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: Runtime Error)

using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;

namespace Sandbox
{
    internal class Program
    {
        private static readonly int MaxNumber = 10001;

        private static readonly List<int>[] XtoY = Enumerable.Range(0, MaxNumber).Select(_ => new List<int>()).ToArray();
        private static readonly List<int>[] YtoX = Enumerable.Range(0, MaxNumber).Select(_ => new List<int>()).ToArray();
        private static readonly bool[] VisitedX = new bool[MaxNumber];
        private static readonly bool[] VisitedY = new bool[MaxNumber];

        private static void Main(string[] args)
        {
            var scanner = new Scanner();
            var n = scanner.GetNextAsInt();
            var maxX = int.MinValue;
            var maxY = int.MinValue;

            for (var i = 0; i < n; i++)
            {
                var xi = scanner.GetNextAsInt();
                var yi = scanner.GetNextAsInt();
                XtoY[xi].Add(yi);
                YtoX[yi].Add(xi);
                maxX = Math.Max(xi, maxX);
                maxY = Math.Max(xi, maxY);
            }

            var result = 0L;
            for (var xx = 1; xx <= maxX; xx++)
            {
                var countX = 0;
                var countY = 0;

                DfsX(xx, ref countX, ref countY);

                result += (long)countX * (long)countY;
            }

            result -= n;

            Console.WriteLine(result);
        }

        private static void DfsX(int x, ref int countX, ref int countY)
        {
            if (VisitedX[x])
            {
                return;
            }

            countX++;
            VisitedX[x] = true;
            foreach (var yy in XtoY[x])
            {
                DfsY(yy, ref countX, ref countY);
            }
        }

        private static void DfsY(int y, ref int countX, ref int countY)
        {
            if (VisitedY[y])
            {
                return;
            }

            countY++;
            VisitedY[y] = true;
            foreach (var xx in YtoX[y])
            {
                DfsX(xx, ref countX, ref countY);
            }
        }

        #region String Scanner

        public class Scanner
        {
            private const char Separator = ' ';
            private readonly StreamReader _Stream = new StreamReader(Console.OpenStandardInput());
            private int _Pos;
            private string[] _Line = new string[0];

            #region get a element

            public string GetNext()
            {
                // ReSharper disable once InvertIf
                if (this._Pos >= this._Line.Length)
                {
                    // ReSharper disable once PossibleNullReferenceException
                    this._Line = this._Stream.ReadLine().Split(Separator);
                    this._Pos = 0;
                }

                return this._Line[this._Pos++];
            }

            public int GetNextAsInt()
            {
                return int.Parse(this.GetNext());
            }

            public long GetNextAsLong()
            {
                return long.Parse(this.GetNext());
            }

            public double GetNextAsDouble()
            {
                return double.Parse(this.GetNext());
            }

            #endregion

            #region get array

            public string[] ToArrayFromNextLine()
            {
                if (this._Pos >= this._Line.Length)
                {
                    // ReSharper disable once PossibleNullReferenceException
                    this._Line = this._Stream.ReadLine().Split(Separator);
                }

                this._Pos = this._Line.Length;
                return this._Line;
            }

            public int[] ToIntArrayFromNextLine()
            {
                return ToIntArray(this.ToArrayFromNextLine());
            }

            public long[] ToLongArrayFromNextLine()
            {
                return ToLongArray(this.ToArrayFromNextLine());
            }

            public double[] ToDoubleArrayFromNextLine()
            {
                return ToDoubleArray(this.ToArrayFromNextLine());
            }

            #endregion

            #region convert array

            private static int[] ToIntArray(string[] array)
            {
                var result = new int[array.Length];
                for (var i = 0; i < array.Length; i++)
                {
                    result[i] = int.Parse(array[i]);
                }

                return result;
            }

            private static long[] ToLongArray(string[] array)
            {
                var result = new long[array.Length];
                for (var i = 0; i < array.Length; i++)
                {
                    result[i] = long.Parse(array[i]);
                }

                return result;
            }

            private static double[] ToDoubleArray(string[] array)
            {
                var result = new double[array.Length];
                for (var i = 0; i < array.Length; i++)
                {
                    result[i] = double.Parse(array[i]);
                }

                return result;
            }

            #endregion
        }

        #endregion
    }
}