=0:
    par[find(p)][1]+=x
    par[find(p)][2]+=y
for p,x,y in par:
  if p<-1:
    ans+=x*y
print(ans)