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 Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.util.Scanner;

public class Main{
  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);
    // get value from StandardIn
    int n = Integer.parseInt(sc.next());
    int x[] = new int[n];
    int length[] = new int[n];
    int count[] = new int[n];
    for(int i=0;i<n;i++){
      x[i] = Integer.parseInt(sc.next());
      length[i] = Integer.parseInt(sc.next());
      count[i] = 0;
    }

    int maxKill = 1;
    int delNum = 0;

    while(true){
      // 一台ずつ腕伸ばせる範囲に何台ロボットあるか数える
      for(int i=0; i<n; i++){
        int min = x[i] - length[i];
        int max = x[i] + length[i];
        // System.out.println("min:" + min);
        // System.out.println("max:" + max);
        // 範囲内にロボットあればインクリメント
        for(int j=0; j<n; j++){
          if(x[j] + length[j] > min && x[j]-length[j] < max){
            count[i]++;
          }
        }
        // 殺した数が多ければ暫定一位
        // System.out.println("kill:" + count[i]);
        if(maxKill < count[i]){
          maxKill = count[i];
          delNum = i;
        }
      }
      // System.out.println(n);
      if(maxKill == 1){
        break;
      }
      // 一番多く殺してたロボットを除外。詰める。
      for(int i=delNum; i<n-1; i++){
        x[i] = x[i+1];
        length[i] = length[i+1];
      }
      n--;
      maxKill = 1;
      for(int i=0; i<n; i++){
        count[i] = 0;
      }
    }
    System.out.println(n);
  }
}