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.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Numerics;

class Program
{
    static void Main(string[] args)
    {
        var wrong_answer = new wrong_answer();
        wrong_answer.Solve();
    }
}

public class wrong_answer
{
    const int INF = 1 << 29;
    const long INFL = 1L << 60;
    const int MOD = 1000000007;
    const int MOD2 = 998244353;

    myinout IO = new myinout();
    Math2 mmath = new Math2();

    //functions





    public void Solve()
    {

        var n = IO.long1;
        long last = -INF;
        long ans = 0;
        var xl = new long[n,2];
        var l = new long[n];
        var x = new long[n];

        for (int i = 0; i < n; ++i)
        {
            var o = IO.longm;
            x[i] = o[0];
            l[i] = o[1];
        }
        Array.Sort(x,l);
        for (int i = 0; i < n; ++i)
        {


            if (last <= x[i]-l[i] + 1)
            {
                last = x[i] + l[i];
                ans++;
            }
        }


        IO.wri(ans);
    }




}










public class Math2
{
    public long[] fact;
    public long[] invfact;
    public void factoricalmodset(long N, long MOD = 1000000007)
    {
        fact = new long[N + 1];
        invfact = new long[N + 1];
        fact[0] = 1;

        for (long i = 1; i <= N; ++i)
        {
            fact[i] = fact[i - 1] * i % MOD;
        }
        invfact[N] = pow(fact[N], MOD - 2);

        for (long i = N; i > 0; --i)
        {
            invfact[i - 1] = invfact[i] * i % MOD;
        }

    }

    public long nCr(long n, long r, long MOD = 1000000007)
    {
        return (fact[n] * invfact[r] % MOD * invfact[n - r] % MOD);
    }

    public long pow(long i, long n, long MOD = 1000000007)
    {
        long res = 1;
        while (n > 0)
        {
            if ((n & 1) != 0) res = res * i % MOD;
            i = i * i % MOD;
            n >>= 1;
        }
        return res;
    }

    public long gcd(long i, long y)
    {
        while (y != 0)
        {
            var r = i % y;
            i = y;
            y = r;
        }
        return i;
    }

    public long lcm(long i, long y)
    {
        return i * y / gcd(i, y);
    }

    public Dictionary<long, int> primefactorization(long N)
    {
        var ret = new Dictionary<long, int>();

        for (long i = 2; i * i <= N; ++i)
        {
            int cnt = 0;
            while (N % i == 0)
            {
                cnt++;
                N /= i;
            }
            if (cnt != 0) ret[i] = cnt;

        }
        if (N >= 2) ret[N] = 1;

        return ret;

    }

    public List<long> divisorenumrate(long N)
    {
        var ret = new List<long>();

        for (long i = 1; i * i <= N; ++i)
        {

            if (N % i == 0)
            {
                ret.Add(i);
                ret.Add(N / i);
            }

        }

        return ret;

    }

    public void swap<T>(ref T a, ref T b)
    {
        var i = a;
        a = b;
        b = i;
    }

}

class myinout
{
    //in
    public string str => Console.ReadLine();

    public string[] strm => str.Split(' ');

    public long[] longm => strm.Select(long.Parse).ToArray();
    public int[] intm => strm.Select(int.Parse).ToArray();
    public char[] charm => str.ToArray();
    public double[] doublem => strm.Select(double.Parse).ToArray();
    public long long1 => longm[0];
    public int int1 => intm[0];
    public char char1 => charm[0];
    public double double1 => doublem[0];



    //out
    public void wri<T>(T i)
    {
        Console.WriteLine(i);
    }
    public void wri<T>(T[] i)
    {
        Console.WriteLine(string.Join(" ", i));
    }

    public void yn(bool i)
    {
        if (i) wri("Yes");
        else wri("No");
    }

}