There are N dots in a two-dimensional plane. The coordinates of the i-th dot are (x_i, y_i).

We will repeat the following operation as long as possible:

* Choose four integers a, b, c, d (a \neq c, b \neq d) such that there are dots at exactly three of the positions (a, b), (a, d), (c, b) and (c, d), and add a dot at the remaining position.



We can prove that we can only do this operation a finite number of times. Find the maximum number of times we can do the operation.

Constraints

* 1 \leq N \leq 10^5
* 1 \leq x_i, y_i \leq 10^5
* If i \neq j, x_i \neq x_j or y_i \neq y_j.
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N
x_1 y_1
:
x_N y_N


Output

Print the maximum number of times we can do the operation.

Examples

Input

3
1 1
5 1
5 5


Output

1


Input

2
10 10
20 20


Output

0


Input

9
1 1
2 1
3 1
4 1
5 1
1 2
1 3
1 4
1 5


Output

16
n = int(input())
xy = {}
for i in range(n):
  x,y = map(int,input().split())
  xy[x] = xy.get(x,[]) + [y]
d = {}
for x in xy:
  v0 = xy[x][0]
  while d.get(v0,v0) != v0:
    v0 = d[v0]
  for v in xy[x]:
    v1 = d.get(v,v)
    while d.get(v1,v1) != v1:
      v1 = d[v1]
    d[v1] = v0
for y in d:
  yp = d[y]
  y2 = [y]
  while yp != d[yp]:
    y2 += [yp]
    yp = d[yp]
  for y3 in y2:
    d[y3] = yp
e = {}
for y in d:
  e[d[y]] = e.get(d[y],0)+1
ans = 0
for x in xy:
  ans += e[d[xy[x][0]]] - len(xy[x])
print(ans)