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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Runtime.CompilerServices;
using static System.Math;
using System.Text;

namespace Program
{
    public static class ABC131F
    {
        class UF
        {
            public Dictionary<long, long> _par = new Dictionary<long, long>();
            public Dictionary<long, long> _count = new Dictionary<long, long>();
            public Dictionary<long, Tuple<HashSet<long>, HashSet<long>>> _data = new Dictionary<long, Tuple<HashSet<long>, HashSet<long>>>();
            public long Root(long key)
            {
                if (_par[key] == key) return key;
                return _par[key] = Root(_par[key]);
            }
            public long Count(long key)
            {
                return _count[Root(key)];
            }
            public void Unite(long key1, long x1, long y1, long key2, long x2, long y2)
            {
                var k1 = _par.ContainsKey(key1);
                if (key1 == key2)
                {
                    if (!k1)
                    {
                        _par[key1] = key1;
                        _count[key1] = 1;
                        _data[key1] = Tuple.Create(new HashSet<long>(), new HashSet<long>());
                        _data[key1].Item1.Add(x1);
                        _data[key1].Item2.Add(y1);
                    }
                    return;
                }
                var k2 = _par.ContainsKey(key2);
                if (!k1 && !k2)
                {
                    _par[key1] = key1;
                    _par[key2] = key1;
                    _count[key1] = 2;
                    _data[key1] = Tuple.Create(new HashSet<long>(), new HashSet<long>());
                    _data[key1].Item1.Add(x1);
                    _data[key1].Item2.Add(y1);
                    _data[key1].Item1.Add(x2);
                    _data[key1].Item2.Add(y2);
                }
                else if (!k1 && k2)
                {
                    var rt = Root(key2);
                    _par[key1] = rt;
                    _count[rt]++;
                    _data[rt].Item1.Add(x1);
                    _data[rt].Item2.Add(y1);
                }
                else if (k1 && !k2)
                {
                    var rt = Root(key1);
                    _par[key2] = rt;
                    _count[rt]++;
                    _data[rt].Item1.Add(x2);
                    _data[rt].Item2.Add(y2);
                }
                else
                {
                    var r1 = Root(key1);
                    var r2 = Root(key2);
                    if (r1 == r2) return;
                    _count[r2] += _count[r1];
                    _par[r1] = r2;
                    var tmp = _data[r1];
                    var tmp2 = _data[r2];
                    foreach (var item in tmp.Item1)
                    {
                        tmp2.Item1.Add(item);
                    }
                    foreach (var item in tmp.Item2)
                    {
                        tmp2.Item2.Add(item);
                    }
                }
            }
        }
        static public void Solve()
        {
            var N = NextInt;
            var xy = Enumerable.Repeat(0, N).Select(_ => new { x = NextLong, y = NextLong }).ToList();
            var xDic = xy.GroupBy(e => e.x).ToDictionary(e => e.Key, e => e.Select(e2 => e2.y).ToList());
            var yDic = xy.GroupBy(e => e.y).ToDictionary(e => e.Key, e => e.Select(e2 => e2.x).ToList());
            var uf = new UF();
            foreach (var item in xDic)
            {
                if (item.Value.Count > 1)
                {
                    var keymaster = 0L;
                    foreach (var y in item.Value)
                    {
                        if (keymaster == 0L)
                        {
                            keymaster = item.Key * 10000000 + y;
                        }
                        foreach (var x in yDic[y])
                        {
                            var key = x * 10000000 + y;
                            uf.Unite(keymaster, item.Key, y, key, x, y);
                        }
                    }
                }
            }
            var inputPointCount = 0L;
            var totalPointCount = 0L;
            foreach (var item in uf._par)
            {
                if (item.Key != item.Value) continue;
                if (uf.Count(item.Key) > 2)
                {
                    inputPointCount += uf.Count(item.Key);
                    totalPointCount += uf._data[item.Key].Item1.LongCount() * uf._data[item.Key].Item2.LongCount();
                }
            }
            Console.WriteLine(totalPointCount - inputPointCount);
        }

        static public void Main(string[] args)
        {
            if (args.Length == 0)
            {
                var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
                Console.SetOut(sw);
            }
            Solve();
            Console.Out.Flush();
        }
        static class Console_
        {
            private static Queue<string> param = new Queue<string>();
            public static string NextString()
            {
                if (param.Count == 0) foreach (var item in Console.ReadLine().Split(' ')) param.Enqueue(item);
                return param.Dequeue();
            }
        }
        static int NextInt => int.Parse(Console_.NextString());
        static long NextLong => long.Parse(Console_.NextString());
        static double NextDouble => double.Parse(Console_.NextString());
        static string NextString => Console_.NextString();
    }
}