//////////////////////////////////////// /// tu3 pro-con template /// //////////////////////////////////////// #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; //// MACRO //// #define countof(a) (sizeof(a)/sizeof(a[0])) #define REP(i,n) for (int i = 0; i < (n); i++) #define RREP(i,n) for (int i = (n)-1; i >= 0; i--) #define FOR(i,s,n) for (int i = (s); i < (n); i++) #define RFOR(i,s,n) for (int i = (n)-1; i >= (s); i--) #define pos(c,i) c.being() + (i) #define allof(c) c.begin(), c.end() #define aallof(a) a, countof(a) #define partof(c,i,n) c.begin() + (i), c.begin() + (i) + (n) #define apartof(a,i,n) a + (i), a + (i) + (n) #define long long long #define EPS 1e-9 #define INF (1L << 28) #define LINF (1LL << 60) #define PREDICATE(t,a,exp) [&](const t & a) -> bool { return exp; } #define COMPARISON_T(t) bool(*)(const t &, const t &) #define COMPARISON(t,a,b,exp) [&](const t & a, const t & b) -> bool { return exp; } #define CONVERTER(TSrc,t,TDest,exp) [&](const TSrc &t)->TDest { return exp; } inline int sign_of(double x) { return (abs(x) < EPS ? 0 : x > 0 ? 1 : -1); } inline bool inRange(int val, int min, int max) { return val >= min && val < max; } inline bool inRange(double val, double min, double max) { return val - min > -EPS && val - max < EPS; } inline bool inRange(int x, int y, int W, int H) { return x >= 0 && x < W && y >= 0 && y < H; } // W,H含まない template struct vevector : public vector> { vevector(int n = 0, int m = 0, const T &initial = T()) : vector>(n, vector(m, initial)) { } }; template struct vevevector : public vector> { vevevector(int n = 0, int m = 0, int l = 0, const T &initial = T()) : vector>(n, vevector(m, l, initial)) { } }; template struct vevevevector : public vector> { vevevevector(int n = 0, int m = 0, int l = 0, int k = 0, const T &initial = T()) : vector>(n, vevevector(m, l, k, initial)) { } }; //// i/o helper //// namespace std { template inline istream & operator >> (istream & in, pair &p) { in >> p.first >> p.second; return in; } template inline ostream & operator << (ostream &out, const pair &p) { out << p.first << " " << p.second; return out; } } template T read() { T t; cin >> t; return t; } template vector read(int n) { vector v; REP(i, n) { v.push_back(read()); } return v; } template vevector read(int n, int m) { vevector v; REP(i, n) v.push_back(read(m)); return v; } template vector readjag() { return read(read()); } template vevector readjag(int n) { vevector v; REP(i, n) v.push_back(readjag()); return v; } template struct iter_pair_t { T beg, end; }; template iter_pair_t iter_pair(T beg, T end) { return iter_pair_t{beg, end}; } template ostream & operator << (ostream &out, const iter_pair_t &v) { std::copy(v.beg, v.end, ostream_iterator(out, " ")); return out; } template ostream & operator << (ostream &out, const vector &v) { return out << iter_pair(begin(v), end(v)); } template ostream & operator << (ostream &out, const set &v) { return out << iter_pair(begin(v), end(v)); } template ostream & operator << (ostream &out, const map &v) { return out << iter_pair(begin(v), end(v)); } struct _Reader { istream &cin;template _Reader operator ,(T &rhs) { cin >> rhs; return *this; } }; struct _Writer { ostream &cout; bool f{false }; template _Writer operator ,(const T &rhs) { cout << (f ? " " : "") << rhs; f = true; return *this; } }; #define READ(t,...) t __VA_ARGS__; (_Reader{cin}), __VA_ARGS__ #define WRITE(...) (_Writer{cout}), __VA_ARGS__; cout << endl #define DEBUG(...) (_Writer{cerr}), __VA_ARGS__; cerr << endl void solve(); int main() { cin.tie(0); ios_base::sync_with_stdio(false); cout << setprecision(std::numeric_limits::max_digits10); solve(); return 0; } // 平面上の点。もしくは平面上のベクトル。 