結果

問題 No.96 圏外です。
ユーザー maspy
提出日時 2022-04-11 04:04:24
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 399 ms / 5,000 ms
コード長 20,852 bytes
コンパイル時間 3,640 ms
コンパイル使用メモリ 231,440 KB
最終ジャッジ日時 2025-01-28 17:24:58
ジャッジサーバーID
（参考情報） 		judge2 / judge3
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ファイルパターン 結果
other AC * 28
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ソースコード

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プレゼンテーションモードにする

#line 1 "/home/maspy/compro/library/my_template.hpp"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using pi = pair<ll, ll>;
using vi = vector<ll>;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;
template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
template <class T>
using vvvc = vector<vvc<T>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using vvvvvc = vector<vvvvc<T>>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;
#define vec(type, name, ...) vector<type> name(__VA_ARGS__)
#define vv(type, name, h, ...) \
  vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...)   \
  vector<vector<vector<type>>> name( \
      h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...)       \
  vector<vector<vector<vector<type>>>> name( \
      a, vector<vector<vector<type>>>(       \
             b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))
#define FOR_(n) for (ll _ = 0; (_) < (ll)(n); ++(_))
#define FOR(i, n) for (ll i = 0; (i) < (ll)(n); ++(i))
#define FOR3(i, m, n) for (ll i = (m); (i) < (ll)(n); ++(i))
#define FOR_R(i, n) for (ll i = (ll)(n)-1; (i) >= 0; --(i))
#define FOR3_R(i, m, n) for (ll i = (ll)(n)-1; (i) >= (ll)(m); --(i))
#define FOR_subset(t, s) for (ll t = s; t >= 0; t = (t == 0 ? -1 : (t - 1) & s))
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if
#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second
#define stoi stoll
template <typename T>
T SUM(vector<T> &A) {
  T sum = T(0);
  for (auto &&a: A) sum += a;
  return sum;
}
#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end())
int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x==0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x==0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x==0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x==0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x==0 ? -1 : 31 - __builtin_clz(x)); }
int lowbit(u32 x) { return (x==0 ? -1 : 31 - __builtin_clz(x)); }
int lowbit(ll x) { return (x==0 ? -1 : 63 - __builtin_clzll(x)); }
int lowbit(u64 x) { return (x==0 ? -1 : 63 - __builtin_clzll(x)); }
template <typename T, typename U>
T ceil(T x, U y) {
  return (x > 0 ? (x + y - 1) / y : x / y);
}
template <typename T, typename U>
T floor(T x, U y) {
  return (x > 0 ? x / y : (x - y + 1) / y);
}
template <typename T, typename U>
pair<T, T> divmod(T x, U y) {
  T q = floor(x, y);
  return {q, x - q * y};
}
ll binary_search(function<bool(ll)> check, ll ok, ll ng) {
  assert(check(ok));
  while (abs(ok - ng) > 1) {
    auto x = (ng + ok) / 2;
    if (check(x))
      ok = x;
    else
      ng = x;
  }
  return ok;
}
template <class T, class S>
inline bool chmax(T &a, const S &b) {
  return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
  return (a > b ? a = b, 1 : 0);
}
vi s_to_vi(string S, char first_char = 'a') {
  vi A(S.size());
  FOR(i, S.size()) { A[i] = S[i] - first_char; }
  return A;
}
template <typename T>
