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 UnionFind;

struct City
{
    public int id { get; private set; }
    public int x { get; private set; }
    public int y { get; private set; }

    public City(int id, int x, int y)
    {
        this.id = id;
        this.x = x;
        this.y = y;
    }
}

struct Edge
{
    public int a { get; private set; }
    public int b { get; private set; }
    public long cost { get; private set; }

    public Edge(int a, int b, long cost)
    {
        this.a = a;
        this.b = b;
        this.cost = cost;
    }
}

class Program
{
    static int N;
    static List<City> cities;
    static List<Edge> es;

    static void Main()
    {
        /* 入力の受け取り、変数の初期化 */
        N = int.Parse(Console.ReadLine());
        cities = new List<City>();
        for (int i = 0; i < N; i++)
        {
            int[] input = Console.ReadLine().Split().Select(int.Parse).ToArray();
            cities.Add(new City(i, input[0], input[1]));
        }
        es = new List<Edge>();

        /* 街をx順にソートし、隣街との間に辺を張る */
        cities.Sort((a, b) => a.x - b.x);
        for (int i = 0; i < N - 1; i++)
        {
            int s = cities[i].id;
            int g = cities[i + 1].id;
            long l = Math.Abs(cities[i].x - cities[i + 1].x);
            es.Add(new Edge(s, g, l));
        }

        /* 街をy順にソートし、隣街との間に辺を張る */
        cities.Sort((a, b) => a.y - b.y);
        for (int i = 0; i < N - 1; i++)
        {
            int s = cities[i].id;
            int g = cities[i + 1].id;
            long l = Math.Abs(cities[i].y - cities[i + 1].y);
            es.Add(new Edge(s, g, l));
        }

        /* クラスカル法で答えを求める */
        Console.WriteLine(Kruskal());
    }

    /* グラフesに対し、クラスカル法で最小全域木を求め、総コストを返す */
    static long Kruskal()
    {
        es.Sort((a, b) => (a.cost > b.cost) ? 1 : (a.cost == b.cost) ? 0 : -1);

        UF uf = new UF(N);
        long min_cost = 0;

        foreach (var e in es)
        {
            if (!uf.Same(e.a, e.b))
            {
                min_cost += e.cost;
                uf.Unite(e.a, e.b);
            }
        }

        return min_cost;
    }
}

namespace UnionFind
{
    class UF
    {
        private int[] 親; //親[i] : iの親の番号

        public UF(int N) //コンストラクタ、すべてが根として初期化
        {
            親 = new int[N];
            for (int i = 0; i < N; i++)
                親[i] = i;
        }

        public int Root(int x) //xの属する木の根を返す
        {
            if (親[x] == x) return x;
            return 親[x] = Root(親[x]);
        }

        public void Unite(int x, int y) //xとyの木を統合
        {
            int rx = Root(x);
            int ry = Root(y);
            if (rx == ry) return;
            親[rx] = ry;
        }

        public bool Same(int x, int y) //xとyが同じ木に属するかどうかを返す
        {
            return Root(x) == Root(y);
        }
    }
}