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)

//#pragma GCC optimize("Ofast")
//#pragma GCC target("avx,avx2,fma")
#include <bits/stdc++.h>
#define all(x) std::begin(x), std::end(x)
#define isz(x) (int)std::size(x)
const auto io_sync_off = [](){std::ios_base::sync_with_stdio(0);std::cin.tie(0);return 0;}();
// Debug defines:
#define watch(x) std::cerr << std::setw(12) << #x << " = " << std::setw(12) << x
#define watchln(x) watch(x) << std::endl
#define watchsp(x) watch(x) << " "
#define cerr cerr && debug && std::cerr
// Defines:
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using vi = std::vector<int>;
using vl = std::vector<ll>;
using vvi = std::vector<vi>;
using vvl = std::vector<vl>;
using pii = std::pair<int,int>;
using pil = std::pair<int,ll>;
using pli = std::pair<ll,int>;
using pll = std::pair<ll,ll>;
// Comparators:
template<typename A, typename B> bool operator >(const A& a, const B& b) { return b < a; }
template<typename A, typename B> bool operator<=(const A& a, const B& b) { return !(a > b); }
template<typename A, typename B> bool operator>=(const A& a, const B& b) { return !(a < b); }
template<typename A, typename B> bool operator!=(const A& a, const B& b) { return a < b || b < a; }
template<typename A, typename B> bool operator==(const A& a, const B& b) { return !(a != b); }
namespace std {
    // Containers:
    template <typename T> constexpr auto size(const T& t) -> decltype(t.size());
    // 2D arrays:
    template<typename T, int N, int M> auto size(const T (&)[N][M]) { return N * M; }
    template<typename T, int N, int M> auto begin(T (&a)[N][M]) { return &a[0][0]; }
    template<typename T, int N, int M> auto end(T (&a)[N][M]) { return &a[0][0] + N * M; }
    // 3D arrays:
    template<typename T, int N, int M, int K> auto size(const T (&)[N][M][K]) { return N * M * K; }
    template<typename T, int N, int M, int K> auto begin(T (&a)[N][M][K]) { return &a[0][0][0]; }
    template<typename T, int N, int M, int K> auto end(T (&a)[N][M][K]) { return &a[0][0][0] + N * M * K; }
    // Algorithms:
    template<typename C> void reuniq(C& c) { c.erase(unique(all(c)), end(c)); }
    template<typename C, typename X> int lowpos(const C& c, X x) {
        return int(lower_bound(all(c), x) - begin(c));
    }
    template<typename C, typename X> int uppos(const C& c, X x) {
        return int(upper_bound(all(c), x) - begin(c));
    }
    template<typename X, typename Y> X& remin(X& x, const Y& y) { return x = (y < x) ? y : x; }
    template<typename X, typename Y> X& remax(X& x, const Y& y) { return x = (x < y) ? y : x; }
}
// Numeric:
namespace Numeric {
    template<typename T, typename N> 
    T pow(T a, N n) {
        T r(1);
        while (n > 0) {
            if (n & 1) { r *= a; }
            a *= a; n >>= 1;
        }
        return r;
    }
    template<int mod>
    struct IntMod {
        int value;
        IntMod(int value_ = 0) : value(value_) {
            if (value >= mod) value -= mod;
            if (value < 0) value += mod;
        }
        IntMod& operator+=(IntMod num) {
            value += num.value;
            if (value >= mod) value -= mod;
            return *this;
        }
        IntMod& operator-=(IntMod num) {
            value -= num.value;
            if (value < 0) value += mod;
            return *this;
        }
        IntMod operator+(IntMod num) const { return IntMod(*this) += num; }
        IntMod operator-(IntMod num) const { return IntMod(*this) -= num; }
        IntMod operator*(IntMod num) const { return IntMod(int(value * 1LL * num.value % mod)); }
        IntMod& operator*=(IntMod num) { return *this = *this * num; }
        IntMod operator/(IntMod num) const { return *this * pow(num, mod-2); }
        IntMod& operator/=(IntMod num) { return *this = *this / num; }
    };
    template<int mod> bool operator<(IntMod<mod> a,IntMod<mod> b) { return a.value < b.value; }
    template<int mod>
    std::ostream& operator<<(std::ostream& os, const IntMod<mod>& num) {
        return os << num.value;
    }
}
// Rand:
namespace Rand {
    const auto seed = std::chrono::high_resolution_clock::now().time_since_epoch().count();
    std::mt19937 gen(seed ^ ull(new ull));
}
// Hash:
namespace Hash {
    const ull mod = (ull(1) << 61) - 1; // prime mod of hashing
    std::vector<ull> pow;
    const int base = [&](){
        pow = {1};
        std::uniform_int_distribution<int> dist((int)1.5e9, (int)2e9);
        int tmp = dist(Rand::gen);
        return tmp % 2 == 0 ? tmp - 1 : tmp;
    }();
    
