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.*;
import java.io.*;

	
public class Main {
	public static void main(String[] args) throws Exception {
		FastScanner sc = new FastScanner();
		PrintWriter out = new PrintWriter(System.out);
		
    	int vn=sc.nexI();
        	
    	long[] xs = new long[vn];
    	long[] ys = new long[vn];
    	
	   	for(int i=0; i<vn; i++){
	   	    xs[i] = sc.nexL();
	   	    ys[i] = sc.nexL();
	   	}
    	   	
		int[] parent = new int[vn];
	   	for(int i=0; i<vn; i++){
	   	    parent[i]=i;
	   	}
	   	
	   	Edge[] xln = new Edge[vn];
	   	Edge[] yln = new Edge[vn];
	   	
	   	for(int i=0; i<vn; i++){
	   	    xln[i] = new Edge(i, xs[i]);
	   	    yln[i] = new Edge(i, ys[i]);
	   	}
	   	Arrays.sort(xln, new Comparator_Edge());
	   	Arrays.sort(yln, new Comparator_Edge());
   
	    Queue<Edge> edges = new PriorityQueue<>(new Comparator_Edge());
	    
	    for(int i=1; i<vn; i++){
	        edges.add(new Edge(xln[i-1].v2, xln[i].v2, xln[i].weight-xln[i-1].weight));
	        edges.add(new Edge(yln[i-1].v2, yln[i].v2, yln[i].weight-yln[i-1].weight));
	    }
	    
	    long ans=0;
	    while(edges.size()>0){
	        Edge e = edges.poll();
	        if(!is_same_uf(parent,e.from, e.v2)){
	            ans += e.weight;
	            unite_uf(parent,e.from, e.v2);
	        }
	    }
		out.println(ans);
		out.flush();
	}
    
    private static int get_root_uf(int[] parent, int index){
        if(parent[index] == index) return index;
        int root = get_root_uf(parent, parent[index]);
        parent[index] = root;
        return root;
    }
    
    private static boolean is_same_uf(int[] parent, int x, int y){
        if(get_root_uf(parent,x) == get_root_uf(parent,y)) return true;
        else return false;
    }
    
    private static void unite_uf(int[] parent, int receiver, int attacker){
        parent[get_root_uf(parent,attacker)] = get_root_uf(parent, receiver);
        return;
    }

	private static int INF = (int)1e8;
	private static long INFL = (long)1e17;
	private static int e97 = (int)1e9 + 7;
	
	
	private static int abs(int a){  return (a>=0) ? a: -a;  }
	private static long abs(long a){    return (a>=0) ? a: -a;  }
	
	private static int min(int a, int b){   return (a>b) ? b : a;   }
	private static long min(long a, long b){    return (a>b) ? b : a;   }
	
	private static int max(int a, int b){   return (a>b) ? a : b;   }
	private static long max(long a, long b){    return (a>b) ? a : b;   }
	
	private static int minN(int... ins){
		int min = ins[0];
		for(int i=1; i<ins.length; i++){    if(ins[i] < min) min = ins[i];  }
		return min;
	}
	private static int maxN(int... ins){
		int max = ins[0];
		for(int i=1; i<ins.length; i++){    if(ins[i] > max) max = ins[i];  }
		return max;
	}
	private static long minN(long... ins){
		long min = ins[0];
		for(int i=1; i<ins.length; i++){    if(ins[i] < min) min = ins[i];  }
		return min;
	}
	private static long maxN(long... ins){
		long max = ins[0];
		for(int i=1; i<ins.length; i++){    if(ins[i] > max) max = ins[i];  }
		return max;
	}
	
	private static int minExAd(int[] dt, int ad){
	    int min=Integer.MAX_VALUE;
		for(int i=0; i<dt.length; i++){ if((i != ad) && (dt[i] < min)) min = dt[i]; }
		return min;
	}
	private static long minExAd(long[] dt, int ad){
	    long min=Long.MAX_VALUE;
		for(int i=0; i<dt.length; i++){ if((i != ad) && (dt[i] < min)) min = dt[i]; }
		return min;
	}
	private static int minExVal(int[] dt, int ex_val){
	    int min=Integer.MAX_VALUE;
		for(int i=0; i<dt.length; i++){ if((dt[i] != ex_val) && (dt[i] < min)) min = dt[i]; }
		return min;
	}
	private static long minExVal(long[] dt, long ex_val){
	    long min=Long.MAX_VALUE;
		for(int i=0; i<dt.length; i++){ if((dt[i] != ex_val) && (dt[i] < min)) min = dt[i]; }
		return min;
	}
	
