test/sample_test/arc010_4.test.cpp

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• Last update: 2024-10-12 14:04:05+09:00
• Link: https://atcoder.jp/contests/arc010/tasks/arc010_4

Depends on

• kD-Tree (src/DataStructure/KDTree.hpp)
• グラフ (src/Graph/Graph.hpp)
• 強連結成分分解 (src/Graph/StronglyConnectedComponents.hpp)
• メンバの有無を判定するテンプレート 他 (src/Internal/HAS_CHECK.hpp)
• CSR 表現を用いた二次元配列 他 (src/Internal/ListRange.hpp)
• int から long long などのテンプレート (src/Internal/long_traits.hpp)
• tupleやarrayに関するテンプレート 他 (src/Internal/tuple_traits.hpp)

Code

// competitive-verifier: STANDALONE

// https://atcoder.jp/contests/arc010/tasks/arc010_4
// 最近傍探索
#include <sstream>
#include <string>
#include <cassert>
#include <algorithm>
#include <vector>
#include <array>
#include "src/DataStructure/KDTree.hpp"
#include "src/Graph/StronglyConnectedComponents.hpp"
using namespace std;
bool test(int (*solve)(stringstream&, stringstream&), string in, string expected) {
 stringstream scin(in), scout;
 solve(scin, scout);
 return scout.str() == expected;
}
namespace TEST {
signed main(stringstream& scin, stringstream& scout) {
 int N;
 scin >> N;
 vector<array<int, 2>> f(N);
 for (int i= 0; i < N; ++i) scin >> f[i][0] >> f[i][1];
 int M;
 scin >> M;
 vector<array<int, 2>> s(M);
 for (int i= 0; i < M; ++i) scin >> s[i][0] >> s[i][1];
 KDTree<int, 2> kdt(s);
 vector<long long> lim(N, 1ll << 60);
 auto dist2= [&](int x1, int y1, int x2, int y2) {
  long long dx= x1 - x2, dy= y1 - y2;
  return dx * dx + dy * dy;
 };
 if (M)
  for (int i= 0; i < N; ++i) {
   auto [x, y]= f[i];
   auto [xx, yy]= kdt.nearest_neighbor(x, y);
   lim[i]= dist2(x, y, xx, yy);
  }
 Graph g(N);
 for (int i= N; i--;)
  for (int j= i; j--;) {
   auto d= dist2(f[i][0], f[i][1], f[j][0], f[j][1]);
   if (lim[i] > d) g.add_edge(i, j);
   if (lim[j] > d) g.add_edge(j, i);
  }
 StronglyConnectedComponents scc(g);
 auto dag= scc.dag(g);
 int C= scc.size();
 vector<int> start(C, true);
 auto adj= dag.adjacency_vertex(1);
 for (int i= C; i--;)
  for (int j: adj[i]) start[j]= false;
 int ans= 0;
 for (int i= C; i--;) ans+= start[i];
 scout << ans << '\n';
 return 0;
}
}
signed main() {
 assert(test(TEST::main, "3\n1 1\n1 2\n2 1\n0\n", "1\n"));
 assert(test(TEST::main, "2\n1 1\n1 2\n1\n2 1\n", "1\n"));
 assert(test(TEST::main, "5\n1 1\n1 2\n2 3\n3 3\n5 3\n2\n2 1\n4 4\n", "2\n"));
 assert(test(TEST::main, "10\n-10 5\n2 9\n-4 4\n10 -9\n8 3\n5 6\n4 -5\n6 8\n-8 10\n-4 -2\n10\n-1 2\n-2 -7\n9 -3\n-5 5\n6 -10\n-10 9\n7 4\n2 1\n-10 1\n-5 2\n", "8\n"));
 return 0;
}

#line 1 "test/sample_test/arc010_4.test.cpp"
// competitive-verifier: STANDALONE

// https://atcoder.jp/contests/arc010/tasks/arc010_4
// 最近傍探索
#include <sstream>
#include <string>
#include <cassert>
#include <algorithm>
#include <vector>
#include <array>
#line 4 "src/DataStructure/KDTree.hpp"
#include <numeric>
#include <map>
#include <set>
#line 8 "src/DataStructure/KDTree.hpp"
#include <cstdint>
#line 2 "src/Internal/HAS_CHECK.hpp"
#include <type_traits>
#define MEMBER_MACRO(member, Dummy, name, type1, type2, last) \
 template <class tClass> struct name##member { \
