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)

#include<bits/stdc++.h>
using namespace std;
#define fi first
#define se second
#define fastio ios_base::sync_with_stdio(false); cin.tie(0)
#define loop(i, a, b) for(lli i=a; i<b; i++)
#define loopb(i, a, b) for(lli i=a; i>=b; i--)
#define pb push_back
#define umap unordered_map
typedef long long int lli;
typedef pair<lli, lli> pii;
typedef vector<lli> vll;
// use to avoid collision
struct custom_hash {
    static uint64_t splitmix64(uint64_t x) {
        // http://xorshift.di.unimi.it/splitmix64.c
        x += 0x9e3779b97f4a7c15;
        x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
        x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
        return x ^ (x >> 31);
    }
 
    size_t operator()(uint64_t x) const {
        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
        return splitmix64(x + FIXED_RANDOM);
    }
};
// for pair in unordered_map
struct hash_pair {
    static uint64_t splitmix64(uint64_t x) {
    // http://xorshift.di.unimi.it/splitmix64.c
    x += 0x9e3779b97f4a7c15;
    x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
    x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
    return x ^ (x >> 31);
	}
    template <class T1, class T2>
    size_t operator()(const pair<T1, T2>& p) const{
        auto hash1 = hash<T1>{}(p.first);
        auto hash2 = hash<T2>{}(p.second);
        uint64_t x = hash1 ^ hash2;
        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
        return splitmix64(x + FIXED_RANDOM);
    }
};
lli M = 1e9 + 7;
lli power(lli x, lli y){
    lli res = 1;
    x = x ;
    while (y > 0) {
        if (y & 1)
            res = (res*x)%M ;
        y = y>>1;
        x = (x*x)%M;
    }
    return res%M;
}
lli gcd(lli a, lli b, lli &x, lli& y){
	if(a == 0){
		x = 0;
		y = 1;
		return b;
	}
	lli x1, y1;
	lli d = gcd(b%a, a, x1, y1);
	x = y1 - (b/a)*x1;
	y = x1;
	return d;
}
lli solve(){
	lli n;
	cin>>n;
	vll A(n), B(n);
	loop(i, 0, n){
		lli u, v;
		cin>>u>>v;
		A[i] = u-v+1;
		B[i] = u+v-1;
	}
	sort(A.begin(), A.end());
	sort(B.begin(), B.end());
	int plat_needed = 0, result = 0; 
   int i = 1, j = 0; 
  
   // Similar to merge in merge sort to process  
   // all events in sorted order 
   while (i < n && j < n) 
   { 
      // If next event in sorted order is arrival,  
      // increment count of platforms needed 
      if (A[i] <= B[j]) 
      { 
          plat_needed++; 
          i++; 
  
          // Update result if needed  
          if (plat_needed > result)  
              result = plat_needed; 
      } 
  
      // Else decrement count of platforms needed 
      else
      { 
          plat_needed--; 
          j++; 
      } 
   } 
   cout<<n-result<<"\n";
   return 0;
}
int main(){
	fastio;
	lli t;
	// cin>>t;
	t = 1;
	while(t>0){
		t--;
		solve();
	}
}