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)

//#pragma GCC optimize("O3")
//#pragma GCC target("avx")

#include <algorithm>
#include <cmath>
#include <functional>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <string>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std;

// Types
using ll = long long int;
using str = string;
template <class T> using u_set = unordered_set<T>;
template <class K, class V> using u_map = unordered_map<K, V>;
template <class V> using graph = u_map<V, u_set<V>>;
template <class F,
          typename enable_if<is_function<F>::value, nullptr_t>::type = nullptr>
using fun = function<F>;

namespace io {
// Input
using IS = istream;
IS &in(IS &);
IS &in(IS &i) { return i; }
template <class T, class... Ts> IS &in(IS &i, T &a, Ts &... as) {
  return in(i >> a, as...);
}
template <class V> IS &operator>>(IS &i, vector<V> &a) {
  for_each(a.begin(), a.end(), [&i](auto &e) { i >> e; });
  return i;
}
template <class F, class S> IS &operator>>(IS &i, pair<F, S> &p) {
  return in(i, p.first, p.second);
}
template <class... Ts, size_t... I>
IS &tuple_in(IS &i, tuple<Ts...> &t, index_sequence<I...>) {
  return in(i, get<I>(t)...);
}
template <class... Ts> IS &operator>>(IS &i, tuple<Ts...> &t) {
  return tuple_in(i, t, make_index_sequence<sizeof...(Ts)>());
}
// Output
using OS = ostream;
OS &out(OS &o) { return o << endl; }
template <class T> OS &out(OS &o, T const &a) { return o << a << endl; }
template <class T, class... Ts> OS &out(OS &o, T const &a, Ts const &... as) {
  return out(o << a << " ", as...);
}
template <class F, class S> OS &operator<<(OS &o, pair<F, S> const &p) {
  return o << p.first << ":" << p.second;
}
template <class... Ts> OS &args_out(OS &o, Ts const &... ts);
OS &args_out(OS &o) { return o; }
template <class T> OS &args_out(OS &o, T const &t) { return o << t; }
template <class T0, class T1, class... Ts>
OS &args_out(OS &o, T0 const &t0, T1 const &t1, Ts const &... ts) {
  return args_out(o << t0 << ",", t1, ts...);
}
template <class... Ts, size_t... I>
OS &tuple_out(OS &o, tuple<Ts...> const &t, index_sequence<I...>) {
  return args_out(o, get<I>(t)...);
}
template <class... Ts> OS &operator<<(OS &o, tuple<Ts...> const &t) {
  return tuple_out(o << "(", t, make_index_sequence<sizeof...(Ts)>()) << ")";
}
template <
    class C,
    class T = typename iterator_traits<typename C::iterator>::value_type,
    typename enable_if<!is_same<C, str>::value, nullptr_t>::type = nullptr>
OS &operator<<(OS &o, C const &a) {
  return a.empty() ? (o << "[]") : ([&o, &a]() -> OS & {
    o << "[" << *a.begin();
    for_each(next(a.begin()), a.end(), [&o](auto const &e) { o << "," << e; });
    return o << "]";
  }());
}
} // namespace io
auto input = [](auto &... a) { io::in(cin, a...); };
auto print = [](auto const &... a) { io::out(cout, a...); };
#ifdef JUMPAKU_DEBUG
auto dump = [](auto const &... a) { io::out(cerr, a...); };
#else
auto dump = [](auto const &...) {};
#endif

// Hash
namespace hashcode {
template <class... Ts> uint64_t hash_args(uint64_t h, Ts const &... ts);
uint64_t hash_args(uint64_t h) { return h; }
template <class T, class... Ts>
uint64_t hash_args(uint64_t h, T const &t, Ts const &... ts) {
  constexpr hash<T> hasher;
  return hash_args(((h << 19) - h) ^ hasher(t), ts...);
}
template <class... Ts, size_t... I>
uint64_t hash_tuple(tuple<Ts...> const &t, index_sequence<I...>) {
  return hash_args(17, get<I>(t)...);
}
} // namespace hashcode
namespace std {
template <class... Ts> struct hash<tuple<Ts...>> {
  size_t operator()(tuple<Ts...> const &t) const {
    uint64_t h = hashcode::hash_tuple(t, index_sequence_for<Ts...>());
    return h ^ (h >> 32);
  }
};
} // namespace std

