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 BitArray = System.Collections.BitArray;
using BigInteger = System.Numerics.BigInteger;
using TextReader = System.IO.TextReader;
using System.Text;

namespace AtCoderProject
{
    public class Program
    {
        public object Calc()
        {
            var N = consoleReader.Int;
            var towns = consoleReader.Repeat(N).Select(cr => new Point(cr.Split.Int)).ToArray();
            var townX = towns.Select((p, i) => Tuple.Create(p, i)).OrderBy(t => t.Item1.x).Select(t => t.Item2).ToArray();
            var townY = towns.Select((p, i) => Tuple.Create(p, i)).OrderBy(t => t.Item1.y).Select(t => t.Item2).ToArray();
            var roads = new List<Road>(2 * N);
            long cost = 0;
            for (int i = 1; i < N; i++)
            {
                roads.Add(new Road { a = townX[i - 1], b = townX[i], cost = towns[townX[i]].x - towns[townX[i - 1]].x });
                roads.Add(new Road { a = townY[i - 1], b = townY[i], cost = towns[townY[i]].y - towns[townY[i - 1]].y });
            }
            roads.Sort();

            var uf = new UnionFind(N);
            foreach (var r in roads)
            {
                if (uf.IsSameSet(r.a, r.b)) continue;
                uf.UnionSet(r.a, r.b);
                cost += r.cost;
            }

            return cost;
        }
        struct Road : IComparable<Road>
        {
            public int cost;
            public int a;
            public int b;

            public int CompareTo(Road other) => this.cost.CompareTo(other.cost);
        }
        struct Point : IEquatable<Point>
        {
            public int x;
            public int y;
            public Point(int[] arr) : this(arr[0], arr[1]) { }
            public Point(int x, int y)
            {
                this.x = x;
                this.y = y;
            }
            public bool Equals(Point other) => this.x == other.x && this.y == other.y;
            public override bool Equals(object obj)
            {
                if (obj is Point) return Equals((Point)obj);
                return false;
            }
            public override int GetHashCode() => x ^ y;
            public override string ToString() => $"({x}, {y})";
        }

        class UnionFind
        {
            int[] data;
            public UnionFind(int size)
            {
                this.data = Enumerable.Repeat(-1, size).ToArray();
            }

            public int Root(int x)
            {
                if (data[x] < 0) return x;
                return data[x] = Root(data[x]);
            }
            public int Count(int x) => -data[Root(x)];
            public void UnionSet(int x, int y)
            {
                var xRoot = Root(x);
                var yRoot = Root(y);
                if (xRoot == yRoot) return;
                else if (data[yRoot] < data[xRoot])//y側の方が多い場合は逆にする
                {
                    var tmp = yRoot;
                    yRoot = xRoot;
                    xRoot = tmp;
                }
                data[xRoot] += data[yRoot];
                data[yRoot] = xRoot;
            }
            public bool IsSameSet(int x, int y) => Root(x) == Root(y);
        }


        #region いつもの
#pragma warning disable
        private ConsoleReader consoleReader;
        public Program(ConsoleReader consoleReader) { this.consoleReader = consoleReader; }
        static void Main() => Console.WriteLine(new Program(new ConsoleReader(Console.In)).Calc()); static string AllLines<T>(IEnumerable<T> source) => string.Join("\n", source);
    }
    static class Ext
    {
        public static Dictionary<TKey, int> GroupCount<TSource, TKey>(this IEnumerable<TSource> source, Func<TSource, TKey> keySelector) => source.GroupBy(keySelector).ToDictionary(g => g.Key, g => g.Count());
        public static Dictionary<TKey, int> GroupCount<TKey>(this IEnumerable<TKey> source) => source.GroupCount(i => i);
    }
    public class ConsoleReader { private string[] ReadLineSplit() => textReader.ReadLine().Split(Array.Empty<char>(), StringSplitOptions.RemoveEmptyEntries); private string[] line = Array.Empty<string>(); private int linePosition; private TextReader textReader; public ConsoleReader(TextReader tr) { textReader = tr; } public int Int => int.Parse(String); public long Long => long.Parse(String); public double Double => double.Parse(String); public string String { get { if (linePosition >= line.Length) { linePosition = 0; line = ReadLineSplit(); } return line[linePosition++]; } } public class SplitLine { private string[] splited; public SplitLine(ConsoleReader cr) { splited = cr.ReadLineSplit(); cr.line = Array.Empty<string>(); } public int[] Int => String.Select(x => int.Parse(x)).ToArray(); public int[] Int0 => String.Select(x => int.Parse(x) - 1).ToArray(); public long[] Long => String.Select(x => long.Parse(x)).ToArray(); public double[] Double => String.Select(x => double.Parse(x)).ToArray(); public string[] String => splited; } public SplitLine Split => new SplitLine(this); public class RepeatReader : IEnumerable<ConsoleReader> { ConsoleReader cr; int count; public RepeatReader(ConsoleReader cr, int count) { this.cr = cr; this.count = count; } public IEnumerator<ConsoleReader> GetEnumerator() => Enumerable.Repeat(cr, count).GetEnumerator(); System.Collections.IEnumerator System.Collections.IEnumerable.GetEnumerator() => GetEnumerator(); public IEnumerable<string> String => this.Select(cr => cr.String); public IEnumerable<int> Int => this.Select(cr => cr.Int); public IEnumerable<int> Int0 => this.Select(cr => cr.Int - 1); public IEnumerable<long> Long => this.Select(cr => cr.Long); public IEnumerable<double> Double => this.Select(cr => cr.Double); } public RepeatReader Repeat(int count) => new RepeatReader(this, count); }
    #endregion
}