  template <class U, Dummy> static type1 check(U *); \
  static type2 check(...); \
  static tClass *mClass; \
  last; \
 }
#define HAS_CHECK(member, Dummy) MEMBER_MACRO(member, Dummy, has_, std::true_type, std::false_type, static const bool value= decltype(check(mClass))::value)
#define HAS_MEMBER(member) HAS_CHECK(member, int dummy= (&U::member, 0))
#define HAS_TYPE(member) HAS_CHECK(member, class dummy= typename U::member)
#define HOGE_OR(member, name, type2) \
 MEMBER_MACRO(member, class dummy= typename U::member, name, typename U::member, type2, using type= decltype(check(mClass))); \
 template <class tClass> using name##member##_t= typename name##member<tClass>::type
#define NULLPTR_OR(member) HOGE_OR(member, nullptr_or_, std::nullptr_t)
#define MYSELF_OR(member) HOGE_OR(member, myself_or_, tClass)
#line 2 "src/Internal/tuple_traits.hpp"
#include <tuple>
#line 5 "src/Internal/tuple_traits.hpp"
#include <cstddef>
template <class T> static constexpr bool tuple_like_v= false;
template <class... Args> static constexpr bool tuple_like_v<std::tuple<Args...>> = true;
template <class T, class U> static constexpr bool tuple_like_v<std::pair<T, U>> = true;
template <class T, size_t K> static constexpr bool tuple_like_v<std::array<T, K>> = true;
template <class T> auto to_tuple(const T &t) {
 if constexpr (tuple_like_v<T>) return std::apply([](auto &&...x) { return std::make_tuple(x...); }, t);
}
template <class T> auto forward_tuple(const T &t) {
 if constexpr (tuple_like_v<T>) return std::apply([](auto &&...x) { return std::forward_as_tuple(x...); }, t);
}
template <class T> static constexpr bool array_like_v= false;
template <class T, size_t K> static constexpr bool array_like_v<std::array<T, K>> = true;
template <class T, class U> static constexpr bool array_like_v<std::pair<T, U>> = std::is_convertible_v<T, U>;
template <class T> static constexpr bool array_like_v<std::tuple<T>> = true;
template <class T, class U, class... Args> static constexpr bool array_like_v<std::tuple<T, U, Args...>> = array_like_v<std::tuple<T, Args...>> && std::is_convertible_v<U, T>;
template <class T> auto to_array(const T &t) {
 if constexpr (array_like_v<T>) return std::apply([](auto &&...x) { return std::array{x...}; }, t);
}
template <class T> using to_tuple_t= decltype(to_tuple(T()));
template <class T> using to_array_t= decltype(to_array(T()));
#line 2 "src/Internal/long_traits.hpp"
// clang-format off
template<class T>struct make_long{using type= T;};
template<>struct make_long<char>{using type= short;};
template<>struct make_long<unsigned char>{using type= unsigned short;};
template<>struct make_long<short>{using type= int;};
template<>struct make_long<unsigned short>{using type= unsigned;};
template<>struct make_long<int>{using type= long long;};
template<>struct make_long<unsigned>{using type= unsigned long long;};
template<>struct make_long<long long>{using type= __int128_t;};
template<>struct make_long<unsigned long long>{using type= __uint128_t;};
template<>struct make_long<float>{using type= double;};
template<>struct make_long<double>{using type= long double;};
