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: Wrong Answer)

import java.util.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        Node ns[] = new Node[n];
        for (int i = 0; i < n; i++) {
            ns[i] = new Node(i, sc.nextLong(), sc.nextLong());
        }

        ArrayList<Edge> es[] = new ArrayList[n];
        for (int i = 0; i < n; i++) {
            es[i] = new ArrayList<>();
        }
        Arrays.sort(ns, (n1, n2) -> Long.compare(n1.x, n2.x));
        createEdge(es, ns, n);
        Arrays.sort(ns, (n1, n2) -> Long.compare(n1.y, n2.y));
        createEdge(es, ns, n);

        boolean used[] = new boolean[n];
        long res = 0;
        PriorityQueue<Edge> queue = new PriorityQueue<>((e1, e2) ->
                Long.compare(e1.cost, e2.cost));
        used[0] = true;
        queue.addAll(es[0]);

        while (!queue.isEmpty()) {
            Edge e = queue.poll();
            if (used[e.to]) continue;
            used[e.to] = true;
            res += e.cost;

            queue.addAll(es[e.to]);
        }
        System.out.println(res);
    }

    static long dist(int i, int j, Node[] ns) {
        return Math.min(Math.abs(ns[i].x - ns[j].x), Math.abs(ns[i].y - ns[j].y));
    }

    static void createEdge(ArrayList<Edge> es[], Node[] ns, int n) {
        for (int i = 1; i < n-1; i++) {
            long dist1 = dist(i, i-1, ns);
            long dist2 = dist(i, i+1, ns);
            int prevID = ns[i-1].id;
            int ID = ns[i].id;
            int nextID = ns[i+1].id;
            Edge e1 = new Edge(prevID, ID, dist1);
            Edge e2 = new Edge(ID, prevID, dist1);
            Edge e3 = new Edge(ID, nextID, dist2);
            Edge e4 = new Edge(nextID, ID, dist2);
            es[prevID].add(e1);
            es[ID].add(e2);es[ID].add(e3);
            es[nextID].add(e4);
        }

    }

    static class Node {
        int id;
        long x, y;
        Node(int id, long x, long y) {
            this.id = id;
            this.x = x;
            this.y = y;
        }

    }

    static class Edge {
        int from, to;
        long cost;
        Edge(int f, int t, long c) {
            from = f;
            to = t;
            cost = c;
        }

    }


}