vector<T> cumsum(vector<T> &A, int off = 1) {
  int N = A.size();
  vector<T> B(N + 1);
  FOR(i, N) { B[i + 1] = B[i] + A[i]; }
  if (off == 0) B.erase(B.begin());
  return B;
}
template <typename T, typename CNT = int>
vc<CNT> bincount(vc<T> &A, int size) {
  vc<CNT> C(size);
  for (auto &&x: A) { ++C[x]; }
  return C;
}
template <typename T>
vector<int> argsort(vector<T> &A) {
  // stable
  vector<int> ids(A.size());
  iota(all(ids), 0);
  sort(all(ids),
       [&](int i, int j) { return A[i] < A[j] || (A[i] == A[j] && i < j); });
  return ids;
}
#line 1 "/home/maspy/compro/library/other/io.hpp"
// based on yosupo's fastio
#include <unistd.h>
namespace detail {
template <typename T, decltype(&T::is_modint) = &T::is_modint>
std::true_type check_value(int);
template <typename T>
std::false_type check_value(long);
} // namespace detail
template <typename T>
struct is_modint : decltype(detail::check_value<T>(0)) {};
template <typename T>
using is_modint_t = enable_if_t<is_modint<T>::value>;
template <typename T>
using is_not_modint_t = enable_if_t<!is_modint<T>::value>;
struct Scanner {
  FILE *fp;
  char line[(1 << 15) + 1];
  size_t st = 0, ed = 0;
  void reread() {
    memmove(line, line + st, ed - st);
    ed -= st;
    st = 0;
    ed += fread(line + ed, 1, (1 << 15) - ed, fp);
    line[ed] = '\0';
  }
  bool succ() {
    while (true) {
      if (st == ed) {
        reread();
        if (st == ed) return false;
      }
      while (st != ed && isspace(line[st])) st++;
      if (st != ed) break;
    }
    if (ed - st <= 50) {
      bool sep = false;
      for (size_t i = st; i < ed; i++) {
        if (isspace(line[i])) {
          sep = true;
          break;
        }
      }
      if (!sep) reread();
    }
    return true;
  }
  template <class T, enable_if_t<is_same<T, string>::value, int> = 0>
  bool read_single(T &ref) {
    if (!succ()) return false;
    while (true) {
      size_t sz = 0;
      while (st + sz < ed && !isspace(line[st + sz])) sz++;
      ref.append(line + st, sz);
      st += sz;
      if (!sz || st != ed) break;
      reread();
    }
    return true;
  }
  template <class T, enable_if_t<is_integral<T>::value, int> = 0>
  bool read_single(T &ref) {
    if (!succ()) return false;
    bool neg = false;
    if (line[st] == '-') {
      neg = true;
      st++;
    }
    ref = T(0);
    while (isdigit(line[st])) { ref = 10 * ref + (line[st++] & 0xf); }
    if (neg) ref = -ref;
    return true;
  }
  template <class T, is_modint_t<T> * = nullptr>
  bool read_single(T &ref) {
    long long val = 0;
    bool f = read_single(val);
    ref = T(val);
    return f;
  }
  bool read_single(double &ref) {
    string s;
    if (!read_single(s)) return false;
    ref = std::stod(s);
    return true;
  }
  bool read_single(char &ref) {
    string s;
    if (!read_single(s) || s.size() != 1) return false;
    ref = s[0];
    return true;
  }
  template <class T>
  bool read_single(vector<T> &ref) {
    for (auto &d: ref) {
      if (!read_single(d)) return false;
    }
    return true;
  }
  template <class T, class U>
  bool read_single(pair<T, U> &p) {
    return (read_single(p.first) && read_single(p.second));
  }
  template <class A, class B, class C>
  bool read_single(tuple<A, B, C> &p) {
    return (read_single(get<0>(p)) && read_single(get<1>(p))
            && read_single(get<2>(p)));
  }
  template <class A, class B, class C, class D>
