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.Linq;
using System.IO;
using static System.Console;
using static System.Math;
 
public class Solve{
    static public int mod = 1000000007;
    public static void Main(){
        // 方針
        //
        var n = rint();
        var zax = new int[n];
        var zay = new int[n];
        var numx = new int[n];
        var numy = new int[n];
        for(int i=0;i<n;i++){
            numx[i] = i;
            numy[i] = i;
        }
        for(int i=0;i<n;i++){
            var a = inta();
            zax[i] = a[0];
            zay[i] = a[1];
        }
        Array.Sort(zax,numx);
        Array.Sort(zay,numy);
        //WriteLine(string.Join(" ",zay));
        //WriteLine(string.Join(" ",numy));
        
        var pq3 = new PriorityQueue3();
        var uf = new UnionFind(n);
        
        for(int i=0;i<n-1;i++){
            pq3.Enqueue(Abs(zax[i]-zax[i+1]),numx[i],numx[i+1]);
            pq3.Enqueue(Abs(zay[i]-zay[i+1]),numy[i],numy[i+1]);
        }
        
        long ans = 0;
        while(pq3.Count() > 0){
            var de = pq3.Dequeue();
            long distance = de[0];
            var num1 = de[1];
            var num2 = de[2];
            if(!uf.same(num1,num2)){
                ans += distance;
                uf.unite(num1,num2);
            }
        }
        
        WriteLine(ans);
        
	
	
    }
    public static void swap(ref int a,ref int b){int temp = a;a= b;b = temp;}
    static void charswap(ref char a,ref char b){char temp = a;a= b;b = temp;}
    static int ncr(int n,int r){if(n<r)return 0;r = Min(r,n-r);long nn = 1;for(int i=n-r+1;i<=n;i++){nn = nn*i%mod;}long rr = 1;for(int i=1;i<=r;i++){rr = rr*i%mod;}rr = square((int)rr,mod-2);nn = nn * rr %mod;return (int)nn;}
    // a^b mod
    static int square(int a,int b){string binary = Convert.ToString(b,2);int bileng = binary.Length;long a_power = a;long value = 1;for(int i=bileng-1;i>=0;i--){if(binary[i] == '1'){value = value*a_power%mod;}a_power = a_power*a_power%mod;}return (int)value;}
    static int square2(int a,int b){long output = 1;var list = new List<long>();int sh = 1;long n = a;list.Add(a);while(sh < b){sh *= 2;n = n*n%mod;list.Add(n);}for(int i=list.Count-1;i>=0;i--){if(b > sh){b -= sh;sh /= 2;output = output*list[i]%mod;}}return (int)output;}
    //各種読取
    static string rstr(){ return ReadLine(); }
    static int rint(){ return int.Parse(ReadLine()); }
    static long rlong(){ return long.Parse(ReadLine()); }
    static string[] stra(){ return ReadLine().Split(' '); }
    static char[] chara(){ string[] a=stra();string b="";for(int i=0;i<a.Length;i++){b+=a[i];}return b.ToCharArray();}
    static int[] inta(){ string[] read_str_array = ReadLine().Split(' '); int[] return_int_array = new int[read_str_array.Length]; for(int countup_i=0;countup_i<read_str_array.Length;countup_i++){ return_int_array[countup_i] = int.Parse(read_str_array[countup_i]); } return return_int_array; }
    static int[,] inta2(int num_array,int in_array){ int[,] int_array2 = new int[num_array,in_array]; for(int i=0;i<num_array;i++){ int[] temp_array = inta(); for(int j=0;j<in_array;j++){ int_array2[i,j] = temp_array[j]; } } return int_array2; }
    static long[] longa(){ string[] read_str_array = ReadLine().Split(' '); long[] return_long_array = new long[read_str_array.Length]; for(long countup_i=0;countup_i<read_str_array.Length;countup_i++){ return_long_array[countup_i] = long.Parse(read_str_array[countup_i]); } return return_long_array; }
    static double[] doublea(){ string[] read_str_array = ReadLine().Split(' '); double[] return_double_array = new double[read_str_array.Length]; for(long countup_i=0;countup_i<read_str_array.Length;countup_i++){ return_double_array[countup_i] = long.Parse(read_str_array[countup_i]); } return return_double_array; }
    // -----------------------------
    static long divideup(long divided,long divid){ long temp_divide = divided/divid; if(divided % divid > 0){ temp_divide++; } return temp_divide; }
    static long GCD(long a,long b){ if(a < b){ long temp = a; a = b; b = temp; } if(a % b == 0){ return b; } else{ long temp = b; b = a%b; a = temp; return GCD(a,b); } }
    static long LCM(long a,long b){ return a * b / GCD(a,b); }
    static void WriteArray(int[,] a,int b,int c){for(int i=0;i<b;i++){for(int j=0;j<c;j++){if(j!=0) Write(" ");Write(a[i,j]);}WriteLine();}}
}

