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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;

namespace MyProject
{
    class Program
    {
        static void Main(string[] args)
        {
#if Local
            var sw = new Stopwatch();
            sw.Start();
            Console.SetIn(new StreamReader("input.in"));
#endif

            var solver = new Solver();
            solver.Solve();
#if Local
            Console.WriteLine($"{sw.ElapsedMilliseconds}ms");
#endif
        }
    }

    class Solver
    {
        private bool IsNg(Tuple<int, int> robot1, Tuple<int, int> robot2)
        {
            if (robot1.Item1 < robot2.Item1)
            {
                if (robot1.Item1 + robot1.Item2 > robot2.Item1 - robot2.Item2)
                {
                    return true;
                }
                else
                {
                    return false;
                }
            }
            else
            {
                if (robot2.Item1 + robot2.Item2 > robot1.Item1 - robot1.Item2)
                {
                    return true;
                }
                else
                {
                    return false;
                }
            }
        }

        private List<Tuple<int, int>> robots = new List<Tuple<int, int>>();
        private List<int> remList = new List<int>();
        private Dictionary<int, int> ngCounts = new Dictionary<int, int>();

        private int GetNgCount(int i)
        {
            int ngCount = 0;
            foreach (var j in Enumerable.Range(0, this.robots.Count))
            {
                if (i == j)
                {
                    continue;
                }

                if (this.IsNg(this.robots[i], this.robots[j]))
                {
                    ngCount++;
                }
            }

            return ngCount;
        }

        public void Solve()
        {
            var N = int.Parse(Console.ReadLine());
            foreach (var i in Enumerable.Range(0, N))
            {
                var item = Console.ReadLine().Split().Select(elem => int.Parse(elem)).ToArray();
                var X = item[0];
                var L = item[1];
                robots.Add(new Tuple<int, int>(X, L));
            }

            foreach (var i in Enumerable.Range(0, N))
            {
                this.ngCounts[i] = this.GetNgCount(i);
            }

            // NGの多いものから順に消していく
            foreach (var i in this.ngCounts.Where(elem => elem.Value > 0).OrderByDescending(elem => elem.Value).Select(elem => elem.Key))
            {
                this.remList.Add(i);
                if (this.AllOk())
                {
                    break;
                }
            }

            Console.WriteLine(this.robots.Count - this.remList.Count);
        }

        private bool AllOk()
        {
            foreach (var i in Enumerable.Range(0, this.robots.Count))
            {
                foreach (var j in Enumerable.Range(0, this.robots.Count))
                {
                    if (i == j)
                    {
                        continue;
                    }

                    if (this.remList.Contains(i) || this.remList.Contains(j))
                    {
                        continue;
                    }

                    if (this.IsNg(this.robots[i], this.robots[j]))
                    {
                        return false;
                    }
                }
            }

            return true;
        }
    }
}