	private static boolean same3(long a, long b, long c){
    	if(a!=b) return false;
    	if(b!=c) return false;
    	if(c!=a) return false;
    	return true;
	}
	private static boolean dif3(long a, long b, long c){
    	if(a==b) return false;
    	if(b==c) return false;
    	if(c==a) return false;
    	return true;
	}
	
	private static int factorial(int n) {
		int ans=1;
		for(int i=n; i>0; i--){ ans*=i; }
		return ans;
	}
	
	private static long gcd(long m, long n) {
		if(m < n) return gcd(n, m);
		if(n == 0) return m;
		return gcd(n, m % n);
	}
	
	private static int pow2(int in){    return in*in;   }
	private static long pow2(long in){  return in*in;   }
	private static double pow2(double in){    return in*in;   }
	
	private static int getDigit2(long num){
		long cf = 1;
		int d=0;
		while(num >= cf){
			d++;
			cf = 1<<d;
		}
		return d; //numはd桁の数で、2^dより小さい
	}
	
	private static int getDigit10(long num){
		long cf = 1;
		int d=0;
		while(num >= cf){
			d++;
			cf*=10;
		}
		return d; //numはd桁の数で、10^dより小さい
	}
	
	private static boolean isINF(int in){
    	if((in*20)>INF) return true;
    	else return false;
	}
	private static boolean isINFL(long in){
    	if((in*10000)>INFL) return true;
    	else return false;
	}
	
	private static long pow10E97(long ob, int soeji){
		if(soeji==2) return (ob*ob)%e97;
		
		int d = getDigit2(soeji);
		long[] ob_pow_2pow = new long[d];
		
		ob_pow_2pow[0] = ob;
		for(int i=1; i<d; i++){ ob_pow_2pow[i] = (ob_pow_2pow[i-1]*ob_pow_2pow[i-1])%e97;   }
		
		long ans=1;
		for(int i=d-1; i>=0; i--){
			if(soeji >= (1<<i)){
				soeji -= (1<<i);
				ans = (ans*ob_pow_2pow[i])%e97;
			}
 		}
		return ans;
	}
	
	
	private static int flag(int pos){   return (1<<pos);    }
	private static boolean isFlaged(int bit, int pos){
    	if((bit&(1<<pos)) > 0) return true;
    	else return false;
	}
	private static int deflag(int bit, int pos){    return bit&~(1<<pos);   }
	
	private static void showflag(int bit){
    	for(int i=0; i<getDigit2(bit); i++){
        	if(isFlaged(bit,i)) System.out.print("O");
        	else System.out.print(".");
    	}
	}
	
	
	private static void fill(boolean[] ob, boolean res){
		for(int i=0; i<ob.length; i++){ ob[i] = res;    }
		return;
	}
	private static void fill(int[] ob, int res){
		for(int i=0; i<ob.length; i++){ ob[i] = res;    }
		return;
	}
	private static void fill(long[] ob, long res){
		for(int i=0; i<ob.length; i++){ ob[i] = res;    }
		return;
	}
	private static void fill(char[] ob, char res){
		for(int i=0; i<ob.length; i++){ ob[i] = res;    }
		return;
	}
	private static void fill(boolean[][] ob, boolean res){
		for(int i=0; i<ob.length; i++){ for(int j=0; j<ob[0].length; j++){  ob[i][j] = res; }   }
		return;
	}
	private static void fill(int[][] ob, int res){
		for(int i=0; i<ob.length; i++){ for(int j=0; j<ob[0].length; j++){  ob[i][j] = res; }   }
		return;
	}
	private static void fill(long[][] ob, long res){
		for(int i=0; i<ob.length; i++){ for(int j=0; j<ob[0].length; j++){  ob[i][j] = res; }   }
		return;
	}
	private static void fill(char[][] ob, char res){
		for(int i=0; i<ob.length; i++){ for(int j=0; j<ob[0].length; j++){  ob[i][j] = res; }   }
		return;
	}
	private static void fill(int[][][] ob, int res){
		for(int i=0; i<ob.length; i++){
			for(int j=0; j<ob[0].length; j++){
				for(int k=0; k<ob[0][0].length; k++){
			        ob[i][j][k] = res;
				}
			}
		}
		return;
	}
	private static void fill(long[][][][] ob, long res){
		for(int i=0; i<ob.length; i++){
			for(int j=0; j<ob[0].length; j++){
				for(int k=0; k<ob[0][0].length; k++){
    				for(int l=0; l<ob[0][0][0].length; l++){
    				    ob[i][j][k][l]=res;
    				}
				}
			}
		}
		return;
	}
	
