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: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.IO;
using System.Numerics;

class Program
{
    const int MOD = 1000000007;
    static void Main(string[] args)
    {
        new Program().Solve();
    }

    void Solve()
    {

        //http://drken1215.hatenablog.com/entry/2019/06/23/004700
        Scanner cin = new Scanner();
        int n = cin.NextInt();
        int MAX = 110000;

        UnionFind uf = new UnionFind(MAX * 2);
        for (int i = 0; i < n; i++)
        {
            uf.Merge(cin.NextInt(), cin.NextInt() + MAX);
        }

        List<int> index = Enumerable.Range(0, MAX * 2).ToList();
        Dictionary<int, long> mx = index.ToDictionary(i => i, i => 0L);
        Dictionary<int, long> my = index.ToDictionary(i => i, i => 0L);

        for (int i = 0; i < MAX; i++)
        {
            mx[uf.Root(i)]++;
        }

        for (int i = MAX; i < MAX * 2; i++)
        {
            my[uf.Root(i)]++;
        }

        long result = 0;
        for (int i = 0; i < MAX * 2; i++)
        {
            result += mx[i] * my[i];
        }
        Console.WriteLine(result - n);
    }
}

class Util
{
    public static void Swap(ref int a, ref int b)
    {
        a ^= b; // a = a ^ b
        b ^= a; // b = b ^ (a ^ b) // this is a.
        a ^= b; // a = (a ^ b) ^ (b ^ (a ^ b)) // this is b.
    }
}

class UnionFind
{
    private List<int> parentVertexes = new List<int>();

    public UnionFind(int n)
    {
        parentVertexes = Enumerable.Repeat(-1, n).ToList();
    }

    public int Root(int vertexIndex)
    {
        if(parentVertexes[vertexIndex] < 0)
        {
            return vertexIndex;
        }

        parentVertexes[vertexIndex] = Root(parentVertexes[vertexIndex]);
        return parentVertexes[vertexIndex];

    }

    public bool IsSame(int x, int y)
    {
        return Root(x) == Root(y);
    }

    public bool Merge(int x, int y)
    {
        // replace targets with roots
        x = Root(x);
        y = Root(y);
        if (IsSame(x, y))
        {
            return false;
        }
        if (parentVertexes[x] > parentVertexes[y])
        {
            // merge technique
            Util.Swap(ref x, ref y);
        }

        parentVertexes[x] += parentVertexes[y];
        parentVertexes[y] = x;
        return true;
    }

}


class Scanner
{
    string[] s;
    int i;

    char[] cs = new char[] { ' ' };

    public Scanner()
    {
        s = new string[0];
        i = 0;
    }

    public string Next()
    {
        if (i < s.Length) return s[i++];
        string st = Console.ReadLine();
        while (st == "") st = Console.ReadLine();
        s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
        if (s.Length == 0) return Next();
        i = 0;
        return s[i++];
    }

    public int NextInt()
    {
        return int.Parse(Next());
    }

    public char[] ArrayChar()
    {
        return Next().ToCharArray();
    }
    public int[] ArrayInt(int N, int add = 0)
    {
        int[] Array = new int[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = NextInt() + add;
        }
        return Array;
    }

    public long NextLong()
    {
        return long.Parse(Next());
    }

    public long[] ArrayLong(int N, long add = 0)
    {
        long[] Array = new long[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = NextLong() + add;
        }
        return Array;
    }

    public double NextDouble()
    {
        return double.Parse(Next());
    }


    public double[] ArrayDouble(int N, double add = 0)
    {
        double[] Array = new double[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = NextDouble() + add;
        }
        return Array;
    }
}