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 System.IO;
using System.Globalization;
using System.Diagnostics;
using static System.Console;
using Pair = System.Collections.Generic.KeyValuePair<int, int>;
//using System.Numerics;

class Program
{
    static void Main()
    {
        //SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
        new Program().Solve();
        Out.Flush();
    }
    Scanner cin = new Scanner();
    Random rnd = new Random();
    Stopwatch sw = new Stopwatch();
    readonly int[] dd = { 0, 1, 0, -1, 0 };
    readonly int mod = 1000000007;
    readonly string alfa = "abcdefghijklmnopqrstuvwxyz";

    int N;
    void Solve()
    {
        N = cin.Nextint;
        var X = new int[N];
        var Y = new int[N];
        var A = Enumerable.Range(0, N).ToArray();
        var B = Enumerable.Range(0, N).ToArray();
        for (int i = 0; i < N; i++)
        {
            X[i] = cin.Nextint;
            Y[i] = cin.Nextint;
        }
        Array.Sort(X, A);
        Array.Sort(Y, B);
        int idx = 0;
        var Cost = new int[2 * N - 2];
        var P = new Pair[2 * N - 2];

        for (int i = 1; i < N; i++)
        {
            Cost[idx] = X[i] - X[i - 1];
            P[idx] = new Pair(A[i - 1], A[i]);
            idx++;
        }
        for (int i = 1; i < N; i++)
        {
            Cost[idx] = Y[i] - Y[i - 1];
            P[idx] = new Pair(B[i - 1], B[i]);
            idx++;
        }

        Array.Sort(Cost, P);

        long ans = 0;
        var U = new UnionFind(N);
        for (int i = 0; i < idx; i++)
        {
            if (!U.Same(P[i].Key, P[i].Value))
            {
                U.Unite(P[i].Key, P[i].Value);
                ans += Cost[i];
            }
        }

        WriteLine(ans);
    }

}

class UnionFind
{
    internal int[] rank;
    internal int[] p;
    internal int[] weight;
    public UnionFind(int size)
    {
        rank = new int[size];
        p = new int[size];
        weight = new int[size];
        for (int i = 0; i < size; i++)
        {
            rank[i] = 0;
            p[i] = i;
            weight[i] = 1;
        }
    }
    public void Unite(int x, int y)
    {
        x = FindSet(x);
        y = FindSet(y);
        if (x == y) return;
        if (rank[x] > rank[y])
        {
            p[y] = x;
            weight[x] += weight[y];
        }

        if (rank[x] < rank[y])
        {
            p[x] = y;
            weight[y] += weight[x];
        }
        if (rank[x] == rank[y])
        {
            p[x] = y;
            rank[y]++;
            weight[y] += weight[x];
        }
    }
    public bool Same(int x, int y)
    {
        return FindSet(x) == FindSet(y);
    }
    public int FindSet(int x)
    {
        var H = new HashSet<int>();
        while (p[x] != x)
        {
            H.Add(x);
            x = p[x];
        }
        foreach (var h in H)
        {
            p[h] = x;
        }
        return x;
    }
    public int Weight(int x)
    {
        return weight[FindSet(x)];
    }
}

class Scanner
{
    string[] s; int i;
    char[] cs = new char[] { ' ' };
    public Scanner() { s = new string[0]; i = 0; }
    public string[] Scan { get { return ReadLine().Split(); } }
    public int[] Scanint { get { return Array.ConvertAll(Scan, int.Parse); } }
    public long[] Scanlong { get { return Array.ConvertAll(Scan, long.Parse); } }
    public double[] Scandouble { get { return Array.ConvertAll(Scan, double.Parse); } }
    public string Next
    {
        get
        {
            if (i < s.Length) return s[i++];
            string st = ReadLine();
            while (st == "") st = ReadLine();
            s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
            i = 0;
            return Next;
        }
    }
    public int Nextint { get { return int.Parse(Next); } }
    public long Nextlong { get { return long.Parse(Next); } }
    public double Nextdouble { get { return double.Parse(Next); } }
}