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.IO;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
namespace ProCon
{

    class Program
    {

        static void Main(string[] args)
        {
            int num = int.Parse(Console.ReadLine());

            List<TwoNums> listX = new List<TwoNums>();
            List<TwoNums> listY = new List<TwoNums>();

            for (int i = 0; i < num; ++i)
            {
                string[] input = Console.ReadLine().Split(' ');
                listX.Add(new TwoNums(i, int.Parse(input[0])));
                listY.Add(new TwoNums(i, int.Parse(input[1])));
            }
            listX.Sort((a, b) => a.Value2 - b.Value2);
            listY.Sort((a, b) => a.Value2 - b.Value2);
            Graph graph = new Graph(num);
            for (int i = 0; i < num - 1; ++i)
            {
                graph.AddLine(listX[i].Value1, listX[i + 1].Value1, listX[i + 1].Value2 - listX[i].Value2);
                graph.AddLine(listY[i].Value1, listY[i + 1].Value1, listY[i + 1].Value2 - listY[i].Value2);
            }
            Console.WriteLine(graph.GetMinimamAllTree());
        }
    }
    struct TwoNums
    {
        public TwoNums(int n, int m)
        {
            Value1 = n;
            Value2 = m;
        }
        public int Value1 { get; private set; }
        public int Value2 { get; private set; }
    }
    class Graph
    {
        struct Line
        {
            public Line(int i1, int i2, int cost)
            {
                Index1 = i1;
                Index2 = i2;
                Cost = cost;
            }
            public int Index1{ get; private set; }
            public int Index2{ get; private set; }
            public int Cost { get; private set; }
            
        }
        public Graph(int nodesNum)
        {
            Lines = new List<Line>();
            NodesNum = nodesNum;
        }
        public void MakeNodes(int num)
        {
            NodesNum = num;
        }
        public void AddLine(int i1, int i2, int cost)
        {
            Lines.Add(new Line(i1, i2, cost));
        }
        public int GetMinimamAllTree()
        {
            int[] group = new int[NodesNum];
            for(int i = 0; i < NodesNum; ++i)
            {
                group[i] = i;
            }
            int ConnectNum = 0;
            int cost = 0;
            Lines.Sort((a,b)=>a.Cost - b.Cost);
            for( int i=0;i<Lines.Count;++i)
            {
                if(group[Lines[i].Index1] != group[Lines[i].Index2])
                {
                    cost += Lines[i].Cost;
                    ConnectNum++;
                    if ( ConnectNum >= NodesNum - 1)
                    {
                        return cost;
                    }
                    group[Math.Min(Lines[i].Index1, Lines[i].Index2)] = group[Math.Max(Lines[i].Index1, Lines[i].Index2)];
                } 
            }
            return -1;
        }
        int NodesNum;
        List<Line> Lines;
    }
}