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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

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

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);
    }
}

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;
    }
}

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

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

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

public class Main {

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

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

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

    static int N;
    static List<Edge> edges;

    public static void main(String[] args) {
        FastScanner fs = new FastScanner();
        N = fs.nextInt();
        edges = new ArrayList<>();
        List<Pair> X = new ArrayList<>();
        List<Pair> Y = new ArrayList<>();
        for (int i = 0; i < N; ++i) {
            int x = fs.nextInt();
            int y = fs.nextInt();
            X.add(new Pair(x, i));
            Y.add(new Pair(y, i));
        }

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

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

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

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;}
    public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; 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() {
        if (!hasNext()) throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while(true){
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            }else if(b == -1 || !isPrintableChar(b)){
                return minus ? -n : n;
            }else{
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }

    public int nextInt() {
        long nl = nextLong();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
        return (int) nl;
    }

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