class UnionFind{
    private int[] _unionfind;
    private int[] _unionfind_size;
    
    public UnionFind(int a){
        _unionfind = new int[a];
        _unionfind_size = new int[a];
        for(int i=0;i<a;i++){
            _unionfind[i] = i;
            _unionfind_size[i] = 1;
        }
    }
    
    public int root(int x){
        if(_unionfind[x] == x) return x;
        return _unionfind[x] = root(_unionfind[x]);
    }
    
    public void unite(int a,int b){
        a = root(a);
        b = root(b);
        if(a == b) return;
        if(_unionfind_size[a] < _unionfind_size[b]){
            int temp = a;
            a = b;
            b = temp;
        }
        _unionfind[b] = a;
        _unionfind_size[a] += _unionfind_size[b];
    }
    
    public bool same(int a,int b){
        return root(a) == root(b);
    }
    
    public int size(int x){
        return _unionfind_size[root(x)];
    }
}

class PriorityQueue{
    private List<int> _priorityqueue = new List<int>();
    
    public void Enqueue(int a){
        _priorityqueue.Add(a);
        int num = _priorityqueue.Count-1;
        while(true){
            if(num == 0) break;
            if(_priorityqueue[(num-1)/2] < _priorityqueue[num]){ //大小逆の時弄るとこ
                int temp = _priorityqueue[(num-1)/2];
                _priorityqueue[(num-1)/2] = _priorityqueue[num];
                _priorityqueue[num] = temp;
                num = (num-1)/2;
            }else{
                break;
            }
        }
    }
    
    public int Dequeue(){
        int re = _priorityqueue[0];
        int temp = _priorityqueue[0];
        _priorityqueue[0] = _priorityqueue[_priorityqueue.Count-1];
        _priorityqueue[_priorityqueue.Count-1] = temp;
        _priorityqueue.RemoveAt(_priorityqueue.Count-1);
        int num = 0;
        while(true){
            int swapnum = -1;
            if((num+1)*2 < _priorityqueue.Count){
                if(_priorityqueue[num*2+1] > _priorityqueue[(num+1)*2]){ //大小逆の時弄るとこ
                    swapnum = num*2+1;
                }else{
                    swapnum = (num+1)*2;
                }
            }else if(num*2+1 < _priorityqueue.Count){
                swapnum = num*2+1;
            }
            if(swapnum == -1) break;
            if(_priorityqueue[swapnum] > _priorityqueue[num]){ //大小逆の時弄るとこ
                temp = _priorityqueue[swapnum];
                _priorityqueue[swapnum] = _priorityqueue[num];
                _priorityqueue[num] = temp;
                num = swapnum;
            }else{
                break;
            }
        }
        return re;
    }
    
    public int Peek(){
        return _priorityqueue[0];
    }
    
    public int Count(){
        return _priorityqueue.Count;
    }
}
class PriorityQueue2{
    private List<int> _priorityqueue = new List<int>();
    private List<int> _accompany_info = new List<int>();
    
    public void Enqueue(int a,int b){
        _priorityqueue.Add(a);
        _accompany_info.Add(b);
        int num = _priorityqueue.Count-1;
        while(true){
            if(num == 0) break;
            if(_priorityqueue[(num-1)/2] > _priorityqueue[num]){ //大小逆の時弄るとこ
                int temp = _priorityqueue[(num-1)/2];
                  _priorityqueue[(num-1)/2] = _priorityqueue[num];
                  _priorityqueue[num] = temp;
                temp = _accompany_info[(num-1)/2];
                  _accompany_info[(num-1)/2] = _accompany_info[num];
                  _accompany_info[num] = temp;
                num = (num-1)/2;
            }else{
                break;
            }
        }
    }
    
