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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Text;
using System.Linq;
using System.Collections;
using System.Collections.Generic;


class Program {


	static long mod = 1000000007;
	//static long mod =998244353; 
	static void Main(string[] args) {

		char[] cs = new char[] { ' ' };
		//char[] cs = new char[] { ' ', ',' };

		//int n = int.Parse(Console.ReadLine());
		//int val = int.Parse(Console.ReadLine());
		//int[] vals = parseAry(Console.ReadLine().Split(cs));
		//string str = Console.ReadLine();
		//string[] strs = Console.ReadLine().Split(cs);

		//string res = "";
		int res = 0;

		int n = int.Parse(Console.ReadLine());
		int x;// = new int[n];
		int len;// = new int[n];

		List<KeyValuePair<int, int>> list = new List<KeyValuePair<int, int>>();
		for ( int i = 0; i < n; i++ ) {
			int[] vals = parseAry(Console.ReadLine().Split(cs));
			x = vals[0];
			len = vals[1];
			list.Add(new KeyValuePair<int, int>(x-len+1, len*2-1));
		}

		list.Sort((a, b) => a.Key.CompareTo(b.Key));  //昇順

		int remove = 0;
		for ( int i = 0; i < n-1; i++ ) {
			int r=1;
			KeyValuePair<int,int> now = list[i];
			KeyValuePair<int,int> nex = list[i + r];

			for ( int k = 0; k < now.Value; k++ ) {
				if ( now.Key + k == nex.Key ) {
					remove++;
					r++;
					if ( i + r >= n ) { break; }
					if ( now.Key + now.Value < nex.Key + nex.Value ) {
						nex = list[i + r];
						k--;
						continue;
					} else {
						now = nex;
						nex = list[i + r];
						k = -1;
						continue;
					}
				
				}

			}
			i += r - 1;
		}




			Console.WriteLine(n-remove);

		return;

	}


	//	int配列をスペース区切りの文字列に変換
	static string stringBuilderArrayInt(int[] a) {
		StringBuilder sb = new StringBuilder();

		for ( int i = 0; i < a.Length; i++ ) {
			sb.Append(a[i] + " "); 
		}
		if ( sb.Length > 1 ) {
			sb = sb.Remove(sb.Length - 1, 1);
		}
		return sb.ToString(); ;
	}


	//	文字列strをindex番目からdで上書き
	static string strOverWrite(string str, int i, string s) {
		return str.Remove(i, s.Length).Insert(i, s);
	}

	//　String[]  ----->  int[]
	static int[] parseAry(string[] str) {
		int[] nums = new int[str.Length];
		for ( int i = 0; i < str.Length; i++ ) { nums[i] = int.Parse(str[i]); }
		return nums;
	}
	//　String[]  ----->  long[]
	static long[] parseAryL(string[] str) {
		long[] nums = new long[str.Length];
		for ( int i = 0; i < str.Length; i++ ) { nums[i] = long.Parse(str[i]); }
		return nums;
	}

	//文字列を1文字ずつString[]に入れる
	static string[] strAry(String str) {
		string[] re = new string[str.Length];
		for ( int i = 0; i < str.Length; i++ ) { re[i] = str[i].ToString(); }
		return re;
	}



}