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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.List;

public class Main {
	static List<Integer> path;

	public static void main(String[] args) throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(br.readLine());
		City[] arr = new City[n];
		for (int i = 0; i < n; i++) {
			String[] sa = br.readLine().split(" ");
			City o = new City();
			o.i = i;
			o.x = Integer.parseInt(sa[0]);
			o.y = Integer.parseInt(sa[1]);
			arr[i] = o;
		}
		br.close();

		List<Road> list = new ArrayList<Road>(2 * n);

		Arrays.parallelSort(arr, new Comparator<City>() {
			public int compare(City o1, City o2) {
				return o1.x - o2.x;
			}
		});
		for (int i = 1; i < arr.length; i++) {
			City o1 = arr[i - 1];
			City o2 = arr[i];
			Road e = new Road();
			e.i = o1.i;
			e.j = o2.i;
			e.c = o2.x - o1.x;
			list.add(e);
		}

		Arrays.parallelSort(arr, new Comparator<City>() {
			public int compare(City o1, City o2) {
				return o1.y - o2.y;
			}
		});
		for (int i = 1; i < arr.length; i++) {
			City o1 = arr[i - 1];
			City o2 = arr[i];
			Road e = new Road();
			e.i = o1.i;
			e.j = o2.i;
			e.c = o2.y - o1.y;
			list.add(e);
		}

		Collections.sort(list, new Comparator<Road>() {
			public int compare(Road e1, Road e2) {
				return e1.c - e2.c;
			}
		});

		int[] parent = new int[n];
		for (int i = 0; i < parent.length; i++) {
			parent[i] = i;
		}

		long ans = 0;
		for (Road e : list) {
			if (find(parent, e.i) != find(parent, e.j)) {
				union(parent, e.i, e.j);
				ans += e.c;
			}
		}
		System.out.println(ans);
	}

	static class City {
		int i, x, y;
	}

	static class Road {
		int i, j, c;
	}

	static void union(int[] parent, int x, int y) {
		int px = find(parent, x);
		int py = find(parent, y);
		if (px != py) {
			parent[px] = py;
		}
	}

	static int find(int[] parent, int x) {
		if (parent[x] == x) {
			return x;
		}
		parent[x] = find(parent, parent[x]);
		return parent[x];
	}
}