    public int[] Dequeue(){
        var re = new int[]{_priorityqueue[0],_accompany_info[0]};
        var qcount = _priorityqueue.Count;
        var temp = _priorityqueue[0]; _priorityqueue[0] = _priorityqueue[qcount-1]; _priorityqueue[qcount-1] = temp;
        temp = _accompany_info[0]; _accompany_info[0] = _accompany_info[qcount-1]; _accompany_info[qcount-1] = temp;
        _priorityqueue.RemoveAt(qcount-1);
        _accompany_info.RemoveAt(qcount-1);
        int num = 0;
        while(true){
            int swapnum = -1;
            if((num+1)*2 < _priorityqueue.Count){
                if(_priorityqueue[num*2+1] < _priorityqueue[(num+1)*2]){ //大小逆の時弄るとこ
                    swapnum = num*2+1;
                }else{
                    swapnum = (num+1)*2;
                }
            }else if(num*2+1 < _priorityqueue.Count){
                swapnum = num*2+1;
            }
            if(swapnum == -1) break;
            if(_priorityqueue[swapnum] < _priorityqueue[num]){ //大小逆の時弄るとこ
                temp = _priorityqueue[swapnum];_priorityqueue[swapnum] = _priorityqueue[num];_priorityqueue[num] = temp;
                temp = _accompany_info[swapnum];_accompany_info[swapnum] = _accompany_info[num];_accompany_info[num] = temp;
                num = swapnum;
            }else{
                break;
            }
        }
        return re;
    }
    
    public int[] Peek(){
        var temp = new int[]{_priorityqueue[0],_accompany_info[0]};
        return temp;
    }
    
    public int Count(){
        return _priorityqueue.Count;
    }
}
class PriorityQueue3{
    private List<int> _priorityqueue = new List<int>();
    private List<int> _accompany_info = new List<int>();
    private List<int> _accompany_info2 = new List<int>();
    
    public void Enqueue(int a,int b,int c){
        _priorityqueue.Add(a);
        _accompany_info.Add(b);
        _accompany_info2.Add(c);
        int num = _priorityqueue.Count-1;
        while(true){
            if(num == 0) break;
            if(_priorityqueue[(num-1)/2] > _priorityqueue[num]){ //大小逆の時弄るとこ
                int temp = _priorityqueue[(num-1)/2];
                  _priorityqueue[(num-1)/2] = _priorityqueue[num];
                  _priorityqueue[num] = temp;
                temp = _accompany_info[(num-1)/2];
                  _accompany_info[(num-1)/2] = _accompany_info[num];
                  _accompany_info[num] = temp;
                  temp = _accompany_info2[(num-1)/2];
                  _accompany_info2[(num-1)/2] = _accompany_info2[num];
                  _accompany_info2[num] = temp;
                num = (num-1)/2;
            }else{
                break;
            }
        }
    }
    
    public int[] Dequeue(){
        var re = new int[]{_priorityqueue[0],_accompany_info[0],_accompany_info2[0]};
        var qcount = _priorityqueue.Count;
        var temp = _priorityqueue[0]; _priorityqueue[0] = _priorityqueue[qcount-1]; _priorityqueue[qcount-1] = temp;
        temp = _accompany_info[0]; _accompany_info[0] = _accompany_info[qcount-1]; _accompany_info[qcount-1] = temp;
        temp = _accompany_info2[0]; _accompany_info2[0] = _accompany_info2[qcount-1]; _accompany_info2[qcount-1] = temp;
        _priorityqueue.RemoveAt(qcount-1);
        _accompany_info.RemoveAt(qcount-1);
        _accompany_info2.RemoveAt(qcount-1);
        int num = 0;
        while(true){
            int swapnum = -1;
            if((num+1)*2 < _priorityqueue.Count){
                if(_priorityqueue[num*2+1] < _priorityqueue[(num+1)*2]){ //大小逆の時弄るとこ
                    swapnum = num*2+1;
                }else{
                    swapnum = (num+1)*2;
                }
            }else if(num*2+1 < _priorityqueue.Count){
                swapnum = num*2+1;
            }
            if(swapnum == -1) break;
            if(_priorityqueue[swapnum] < _priorityqueue[num]){ //大小逆の時弄るとこ
                temp = _priorityqueue[swapnum];_priorityqueue[swapnum] = _priorityqueue[num];_priorityqueue[num] = temp;
                temp = _accompany_info[swapnum];_accompany_info[swapnum] = _accompany_info[num];_accompany_info[num] = temp;
                temp = _accompany_info2[swapnum];_accompany_info2[swapnum] = _accompany_info2[num];_accompany_info2[num] = temp;
                num = swapnum;
            }else{
                break;
            }
        }
        return re;
    }
    
    public int[] Peek(){
        var temp = new int[]{_priorityqueue[0],_accompany_info[0],_accompany_info2[0]};
        return temp;
    }
    
    public int Count(){
        return _priorityqueue.Count;
    }
}