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.Generic;
using System.Linq;
using static Input;

public class Prog
{
    private const int INF = 1000000007;
    private const long INFINITY = 9223372036854775807;
    public struct Pair { public int x, y; public Pair(int xx, int yy) { x = xx; y = yy; } }
    private static int[] dx = { 1, 0, -1, 0 };
    private static int[] dy = { 0, -1, 0, 1 };
    public static void Main()
    {
        int N = NextInt();
        List<int[]> citys = new List<int[]>();
        for (int i = 0; i < N; i++)
        {
            int xi = NextInt();
            int yi = NextInt();
            citys.Add(new int[3] { i, xi, yi });
        }
        var x_city = citys.OrderBy(v => v[1]).ToList();
        var y_city = citys.OrderBy(v => v[2]).ToList();
        PriorityQueue<int, int[]> e = new PriorityQueue<int, int[]>();
        //座標でソート、近い場所以外の道を建設するのはあうと
        //PQ(長さ,(都市A,都市B))
        for (int i = 1; i < N; i++)
        {
            var A = x_city[i - 1][1];
            var B = y_city[i - 1][2];
            var C = x_city[i][1];
            var D = y_city[i][2];
            e.Add(C - A, new int[3] { C - A, x_city[i - 1][0], x_city[i][0] });
            e.Add(D - B, new int[3] { D - B, y_city[i - 1][0], y_city[i][0] });
        }
        //連結判定
        UnionFind UF = new UnionFind(N);
        long ans = 0;
        while (e.Count() != 0)
        {
            var data = e.Take();
            if (!UF.Same(data[1], data[2]))
            {
                UF.Unite(data[1], data[2]);
                ans += data[0];
            }
        }
        Console.WriteLine(ans);
    }
}

public class PriorityQueue<Tkey, Tvalue> where Tkey : IComparable
{
    private List<Tkey> keys = new List<Tkey>();
    private List<Tvalue> values = new List<Tvalue>();
    private int size = 0;
    private static bool Descending;
    private static int Compare(Tkey a, Tkey b) { return (Descending ? a.CompareTo(b) : b.CompareTo(a)); }

    public PriorityQueue(bool b = true) { Clear(); Descending = b; }
    public int Count() { return size; }
    public void Clear() { keys = new List<Tkey>(); values = new List<Tvalue>(); size = 0; }
    public void Add(Tkey e, Tvalue v)
    {
        keys.Add(e);
        values.Add(v);
        int x = size;
        size += 1;
        while (x != 0)
        {
            int par = (x % 2 == 0 ? x - 2 : x - 1) / 2;
            if (Compare(keys[par], e) <= 0) break;
            Tkey a = keys[x]; keys[x] = keys[par]; keys[par] = a;
            Tvalue b = values[x]; values[x] = values[par]; values[par] = b;
            x = par;
        }
    }
    public void Poll()
    {
        Tkey k = keys[size - 1];
        Tvalue v = values[size - 1];
        int x = 0;
        size--;
        if (size == 0) { Clear(); return; }
        keys.RemoveAt(size);
        values.RemoveAt(size);
        while (true)
        {
            int l = x * 2 + 1;
            int r = x * 2 + 2;
            if (size - 1 < l) break;
            int y = 0;
            if (size - 1 == l) { y = l; }
            else if (Compare(keys[l], keys[r]) == 1) { y = r; }
            else { y = l; }
            if (Compare(keys[y], k) > 0) break;
            keys[x] = keys[y];
            values[x] = values[y];
            x = y;
        }
        keys[x] = k;
        values[x] = v;
    }
    public Tvalue Take() { Tvalue ret = values[0]; Poll(); return ret; }
    public Tvalue Peek() { return values[0]; }
    public void Debug()
    {
        Console.Write("key   : ");
        foreach (var k in keys) Console.Write(k + " ");
        Console.WriteLine();
        Console.Write("value : ");
        foreach (var k in values) Console.Write(k + " ");
        Console.WriteLine();
    }
}

public class UnionFind
{
    public List<int> parent = new List<int>();

    public UnionFind(int N)
    {
        for (int i = 0; i < N; i++) parent.Add(i);
    }

    private int Root(int a)
    {
        if (parent[a] == a) return a;
        else return parent[a] = Root(parent[a]);
    }

    public void Unite(int a, int b)
    {
        a = Root(a);
        b = Root(b);
        if (a == b) return;
        parent[a] = parent[b];
    }

    public bool Same(int a, int b) { return (Root(a) == Root(b)); }
}

public class Input
{
    private static Queue<string> q = new Queue<string>();
    private static void Confirm() { if (q.Count == 0) foreach (var s in Console.ReadLine().Split(' ')) q.Enqueue(s); }
    public static int NextInt() { Confirm(); return int.Parse(q.Dequeue()); }
    public static long NextLong() { Confirm(); return long.Parse(q.Dequeue()); }
    public static char NextChar() { Confirm(); return char.Parse(q.Dequeue()); }
    public static string NextString() { Confirm(); return q.Dequeue(); }
    public static double NextDouble() { Confirm(); return double.Parse(q.Dequeue()); }
    public static int[] LineInt() { return Console.ReadLine().Split(' ').Select(int.Parse).ToArray(); }
    public static long[] LineLong() { return Console.ReadLine().Split(' ').Select(long.Parse).ToArray(); }
    public static string[] LineString() { return Console.ReadLine().Split(' ').ToArray(); }
    public static double[] LineDouble() { return Console.ReadLine().Split(' ').Select(double.Parse).ToArray(); }
}