Problem:
Score : 600 points

Problem Statement

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.

Sample Input 1

3
1 1
5 1
5 5

Sample Output 1

1

By choosing a = 1, b = 1, c = 5, d = 5, we can add a dot at (1, 5). We cannot do the operation any more, so the maximum number of operations is 1.

Sample Input 2

2
10 10
20 20

Sample Output 2

0

There are only two dots, so we cannot do the operation at all.

Sample Input 3

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

Sample Output 3

16

We can do the operation for all choices of the form a = 1, b = 1, c = i, d = j (2 \leq i,j \leq 5), and no more. Thus, the maximum number of operations is 16.

Solution in Python (3.4.3) (judge verdict: Accepted)

import sys
# input = sys.stdin.readline
sys.setrecursionlimit(pow(10, 6))

xedges = [[] for _ in range(100001)]
yedges = [[] for _ in range(100001)]
xvisited = [False for _ in range(100001)]
yvisited = [False for _ in range(100001)]

def dfs(i, xy):
  if xy == 0:
    xvisited[i] = True
  else:
    yvisited[i] = True
  xc, yc, ec = (xy+1)%2, xy%2, 0
  if xy == 0:
    ec += len(xedges[i])
    for toy in xedges[i]:
      if not yvisited[toy]:
        _xc, _yc, _ec = dfs(toy, 1)
        xc += _xc
        yc += _yc
        ec += _ec
  else :
    ec += len(yedges[i])
    for tox in yedges[i]:
      if not xvisited[tox]:
        _xc, _yc, _ec = dfs(tox, 0)
        xc += _xc
        yc += _yc
        ec += _ec
  return xc, yc, ec

def main():
  n = int(input())
  for _ in range(n):
    x, y = map(int, input().split())
    xedges[x].append(y)
    yedges[y].append(x)

  ans = 0
  for i in range(1, 100001):
    if not xvisited[i] and len(xedges[i]) != 0:
      xc, yc, ec = dfs(i, 0)
      ans += xc*yc-ec//2
    elif not yvisited[i] and len(yedges[i]) != 0:
      xc, yc, ec = dfs(i, 1)
      ans += xc*yc-ec//2

  print(ans)


if __name__ == '__main__':
  main()