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:
def find(x):
  if x==Tree[x]:
      return x
  else:
      Tree[x]=find(Tree[x])
      return Tree[x]
def unite(x,y):
  s1=find(x)
  s2=find(y)
  if s1!=s2:
    Tree[s2]=s1
    size[s1][0]+=size[s2][0]
    size[s1][1]+=size[s2][1]
H,W=map(int,input().split())
Tree=[i for i in range(H*W)]
S=[]
size=[[0,0] for i in range(H*W)]
for i in range(H):
  S.append(input())
  for j in range(W):
    t=i*W+j
    if S[-1][j]==".":
      size[t][0]=1
    else:
      size[t][1]=1
for i in range(1,W):
  if S[0][i]!=S[0][i-1]:
    unite(i,i-1)
for i in range(1,H):
  if S[i][0]!=S[i-1][0]:
    unite(i*W,(i-1)*W)
for i in range(1,H):
  for j in range(1,W):
    if S[i][j]!=S[i][j-1]:
      t=i*W+j
      unite(t,t-1)
    if S[i][j]!=S[i-1][j]:
      t=i*W+j
      unite(t,t-W)
ans=0
for i in range(H*W):
  if i==Tree[i]:
    ans+=size[i][0]*size[i][1]
print(ans)