  bool read_single(tuple<A, B, C, D> &p) {
    return (read_single(get<0>(p)) && read_single(get<1>(p))
            && read_single(get<2>(p)) && read_single(get<3>(p)));
  }
  void read() {}
  template <class H, class... T>
  void read(H &h, T &... t) {
    bool f = read_single(h);
    assert(f);
    read(t...);
  }
  Scanner(FILE *fp) : fp(fp) {}
};
struct Printer {
  Printer(FILE *_fp) : fp(_fp) {}
  ~Printer() { flush(); }
  static constexpr size_t SIZE = 1 << 15;
  FILE *fp;
  char line[SIZE], small[50];
  size_t pos = 0;
  void flush() {
    fwrite(line, 1, pos, fp);
    pos = 0;
  }
  void write(const char &val) {
    if (pos == SIZE) flush();
    line[pos++] = val;
  }
  template <class T, enable_if_t<is_integral<T>::value, int> = 0>
  void write(T val) {
    if (pos > (1 << 15) - 50) flush();
    if (val == 0) {
      write('0');
      return;
    }
    if (val < 0) {
      write('-');
      val = -val; // todo min
    }
    size_t len = 0;
    while (val) {
      small[len++] = char(0x30 | (val % 10));
      val /= 10;
    }
    for (size_t i = 0; i < len; i++) { line[pos + i] = small[len - 1 - i]; }
    pos += len;
  }
  void write(const string &s) {
    for (char c: s) write(c);
  }
  void write(const char *s) {
    size_t len = strlen(s);
    for (size_t i = 0; i < len; i++) write(s[i]);
  }
  void write(const double &x) {
    ostringstream oss;
    oss << setprecision(15) << x;
    string s = oss.str();
    write(s);
  }
  void write(const long double &x) {
    ostringstream oss;
    oss << setprecision(15) << x;
    string s = oss.str();
    write(s);
  }
  template <class T, is_modint_t<T> * = nullptr>
  void write(T &ref) {
    write(ref.val);
  }
  template <class T>
  void write(const vector<T> &val) {
    auto n = val.size();
    for (size_t i = 0; i < n; i++) {
      if (i) write(' ');
      write(val[i]);
    }
  }
  template <class T, class U>
  void write(const pair<T, U> &val) {
    write(val.first);
    write(' ');
    write(val.second);
  }
  template <class A, class B, class C>
  void write(const tuple<A, B, C> &val) {
    auto &[a, b, c] = val;
    write(a);
    write(' ');
    write(b);
    write(' ');
    write(c);
  }
  template <class A, class B, class C, class D>
  void write(const tuple<A, B, C, D> &val) {
    auto &[a, b, c, d] = val;
    write(a);
    write(' ');
    write(b);
    write(' ');
    write(c);
    write(' ');
    write(d);
  }
  template <class T, size_t S>
  void write(const array<T, S> &val) {
    auto n = val.size();
    for (size_t i = 0; i < n; i++) {
      if (i) write(' ');
      write(val[i]);
    }
  }
  void write(i128 val) {
    string s;
    while (val) {
      s += '0' + int(val % 10);
      val /= 10;
    }
    reverse(all(s));
    if (len(s) == 0) s = "0";
    write(s);
  }
};
Scanner scanner = Scanner(stdin);
Printer printer = Printer(stdout);
void flush() { printer.flush(); }
void print() { printer.write('\n'); }
template <class Head, class... Tail>
void print(Head &&head, Tail &&... tail) {
  printer.write(head);
  if (sizeof...(Tail)) printer.write(' ');
  print(forward<Tail>(tail)...);
}
void read() {}
template <class Head, class... Tail>
void read(Head &head, Tail &... tail) {
  scanner.read(head);
  read(tail...);
}
#define INT(...)   \
  int __VA_ARGS__; \
  read(__VA_ARGS__)
#define LL(...)   \
  ll __VA_ARGS__; \
  read(__VA_ARGS__)
#define STR(...)      \
  string __VA_ARGS__; \