struct P2 { double x, y; P2(double x = 0, double y = 0) : x(x), y(y) { } P2(complex c) : x(c.real()), y(c.imag()) { } P2 operator +() const { return *this; } P2 operator +(const P2 &_) const { return P2(x + _.x, y + _.y); } P2 operator -() const { return P2(-x, -y); } P2 operator -(const P2 &_) const { return *this + -_; } P2 operator *(double _) const { return P2(x*_, y*_); } P2 operator /(double _) const { return P2(x / _, y / _); } double dot(const P2 &_) const { return x * _.x + y * _.y; } // 内積 double cross(const P2 &_) const { return x * _.y - y * _.x; } // 外積 double sqlength() const { return dot(*this); } // 二乗長さ double length() const { return sqrt(sqlength()); } // 長さ P2 orthogonal() const { return P2(y, -x); } P2 direction() const { return *this / length(); } // 方向ベクトル double arg() const { return atan2(y, x); } static P2 polar(double length, double theta) { return P2(std::polar(length, theta)); } }; inline istream & operator>>(istream & in, P2 & p) { in >> p.x >> p.y; return in; } inline ostream & operator<<(ostream & out, const P2 & p) { out << p.x << ' ' << p.y; return out; } inline double abs(P2 p2) { return p2.length(); } // 長さ inline P2 orthogonal(P2 p) { return p.orthogonal(); } // 垂直 inline complex orthogonal(complex c) { return c * complex(0, 1); } // 垂直 // 点集合の凸包 O(n log n) typedef int Index; vector convex_hull(const vector &points) { int N = points.size(); if (N == 0) { return { }; } if (N == 1) { return { 0 }; } if (N == 2) { return { 0,1 }; } vector pidx(N); REP(i, N) { pidx[i] = i; } auto cmpP2 = COMPARISON(P2, a, b, a.x != b.x ? a.x < b.x : a.y < b.y); sort(allof(pidx), COMPARISON(Index, a, b, cmpP2(points[a], points[b]))); vector ret; ret.reserve(N * 2); auto cw = [](P2 a, P2 b, P2 c) { return (b - a).cross(c - a) > EPS; }; auto f = [&](int K, int i) { while (ret.size() > K) { P2 a = points[ret[ret.size() - 2]]; P2 b = points[ret[ret.size() - 1]]; P2 c = points[pidx[i]]; if (cw(a, b, c)) { break; } ret.pop_back(); } ret.push_back(pidx[i]); }; REP(i, N) { f(1, i); } int K = ret.size(); RREP(i, N - 1) { f(K, i); } ret.pop_back(); return ret; } // convex_hull + キャリパー法。O(n long n) + O(n) // 点集合のうち一番遠いペアの距離 double convex_diameter(const vector &points) { vector vi = convex_hull(points); int N = vi.size(); vector p(N); REP(i, N) { p[i] = points[vi[i]]; } if (N <= 1) { return 0; } if (N == 2) { return (p[0] - p[1]).length(); } int si = 0, sj = 0; auto cmpP2 = COMPARISON(P2, a, b, a.x != b.x ? a.x < b.x : a.y < b.y); REP(k, N) { if (cmpP2(p[k], p[si])) { si = k; } if (cmpP2(p[sj], p[k])) { sj = k; } } int i = si, j = sj; int maxI = 0, maxJ = 0; double maxD = -INF; do { double d = (p[i] - p[j]).sqlength(); if (d > maxD) { maxD = d; maxI = i; maxJ = j; } int ni = (i + 1) % N; int nj = (j + 1) % N; if ((p[ni] - p[i]).cross(p[nj] - p[j]) >= 0) { j = nj; } else { i = ni; } } while (i != si || j != sj); return (p[maxI] - p[maxJ]).length(); } /// ユニオンファインド森。ユニオンファインドが必要な問題が解ける。 struct UnionFindForest { vector p; UnionFindForest(int n) : p(n, -1) { } int rootOf(int i) { return p[i] < 0 ? i : (p[i] = rootOf(p[i])); } int countOf(int i) { return -p[rootOf(i)]; } bool linked(int a, int b) { return rootOf(a) == rootOf(b); } bool link(int a, int b) { int x = rootOf(a), y = rootOf(b); if (x != y) { p[x] += p[y]; p[y] = x; } return x != y; } }; //////////////////// /// template end /// //////////////////// void solve() { READ(int, N); auto X = read(N); if (N == 0) { WRITE(1); return; } sort(allof(X), COMPARISON(P2, a, b, a.x != b.x ? a.x < b.x : a.y < b.y)); int H = 2001, W = 2001; vevevector buckets(W, H); REP(i, N) { P2 p = X[i]; int x = (p.x + 10000) / 10 + EPS; int y = (p.y + 10000) / 10 + EPS; buckets[x][y].push_back(i); } UnionFindForest g(N); int dx[] = { -1,0,1,-1,0,1,-1,0,1 }; int dy[] = { -1,-1,-1,0,0,0,1,1,1 }; REP(x, W) { REP(y, H) { for(int i : buckets[x][y]) { //if (g.rootOf(i) != i) { continue; } REP(k, 9) { int xx = x + dx[k]; int yy = y + dy[k]; if (inRange(xx, yy, W, H)) { for (int j : buckets[xx][yy]) { if ((X[i] - X[j]).sqlength() <= 100) { g.link(i, j); } } } } linked:; } } } map> S; REP(i, N) { S[g.rootOf(i)].push_back(X[i]); } double maxDistance = 0; for(auto &p : S) { maxDistance = max(maxDistance, convex_diameter(p.second)); } WRITE(maxDistance + 2); }