	static void show_b2(boolean[][] dt, int lit_x, int lit_y){
		PrintWriter out = new PrintWriter(System.out);
		for(int i=0; i<dt[0].length; i++){
			for(int j=0; j<dt.length; j++){
				if((i==lit_y) && (j==lit_x)) out.print("X");
				else if(dt[j][i]) out.print("O");
				else out.print(".");
			}
			out.println();
		}
		out.flush();
	}
	static void show_L2(long[][] dt, String cmnt){
		PrintWriter out = new PrintWriter(System.out);
		for(int i=0; i<dt[0].length; i++){
			for(int j=0; j<dt.length; j++){
				out.print(dt[j][i]+",");
			}
			out.println("<-"+cmnt+":"+i);
		}
		out.flush();
	}
	static void disp_que(ArrayDeque<Integer> dt){		//上手くいかなかった時用
		int a=0;
		while(dt.size()>0){
			a=dt.removeLast();
			System.out.print(a);
		}
		System.out.println("\n");
	}
	
	
	private static void nextPerm(ArrayList<Integer> former){
		int pivot=-1;
		int ln = former.size();
		for(int i = ln; i>1; i--){
			if(former.get(i-2) < former.get(i-1)){
				pivot = i-2;
				break;
			}
		}
		if(pivot==-1){
    		former = null;
    		return;
		}
		int pivot_fig = former.get(pivot);
		
		int min_pos=pivot+1;
		int min=former.get(min_pos);
		for(int i=ln-1; i > pivot+1; i--){
			if((former.get(i) < min)&&(former.get(i) > pivot_fig)){
				min_pos=i;
				min=former.get(min_pos);
			}
		}
		Collections.swap(former, pivot, min_pos);
		Collections.sort(former.subList(pivot+1, ln));
		return;
	}
    private static ArrayList<boolean[]> combi_enum(int ln, boolean[] former, int now_pos, int rest){
        ArrayList<boolean[]> ans = new ArrayList<>();
        boolean[] ans1 = new boolean[former.length+1];
	   	for(int i=0; i<former.length; i++){
	   	    ans1[i] = former[i];
	   	}
        if(ln==(now_pos+1)){
            switch(rest){
                case 0:
                    ans1[former.length] = false;
                    ans.add(ans1);
                    break;
                case 1:
                    ans1[former.length] = true;
                    ans.add(ans1);
                    break;
            }
        }else{
            if(rest == 0){
                ans1[former.length] = false;
                ans.addAll(combi_enum(ln, ans1, now_pos+1, rest));
            }else{
                ans1[former.length] = false;
                ans.addAll(combi_enum(ln, ans1.clone(), now_pos+1, rest));
                ans1[former.length] = true;
                ans.addAll(combi_enum(ln, ans1.clone(), now_pos+1, rest-1));
            }
        }
        return ans;
    }
	
	public static int biSearch(int[] dt, int target){
		int left=0, right=dt.length-1;
		int mid=-1;
		while(left<=right){
			mid = (right+left)/2;
			if(dt[mid] == target) return mid;
			if(dt[mid] < target) left=mid+1;
			else right=mid-1;
		}
		return -1;
	}
	public static int biSearchMax(long[] dt, long target){
		int left=-1, right=dt.length;
		int mid=-1;
		