template<class T> using make_long_t= typename make_long<T>::type;
// clang-format on
#line 12 "src/DataStructure/KDTree.hpp"
namespace kdtree_internal {
template <class pos_t, size_t K, class M, class A, class B> class KDTreeImpl {};
template <class pos_t, size_t K, class M, class... PK, class... PK2> class KDTreeImpl<pos_t, K, M, std::tuple<PK...>, std::tuple<PK2...>> {
 HAS_MEMBER(op);
 HAS_MEMBER(ti);
 HAS_MEMBER(mp);
 HAS_MEMBER(cp);
 HAS_TYPE(T);
 HAS_TYPE(E);
 MYSELF_OR(T);
 NULLPTR_OR(E);
 using Sec= std::array<pos_t, 2>;
 using Pos= std::array<pos_t, K>;
 using Range= std::array<Sec, K>;
 using long_pos_t= make_long_t<pos_t>;
 template <class L> static constexpr bool monoid_v= std::conjunction_v<has_T<L>, has_op<L>, has_ti<L>>;
 template <class L> static constexpr bool dual_v= std::conjunction_v<has_T<L>, has_E<L>, has_mp<L>, has_cp<L>>;
 struct Node_BB {
  int ch[2]= {-1, -1};
  Pos pos;
  pos_t range[K][2];
 };
 template <class U> struct Node_B: Node_BB {
  U val;
 };
 template <class D, bool sg, bool du> struct Node_D: Node_B<M> {};
 template <bool sg, bool du> struct Node_D<void, sg, du>: Node_BB {};
 template <class D> struct Node_D<D, 1, 0>: Node_B<typename M::T> {
  typename M::T sum;
 };
 template <class D> struct Node_D<D, 0, 1>: Node_B<typename M::T> {
  typename M::E laz;
  bool flg= false;
 };
 template <class D> struct Node_D<D, 1, 1>: Node_B<typename M::T> {
  typename M::T sum;
  typename M::E laz;
  bool flg= false;
 };
 using Node= Node_D<M, monoid_v<M>, dual_v<M>>;
 using Iter= typename std::vector<int>::iterator;
 using T= std::conditional_t<std::is_void_v<M>, std::nullptr_t, myself_or_T_t<M>>;
 using E= nullptr_or_E_t<M>;
 template <class P> using canbe_Pos= std::is_convertible<to_tuple_t<P>, std::tuple<PK...>>;
 template <class P> using canbe_PosV= std::is_convertible<to_tuple_t<P>, std::tuple<PK..., T>>;
 template <class P, class U> static constexpr bool canbe_Pos_and_T_v= std::conjunction_v<canbe_Pos<P>, std::is_convertible<U, T>>;
 std::vector<Node> ns;
 static inline T def_val() {
  if constexpr (monoid_v<M>) return M::ti();
  else return T();
 }
 template <bool z, size_t k, class P> static inline auto get_(const P &p) {
  if constexpr (z) return std::get<k>(p);
  else return std::get<k>(p.first);
 }
 template <class P, size_t... I> Range to_range(const P &p, std::index_sequence<I...>) { return {(assert(std::get<I + I>(p) <= std::get<I + I + 1>(p)), Sec{std::get<I + I>(p), std::get<I + I + 1>(p)})...}; }
 inline void update(int t) {
  ns[t].sum= ns[t].val;
  if (ns[t].ch[0] != -1) ns[t].sum= M::op(ns[t].sum, ns[ns[t].ch[0]].sum);
  if (ns[t].ch[1] != -1) ns[t].sum= M::op(ns[t].sum, ns[ns[t].ch[1]].sum);
 }
 inline void propagate(int t, const E &x) {
  if (t == -1) return;
  if (ns[t].flg) M::cp(ns[t].laz, x);
  else ns[t].laz= x, ns[t].flg= true;
  M::mp(ns[t].val, x);
  if constexpr (monoid_v<M>) M::mp(ns[t].sum, x);
 }
 inline void push(int t) {
  if (ns[t].flg) ns[t].flg= false, propagate(ns[t].ch[0], ns[t].laz), propagate(ns[t].ch[1], ns[t].laz);
 }
 template <bool z, class P, size_t k> inline void set_range(int t, int m, Iter bg, Iter ed, const P *p) {