  read(__VA_ARGS__)
#define CHAR(...)      \
  char __VA_ARGS__; \
  read(__VA_ARGS__)
#define DBL(...)      \
  double __VA_ARGS__; \
  read(__VA_ARGS__)
#define VEC(type, name, size) \
  vector<type> name(size);    \
  read(name)
#define VV(type, name, h, w)                     \
  vector<vector<type>> name(h, vector<type>(w)); \
  read(name)
void YES(bool t = 1) { print(t ? "YES" : "NO"); }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { print(t ? "Yes" : "No"); }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { print(t ? "yes" : "no"); }
void no(bool t = 1) { yes(!t); }
#line 1 "/home/maspy/compro/library/ds/hashmap.hpp"
template <typename Val, int LOG = 20>
struct HashMapLL {
  int N;
  ll* keys;
  Val* vals;
  vc<int> IDS;
  bitset<1 << LOG> used;
  const int shift;
  const uint64_t r = 11995408973635179863ULL;
  HashMapLL()
      : N(1 << LOG), keys(new ll[N]), vals(new Val[N]), shift(64 - __lg(N)) {}
  int hash(ll x) {
    static const uint64_t FIXED_RANDOM
        = std::chrono::steady_clock::now().time_since_epoch().count();
    return (uint64_t(x + FIXED_RANDOM) * r) >> shift;
  }
  int index(const ll& key) {
    int i = 0;
    for (i = hash(key); used[i] && keys[i] != key; (i += 1) &= (N - 1)) {}
    return i;
  }
  Val& operator[](const ll& key) {
    int i = index(key);
    if (!used[i]) IDS.eb(i), used[i] = 1, keys[i] = key, vals[i] = Val{};
    return vals[i];
  }
  bool contain(const ll& key) {
    int i = index(key);
    return used[i] && keys[i] == key;
  }
  bool count(const ll& key) {
    int i = index(key);
    return used[i] && keys[i] == key;
  }
  void reset(){
    for(auto&& i : IDS) used[i] = 0;
    IDS.clear();
  }
};
#line 2 "/home/maspy/compro/library/ds/unionfind.hpp"
struct UnionFind {
  int num;
  int comp;
  vc<int> size, par;
  UnionFind(int n) : num(n), comp(n), size(n, 1), par(n) {
    iota(par.begin(), par.end(), 0);
  }
  int find(int x) {
    while (par[x] != x) {
      par[x] = par[par[x]];
      x = par[x];
    }
    return x;
  }
  int operator[](int x) { return find(x); }
  bool merge(ll x, ll y) {
    x = find(x);
    y = find(y);
    if (x == y) { return false; }
    comp--;
    if (size[x] < size[y]) swap(x, y);
    size[x] += size[y];
    size[y] = 0;
    par[y] = x;
    return true;
  }
  vc<int> find_all() {
    vc<int> A(num);
    FOR(i, num) A[i] = find(i);
    return A;
  }
};
#line 1 "/home/maspy/compro/library/ds/cht.hpp"
template <typename T>
struct Line {
  mutable T k, m, p;
  bool operator<(const Line& o) const { return k < o.k; }
  bool operator<(T x) const { return p < x; }
};
template <typename T>
T lc_inf() {
  return numeric_limits<T>::max();
}
template <>
long double lc_inf<long double>() {
  return 1 / .0;
}
template <typename T>
T lc_div(T a, T b) {
  return a / b - ((a ^ b) < 0 and a % b);
}
template <>
long double lc_div(long double a, long double b) {
  return a / b;
};
template <>
double lc_div(double a, double b) {
  return a / b;
};
template <typename T, bool MINIMIZE = true>
struct LineContainer : multiset<Line<T>, less<>> {
  using super = multiset<Line<T>, less<>>;
  using super::begin, super::end, super::insert, super::erase;
  using super::empty, super::lower_bound;
  const T inf = lc_inf<T>();
  bool insect(typename super::iterator x, typename super::iterator y) {
    if (y == end()) return x->p = inf, false;
    if (x->k == y->k)
