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: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Text;
using System.Linq;
using static MyIO;


public class D
{
	public static void Main()
	{
		int N = GetInt();
		var cities = new List<Tuple<int, int, int>>(N);
		for(int i = 0; i < N; i++)
			cities.Add(Tuple.Create(GetInt(), GetInt(), i));

		var edges = new List<Edge>(2 * N);

		cities.Sort((p, q) => p.Item1 - q.Item1);
		for(int i = 0; i < N - 1; i++)
		{
			int a = cities[i].Item3;
			int c = cities[i+1].Item3;
			edges.Add(new Edge(a, c, cities[i+1].Item1 - cities[i].Item1));
		}

		cities.Sort((p, q) => p.Item2 - q.Item2);
		for(int i = 0; i < N - 1; i++)
		{
			int b = cities[i].Item3;
			int d = cities[i+1].Item3;
			edges.Add(new Edge(b, d, cities[i+1].Item2 - cities[i].Item2));
		}

		Console.WriteLine(Kruskal(N, edges));
	}

	public static int Kruskal(int N, List<Edge> edges)
	{
		edges.Sort((x, y) => x.Cost - y.Cost);
		var uf = new UnionFind(N);
		int res = 0;
		for(int i = 0; i < edges.Count; i++)
		{
			Edge edge = edges[i];
			if(!uf.IsSame(edge.S, edge.T))
			{
				uf.Merge(edge.S, edge.T);
				res += edge.Cost;
			}
		}
		return res;
	} 
}


public struct Edge
{
	public int S;
	public int T;
	public int Cost;

	public Edge(int s, int t, int cost)
	{
		S = s;
		T = t;
		Cost = cost;
	}
}


public class UnionFind
{
	private int[] par = null;
	private int[] rank = null;
	private int[] ccSize = null;
	
	public UnionFind(int n)
	{
		par = new int[n];
		rank = new int[n];
		ccSize = new int[n];
		for(int i = 0; i < n; i++)
		{
			par[i] = i;
			rank[i] = 0;
			ccSize[i] = 1;
		}
	}

	public bool IsSame(int x, int y)
	{
		return (Root(x) == Root(y));
	}

	public int Root(int x)
	{
		if(par[x] == x)
			return x;

		int r = Root(par[x]);
		par[x] = r;
		return r;
	}
	
	public bool Merge(int x, int y)
	{
		int rx = Root(x);
		int ry = Root(y);
		if(rx == ry)
			return false;
		
		if(rank[rx] < rank[ry])
		{
			int tmp = rx;
			rx = ry;
			ry = tmp;
		}
		else if(rank[rx] == rank[ry])
			rank[rx]++;

		par[ry] = rx;
		ccSize[rx] = ccSize[rx] + ccSize[ry];
		return true;
	}

	public int Size(int x)
	{
		return ccSize[Root(x)];
	}
}


public static class MyIO
{
	private static string[] args = null;
	private static int num = -1;
	private static int used = -1;

	private static string getArg()
	{
		if(used == num)
		{
			args = Console.ReadLine().Split(' ');
			num = args.Length;
			used = 0;
		}
		return args[used++];
	}

	public static int GetInt(){ return int.Parse(getArg()); }
	public static long GetLong(){ return long.Parse(getArg()); }
	public static double GetDouble(){ return double.Parse(getArg()); }
	public static string GetString(){ return getArg(); }
}