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 getminLT(i):
  if LT[i] == i:
    return i
  else:
    return getminLT(LT[i])

H, W = list(map(int, input().split()))

D = []
for i in range(H):
  D.append(input())

M = [[0] * W for i in range(H)]
LT = [0]
for i in range(H):
  for j in range(W):
    if i == 0 and j == 0:
      continue
    flag = False
    if i != 0:
      if D[i][j] != D[i-1][j]:
        M[i][j] = M[i-1][j]
        flag = True
    if j != 0:
      if D[i][j] != D[i][j-1]:
        M[i][j] = M[i][j-1]
        if flag == True:
          
          LT[max(getminLT(M[i-1][j]), getminLT(M[i][j-1]))] = LT[min(getminLT(M[i][j-1]), getminLT(M[i-1][j]))]
        flag = True
    if flag == False:
        M[i][j] = len(LT)
        LT.append(len(LT))
for i in range(len(LT)):
  LT[i] = getminLT(LT[i])
  
L = [[] for i in range(len(LT))]
for i in range(H):
  for j in range(W):
  	L[LT[M[i][j]]].append((i, j))
#print(M)
#print(LT)
#print(L)
cnt = 0
for i in L:
  E = 0
  A = 0
  for j in i:
    if (j[0] + j[1]) % 2 == 0:
      E += 1
    else:
      A += 1
  cnt += E * A
print(cnt)