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: Accepted)

#include <bits/stdc++.h>
using namespace std;
 
#define int long long
#define REP(i, l, r) for (int i=(l); i<(r); ++i)
#define RREP(i, r, l) for (int i=(r); i>(l); --i)
#define CASET int _T; cin >> _T; REP(caset, 0, _T)
#define print(x) cout << to_string(x) << '\n'
#define vi vector<int>
#define vb vector<bool>
#define vs vector<string>
#define vvi vector<vi>
#define vvb vector<vb>
#define pii pair<int,int>
#define t3i tuple<int,int,int>
#define mii map<int,int>
#define sq(x) (x)*(x)
#define inv(x) powa(x, MOD-2)
 
long long INF = 1LL<<60;
long long MOD = 998244353;

string to_string(char &c) {string x(1, c); return x;}
string to_string(const char s[]) {return (string)s;}
string to_string(string &s) {return s;}
string to_string(vb &v) {string res; for (const bool &x : v) res += to_string(x) + ' '; return res;}
template <class C> string to_string(C &v) {string res; for (auto &x : v) res += to_string(x) + ' '; return res;}
template <typename A, typename B> istream &operator>>(istream &is, pair<A, B> &pr) {is >> pr.first >> pr.second; return is;}
template <typename A> istream &operator>>(istream &is, vector<A> &v) {for (auto &x : v) is >> x; return is;}
ostream &operator<<(ostream &os, char &c) {os << (char)c; return os;}
ostream &operator<<(ostream &os, const char s[]) {os << (string)s; return os;}
ostream &operator<<(ostream &os, string &s) {for (char &c : s) os << (char)c; return os;}
template <typename A, typename B> ostream &operator<<(ostream &os, pair<A, B> pr) {os << '(' << pr.first << ", " << pr.second << ')'; return os;}
ostream &operator<<(ostream &os, vb &v) {
    bool first = true;
    os << '[';
    for (const bool &x : v) {
        if (!first) os << ", ";
        first = false;
        os << x;
    }
    os << ']';
    return os;
}
template <class C> ostream &operator<<(ostream &os, C &v) {
    bool first = true;
    os << '[';
    for (auto &x : v) {
        if (!first) os << ", ";
        first = false;
        os << x;
    }
    os << ']';
    return os;
}
string bin_string(int x) {
    const int d = 32;
    string res(d, ' ');
    REP(i, 0, d) res[d-1-i] = '0'+(x>>i & 1LL);
    return res;
}
int powa(int base, int exp) {
    int res = 1;
    while (exp) {
        if (exp&1) res = res*base % MOD;
        base = base*base % MOD;
        exp >>= 1;
    }
    return res;
}

main() {
    ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
    
    int n;
    cin >> n;
    vector<pii> robots;
    REP(i, 0, n) {
        int x, s;
        cin >> x >> s;
        robots.push_back({x-s, x+s});
    }
    sort(robots.begin(), robots.end());
    int i=0, j=1;
    vb keep(n, true);
    while (j<n) {
        if (robots[i].second <= robots[j].first) i=j;
        else if (robots[i].second < robots[j].second) {
            keep[j] = false;
        } else {
            keep[i] = false;
            i=j;
        }
        ++j;
    }
    cout << accumulate(keep.begin(), keep.end(), 0LL);
}