// Range
namespace ranges {
template <class T, class Itr> struct iterator_base {
  using difference_type = ll;
  using value_type = T;
  using pointer = T *;
  using reference = T &;
  using iterator_category = random_access_iterator_tag;
  ll i;
  iterator_base(ll const &i = 0) : i(i) {}
  bool operator==(Itr const &itr) const { return i == itr.i; }
  bool operator!=(Itr const &itr) const { return i != itr.i; }
  ll operator-(Itr const &itr) const { return i - itr.i; }
  Itr operator++(int) { return with(i++); }
  Itr operator--(int) { return with(i--); }
  Itr operator+(ll const &n) const { return with(i + n); }
  Itr operator-(ll const &n) const { return with(i - n); }
  Itr &operator+=(ll const &n) {
    i += n;
    return self();
  }
  Itr &operator-=(ll const &n) { return self() += (-n); }
  Itr &operator++() { return self() += 1; }
  Itr &operator--() { return self() -= 1; }

protected:
  virtual Itr with(ll i) const = 0;
  virtual Itr &self() = 0;
};
template <class T> struct seq_base {
  ll const b;
  ll const e;
  seq_base(ll b, ll e) : b(b), e(e) {}
  ll size() const { return e - b; }
  bool empty() const { return size() == 0; }
};
template <class T> struct seq : seq_base<T> {
  struct iterator : iterator_base<T, iterator> {
    seq *s;
    iterator(seq *s, ll const &i) : iterator_base<T, iterator>(i), s(s) {}
    iterator with(ll i) const override { return iterator(s, i); }
    iterator &self() override { return *this; }
    T operator*() const { return (*s)[this->i]; }
  };
  function<T(ll)> const f;
  seq(ll n, function<T(ll)> const &f) : seq(0, n, f) {}
  seq(ll b, ll e, function<T(ll)> const &f) : seq_base<T>(b, e), f(f) {}
  iterator begin() { return iterator(this, this->b); }
  iterator end() { return iterator(this, this->e); }
  ll operator[](ll i) const { return f(i); }
};
struct range : seq_base<ll> {
  struct iterator : iterator_base<ll, iterator> {
    iterator(ll const &i) : iterator_base<ll, iterator>(i) {}
    iterator with(ll i) const override { return iterator(i); }
    iterator &self() override { return *this; }
    ll operator*() const { return i; }
  };
  range(ll n) : range(0LL, n) {}
  range(ll b, ll e) : seq_base<ll>(b, e) {}
  iterator begin() const { return iterator(b); }
  iterator end() const { return iterator(e); }
  ll operator[](ll i) const { return i + b; }
};
} // namespace ranges
using range = ranges::range;
range::iterator end(ll i) { return ranges::range::iterator(i); }
range::iterator begin(ll i) { return end(i); }
template <class F> auto seq(ll b, ll e, F const &f) {
  using T = decltype(f(declval<ll>()));
  return ranges::seq<T>(b, e, f);
}
template <class F> auto seq(ll n, F const &f) { return seq(0, n, f); }
template <class T = ll> vector<T> vec(size_t n, T const &init = T()) {
  return vector<T>(n, init);
}

ll gcd(ll p, ll q) { return (q == 0) ? p : gcd(q, p % q); }
ll lcm(ll p, ll q) { return p / gcd(q, p) * q; }

// MOD
ll pow(ll a, ll n, ll m) {
  if (n == 0)
    return 1;
  if (n & 1)
    return ((a % m) * pow(a, n - 1, m)) % m;
  auto b = pow(a, n / 2, m);
  return (b * b) % m;
}
ll inv(ll a, ll p) { return pow(a, p - 2, p); }

template <ll N, ll M> struct Factrial {
  Factrial() {
    fact[0] = 1;
    for (int i = 1; i <= N; ++i)
      fact[i] = (fact[i - 1] * i) % M;
    finv[N] = inv(fact[N], M);
    for (int i = N; i > 0; --i)
      finv[i - 1] = (finv[i] * i) % M;
  }
  array<ll, N + 1> fact;
  array<ll, N + 1> finv;
  ll comb(ll n, ll m) const {
    if (m < 0 || n < m)
      return 0LL;
    return (fact[n] * ((finv[m] * finv[n - m]) % M)) % M;
  }
};

constexpr ll MOD = 1e9 + 7;

int main() {
  ll N;
  input(N);
  using T = tuple<ll, ll, ll>;
  constexpr ll X = 0, L = 1, R = 2;
  auto cmp = [](auto &ai, auto &aj) { return get<L>(ai) < get<L>(aj); };
  auto A = set<T, decltype(cmp)>(cmp);
  for (auto &&i : range(N)) {
    ll x, l;
    input(x, l);
    A.emplace(x, x - l, x + l);
  }
  auto j = A.begin();
  auto i = j++;
  while (i != A.end() && j != A.end()) {
    ll ri = get<R>(*i);
    ll lj = get<L>(*j);
    ll rj = get<R>(*j);
    if (ri >= rj) {
      A.erase(i);
      i = j++;
    } else if (ri > lj) {
      A.erase(j++);
    } else {
      i = j++;
    }
  }
  print(A.size());
}