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.Text;
using System.Linq;
using static MyIO;


public class F
{
	public static void Main() => (new Solver()).Solve();
}


public class Solver
{
	public static readonly int MAX = 100000;

	public void Solve()
	{
		int N = GetInt();
		int[] x = new int[N];
		int[] y = new int[N];
		for(int i = 0; i < N; i++)
		{
			x[i] = GetInt() - 1;
			y[i] = GetInt() - 1 + MAX;
		}

		var uf = new UnionFind(2 * MAX);
		for(int i = 0; i < N; i++)
		{
			if(!uf.IsSame(x[i], y[i]))
				uf.Merge(x[i], y[i]);
		}

		var set = new HashSet<int>();
		var cntX = new Dictionary<int, long>();
		var cntY = new Dictionary<int, long>();
		for(int i = 0; i < MAX; i++)
		{
			long tmpX = 0;
			cntX.TryGetValue(uf.Root(i), out tmpX);
			cntX[uf.Root(i)] = tmpX + 1;
			set.Add(uf.Root(i));
		}

		for(int i = MAX; i < 2 * MAX; i++)
		{
			long tmpY = 0;
			cntY.TryGetValue(uf.Root(i), out tmpY);
			cntY[uf.Root(i)] = tmpY + 1;
			set.Add(uf.Root(i));
		}

		long ans = 0;
		foreach(int r in set)
		{
			long tmpX = 0;
			cntX.TryGetValue(r, out tmpX);
			long tmpY = 0;
			cntY.TryGetValue(r, out tmpY);
			ans += tmpX * tmpY;
		}

		Console.WriteLine(ans - N);
	}
}


public class UnionFind
{
	private int[] par = null;
	private int[] rank = null;
	private int[] ccSize = null;
	
	public UnionFind(int n)
	{
		par = new int[n];
		rank = new int[n];
		ccSize = new int[n];
		for(int i = 0; i < n; i++)
		{
			par[i] = i;
			rank[i] = 0;
			ccSize[i] = 1;
		}
	}

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

	public int Root(int x)
	{
		if(par[x] == x)
			return x;

		int r = Root(par[x]);
		par[x] = r;
		return r;
	}
	
	public bool Merge(int x, int y)
	{
		int rx = Root(x);
		int ry = Root(y);
		if(rx == ry)
			return false;
		
		if(rank[rx] < rank[ry])
		{
			int tmp = rx;
			rx = ry;
			ry = tmp;
		}
		else if(rank[rx] == rank[ry])
			rank[rx]++;

		par[ry] = rx;
		ccSize[rx] = ccSize[rx] + ccSize[ry];
		return true;
	}

	public int Size(int x)
	{
		return ccSize[Root(x)];
	}
}


public static class MyIO
{
	private static string[] args = null;
	private static int num = -1;
	private static int used = -1;

	private static string getArg()
	{
		if(used == num)
		{
			args = Console.ReadLine().Split(' ');
			num = args.Length;
			used = 0;
		}
		return args[used++];
	}

	public static int GetInt() => int.Parse(getArg());
	public static long GetLong() => long.Parse(getArg());
	public static double GetDouble() => double.Parse(getArg());
	public static string GetString() => getArg();
	public static char GetChar() => getArg()[0];
	public static int[] GetInts(int N) => Enumerable.Range(0, N).Select(_ => GetInt()).ToArray();
	public static long[] GetLongs(int N) => Enumerable.Range(0, N).Select(_ => GetLong()).ToArray();
	public static double[] GetDoubles(int N) => Enumerable.Range(0, N).Select(_ => GetDouble()).ToArray();
	public static string[] GetStrings(int N) => Enumerable.Range(0, N).Select(_ => GetString()).ToArray();
}