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.*;
import java.lang.*;
import java.util.*;
import java.util.Arrays;
import java.math.*;

class Edge {
	public int u, v, w;
	public Edge(int u, int v, int w) {
		this.u = u;
		this.v = v;
		this.w = w;
	}
}

class CompKey_e implements Comparator<Edge> {
	public int compare(Edge x, Edge y) {
		return x.w-y.w;
	}
}

class CompKey implements Comparator<Integer> {
	int[] val;
	public CompKey(int[] val) {	
		this.val = val;
	}
	public int compare(Integer x, Integer y) {
		return this.val[x]-this.val[y];
	}
}

class DisjointSet {
	int[] p;
	public DisjointSet(int n) {
		p = new int[n];
		for (int i = 0; i < n; ++i)
			p[i] = -1;
	}
	public int getRoot(int u) {
		if (p[u] == -1) return u;
		return p[u] = getRoot(p[u]);
	}
	public boolean isConnected(int u, int v) {
		u = getRoot(u); 
		v = getRoot(v);
		if (u == v) return true;
		p[u] = v;
		return false;
	}
}

class Main {
	static BufferedReader jvin = new BufferedReader(new InputStreamReader(System.in));
	static PrintWriter jvout = new PrintWriter(System.out);
	
	int N;
	int[] X_Coor, Y_Coor;
	Integer[] X_id, Y_id;
	Edge[] E;
	DisjointSet d;
	
	public static void main(String[] args) throws IOException {
		Main instance = new Main();
		instance.passStaticVar();
	}


	public void passStaticVar() throws IOException {
		N = Integer.parseInt(jvin.readLine());
		X_Coor = new int[N]; X_id = new Integer[N];
		Y_Coor = new int[N]; Y_id = new Integer[N];
		for (int i = 0; i < N; ++i) {
			String[] t = jvin.readLine().split(" ");
			X_Coor[i] = Integer.parseInt(t[0]);
			Y_Coor[i] = Integer.parseInt(t[1]);
			X_id[i] = Y_id[i] = i;
		}
		
		Arrays.sort(X_id, new CompKey(X_Coor));
		Arrays.sort(Y_id, new CompKey(Y_Coor));
		E = new Edge[2*N-2];
		int m = 0;
		for (int i = 1; i < N; ++i) {
			E[m++] = new Edge(X_id[i], X_id[i-1], X_Coor[X_id[i]]-X_Coor[X_id[i-1]]);
			E[m++] = new Edge(Y_id[i], Y_id[i-1], Y_Coor[Y_id[i]]-Y_Coor[Y_id[i-1]]);
		}
		Arrays.sort(E, new CompKey_e());
		d = new DisjointSet(N);
		long res = 0;
		for (int i = 0; i < m; ++i) 
			if (!d.isConnected(E[i].u, E[i].v)) 
				res += E[i].w;
		jvout.println(res);
		jvout.flush();
	}
}