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.*;
import java.nio.CharBuffer;
import java.util.Arrays;
import java.util.HashMap;
import java.util.HashSet;
import java.util.NoSuchElementException;

public class Main {

    public static void main(String[] args) {
        SimpleScanner scanner = new SimpleScanner(System.in);
        PrintWriter writer = new PrintWriter(System.out);

        int n = scanner.nextInt();
        HashMap<Integer, HashSet<Integer>> xMap = new HashMap<>();
        HashMap<Integer, HashSet<Integer>> yMap = new HashMap<>();
        int[][] point = new int[n][2];
        for (int i = 0; i < n; ++i) {
            int x = scanner.nextInt();
            int y = scanner.nextInt();
            point[i][0] = x;
            point[i][1] = y;
            xMap.putIfAbsent(x, new HashSet<>());
            xMap.get(x).add(i);
            yMap.putIfAbsent(y, new HashSet<>());
            yMap.get(y).add(i);
        }
        boolean[] visited = new boolean[n];
        Arrays.fill(visited, false);
        long ans = 0;
        for (int i = 0; i < n; ++i) {
            if (!visited[i]) {
                HashSet<Integer> diffX = new HashSet<>();
                HashSet<Integer> diffY = new HashSet<>();
                dfs(i, point, visited, xMap, yMap, diffX, diffY);
                ans += (long) diffX.size() * diffY.size();
            }
        }
        writer.println(ans - n);

        writer.close();
    }

    private static void dfs(int u, int[][] point, boolean[] visited, HashMap<Integer, HashSet<Integer>> xMap, HashMap<Integer, HashSet<Integer>> yMap, HashSet<Integer> diffX, HashSet<Integer> diffY) {
        visited[u] = true;
        if (diffX.add(point[u][0]))
            for (int v : xMap.get(point[u][0]))
                dfs(v, point, visited, xMap, yMap, diffX, diffY);
        if (diffY.add(point[u][1]))
            for (int v : yMap.get(point[u][1]))
                dfs(v, point, visited, xMap, yMap, diffX, diffY);
    }

    private static class SimpleScanner {

        private static final int BUFFER_SIZE = 10240;

        private Readable in;
        private CharBuffer buffer;
        private boolean eof;

        SimpleScanner(InputStream in) {
            this.in = new BufferedReader(new InputStreamReader(in));
            buffer = CharBuffer.allocate(BUFFER_SIZE);
            buffer.limit(0);
            eof = false;
        }


        private char read() {
            if (!buffer.hasRemaining()) {
                buffer.clear();
                int n;
                try {
                    n = in.read(buffer);
                } catch (IOException e) {
                    n = -1;
                }
                if (n <= 0) {
                    eof = true;
                    return '\0';
                }
                buffer.flip();
            }
            return buffer.get();
        }

        void checkEof() {
            if (eof)
                throw new NoSuchElementException();
        }

        char nextChar() {
            checkEof();
            char b = read();
            checkEof();
            return b;
        }

        String next() {
            char b;
            do {
                b = read();
                checkEof();
            } while (Character.isWhitespace(b));
            StringBuilder sb = new StringBuilder();
            do {
                sb.append(b);
                b = read();
            } while (!eof && !Character.isWhitespace(b));
            return sb.toString();
        }

        int nextInt() {
            return Integer.valueOf(next());
        }

        long nextLong() {
            return Long.valueOf(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }
    }
}