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.IOException;
import java.io.InputStream;
import java.util.Arrays;
import java.util.NoSuchElementException;
import java.util.PriorityQueue;
 
public class Main {
	private static FastScanner sc = new FastScanner();
	static City[] c;
	
	public static void main(String[] args) {
		int N = sc.nextInt();
		
		c = new City[N];
		for(int i=0; i<N; i++) {
			c[i] = new City(sc.nextInt(), sc.nextInt(), i);
		}
		
		PriorityQueue<Road> r = new PriorityQueue<>((a, b) -> a.cost - b.cost);
		
		City[] ca = c.clone();
		
		Arrays.sort(ca, (a, b) -> a.x - b.x);
		for(int i=0; i<N-1; i++) {
			r.add(new Road(ca[i+1].x - ca[i].x, ca[i].id, ca[i+1].id));
		}
		
		Arrays.sort(ca, (a, b) -> a.y - b.y);
		for(int i=0; i<N-1; i++) {
			r.add(new Road(ca[i+1].y - ca[i].y, ca[i].id, ca[i+1].id));
		}
		
		long ans = 0;
		while(!r.isEmpty()) {
			Road road = r.poll();
			int p1 = c[road.id1].findParent();
			int p2 = c[road.id2].findParent();
			
			if(p1 != p2) {
				c[p2].parent = p1;
				ans += road.cost;
//				System.out.println(p1 + " " + p2 + " " + ans);
			}
		}
		
		System.out.println(ans);
	}
	
	static class City {
		int id;
		int x;
		int y;
		int parent = -1;
		
		City(int x, int y, int id) {
			this.x = x;
			this.y = y;
			this.id = id;
		}
		
		public int findParent() {
			if(parent == -1) {
				return id;
			}
			int p = c[parent].findParent();
			parent = p;
			return p;
		}
	}

	static class Road {
		int cost;
		int id1;
		int id2;
		
		Road(int cost, int id1, int id2) {
			this.cost = cost;
			this.id1 = id1;
			this.id2 = id2;
		}
	}
	
	static class FastScanner {
        private final InputStream in = System.in;
        private final byte[] buffer = new byte[1024];
        private int ptr = 0;
        private int buflen = 0;
        private boolean hasNextByte() {
            if(ptr < buflen) {
                return true;
            } else {
                ptr = 0;
                try {
                    buflen = in.read(buffer);
                } catch(IOException e) {
                    e.printStackTrace();
                }
                if(buflen <= 0) {
                    return false;
                }
            }
            return true;
        }
        private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
        private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
        private void skipUnprintable() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;}
        public boolean hasNext() { skipUnprintable(); return hasNextByte();}
        public String next() {
            if (!hasNext()) throw new NoSuchElementException();
            StringBuilder sb = new StringBuilder();
            int b = readByte();
            while(isPrintableChar(b)) {
                sb.appendCodePoint(b);
                b = readByte();
            }
            return sb.toString();
        }
        public long nextLong() {
            return Long.parseLong(next());
        }
        public int nextInt(){
            return Integer.parseInt(next());
        }
        public double nextDouble(){
            return Double.parseDouble(next());
        }
    }
}