  auto [mn, mx]= std::minmax_element(bg, ed, [&](int a, int b) { return get_<z, k>(p[a]) < get_<z, k>(p[b]); });
  ns[t].range[k][0]= get_<z, k>(p[*mn]), ns[t].range[k][1]= get_<z, k>(p[*mx]), ns[t].pos[k]= get_<z, k>(p[m]);
 }
 template <bool z, class P, size_t... I> inline void set_range_lp(int t, int m, Iter bg, Iter ed, const P *p, std::index_sequence<I...>) { (void)(int[]){(set_range<z, P, I>(t, m, bg, ed, p), 0)...}; }
 template <bool z, uint8_t div, class P> inline int build(int &ts, Iter bg, Iter ed, const P *p, const T &v= def_val()) {
  if (bg == ed) return -1;
  auto md= bg + (ed - bg) / 2;
  int t= ts++;
  std::nth_element(bg, md, ed, [&](int a, int b) { return get_<z, div>(p[a]) < get_<z, div>(p[b]); }), set_range_lp<z>(t, *md, bg, ed, p, std::make_index_sequence<K>());
  if constexpr (z) {
   if constexpr (!std::is_void_v<M>) {
    if constexpr (std::tuple_size_v<P> == K + 1) ns[t].val= std::get<K>(p[*md]);
    else ns[t].val= v;
   }
  } else ns[t].val= p[*md].second;
  static constexpr uint8_t nx= div + 1 == K ? 0 : div + 1;
  ns[t].ch[0]= build<z, nx>(ts, bg, md, p, v), ns[t].ch[1]= build<z, nx>(ts, md + 1, ed, p, v);
  if constexpr (monoid_v<M>) update(t);
  return t;
 }
 template <bool z, uint8_t div, class P> inline int build(Iter bg, Iter ed, const P *p, int &ts) {
  if (bg == ed) return -1;
  auto md= bg + (ed - bg) / 2;
  int t= ts++;
  std::nth_element(bg, md, ed, [&](int a, int b) { return get_<z, div>(p[a]) < get_<z, div>(p[b]); }), set_range_lp<z>(t, bg, ed, p, std::make_index_sequence<K>());
  if constexpr (z) {
   if constexpr (!std::is_void_v<M>) {
    if constexpr (std::tuple_size_v<P> == K + 1) ns[t].val= std::get<K>(p[t]);
    else ns[t].val= def_val();
   }
  } else ns[t].val= p[t].second;
  static constexpr uint8_t nx= div + 1 == K ? 0 : div + 1;
  ns[t].ch[0]= build<z, nx>(bg, md, p, ts), ns[t].ch[1]= build<z, nx>(md + 1, ed, p, ts);
  if constexpr (monoid_v<M>) update(t);
  return t;
 }
 static inline auto in_cuboid(const Range &r) {
  return [r](const Pos &pos) {
   for (uint8_t k= K; k--;)
    if (r[k][1] < pos[k] || pos[k] < r[k][0]) return false;
   return true;
  };
 }
 static inline auto out_cuboid(const Range &r) {
  return [r](const pos_t rr[K][2]) {
   for (uint8_t k= K; k--;)
    if (rr[k][1] < r[k][0] || r[k][1] < rr[k][0]) return true;
   return false;
  };
 }
 static inline auto inall_cuboid(const Range &r) {
  return [r](const pos_t rr[K][2]) {
   for (uint8_t k= K; k--;)
    if (rr[k][0] < r[k][0] || r[k][1] < rr[k][1]) return false;
   return true;
  };
 }
 static inline long_pos_t min_dist2(const pos_t r[K][2], const Pos &pos) {
  long_pos_t d2= 0, dx;
  for (uint8_t k= K; k--;) dx= std::clamp(pos[k], r[k][0], r[k][1]) - pos[k], d2+= dx * dx;
  return d2;
 }
 static inline auto in_ball(const Pos &c, long_pos_t r2) {
  return [c, r2](const Pos &pos) {
   long_pos_t d2= 0, dx;
   for (uint8_t k= K; k--;) dx= pos[k] - c[k], d2+= dx * dx;
   return d2 <= r2;
  };
 }
 static inline auto inall_ball(const Pos &c, long_pos_t r2) {
  return [c, r2](const pos_t rr[K][2]) {