      x->p = (x->m > y->m ? inf : -inf);
    else
      x->p = lc_div(y->m - x->m, x->k - y->k);
    return x->p >= y->p;
  }
  void add(T k, T m) {
    if (MINIMIZE) { k = -k, m = -m; }
    auto z = insert({k, m, 0}), y = z++, x = y;
    while (insect(y, z)) z = erase(z);
    if (x != begin() and insect(--x, y)) insect(x, y = erase(y));
    while ((y = x) != begin() and (--x)->p >= y->p) insect(x, erase(y));
  }
  T query(T x) {
    assert(!empty());
    auto l = *lower_bound(x);
    T v = (l.k * x + l.m);
    return (MINIMIZE ? -v : v);
  }
};
template <typename T>
using CHT_min = LineContainer<T, true>;
template <typename T>
using CHT_max = LineContainer<T, false>;
/*
long long / double で動くと思う。クエリあたり O(log N)
・add(a, b)：ax + by の追加
・get_max(x,y)：max_{a,b} (ax + by)
・get_min(x,y)：max_{a,b} (ax + by)
*/
template <typename T>
struct CHT_xy {
  using ld = long double;
  CHT_min<ld> cht_min;
  CHT_max<ld> cht_max;
  T amax = -1e18, amin = 1e18, bmax = -1e18, bmin = 1e18;
  void add(T a, T b) {
    cht_min.add(b, a);
    cht_max.add(b, a);
    chmax(amax, a), chmin(amin, a), chmax(bmax, b), chmin(bmin, b);
  }
  T get_max(T x, T y) {
    if (x == 0) { return max(bmax * y, bmin * y); }
    ld z = ld(y) / x;
    if (x > 0) {
      auto l = cht_max.lower_bound(z);
      ll a = l->m, b = l->k;
      return a * x + b * y;
    }
    auto l = cht_min.lower_bound(z);
    ll a = -(l->m), b = -(l->k);
    return a * x + b * y;
  }
  T get_min(T x, T y) { return -get_max(-x, -y); }
};
#line 2 "/home/maspy/compro/library/geo/base.hpp"
template<typename X = long long>
struct Point {
  X x, y;
  Point(X x=0, X y=0) : x(x), y(y) {}
  template <typename S, typename T>
  Point(pair<S, T> p) : x(p.fi), y(p.se) {}
  Point operator+(Point p) const { return {x + p.x, y + p.y}; }
  Point operator-(Point p) const { return {x - p.x, y - p.y}; }
  X det(Point p) const { return x * p.y - y * p.x; }
  X dot(Point p) const { return x * p.x + y * p.y; }
  pair<double,double> polar(){
    double r = sqrt(x * x + y * y);
    double theta = atan2(y, x);
    return {r, theta};
  }
  bool operator<(Point p) const {
    if (x != p.x) return x < p.x;
    return y < p.y;
  }
  bool operator==(Point p) const { return x == p.x && y == p.y; }
  Point operator-() const { return {-x, -y}; }
};
#line 2 "/home/maspy/compro/library/geo/convexhull.hpp"
template<typename T>
vector<T> ConvexHull(vector<pair<T, T>>& XY, string mode = "full",
                      bool inclusive = false, bool sorted = false) {
  assert(mode == "full" || mode == "lower" || mode == "upper");
  ll N = XY.size();
  if (N == 1) return {0};
  if (N == 2) return {0, 1};
  vc<int> I = argsort(XY);
  auto check = [&](ll i, ll j, ll k) -> bool {
    auto xi = XY[i].fi, yi = XY[i].se;
    auto xj = XY[j].fi, yj = XY[j].se;
    auto xk = XY[k].fi, yk = XY[k].se;
    auto dx1 = xj - xi, dy1 = yj - yi;
    auto dx2 = xk - xj, dy2 = yk - yj;
    ll det = dx1 * dy2 - dy1 * dx2;
    return (inclusive ? det >= 0 : det > 0);
  };
  auto calc = [&]() {
    vector<int> P;
    for (auto&& k: I) {
      while (P.size() > 1) {
        auto i = P[P.size() - 2];
        auto j = P[P.size() - 1];
        if (check(i, j, k)) break;
        P.pop_back();
      }
      P.eb(k);
    }
    return P;
  };
  vc<int> P;
  if (mode == "full" || mode == "lower") {
    vc<int> Q = calc();
    P.insert(P.end(), all(Q));
  }
  if (mode == "full" || mode == "upper") {
