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: Accepted)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.HashMap;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.HashSet;
import java.util.AbstractCollection;
import java.util.StringTokenizer;
import java.util.Map;
import java.util.Map.Entry;
import java.io.BufferedReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author anand.oza
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        FMustBeRectangular solver = new FMustBeRectangular();
        solver.solve(1, in, out);
        out.close();
    }

    static class FMustBeRectangular {
        static final int MAX = 100_000;
        HashMap<Integer, HashSet<Integer>> xToY;
        HashMap<Integer, HashSet<Integer>> yToX;

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            xToY = new HashMap<>();
            yToX = new HashMap<>();

            for (int i = 0; i < n; i++) {
                int x = in.nextInt(), y = in.nextInt();
                addXY(x, y);
                addYX(x, y);
            }

            UnionFind equalX = new UnionFind(MAX + 1);

//        System.out.println(xToY);
//        System.out.println(yToX);

            for (Map.Entry<Integer, HashSet<Integer>> e : xToY.entrySet()) {
                int x = e.getKey();
                for (int y : e.getValue()) {
                    for (int x2 : yToX.get(y)) {
                        equalX.union(x, x2);
                    }
                }
            }

            HashMap<Integer, HashSet<Integer>> xToYAfter = new HashMap<>();

            for (int i = 1; i <= MAX; i++) {
                if (!xToY.containsKey(i))
                    continue;

                int x = equalX.rep(i);
                if (!xToYAfter.containsKey(x)) {
                    xToYAfter.put(x, new HashSet<>());
                }
                xToYAfter.get(x).addAll(xToY.get(i));
            }

            long answer = 0;
            for (Map.Entry<Integer, HashSet<Integer>> e : xToYAfter.entrySet()) {
                answer += ((long) e.getValue().size()) * equalX.size(e.getKey());
            }
            answer -= n;

            out.println(answer);
        }

        private void addXY(int x, int y) {
            if (!xToY.containsKey(x))
                xToY.put(x, new HashSet<>());
            xToY.get(x).add(y);
        }

        private void addYX(int x, int y) {
            if (!yToX.containsKey(y))
                yToX.put(y, new HashSet<>());
            yToX.get(y).add(x);
        }

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }

    static class UnionFind {
        private int[] __rep;
        private int[] __size;

        public UnionFind(int n) {
            __rep = new int[n];
            __size = new int[n];
            for (int i = 0; i < n; i++) {
                __rep[i] = i;
                __size[i] = 1;
            }
        }

        public int rep(int x) {
            if (__rep[x] == x) {
                return x;
            }

            int r = rep(__rep[x]);
            __rep[x] = r;
            return r;
        }

        public int size(int x) {
            return __size[rep(x)];
        }

        public void union(int x, int y) {
            x = rep(x);
            y = rep(y);

            if (x == y) {
                return;
            }

            if (size(x) < size(y)) {
                int t = x;
                x = y;
                y = t;
            }

            // now size(x) >= size(y)

            __rep[y] = x;
            __size[x] += __size[y];
        }

    }
}