   long_pos_t d2= 0, dx0, dx1;
   for (uint8_t k= K; k--;) dx0= rr[k][0] - c[k], dx1= rr[k][1] - c[k], d2+= std::max(dx0 * dx0, dx1 * dx1);
   return d2 <= r2;
  };
 }
 static inline auto out_ball(const Pos &c, long_pos_t r2) {
  return [c, r2](const pos_t r[K][2]) { return min_dist2(r, c) > r2; };
 }
 inline void nns(int t, const Pos &pos, std::pair<int, long_pos_t> &ret) const {
  if (t == -1) return;
  long_pos_t d2= min_dist2(ns[t].range, pos);
  if (ret.first != -1 && d2 >= ret.second) return;
  long_pos_t dx= d2= 0;
  for (uint8_t k= K; k--;) dx= pos[k] - ns[t].pos[k], d2+= dx * dx;
  if (ret.first == -1 || d2 < ret.second) ret= {t, d2};
  bool f= 0;
  if (auto [l, r]= ns[t].ch; l != -1 && r != -1) f= min_dist2(ns[l].range, pos) > min_dist2(ns[r].range, pos);
  nns(ns[t].ch[f], pos, ret), nns(ns[t].ch[!f], pos, ret);
 }
 template <class In, class Out> inline void col(int t, const In &in, const Out &out, std::vector<T> &ret) const {
  if (t == -1 || out(ns[t].range)) return;
  if (in(ns[t].pos)) ret.push_back(ns[t].val);
  col(ns[t].ch[0], in, out, ret), col(ns[t].ch[1], in, out, ret);
 }
 template <class In, class InAll, class Out> inline T fld(int t, const In &in, const InAll &inall, const Out &out) {
  if (t == -1 || out(ns[t].range)) return def_val();
  if (inall(ns[t].range)) return ns[t].sum;
  if constexpr (dual_v<M>) push(t);
  T ret= M::op(fld(ns[t].ch[0], in, inall, out), fld(ns[t].ch[1], in, inall, out));
  return in(ns[t].pos) ? M::op(ret, ns[t].val) : ret;
 }
 template <class In, class InAll, class Out> inline void app(int t, const In &in, const InAll &inall, const Out &out, const E &x) {
  if (t == -1 || out(ns[t].range)) return;
  if (inall(ns[t].range)) return propagate(t, x);
  if (push(t); in(ns[t].pos)) M::mp(ns[t].val, x);
  app(ns[t].ch[0], in, inall, out, x), app(ns[t].ch[1], in, inall, out, x);
  if constexpr (monoid_v<M>) update(t);
 }
 template <bool z> inline bool set(int t, const Pos &pos, const T &x) {
  if (t == -1) return false;
  bool isok= true;
  for (uint8_t k= K; k--; isok&= pos[k] == ns[t].pos[k])
   if (ns[t].range[k][1] < pos[k] || pos[k] < ns[t].range[k][0]) return false;
  if constexpr (dual_v<M>) push(t);
  if (isok) {
   if constexpr (z) ns[t].val= x;
   else ns[t].val= M::op(ns[t].val, x);
  } else if (!(isok= set<z>(ns[t].ch[0], pos, x))) isok= set<z>(ns[t].ch[1], pos, x);
  if constexpr (monoid_v<M>)
   if (isok) update(t);
  return isok;
 }
 inline std::pair<T, bool> get(int t, const Pos &pos) {
  if (t == -1) return {T(), false};
  bool myself= true;
  for (uint8_t k= K; k--; myself&= pos[k] == ns[t].pos[k])
   if (ns[t].range[k][1] < pos[k] || pos[k] < ns[t].range[k][0]) return {T(), false};
  if (myself) return {ns[t].val, true};
  if constexpr (dual_v<M>) push(t);
  auto ret= get(ns[t].ch[0], pos);
  return !ret.second ? get(ns[t].ch[1], pos) : ret;
 }
public:
 template <class P, typename= std::enable_if_t<std::disjunction_v<canbe_Pos<P>, canbe_PosV<P>>>> KDTreeImpl(const P *p, size_t n): ns(n) {
  std::vector<int> ids(n);
  int ts= 0;
