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 static System.Math;
using static System.Console;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            var n = int.Parse(ReadLine());
            var cities = new int[n][];
            var parents = new int[n];
            var costs = new Dictionary<int, Dictionary<int, int>>();
            for (var i = 0; i < n; i++)
            {
                var line = ReadLine().Split(' ').Select(value => int.Parse(value)).ToArray();
                cities[i] = new int[3] { i, line[0], line[1] };
                parents[i] = i;
                costs.Add(i, new Dictionary<int, int>());
            }

            cities = cities.OrderBy(array => array[1]).ToArray();
            for(var i = 0; i < n - 1; i++)
            {
                if(cities[i][0] < cities[i + 1][0])
                {
                    costs[cities[i][0]].Add(cities[i + 1][0], Abs(cities[i][1] - cities[i + 1][1]));
                }
                else
                {
                    costs[cities[i + 1][0]].Add(cities[i][0], Abs(cities[i][1] - cities[i + 1][1]));
                }
            }
            cities = cities.OrderBy(array => array[2]).ToArray();
            for (var i = 0; i < n - 1; i++)
            {
                if (cities[i][0] < cities[i + 1][0])
                {
                    if (costs[cities[i][0]].ContainsKey(cities[i + 1][0]))
                    {
                        costs[cities[i][0]][cities[i + 1][0]] = Min(costs[cities[i][0]][cities[i + 1][0]], Abs(cities[i][2] - cities[i + 1][2]));
                    }
                    else
                    {
                        costs[cities[i][0]].Add(cities[i + 1][0], Abs(cities[i][2] - cities[i + 1][2]));
                    }
                }
                else
                {
                    if (costs[cities[i + 1][0]].ContainsKey(cities[i][0]))
                    {
                        costs[cities[i + 1][0]][cities[i][0]] = Min(costs[cities[i + 1][0]][cities[i][0]], Abs(cities[i + 1][2] - cities[i][2]));
                    }
                    else
                    {
                        costs[cities[i + 1][0]].Add(cities[i][0], Abs(cities[i + 1][2] - cities[i][2]));
                    }
                }
            }

            var costsList = new List<int[]>();
            foreach (var source in costs)
            {
                foreach (var destination in source.Value)
                {
                    costsList.Add(new int[3] { source.Key, destination.Key, destination.Value });
                }
            }
            costsList = costsList.OrderBy(array => array[2]).ToList();

            var totalCost = 0;
            foreach(var cost in costsList)
            {
                if(GetRoot(parents, cost[0]) != GetRoot(parents, cost[1]))
                {
                    totalCost += cost[2];
                    Union(parents, cost[0], cost[1]);
                }
            }

            WriteLine(totalCost);
        }

        private static int GetRoot(int[] parents, int node)
        {
            if(parents[node] == node)
            {
                return node;
            }
            return parents[node] = GetRoot(parents, parents[node]);
        }

        private static void Union(int[] parents, int x, int y)
        {
            x = GetRoot(parents, x);
            y = GetRoot(parents, y);

            if(x != y)
            {
                parents[x] = y;
            }
        }
    }
}