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.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.*;

public class Main {

    static int N;
    static Cord[] C;

    public static void main(String[] args) {
        FastScanner sc = new FastScanner(System.in);
        N = sc.nextInt();
        C = new Cord[N];
        for (int i = 0; i < N; i++) {
            C[i] = new Cord(i, sc.nextInt(), sc.nextInt());
        }
        System.out.println( solve() );
    }

    static class Cord {
        int n;
        int x;
        int y;

        public Cord(int n, int x, int y) {
            this.n = n;
            this.x = x;
            this.y = y;
        }
    }

    private static long solve() {
        UnionFind uf = new UnionFind(N);

        Arrays.sort(C, Comparator.comparingInt(c -> c.x));
        Dist[] X = new Dist[N-1];
        for (int i = 0; i < N - 1; i++) {
            int j = i+1;
            X[i] = new Dist(C[i], C[j], (C[j].x - C[i].x) );
        }
        Arrays.sort(X, Comparator.comparingInt(d -> d.d));

        Arrays.sort(C, Comparator.comparingInt(c -> c.y));
        Dist[] Y = new Dist[N-1];
        for (int i = 0; i < N - 1; i++) {
            int j = i+1;
            Y[i] = new Dist(C[i], C[j], (C[j].y - C[i].y) );
        }
        Arrays.sort(Y, Comparator.comparingInt(d -> d.d));

        long total = 0;
        int xi = 0;
        int yi = 0;
        f: for (int i = 0; i < N-1; i++) {
            w: while(true) {
                Dist x = X[xi];
                Dist y = Y[yi];
                if( x.d < y.d ) {
                    boolean u = uf.unite(x.from.n, x.to.n);
                    if( u ) {
                        total += x.d;
                        continue f;
                    } else {
                        xi++;
                        continue w;
                    }

                } else {
                    boolean u = uf.unite(y.from.n, y.to.n);
                    if( u ) {
                        total += y.d;
                        continue f;
                    } else {
                        yi++;
                        continue w;
                    }
                }
            }
        }
        return total;
    }

    static class Dist {
        private Cord from;
        private Cord to;
        private int d;

        public Dist(Cord from, Cord to, int d) {
            this.from = from;
            this.to = to;
            this.d = d;
        }
    }

    static class UnionFind {

        private final int[] parent;
        private final int[] rank;

        public UnionFind(int n) {
            parent = new int[n];
            rank = new int[n];
            for (int i = 0; i < n; i++) {
                parent[i] = i;
                rank[i] = 0;
            }
        }

        public boolean isAllUnite() {
            int root = root(0);
            for (int i = 1; i < N; i++) {
                if( root != root(i) ) return false;
            }
            return true;
        }

        public int root(int i) {
            if( parent[i] == i ) {
                return i;
            } else {
                return parent[i] = root(parent[i]);
            }
        }

        public boolean unite(int i, int j) {
            int ri = root(i);
            int rj = root(j);
            if( ri == rj ) return false;

            if( rank[ri] < rank[rj] ) {
                parent[ri] = rj;

            } else {
                parent[rj] = ri;
                if( rank[ri] == rank[rj] ) {
                    rank[ri]++;
                }
            }
            return true;
        }

        public boolean isSame(int a, int b) {
            return root(a) == root(b);
        }
    }

    static class FastScanner {

        private BufferedReader reader;
        private StringTokenizer tokenizer;

        FastScanner(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
            tokenizer = null;
        }

        String next() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        String nextLine() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    return reader.readLine();
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }

            return tokenizer.nextToken("\n");
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        int[] nextIntArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }

        long[] nextLongArray(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++)
                a[i] = nextLong();
            return a;
        }
    }
}