  std::iota(ids.begin(), ids.end(), 0), build<1, 0>(ts, ids.begin(), ids.end(), p);
 }
 template <class P, typename= std::enable_if_t<std::disjunction_v<canbe_Pos<P>, canbe_PosV<P>>>> KDTreeImpl(const std::vector<P> &p): KDTreeImpl(p.data(), p.size()) {}
 template <class P, typename= std::enable_if_t<canbe_Pos<P>::value>> KDTreeImpl(const std::set<P> &p): KDTreeImpl(std::vector(p.begin(), p.end())) {}
 template <class P, class U, typename= std::enable_if_t<canbe_Pos_and_T_v<P, U>>> KDTreeImpl(const P *p, size_t n, U v): ns(n) {
  std::vector<int> ids(n);
  int ts= 0;
  std::iota(ids.begin(), ids.end(), 0), build<1, 0>(ts, ids.begin(), ids.end(), p, v);
 }
 template <class P, class U, typename= std::enable_if_t<canbe_Pos_and_T_v<P, U>>> KDTreeImpl(const std::vector<P> &p, U v): KDTreeImpl(p.data(), p.size(), v) {}
 template <class P, class U, typename= std::enable_if_t<canbe_Pos_and_T_v<P, U>>> KDTreeImpl(const std::set<P> &p, U v): KDTreeImpl(std::vector(p.begin(), p.end()), v) {}
 template <class P, class U, typename= std::enable_if_t<canbe_Pos_and_T_v<P, U>>> KDTreeImpl(const std::pair<P, U> *p, size_t n): ns(n) {
  std::vector<int> ids(n);
  int ts= 0;
  std::iota(ids.begin(), ids.end(), 0), build<0, 0>(ts, ids.begin(), ids.end(), p);
 }
 template <class P, class U, typename= std::enable_if_t<canbe_Pos_and_T_v<P, U>>> KDTreeImpl(const std::vector<std::pair<P, U>> &p): KDTreeImpl(p.data(), p.size()) {}
 template <class P, class U, typename= std::enable_if_t<canbe_Pos_and_T_v<P, U>>> KDTreeImpl(const std::map<P, U> &p): KDTreeImpl(std::vector(p.begin(), p.end())) {}
 std::vector<T> enum_cuboid(PK2... xs) {
  static_assert(!std::is_void_v<M>, "\"enum_cuboid\" is not available");
  std::vector<T> ret;
  auto r= to_range(std::forward_as_tuple(xs...), std::make_index_sequence<K>());
  return col(-ns.empty(), in_cuboid(r), out_cuboid(r), ret), ret;
 }
 std::vector<T> enum_ball(PK... xs, pos_t r) const {
  static_assert(!std::is_void_v<M>, "\"enum_ball\" is not available");
  std::vector<T> ret;
  long_pos_t r2= long_pos_t(r) * r;
  return col(-ns.empty(), in_ball({xs...}, r2), out_ball({xs...}, r2), ret), ret;
 }
 T prod_cuboid(PK2... xs) {
  static_assert(monoid_v<M>, "\"prod_cuboid\" is not available");
  auto r= to_range(std::forward_as_tuple(xs...), std::make_index_sequence<K>());
  return fld(-ns.empty(), in_cuboid(r), inall_cuboid(r), out_cuboid(r));
 }
 T prod_ball(PK... xs, pos_t r) {
  static_assert(monoid_v<M>, "\"prod_ball\" is not available");
  long_pos_t r2= long_pos_t(r) * r;
  return fld(-ns.empty(), in_ball({xs...}, r2), inall_ball({xs...}, r2), out_ball({xs...}, r2));
 }
 void apply_cuboid(PK2... xs, E a) {
  static_assert(dual_v<M>, "\"apply_cuboid\" is not available");
  auto r= to_range(std::forward_as_tuple(xs...), std::make_index_sequence<K>());
  app(-ns.empty(), in_cuboid(r), inall_cuboid(r), out_cuboid(r), a);
 }
 void apply_ball(PK... xs, pos_t r, E a) {
  static_assert(dual_v<M>, "\"apply_ball\" is not available");
  long_pos_t r2= long_pos_t(r) * r;
  app(-ns.empty(), in_ball({xs...}, r2), inall_ball({xs...}, r2), out({xs...}, r2), a);
 }
