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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#define _CRT_SECURE_NO_WARNINGS
#define _USE_MATH_DEFINES
#include <iostream>
#include <iomanip>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <cstdlib>
#include <algorithm>
#include <string>
#include <vector>
#include <stack>
#include <queue>
#include <set>
#include <map>
#include <unordered_map>
#include <functional>
#include <utility>
#include <tuple>
#include <cctype>
#include <bitset>
#include <complex>
#include <cmath>
#include <array>
#include <numeric>
using namespace std;
#define INF 0x3f3f3f3f
#define INFLL 0x3f3f3f3f3f3f3f3fLL
//#define MOD 998244353
#define MOD 1000000007
#define mp make_pair
#define mt make_tuple
#define pb push_back
#define eb emplace_back
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
typedef pair<int, int> pint;
typedef pair<ll,ll> pll;
typedef tuple<int,int,int> tint;
typedef vector<int> vint;
typedef vector<ll> vll;
typedef vector<ull> vull;
typedef vector<pint> vpint;
int dx[8]={0,0,-1,1,1,1,-1,-1};
int dy[8]={-1,1,0,0,1,-1,1,-1};
const int SIZE=100050;
//↑templete
signed main(){

	int N;
	cin>>N;
	vector<pll> A;
	for(int i=0;i<N;i++){
		ll x, l;
		cin>>x>>l;
		A.eb(x, l);
	}
	sort(A.begin(), A.end());
	vll X, L;
	for(int i=0;i<N;i++){
		X.pb(A[i].first);
		L.pb(A[i].second);
	}

	// vll que;
	// que.pb(X[i]+L[i]);
	// for(int i=1;i<N;i++){
	// 	pint R=que.back();
	// 	if(R.second<=X[i+1]+L[i+1]){
	// 		que.pop_back();
	// 		que.pb(X[i]+L[i]);
	// 	}
	// }





	//[)
	pll DP[SIZE]={};
	DP[0]=mp(-1, X[0]+L[0]);
	for(int i=1;i<N;i++){
		DP[i]=min(DP[i-1], mp(-1LL, X[i]+L[i]));
		if(DP[i-1].second <= X[i]-L[i])
			DP[i]=mp(DP[i-1].first-1, X[i]+L[i]);
		if(DP[i-2].second <=X[i]-L[i])
			DP[i]=min(DP[i], mp(DP[i-2].first-1, X[i]+L[i]));
	}
	cout<<-1*DP[N-1].first<<endl;
	return 0;
}