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: Runtime Error)

using System;
using System.Linq;
using System.Collections.Generic;
using System.Numerics;
namespace AtCoder
{
    public class Program
    {
        public static void Main(string[] args)
        {
            var N = Inputer.Int1Char();
            var inp = new List<long[]>();
            var test = new int[100000000];
            for(int i = 0; i < N; i++)
            {
                var tmp = Inputer.LongArray1Line();
                var dis = tmp[0]-tmp[1];
                
                if (dis < 0)
                {
                    dis = 0;
                }
                
                for(long j = dis; j < tmp[0] + tmp[1]; j++)
                {
                    test[j] += 1;
                }
            }
            var max = test.Max();
           
            Console.Write(N-(max-1));
        }





    }


    /// <summary>
    /// 素数かどうか判定する
    /// </summary>
    static class IsPrime
    {
        /// <summary>
        /// 素数かどうか判定
        /// </summary>
        /// <param name="num"></param>
        /// <returns></returns>
        public static bool Is(int num)
        {
            if (num < 2) return false;
            else if (num == 2) return true;
            else if (num % 2 == 0) return false;

            double sqrtNum = Math.Sqrt(num);
            for (int i = 3; i <= sqrtNum; i += 2)
            {
                if (num % i == 0)
                {

                    return false;
                }
            }


            return true;
        }

    }

    /// <summary>
    /// 入力受付
    /// </summary>
    static class Inputer
    {
        /// <summary>
        /// A B C の複数整数からなる1行を受け取る
        /// </summary>
        /// <returns></returns>
        public static int[] IntArray1Line()
        {
            return Console.ReadLine().Split().Select(int.Parse).ToArray();
        }

        /// <summary>
        /// 整数N　のような１つの整数からなる入力を受け取る
        /// </summary>
        /// <returns></returns>
        public static int Int1Char()
        {
            return int.Parse(Console.ReadLine());
        }
        public static double Double1Char()
        {
            return double.Parse(Console.ReadLine());
        }

        /// <summary>
        /// 大きい整数N　のような１つの整数からなる入力を受け取る
        /// </summary>
        /// <returns></returns>
        public static long Long1Char()
        {
            return long.Parse(Console.ReadLine());

        }

        public static List<int> MultLineInt(int Linenum)
        {
            var L = new List<int>();
            for(int i = 0; i < Linenum; i++)
            {
                L.Add(int.Parse(Console.ReadLine()));
            }
            return L;
        } 

        public static long[] LongArray1Line()
        {
            return Console.ReadLine().Split().Select(long.Parse).ToArray();
        }

        public static Char[] CharArray()
        {
            return Console.ReadLine().ToCharArray();
        }

    }

    /// <summary>
    /// 順列を出すやつ
    /// </summary>
    /// <typeparam name="T"></typeparam>
    static class Permutation<T>
    {
        private static void Search(List<T[]> perms, Stack<T> stack, T[] a)
        {
            int N = a.Length;
            if (N == 0)
            {
                perms.Add(stack.Reverse().ToArray());
            }
            else
            {
                var b = new T[N - 1];
                Array.Copy(a, 1, b, 0, N - 1);
                for (int i = 0; i < a.Length; ++i)
                {
                    stack.Push(a[i]);
                    Search(perms, stack, b);
                    if (i < b.Length) { b[i] = a[i]; }
                    stack.Pop();
                }
            }
        }
        public static IEnumerable<T[]> All(IEnumerable<T> src)
        {
            var perms = new List<T[]>();
            Search(perms, new Stack<T>(), src.ToArray());
            return perms;
        }
    }
    
    /// <summary>
    /// 素因数分解
    /// </summary>
    static class PrimeFactors
    {
        public static IEnumerable<long> PrimeFactor(long n)
        {
            long i = 2;
            long tmp = n;

            while (i * i <= n) 
            {
                if (tmp % i == 0)
                {
                    tmp /= i;
                    yield return i;
                }
                else
                {
                    i++;
                }
            }
            if (tmp != 1) yield return tmp;//最後の素数も返す
        }

    }

}