 void set(PK... xs, T v) { assert(ns.size()), assert(set<1>(0, {xs...}, v)); }
 void mul(PK... xs, T v) {
  static_assert(monoid_v<M>, "\"mul\" is not available");
  assert(ns.size()), assert(set<0>(0, {xs...}, v));
 }
 T get(PK... xs) {
  assert(ns.size());
  auto [ret, flg]= get(0, {xs...});
  return assert(flg), ret;
 }
 Pos nearest_neighbor(PK... xs) const {
  assert(ns.size());
  std::pair<int, long_pos_t> ret= {-1, -1};
  return nns(0, {xs...}, ret), ns[ret.first].pos;
 }
};
template <class pos_t, size_t K, class M= void> using KDTree= KDTreeImpl<pos_t, K, M, to_tuple_t<std::array<pos_t, K>>, to_tuple_t<std::array<pos_t, K + K>>>;
}
using kdtree_internal::KDTree;
#line 3 "src/Internal/ListRange.hpp"
#include <iostream>
#include <iterator>
#line 6 "src/Internal/ListRange.hpp"
#define _LR(name, IT, CT) \
 template <class T> struct name { \
  using Iterator= typename std::vector<T>::IT; \
  Iterator bg, ed; \
  Iterator begin() const { return bg; } \
  Iterator end() const { return ed; } \
  size_t size() const { return std::distance(bg, ed); } \
  CT &operator[](int i) const { return bg[i]; } \
 }
_LR(ListRange, iterator, T);
_LR(ConstListRange, const_iterator, const T);
#undef _LR
template <class T> struct CSRArray {
 std::vector<T> dat;
 std::vector<int> p;
 size_t size() const { return p.size() - 1; }
 ListRange<T> operator[](int i) { return {dat.begin() + p[i], dat.begin() + p[i + 1]}; }
 ConstListRange<T> operator[](int i) const { return {dat.cbegin() + p[i], dat.cbegin() + p[i + 1]}; }
};
template <template <class> class F, class T> std::enable_if_t<std::disjunction_v<std::is_same<F<T>, ListRange<T>>, std::is_same<F<T>, ConstListRange<T>>, std::is_same<F<T>, CSRArray<T>>>, std::ostream &> operator<<(std::ostream &os, const F<T> &r) {
 os << '[';
 for (int _= 0, __= r.size(); _ < __; ++_) os << (_ ? ", " : "") << r[_];
 return os << ']';
}
#line 3 "src/Graph/Graph.hpp"
struct Edge: std::pair<int, int> {
 using std::pair<int, int>::pair;
 Edge &operator--() { return --first, --second, *this; }
 int to(int v) const { return first ^ second ^ v; }
 friend std::istream &operator>>(std::istream &is, Edge &e) { return is >> e.first >> e.second, is; }
};
struct Graph: std::vector<Edge> {
 size_t n;
 Graph(size_t n= 0, size_t m= 0): vector(m), n(n) {}
 size_t vertex_size() const { return n; }
 size_t edge_size() const { return size(); }
 size_t add_vertex() { return n++; }
 size_t add_edge(int s, int d) { return emplace_back(s, d), size() - 1; }
 size_t add_edge(Edge e) { return emplace_back(e), size() - 1; }
#define _ADJ_FOR(a, b) \
 for (auto [u, v]: *this) a; \
 for (size_t i= 0; i < n; ++i) p[i + 1]+= p[i]; \
 for (int i= size(); i--;) { \
  auto [u, v]= (*this)[i]; \
  b; \
 }
#define _ADJ(a, b) \
 vector<int> p(n + 1), c(size() << !dir); \
 if (!dir) { \
  _ADJ_FOR((++p[u], ++p[v]), (c[--p[u]]= a, c[--p[v]]= b)) \
 } else if (dir > 0) { \
  _ADJ_FOR(++p[u], c[--p[u]]= a) \
 } else { \
  _ADJ_FOR(++p[v], c[--p[v]]= b) \
 } \
 return {c, p}
 CSRArray<int> adjacency_vertex(int dir) const { _ADJ(v, u); }
 CSRArray<int> adjacency_edge(int dir) const { _ADJ(i, i); }
#undef _ADJ
