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.IO;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using static System.Console;
using static System.Math;
using static Func;
class Z { static void Main() => new K(); }
class K
{
	int F => int.Parse(Str);
	long FL => long.Parse(Str);
	int[] G => Strs.Select(int.Parse).ToArray();
	uint[] GU => Strs.Select(uint.Parse).ToArray();
	decimal[] GD => Strs.Select(decimal.Parse).ToArray();
	long[] GL => Strs.Select(long.Parse).ToArray();
	string Str => ReadLine();
	string[] Strs => Str.Split(new char[] { ' ', '\t' }, StringSplitOptions.RemoveEmptyEntries);
	static ulong One(int k) => 1ul << k;
	static ulong All(int k) => One(k) - 1;
	static bool Has(ulong s, int k) => (s & One(k)) != 0;
	const int MOD = 1000000007;
	public K()
	{
		SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
		Solve();
		Out.Flush();
	}
	void Solve()
	{
		var N = F;
		var ps = new List<Point>();
		for (var i = 0; i < N; i++)
		{
			var I = G;
			ps.Add(new Point(I[0], I[1]));
		}
		var xs = new HashSet<int>(ps.Select(p => p.X)).ToList();
		var ys = new HashSet<int>(ps.Select(p => p.Y)).ToList();
		var X = xs.Count;
		var Y = ys.Count;
		var rx = new Dictionary<int, int>();
		var ry = new Dictionary<int, int>();
		for (var i = 0; i < X; i++) rx[xs[i]] = i;
		for (var i = 0; i < Y; i++) ry[ys[i]] = i;
		var uf = new UnionFindTree(N + X + Y);
		for (var i = 0; i < N; i++)
		{
			uf.UniteCategory(i, N + rx[ps[i].X]);
			uf.UniteCategory(i, N + X + ry[ps[i].Y]);
		}
		var sum = 0L;
		var kx = new Dictionary<int, int>();
		var ky = new Dictionary<int, int>();
		for (var i = 0; i < N + X + Y; i++) kx[uf.GetRootOf(i)] = ky[uf.GetRootOf(i)] = 0;
		for (var i = 0; i < X; i++) kx[uf.GetRootOf(N + i)]++;
		for (var i = 0; i < Y; i++) ky[uf.GetRootOf(N + X + i)]++;
		for (var i = 0; i < N + X + Y; i++) if (i == uf.GetRootOf(i)) sum += kx[i] * (long)ky[i];
		WriteLine(sum - N);
	}
}
class UnionFindTree
{
	int N;
	int[] parent, rank, size;
	public UnionFindTree(int capacity)
	{
		N = capacity;
		parent = new int[N];
		rank = new int[N];
		size = new int[N];
		for (var i = 0; i < N; i++) { parent[i] = i; size[i] = 1; }
	}
	public int GetSize(int x) => size[GetRootOf(x)];
	public int GetRootOf(int x) => parent[x] == x ? x : parent[x] = GetRootOf(parent[x]);
	public bool UniteCategory(int x, int y)
	{
		if ((x = GetRootOf(x)) == (y = GetRootOf(y))) return false;
		if (rank[x] < rank[y]) { parent[x] = y; size[y] += size[x]; }
		else
		{
			parent[y] = x; size[x] += size[y];
			if (rank[x] == rank[y]) rank[x]++;
		}
		return true;
	}
	public bool IsSameCategory(int x, int y) => GetRootOf(x) == GetRootOf(y);
}
struct Point
{
	public readonly int X, Y;
	public Point(int x, int y) { X = x; Y = y; }
}
static class Func
{
	static T[] ConstantArray<T>(int n, T val) { var a = new T[n]; for (var i = 0; i < n; i++) a[i] = val; return a; }
	static T[] MakeArray<T>(int n, Func<int, T> f) { var a = new T[n]; for (var i = 0; i < n; i++) a[i] = f(i); return a; }
	static T[] Recurse<T>(int n, T a0, Func<int, T, T> f) { var a = new T[n]; a[0] = a0; for (var i = 1; i < n; i++) a[i] = f(i, a[i - 1]); return a; }
	static T[] Accumulate<T>(IList<T> a, T zero, Func<T, T, T> f) { var s = new T[a.Count + 1]; s[0] = zero; for (var i = 0; i < a.Count; i++) s[i + 1] = f(s[i], a[i]); return s; }
	public static long GCD(long a, long b)
	{
		var n = (ulong)Math.Abs(a); var m = (ulong)Math.Abs(b);
		if (n == 0) return (long)m; if (m == 0) return (long)n;
		int zm = 0, zn = 0;
		while ((n & 1) == 0) { n >>= 1; zn++; }
		while ((m & 1) == 0) { m >>= 1; zm++; }
		while (m != n)
		{
			if (m > n) { m -= n; while ((m & 1) == 0) m >>= 1; }
			else { n -= m; while ((n & 1) == 0) n >>= 1; }
		}
		return (long)n << Math.Min(zm, zn);
	}
	public static long Inverse(long a, long mod)
	{
		if (a < 0) { a %= mod; if (a < 0) a += mod; }
		var t = SolveLinear(a, mod);
		return t.Item1 > 0 ? t.Item1 : t.Item1 + mod;
	}
	public static long Pow(long a, long b, long mod)
	{
		var p = 1L;
		var x = a;
		while (b > 0)
		{
			if ((b & 1) == 1) p = (p * x) % mod;
			b >>= 1;
			x = (x * x) % mod;
		}
		return p;
	}
	public static Tuple<long, long> SolveLinear(long n, long m)
	{
		if (n < 0) { var p = SolveLinear(-n, m); return p == null ? p : new Tuple<long, long>(-p.Item1, p.Item2); }
		if (m < 0) { var p = SolveLinear(n, -m); return p == null ? p : new Tuple<long, long>(p.Item1, -p.Item2); }
		if (n < m) { var p = SolveLinear(m, n); return p == null ? p : new Tuple<long, long>(p.Item2, p.Item1); }
		long a = 1, b = 0, c = 0, d = 1;
		while (m > 0)
		{
			var r = n % m;
			var q = n / m;
			n = m;
			m = r;
			var tmp = a;
			a = -a * q + b;
			b = tmp;
			tmp = c;
			c = -c * q + d;
			d = tmp;
		}
		return n != 1 ? null : new Tuple<long, long>(d, b);
	}
}