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.util.*;

public class Main {

    static class Edge implements Comparable<Edge> {
        int from, to, cost;

        public Edge(int from, int to, int cost) {
            this.from = from;
            this.to = to;
            this.cost = cost;
        }

        @Override
        public int compareTo(Edge o) {
            return cost - o.cost;
        }
    }

    static class Pair implements Comparable<Pair> {
        int id, pos;

        public Pair(int id, int pos) {
            this.id = id;
            this.pos = pos;
        }

        @Override
        public int compareTo(Pair o) {
            return pos - o.pos;
        }
    }

    static class UnionFind {
        int[] size;
        int[] id;

        public UnionFind(int n) {
            size = new int[n];
            id = new int[n];

            for (int i = 0; i < n; ++i) {
                size[i] = 1;
                id[i] = i;
            }
        }

        void unify(int p, int q) {
            int root1 = find(p);
            int root2 = find(q);

            if (size[root1] > size[root2]) {
                size[root1] += size[root2];
                id[root2] = root1;
            } else {
                size[root2] += size[root1];
                id[root1] = root2;
            }
        }

        int find(int p) {
            int root = p;
            while (root != id[root]) root = id[root];
            while (root != p) {
                int next = id[p];
                id[p] = root;
                p = next;
            }
            return root;
        }

        boolean connected(int p, int q) {
            return find(p) == find(q);
        }
    }

    static long kruskal() {
        long mstCost = 0;
        UnionFind uf = new UnionFind(N);
        PriorityQueue<Edge> pq = new PriorityQueue<>(edges);

        while (!pq.isEmpty()) {
            Edge edge = pq.poll();
            if (uf.connected(edge.from, edge.to)) continue;
            uf.unify(edge.from, edge.to);
            mstCost += edge.cost;

            if (uf.size[uf.find(0)] == N) break;
        }

        return mstCost;
    }

    static int N;
    static List<Edge> edges;

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        N = Integer.parseInt(sc.next());
        List<Pair> X = new ArrayList<>();
        List<Pair> Y = new ArrayList<>();
        edges = new ArrayList<>();

        for (int i = 0; i < N; ++i) {
            X.add(new Pair(i, Integer.parseInt(sc.next())));
            Y.add(new Pair(i, Integer.parseInt(sc.next())));
        }

        Collections.sort(X);
        for (int i = 0; i < N-1; ++i) {
            int from = X.get(i).id;
            int to = X.get(i+1).id;
            edges.add(new Edge(from, to, X.get(i+1).pos - X.get(i).pos));
        }

        Collections.sort(Y);
        for (int i = 0; i < N-1; ++i) {
            int from = Y.get(i).id;
            int to = Y.get(i+1).id;
            edges.add(new Edge(from, to, Y.get(i+1).pos - Y.get(i).pos));
        }

        System.out.println(kruskal());
    }
}