#undef _ADJ_FOR
};
#line 4 "src/Graph/StronglyConnectedComponents.hpp"
class StronglyConnectedComponents {
 std::vector<int> m, q, b;
public:
 StronglyConnectedComponents(const Graph &g) {
  const int n= g.vertex_size();
  m.assign(n, -2), b.resize(n);
  {
   auto adj= g.adjacency_vertex(1);
   std::vector<int> c(adj.p.begin(), adj.p.begin() + n);
   for (int s= 0, k= n, p; s < n; ++s)
    if (m[s] == -2)
     for (m[p= s]= -1; p >= 0;) {
      if (c[p] == adj.p[p + 1]) b[--k]= p, p= m[p];
      else if (int w= adj.dat[c[p]++]; m[w] == -2) m[w]= p, p= w;
     }
  }
  auto adj= g.adjacency_vertex(-1);
  std::vector<char> z(n);
  int k= 0, p= 0;
  q= {0};
  for (int s: b)
   if (!z[s]) {
    for (z[m[k++]= s]= 1; p < k; ++p)
     for (int u: adj[m[p]])
      if (!z[u]) z[m[k++]= u]= 1;
    q.push_back(k);
   }
  for (int i= q.size() - 1; i--;)
   while (k > q[i]) b[m[--k]]= i;
 }
 size_t size() const { return q.size() - 1; }
 ConstListRange<int> block(int k) const { return {m.cbegin() + q[k], m.cbegin() + q[k + 1]}; }
 int operator()(int i) const { return b[i]; }
 Graph dag(const Graph &g) const {
  Graph ret(size());
  for (auto [s, d]: g)
   if (b[s] != b[d]) ret.add_edge(b[s], b[d]);
  return std::sort(ret.begin(), ret.end()), ret.erase(std::unique(ret.begin(), ret.end()), ret.end()), ret;
 }
};
#line 13 "test/sample_test/arc010_4.test.cpp"
using namespace std;
bool test(int (*solve)(stringstream&, stringstream&), string in, string expected) {
 stringstream scin(in), scout;
 solve(scin, scout);
 return scout.str() == expected;
}
namespace TEST {
signed main(stringstream& scin, stringstream& scout) {
 int N;
 scin >> N;
 vector<array<int, 2>> f(N);
 for (int i= 0; i < N; ++i) scin >> f[i][0] >> f[i][1];
 int M;
 scin >> M;
 vector<array<int, 2>> s(M);
 for (int i= 0; i < M; ++i) scin >> s[i][0] >> s[i][1];
 KDTree<int, 2> kdt(s);
 vector<long long> lim(N, 1ll << 60);
 auto dist2= [&](int x1, int y1, int x2, int y2) {
  long long dx= x1 - x2, dy= y1 - y2;
  return dx * dx + dy * dy;
 };
 if (M)
  for (int i= 0; i < N; ++i) {
   auto [x, y]= f[i];
   auto [xx, yy]= kdt.nearest_neighbor(x, y);
   lim[i]= dist2(x, y, xx, yy);
  }
 Graph g(N);
 for (int i= N; i--;)
  for (int j= i; j--;) {
   auto d= dist2(f[i][0], f[i][1], f[j][0], f[j][1]);
   if (lim[i] > d) g.add_edge(i, j);
   if (lim[j] > d) g.add_edge(j, i);
  }
 StronglyConnectedComponents scc(g);
 auto dag= scc.dag(g);
 int C= scc.size();
 vector<int> start(C, true);
 auto adj= dag.adjacency_vertex(1);
 for (int i= C; i--;)
  for (int j: adj[i]) start[j]= false;
 int ans= 0;
 for (int i= C; i--;) ans+= start[i];
 scout << ans << '\n';
 return 0;
}
}
signed main() {
 assert(test(TEST::main, "3\n1 1\n1 2\n2 1\n0\n", "1\n"));
 assert(test(TEST::main, "2\n1 1\n1 2\n1\n2 1\n", "1\n"));
 assert(test(TEST::main, "5\n1 1\n1 2\n2 3\n3 3\n5 3\n2\n2 1\n4 4\n", "2\n"));
 assert(test(TEST::main, "10\n-10 5\n2 9\n-4 4\n10 -9\n8 3\n5 6\n4 -5\n6 8\n-8 10\n-4 -2\n10\n-1 2\n-2 -7\n9 -3\n-5 5\n6 -10\n-10 9\n7 4\n2 1\n-10 1\n-5 2\n", "8\n"));
 return 0;
}

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