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: Accepted)

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

public class Program
{
    int N;
    Robot[] r;
    public void Solve()
    {
        var sc = new Scanner();
        N = sc.NextInt();
        r = new Robot[N];
        for (int i = 0; i < N; i++)
        {
            int x = sc.NextInt();
            int l = sc.NextInt();
            r[i] = new Robot(x, l);

        }


        Array.Sort(r, (a, b) => (a.X + a.L).CompareTo(b.X + b.L));

        int cnt = 1;
        int max = r[0].X + r[0].L;

        for (int i = 1; i < N; i++)
        {
            if (max <= r[i].X - r[i].L)
            {
                cnt++;
                max = r[i].X + r[i].L;
            }
        }

        Console.WriteLine(cnt);
    }



    public static void Main(string[] args) => new Program().Solve();
}

struct Robot
{
    public int X, L;
    public Robot(int x, int l)
    {
        X = x;
        L = l;
    }
}

namespace CompLib.Util
{
    using System;
    using System.Linq;
    class Scanner
    {
        private int _index;
        private string[] _line;
        const char separator = ' ';

        public Scanner()
        {
            _index = 0;
            _line = new string[0];
        }

        public string Next()
        {
            while (_index >= _line.Length)
            {
                _line = Console.ReadLine().Split(separator);
                _index = 0;
            }
            return _line[_index++];
        }
        public int NextInt() => int.Parse(Next());
        public long NextLong() => long.Parse(Next());
        public double NextDouble() => double.Parse(Next());
        public char NextChar() => Next()[0];
        public char[] NextCharArray() => Next().ToCharArray();

        public string[] Array()
        {
            _line = Console.ReadLine().Split(separator);
            _index = _line.Length;
            return _line;
        }
        public int[] IntArray() => Array().Select(int.Parse).ToArray();
        public long[] LongArray() => Array().Select(long.Parse).ToArray();
        public double[] DoubleArray() => Array().Select(double.Parse).ToArray();
    }
}