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 Java8 (OpenJDK 1.8.0) (judge verdict: Runtime Error)

import java.io.InputStream;
import java.io.PrintStream;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.HashSet;
import java.util.List;
import java.util.Map;
import java.util.Objects;
import java.util.Scanner;
import java.util.Set;

public class Main {

  public static void main(String[] args) {
    solve(System.in, System.out);
  }

  private static long MOD = 1000000007;

  static void solve(InputStream is, PrintStream os) {
    Scanner sc = new Scanner(is);

    /* read */
    int n = sc.nextInt();
    Map<Integer, Set<Integer>> xoccurs = new HashMap<>();
    Map<Integer, Set<Integer>> yoccurs = new HashMap<>();

    for (int i = 0; i < n; i++) {
      int x = sc.nextInt();
      int y = sc.nextInt();
      Set<Integer> ySetOfX = xoccurs.getOrDefault(x, new HashSet<>());
      ySetOfX.add(y);
      xoccurs.put(x, ySetOfX);

      Set<Integer> xSetOfY = yoccurs.getOrDefault(y, new HashSet<>());
      xSetOfY.add(x);
      yoccurs.put(y, xSetOfY);
    }

    Set<Integer> xMultiples = new HashSet<>();
    Set<Integer> yMultiples = new HashSet<>();

    for (int x : xoccurs.keySet()) {
      if (xoccurs.get(x).size() == 1) continue;
      Set<Integer> ys = xoccurs.get(x);
      yMultiples.addAll(ys);
      for (int y : ys) {
        Set<Integer> xs = yoccurs.get(y);
        if (xs != null) {
          xMultiples.addAll(xs);
        }
      }
    }

    for (int y : yoccurs.keySet()) {
      if (yoccurs.get(y).size() == 1) continue;
      Set<Integer> xs = xoccurs.get(y);
      xMultiples.addAll(xs);
      for (int x : xs) {
        Set<Integer> ys = xoccurs.get(x);
        if (ys != null) {
          yMultiples.addAll(ys);
        }
      }
    }

    int count = 0;
    for (int x : xMultiples) {
      for (int y : yMultiples) {
        if (!xoccurs.containsKey(x) || !xoccurs.get(x).contains(y)) count++;
      }
    }

    os.println(count);
  }

}