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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text.RegularExpressions;
using System.Threading.Tasks;

class Program
{
    SortedDictionary<int, HashSet<int>> xl, yl;
    void Run()
    {
        var sc = new Scanner();
        int n = sc.NextInt();
        xl = new SortedDictionary<int, HashSet<int>>();
        yl = new SortedDictionary<int, HashSet<int>>();
        for (int i = 0; i < n; i++)
        {
            int x = sc.NextInt();
            int y = sc.NextInt();
            if (!xl.ContainsKey(x)) xl.Add(x, new HashSet<int>());
            xl[x].Add(y);
            if (!yl.ContainsKey(y)) yl.Add(y, new HashSet<int>());
            yl[y].Add(x);
        }
        int res = 0;
        foreach (int xa in xl.Keys.ToList())
        {
            var l = xl[xa].ToList();
            for (int i = 0; i < l.Count; i++)
            {
                for (int j = i + 1; j < l.Count; j++)
                {
                    if (Check(xa, l[i], l[j])) res++;
                }
            }
        }

        Console.WriteLine(res);
    }

    bool Check(int x, int y1, int y2)
    {
        int d = Math.Abs(y2 - y1);
        if (d == 0) return false;
        return Check(x, x + d, y1, y2) || Check(x, x - d, y1, y2);
    }

    bool Check(int x, int xx, int y1, int y2)
    {
        if (xx < 0) return false;
        if (yl[y1].Contains(xx) ^ yl[y2].Contains(xx))
        {
            if (yl[y1].Contains(xx))
            {
                yl[y2].Add(xx);
                xl[xx].Add(y2);
            }
            else
            {
                yl[y1].Add(xx);
                xl[xx].Add(y1);
            }
            return true;
        }
        return false;
    }

    static long Count(long a, long b)
    {
        return a / b;
    }

    static void Main(string[] args)
    {
        new Program().Run();
    }

    static long Gcd(long a, long b)
    {
        if (a < b) return Gcd(b, a);
        if (b == 0) return a;
        return Gcd(b, a % b);
    }

    static long Lcm(long a, long b)
    {
        long d = Gcd(a, b);
        return a * b / d;
    }
}

class Scanner
{
    int index = -1;
    string[] buf;

    public Scanner()
    {
    }

    public int NextInt()
    {
        CheckNext();
        return int.Parse(buf[index++]);
    }

    public long NextLong()
    {
        CheckNext();
        return long.Parse(buf[index++]);
    }

    public double NextDouble()
    {
        CheckNext();
        return double.Parse(buf[index++]);
    }

    public string NextString()
    {
        CheckNext();
        return buf[index++];
    }

    private void CheckNext()
    {
        if (index >= 0 && index < buf.Length) return;

        buf = Console.ReadLine().Split(' ');
        index = 0;
    }
}