    struct PolyHash {
        // -------- Static functions --------
        static inline ull add(ull a, ull b) {
            // Calculate (a + b) % mod, 0 <= a < mod, 0 <= b < mod
            return (a += b) < mod ? a : a - mod;
        }
        
        static inline ull sub(ull a, ull b) {
            // Calculate (a - b) % mod, 0 <= a < mod, 0 <= b < mod
            return (a -= b) < mod ? a : a + mod;
        }

        static inline ull mul(ull a, ull b){
            // Calculate (a * b) % mod, 0 <= a < mod, 0 <= b < mod
            ull l1 = (uint32_t)a, h1 = a >> 32, l2 = (uint32_t)b, h2 = b >> 32;
            ull l = l1*l2, m = l1*h2 + l2*h1, h = h1*h2;
            ull ret = (l & mod) + (l >> 61) + (h << 3) + (m >> 29) + (m << 35 >> 3) + 1;
            ret = (ret & mod) + (ret >> 61);
            ret = (ret & mod) + (ret >> 61);
            return ret-1;
        }
        
        // -------- Variables of class --------
        std::vector<ull> pref; // polynomial hash on prefix
        
        // Constructor from string:
        PolyHash(const std::string& s) 
            : pref(s.size()+1u, 0) 
        {
            // Pre-calculate powers of base:
            while (pow.size() <= s.size()) {
                pow.push_back(mul(pow.back(), base));
            }
            // Calculate polinomial hash on prefix:
            for (int i = 0; i < (int)s.size(); ++i) {
                pref[i+1] = add(mul(pref[i], base), s[i]);
            }
        }
        
        // Constructor from vector:
        template<typename T> PolyHash(const std::vector<T>& v) 
            : pref(v.size()+1u, 0) 
        {
            // Pre-calculate powers of base:
            while (pow.size() <= v.size()) {
                pow.push_back(mul(pow.back(), base));
            }
            // Calculate polinomial hash on prefix:
            for (int i = 0; i < (int)v.size(); ++i) {
                pref[i+1] = add(mul(pref[i], base), v[i]);
            }
        }
        
        // Get hash from [pos, pos+len-1] segment of string
        inline ull operator()(const int pos, const int len) const {
            return sub(pref[pos+len], mul(pref[pos], pow[len]));
        }
    };
}
// Input:
template<typename T> std::istream& operator>>(std::istream& is, std::vector<T>& vec) {
    for (auto &it : vec) is >> it;
    return is;
}
// Output:
template<typename A, typename B> std::ostream& operator<<(std::ostream& os, const std::pair<A,B>& pt) {
    return os << "{" << pt.first << ", " << pt.second << "}";
}
template<typename Iterator>
std::ostream& print_range(std::ostream& os, Iterator begin, Iterator end) {
    os << "{";
    for (auto it = begin; it != end; it++) {
        if (it != begin) { os << ", "; }
        os << *it;
    }
    return os << "}";
}
template<typename T> std::ostream& operator<<(std::ostream& os, const std::vector<T>& vec) {
    return print_range(os, vec.begin(), vec.end());
}
template<typename T> std::ostream& operator<<(std::ostream& os, const std::set<T>& set) {
    return print_range(os, set.begin(), set.end());
}
// Variables:
const int debug = 0;
// -----------------------------------------------------------------------------
const int INF = (int)1e9+7;
struct Robot {
    int l, r;
};
std::ostream& operator<<(std::ostream& os, Robot rob) {
    return os << "{l = " << rob.l << ", r = " << rob.r << "}";
}
int main() {
    // solution
    for (int n; std::cin >> n; ) {
        vi dp(1+n, 0);
        std::vector<Robot> r(1+n, Robot{-INF,-INF});
        for (int i = 1,x,l; i <= n; i++) {
            std::cin >> x >> l;
            r[i].l = x - l;
            r[i].r = x + l;
        }
        std::sort(all(r), [](auto a, auto b) {
            return a.r < b.r;
        });
        vi x(1+n);
        for (int i = 0; i <= n; i++) {
            x[i] = r[i].r;
        }
        watchln(r);
        for (int i = 1; i <= n; i++) {
            dp[i] = std::max(dp[i-1], dp[std::uppos(x,r[i].l)-1]+1);
        }
        watchln(dp);
        std::cout << dp[n] << std::endl;
    }
    return 0;
}