Problem:
Score : 200 points

Problem Statement

In a factory, there are N robots placed on a number line.
Robot i is placed at coordinate X_i and can extend its arms of length L_i in both directions, positive and negative.

We want to remove zero or more robots so that the movable ranges of arms of no two remaining robots intersect.
Here, for each i (1 \leq i \leq N), the movable range of arms of Robot i is the part of the number line between the coordinates X_i - L_i and X_i + L_i, excluding the endpoints.

Find the maximum number of robots that we can keep.

Constraints

1 \leq N \leq 100,000

0 \leq X_i \leq 10^9 (1 \leq i \leq N)

1 \leq L_i \leq 10^9 (1 \leq i \leq N)

If i \neq j, X_i \neq X_j.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
X_1 L_1
X_2 L_2
\vdots
X_N L_N

Output

Print the maximum number of robots that we can keep.

Sample Input 1

4
2 4
4 3
9 3
100 5

Sample Output 1

3

By removing Robot 2, we can keep the other three robots.

Sample Input 2

2
8 20
1 10

Sample Output 2

1

Sample Input 3

5
10 1
2 1
4 1
6 1
8 1

Sample Output 3

5

Solution in Java (OpenJDK 11.0.6) (judge verdict: Accepted)


import java.util.AbstractMap;
import java.util.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.Scanner;

public class Main {

	static Scanner scanner;
	public static void main(String[] args) {
	    scanner = new Scanner(System.in);

	    int n=gi();
	    long[] x=new long[n];
	    long[] l=new long[n];
	    long[] ae=new long[n];
	    List<Pair<Long, Long>> li=new ArrayList<Pair<Long, Long>>();

	    for (int i=0; i<n;i++) {
	    	x[i]=gl();
	    	l[i]=gl();
	    	Pair<Long, Long> p=new Pair<Long,Long>(x[i]+l[i], x[i]-l[i]);
	    	li.add(p);
	    }

	    Collections.sort(li);
	    
	    int c=0;
	    long last=Long.MIN_VALUE;
	    for (int i=0; i< li.size();i++) {
	    	Pair<Long, Long> p= li.get(i);
	    	if (p.getValue()>=last) {
	    		last=p.getKey();
	    		c++;
	    	}
	    }

	    System.out.println(c);
	}

	// 文字列として入力を取得
	public static String gs() {
		return scanner.next();
	}

	// intとして入力を取得
	public static int gi() {
		return Integer.parseInt(scanner.next());
	}

	// longとして入力を取得
	public static long gl() {
		return Long.parseLong(scanner.next());
	}

	// doubleとして入力を取得
	public static double gd() {
		return Double.parseDouble(scanner.next());
	}

	public static class Pair<K, V> extends AbstractMap.SimpleEntry<K, V> implements Comparable<Pair<K, V>>{
		/** serialVersionUID. */
	    private static final long serialVersionUID = 6411527075103472113L;

	    public Pair(final K key, final V value) {
	        super(key, value);
	    }

		@Override
		public int compareTo(Pair<K, V> o) {

			Comparable key = (Comparable)this.getKey();
			Comparable key2 = (Comparable)o.getKey();

			return key.compareTo(key2);
		}


	}
}