		while((right-left)>1){
			mid = left + (right-left)/2;
			if(dt[mid] < target) left=mid;
			else right=mid;
		}
		return left;//target未満の最大のaddress
	}
	public static int biSearchMaxAL(ArrayList<Integer> dt, long target){
		int left=-1, right=dt.size();
		int mid=-1;
		
		while((right-left)>1){
			mid = left + (right-left)/2;
			if(dt.get(mid) < target) left=mid;
			else right=mid;
		}
		return left;//target未満の最大のaddress
	}
	
	
	private static int dfs2(boolean[][] state, int x, int y, int depth){		//薄氷渡り
		int[] tmpltX = {1,-1,0,0};
		int[] tmpltY = {0,0,1,-1};
		int newX = -1, newY = -1;
		
		state[x][y] = false;
		depth++;
		
		int maxDunder_this_brunch = depth, tmpD=0;
		for(int i=0; i < 4; i++){
			newX = x+tmpltX[i];
			newY = y+tmpltY[i];
			if((newX >= 0) && (newY >= 0) && (newX < state.length) && (newY < state[0].length) && state[newX][newY]) tmpD = dfs2(state, newX, newY, depth);
			if(tmpD > maxDunder_this_brunch) maxDunder_this_brunch=tmpD;
		}
		state[x][y] = true;
		return maxDunder_this_brunch;
	}
	
    private static int areaSum(int[][] acum_plus1, int bY_notInclude, int aY_include, int bX_notInclude, int aX_include){
        int ans = acum_plus1[aY_include+1][aX_include+1];
        ans -= acum_plus1[aY_include+1][bX_notInclude+1];
        ans -= acum_plus1[bY_notInclude+1][aX_include+1];
        ans += acum_plus1[bY_notInclude+1][bX_notInclude+1];
        return ans;
    }
    
    
    
    static class Graph0n {
        private ArrayList<Node0n> dt = new ArrayList<>();
        Graph0n(int sz){
	   	    for(int i=0; i<sz; i++){
	   	        Node0n node1 = new Node0n();
	   	        dt.add(node1);
	   	    }
        }
        public void add(int vn, int val){
            dt.get(vn).add(val);
        }
        public int get(int vn, int index){
            return dt.get(vn).get(index);
        }
        public ArrayList<Integer> get(int vn){
            return dt.get(vn).getAll();
        }
        public void clear(){
            for(int i=0; i<dt.size(); i++){
                dt.get(i).clear();
            }
        }
    }
    
    static class Node0n {   //重みなし無向グラフの頂点
        private ArrayList<Integer> next_vs = new ArrayList<>();
        public void add(int val){
            next_vs.add(val);
        }
        public int get(int ad){
            return next_vs.get(ad);
        }
        public ArrayList<Integer> getAll(){
            return next_vs;
        }
        public void clear(){
            next_vs.clear();
        }
    }

    static class Edge {
        int from=-1;
        int v2;
        long weight;
        public Edge(int vn, long w){
            this.v2 = vn;
            this.weight = w;
        }
        public Edge(int cm, int vn, long w){
            this.from = cm;
            this.v2 = vn;
            this.weight = w;
        }
    }
    static class Edge2 {
        int v2;
        long cost1,cost2;
        public Edge2(int vn, long w1, long w2){
            this.v2 = vn;
            this.cost1 = w1;
            this.cost2 = w2;
        }
    }

    static class Comparator_Edge implements Comparator<Edge>{
        public int compare(Edge a, Edge b){
            if(a.weight>b.weight){
                return 1;
            }else if(a.weight<b.weight){
                return -1;
            }
            return 0;
        }
    }
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;}
	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 nexL() {
		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 nexI() {
		long nl = nexL();
		if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
		return (int) nl;
	}
	public double nextDouble() { return Double.parseDouble(next());}
	
	public void ni(long[] array2){
	   	for(int i=0; i<array2.length; i++){
	   	    array2[i] = nexL();
	   	}
	   	return;
	}
	public void ni(int[] array2){
	   	for(int i=0; i<array2.length; i++){
	   	    array2[i] = nexI();
	   	}
	   	return;
	}
}
}