    if (!P.empty()) P.pop_back();
    reverse(all(I));
    vc<int> Q = calc();
    P.insert(P.end(), all(Q));
  }
  if (mode == "upper") reverse(all(P));
  if(len(P) >= 2 && P[0] == P.back()) P.pop_back();
  return P;
}
template<typename X>
vc<int> ConvexHull(vector<Point<X>>& XY, string mode = "full",
                      bool inclusive = false, bool sorted = false) {
  assert(mode == "full" || mode == "lower" || mode == "upper");
  ll N = XY.size();
  if (N == 1) return {0};
  if (N == 2) return {0, 1};
  vc<int> I = argsort(XY);
  auto check = [&](ll i, ll j, ll k) -> bool {
    auto xi = XY[i].x, yi = XY[i].y;
    auto xj = XY[j].x, yj = XY[j].y;
    auto xk = XY[k].x, yk = XY[k].y;
    auto dx1 = xj - xi, dy1 = yj - yi;
    auto dx2 = xk - xj, dy2 = yk - yj;
    ll det = dx1 * dy2 - dy1 * dx2;
    return (inclusive ? det >= 0 : det > 0);
  };
  auto calc = [&]() {
    vc<int> P;
    for (auto&& k: I) {
      while (P.size() > 1) {
        auto i = P[P.size() - 2];
        auto j = P[P.size() - 1];
        if (check(i, j, k)) break;
        P.pop_back();
      }
      P.eb(k);
    }
    return P;
  };
  vc<int> P;
  if (mode == "full" || mode == "lower") {
    vc<int> Q = calc();
    P.insert(P.end(), all(Q));
  }
  if (mode == "full" || mode == "upper") {
    if (!P.empty()) P.pop_back();
    reverse(all(I));
    vc<int> Q = calc();
    P.insert(P.end(), all(Q));
  }
  if (mode == "upper") reverse(all(P));
  if(len(P) >= 2 && P[0] == P.back()) P.pop_back();
  return P;
}
#line 8 "main.cpp"
using P = Point<ll>;
pair<int, int> points_diagonal(vc<P>& XY) {
  ll N = len(XY);
  assert(N >= 1);
  if (N == 1) return {0, 0};
  auto I = ConvexHull(XY, "full");
  CHT_xy<ll> cht;
  pi res = {0, 0};
  ll best = 0;
  for (auto&& i: I) {
    P p = XY[i];
    cht.add(p.x, p.y);
  }
  ll s = 0;
  FOR(k, len(I)) {
    ll i = (k == 0 ? I.back() : I[k - 1]), j = I[k];
    P A = XY[i], B = XY[j];
    ll dx = B.x - A.x, dy = B.y - A.y;
    P vec = {-dy, dx};
    while (1) {
      P p = XY[I[s]], q = XY[I[(s + 1) % len(I)]];
      if (vec.dot(p - q) < 0)
        s = (s + 1) % len(I);
      else
        break;
    }
    P C = XY[I[s]];
    if (chmax(best, (A - C).dot(A - C))) res = {i, I[s]};
    if (chmax(best, (B - C).dot(B - C))) res = {j, I[s]};
  }
  return res;
}
void solve() {
  LL(N);
  if (N == 0) return print(1);
  vc<P> XY(N);
  FOR(i, N) {
    LL(x, y);
    XY[i] = {x, y};
  }
  HashMapLL<int> MP;
  auto to_key = [&](P p) -> ll { return p.x * 1e6 + p.y; };
  FOR(i, N) { MP[to_key(XY[i])] = i; }
  UnionFind uf(N);
  FOR(i, N) {
    P p = XY[i];
    FOR3(dx, 0, 11) FOR3(dy, -10, 11) {
      if (dx * dx + dy * dy > 100) continue;
      if (dx == 0 && dy == 0) continue;
      P q = p;
      q.x += dx, q.y += dy;
      ll key = to_key(q);
      if (!MP.count(key)) continue;
      ll j = MP[key];
      uf.merge(i, j);
    }
  }
  vc<vi> IDS(N);
  FOR(v, N) IDS[uf[v]].eb(v);
  using Re = double;
  Re ANS = 2.0;
  for (auto&& I: IDS) {
    if (len(I) == 0) continue;
    vc<P> xy;
    for (auto&& i: I) xy.eb(XY[i]);
    auto [a, b] = points_diagonal(xy);
    P vec = xy[b] - xy[a];
    chmax(ANS, sqrt(Re(vec.dot(vec))) + 2.0);
  }
  print(ANS);
}
signed main() {
  cin.tie(nullptr);
  ios::sync_with_stdio(false);
  cout << setprecision(15);
  ll T = 1;
  // LL(T);
  FOR(_, T) solve();
  return 0;
}
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