Problem:
Score : 500 points

Problem Statement

There are N towns on a plane. The i-th town is located at the coordinates (x_i,y_i). There may be more than one town at the same coordinates.

You can build a road between two towns at coordinates (a,b) and (c,d) for a cost of min(|a-c|,|b-d|) yen (the currency of Japan). It is not possible to build other types of roads.

Your objective is to build roads so that it will be possible to travel between every pair of towns by traversing roads. At least how much money is necessary to achieve this?

Constraints

2 ≤ N ≤ 10^5

0 ≤ x_i,y_i ≤ 10^9

All input values are integers.

Input

Input is given from Standard Input in the following format:

N
x_1 y_1
x_2 y_2
:
x_N y_N

Output

Print the minimum necessary amount of money in order to build roads so that it will be possible to travel between every pair of towns by traversing roads.

Sample Input 1

3
1 5
3 9
7 8

Sample Output 1

3

Build a road between Towns 1 and 2, and another between Towns 2 and 3. The total cost is 2+1=3 yen.

Sample Input 2

6
8 3
4 9
12 19
18 1
13 5
7 6

Sample Output 2

8

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using static System.Console;
using static System.Convert;
using static System.Math;
//using static System.Globalization.CultureInfo;

class Program
{
    class P:IComparable<P>
    {
        public int index;
        public long Weight;
        public List<int> adj;
        public Dictionary<int, long> weights;
        public P(int index)
        {
            this.index = index;
            adj = new List<int>();
            weights = new Dictionary<int,long>();
            Weight = long.MaxValue;
        }
        public int CompareTo(P p)
            => Weight.CompareTo(p.Weight);
    }
    static void Main(string[] args)
    {
        var num = Input.num;
        var xy = Enumerable.Range(0, num).Select(v => new KeyValuePair<int,int[]>(v,Input.ar)).ToArray(); 
        var ps = Enumerable.Range(0, num).Select(v => new P(v)).ToArray();
        for (var k = 0; k < 2; k++)
        {
            xy = xy.OrderBy(pair => pair.Value[k]).ToArray();
            for (var i = 1; i < num; i++)
                for (var j = 0; j < 2; j++)
                {
                    ps[xy[i - j].Key].adj.Add(xy[i + j - 1].Key);
                    ps[xy[i - j].Key].weights[xy[i + j - 1].Key] = Min(ps[xy[i - j].Key].weights.ContainsKey(xy[i + j - 1].Key) ? ps[xy[i - j].Key].weights[xy[i + j - 1].Key] : long.MaxValue, (long)xy[i].Value[k] - xy[i - 1].Value[k]);
                }
        }
        var pQue = new PriorityQueue<P>(false, new P(-1));
        ps[0].Weight = 0;
        pQue.Enqueue(ps[0]);
        var bo = new bool[num];
        while (!pQue.isEmpty)
        {
            var u = pQue.Dequeue();
            bo[u.index] = true;
            foreach (var ad in u.adj)
                if (!bo[ad] && ps[ad].Weight > u.weights[ad])
                {
                    ps[ad].Weight = u.weights[ad];
                    pQue.Enqueue(ps[ad]);
                }
        }
        WriteLine(ps.Sum(p => p.Weight));
    }
}

public class Input
{
    public static string read => ReadLine();
    public  static int[] ar => Array.ConvertAll(read.Split(' '), int.Parse);
    public  static int num => ToInt32(read);
    public  static long[] arL => Array.ConvertAll(read.Split(' '), long.Parse);
    public  static long numL => ToInt64(read);
    public  const string Alfa = "abcdefghijklmnopqrstuvwxyz";
    public  const int MOD = 1000000007;
}

public class PriorityQueue<T> where T : IComparable<T>
{
    private readonly List<T> items;
    private T MinValue { get; }//一番優先度が低い値

    public bool IsMax { get; }
    public int Size { get { return items.Count; } }
    public bool isEmpty { get { return items.Count == 0; } }
    
    public PriorityQueue(T minValue) : this(true, minValue)
    {

    }

    public PriorityQueue(bool IsMax, T MinValue)
    {
        this.items = new List<T>();
        this.IsMax = IsMax;
        this.MinValue = MinValue;
    }

    private int Parent(int num)
    {
        return (int)Math.Ceiling((double)num / 2) - 1;
    }
    private int Left(int num)
    { 
        return 2 * num + 1;
    }
    private int Right(int num)
    { 
        return 2 * (num + 1);
    }

    private void MaxHeapify(int num)
    {
        var left = Left(num);
        var right = Right(num);
        var largest = 0;
        if (Size >= left + 1 && items[left].CompareTo(items[num]) == 1)
            largest = left;
        else largest = num;
        if (Size >= right + 1 && items[right].CompareTo(items[largest]) == 1)
            largest = right;
        if (largest != num)
        {
            var value = items[largest];
            items[largest] = items[num];
            items[num] = value;
            MaxHeapify(largest);
        }
    }

    private void MinHeapify(int num)
    {
        var left = Left(num);
        var right = Right(num);
        var smallest = 0;
        if (Size >= left + 1 && items[num].CompareTo(items[left]) == 1) smallest = left;
        else smallest = num;
        if (Size >= right + 1 && items[smallest].CompareTo(items[right]) == 1) smallest = right;
        if (smallest != num)
        {
            var value = items[smallest];
            items[smallest] = items[num];
            items[num] = value;
            MinHeapify(smallest);
        }
    }

    private void BuildHeap()
    {
        for (var i = (int)Math.Ceiling((double)Size / 2) - 1; i >= 0; i--)
        {
            if (IsMax) MaxHeapify(i);
            else MinHeapify(i);
        }
    }

    private bool ChangeKey(int index, T reValue)
    {
        if (IsMax && items[index].CompareTo(reValue) == 1)
            return false;
        if (!IsMax && items[index].CompareTo(reValue) == -1)
            return false;
        items[index] = reValue;
        if (IsMax)
        {
            while (index > 0 && items[Parent(index)].CompareTo(items[index]) == -1)
            {
                var value = items[Parent(index)];
                items[Parent(index)] = items[index];
                items[index] = value;
                index = Parent(index);
            }
        }
        else
        {
            while (index > 0 && items[Parent(index)].CompareTo(items[index]) == 1)
            {
                var value = items[Parent(index)];
                items[Parent(index)] = items[index];
                items[index] = value;
                index = Parent(index);
            }
        }
        return true;
    }

    public T Peek { get { return items[0]; } }

    public T Dequeue()
    {
        if (Size <= 0) return default(T);
        var value = items[0];
        items[0] = items[Size - 1];
        items.RemoveAt(Size - 1);
        if (IsMax) MaxHeapify(0);
        else MinHeapify(0);
        return value;
    }

    public bool Enqueue(T key)
    {
        items.Add(MinValue);
        return ChangeKey(Size - 1, key);
    }

    public bool Delete(int index)
    {
        if (index >= Size)
            return false;
        var value = items[index];
        items[index] = items[Size - 1];
        items[Size - 1] = value;
        items.RemoveAt(Size - 1);
        if (IsMax) MaxHeapify(0);
        else MinHeapify(0);
        return true;
    }
}