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
import sys
input = sys.stdin.readline
N = int(input())
s = set()
res = 0

class UnionFind():
  def __init__(self, n):
    self.n = n
    self.root = [-1] * (n + 1)
    self.rnk = [0] * (n + 1)

  def Find_Root(self, x):
    if self.root[x] < 0:
      return x
    else:
      self.root[x] = self.Find_Root(self.root[x])
      return self.root[x]

  def Unite(self, x, y):
    x = self.Find_Root(x)
    y = self.Find_Root(y)
    if x == y:
      return 
    elif self.rnk[x] > self.rnk[y]:
      self.root[x] += self.root[y]
      self.root[y] = x
    else:
      self.root[y] += self.root[x]
      self.root[x] = y
      if self.rnk[x] == self.rnk[y]:
        self.rnk[y] += 1

  def isSameGroup(self, x, y):
    return self.Find_Root(x) == self.Find_Root(y)

  def Count(self, x):
    return -self.root[self.Find_Root(x)]

uf = UnionFind(2 * 10 ** 5)

for _ in range(N):
  u, v = map(int, input().split())
  s.add(u)
  uf.Unite(u, v + 10 ** 5)

ss = set()
c = [0] * (2 * 10 ** 5 + 1)
for x in s:
  y = uf.Find_Root(x)
  ss.add(y)
  c[y] += 1
for x in ss:
  t = uf.Count(x)
  xc = c[x]
  yc = t - xc
  res += xc * yc
print(res - N)