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())
S = []
for i in range(H):
  ss = input()
  S.append(ss)
UF = list(range(H*W))
def par(m):
  if UF[m] == m:
    return m
  r = par(UF[m])
  UF[m] = r
  return r
def unite(m, n):
  i = par(m)
  j = par(n)
  UF[i] = j
for i in range(H):
  for j in range(W):
    if i+1 < H and S[i][j] != S[i+1][j]:
      unite(i*W+j, (i+1)*W+j)
    if j+1 < W and S[i][j] != S[i][j+1]:
      unite(i*W+j, i*W+j+1)
nsb = [0]*(H*W)
nsw = [0]*(H*W)
for i in range(H):
  for j in range(W):
    p = par(i*W+j)
    if S[i][j] == "#":
      nsb[p] += 1
    if S[i][j] == ".":
      nsw[p] += 1
r = 0
for p in range(H*W):
  r += nsb[p]*nsw[p]
print(r)
#  print(UF[i*W:(i+1)*W])