#line 1 "A.cpp" #pragma GCC target("avx2") #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #include using namespace std; using ll = long long; using ull = unsigned long long; template using pq = priority_queue; template using qp = priority_queue, greater>; #define vec(T, A, ...) vector A(__VA_ARGS__); #define vvec(T, A, h, ...) vector> A(h, vector(__VA_ARGS__)); #define vvvec(T, A, h1, h2, ...) vector>> A(h1, vector>(h2, vector(__VA_ARGS__))); #ifndef RIN__LOCAL #define endl "\n" #endif #define spa ' ' #define len(A) A.size() #define all(A) begin(A), end(A) #define fori1(a) for(ll _ = 0; _ < (a); _++) #define fori2(i, a) for(ll i = 0; i < (a); i++) #define fori3(i, a, b) for(ll i = (a); i < (b); i++) #define fori4(i, a, b, c) for(ll i = (a); ((c) > 0 || i > (b)) && ((c) < 0 || i < (b)); i += (c)) #define overload4(a, b, c, d, e, ...) e #define fori(...) overload4(__VA_ARGS__, fori4, fori3, fori2, fori1)(__VA_ARGS__) template vector> ENUMERATE(vector &A, ll s = 0){ vector> ret(A.size()); for(int i = 0; i < A.size(); i++) ret[i] = {i + s, A[i]}; return ret; } vector> ENUMERATE(string &A, ll s = 0){ vector> ret(A.size()); for(int i = 0; i < A.size(); i++) ret[i] = {i + s, A[i]}; return ret; } #define enum1(A) fori(A.size()) #define enum2(a, A) for(auto a:A) #define enum3(i, a, A) for(auto&& [i, a]: ENUMERATE(A)) #define enum4(i, a, A, s) for(auto&& [i, a]: ENUMERATE(A, s)) #define enum(...) overload4(__VA_ARGS__, enum4, enum3, enum2, enum1)(__VA_ARGS__) template vector> ZIP(vector &A, vector &B){ int n = min(A.size(), B.size()); vector> ret(n); for(int i = 0; i < n; i++) ret[i] = {A[i], B[i]}; return ret; } template vector> ENUMZIP(vector &A, vector &B, ll s = 0){ int n = min(A.size(), B.size()); vector> ret(n); for(int i = 0; i < n; i++) ret[i] = {i + s, A[i], B[i]}; return ret; } #define zip4(a, b, A, B) for(auto&& [a, b]: ZIP(A, B)) #define enumzip5(i, a, b, A, B) for(auto&& [i, a, b]: ENUMZIP(A, B)) #define enumzip6(i, a, b, A, B, s) for(auto&& [i, a, b]: ENUMZIP(A, B, s)) #define overload6(a, b, c, d, e, f, g, ...) g #define zip(...) overload6(__VA_ARGS__, enumzip6, enumzip5, zip4, _, _, _)(__VA_ARGS__) vector stoc(string &S){ int n = S.size(); vector ret(n); for(int i = 0; i < n; i++) ret[i] = S[i]; return ret; } #define INT(...) int __VA_ARGS__; inp(__VA_ARGS__); #define LL(...) ll __VA_ARGS__; inp(__VA_ARGS__); #define STRING(...) string __VA_ARGS__; inp(__VA_ARGS__); #define CHAR(...) char __VA_ARGS__; inp(__VA_ARGS__); #define VEC(T, A, n) vector A(n); inp(A); #define VVEC(T, A, n, m) vector> A(n, vector(m)); inp(A); const ll MOD1 = 1000000007; const ll MOD9 = 998244353; template auto min(const T& a){ return *min_element(all(a)); } template auto max(const T& a){ return *max_element(all(a)); } template inline bool chmax(T &a, const S &b) { return (a < b ? a = b, 1 : 0); } template inline bool chmin(T &a, const S &b) { return (a > b ? a = b, 1 : 0); } void FLUSH(){cout << flush;} void print(){cout << endl;} template void print(Head &&head, Tail &&... tail) { cout << head; if (sizeof...(Tail)) cout << spa; print(forward(tail)...); } template void print(vector &A){ int n = A.size(); for(int i = 0; i < n; i++){ cout << A[i]; if(i == n - 1) cout << endl; else cout << spa; } } template void print(vector> &A){ for(auto &row: A) print(row); } template void print(pair &A){ cout << A.first << spa << A.second << endl; } template void print(vector> &A){ for(auto &row: A) print(row); } template void prisep(vector &A, S sep){ int n = A.size(); for(int i = 0; i < n; i++){ cout << A[i]; if(i == n - 1) cout << endl; else cout << sep; } } template void priend(T A, S end){ cout << A << end; } template void priend(T A){ priend(A, spa); } template void inp(T&... a){ (cin >> ... >> a); } template void inp(vector &A){ for(auto &a:A) cin >> a; } template void inp(vector> &A){ for(auto &row:A) inp(row); } template void inp(pair &A){ inp(A.first, A.second); } template void inp(vector> &A){ for(auto &row: A) inp(row.first, row.second); } template T sum(vector &A){ T tot = 0; for(auto a:A) tot += a; return tot; } template pair, map> compression(vector X){ sort(all(X)); X.erase(unique(all(X)), X.end()); map mp; for(int i = 0; i < X.size(); i++) mp[X[i]] = i; return {X, mp}; } #line 2 "Library/C++/data_structure/UnionFind.hpp" struct UnionFind{ int n; vector par; int group; UnionFind(int n) : n(n){ par.assign(n, -1); group = n; } int find(int x){ if(par[x] < 0) return x; par[x] = find(par[x]); return par[x]; } bool unite(int x, int y){ x = find(x); y = find(y); if(x == y) return false; if(par[x] > par[y]) swap(x, y); group--; par[x] += par[y]; par[y] = x; return true; } bool same(int x, int y){ return find(x) == find(y); } int size(int x){ return -par[find(x)]; } vector roots(){ vector ret; for(int i = 0; i < n; i++){ if(i == find(i)) ret.push_back(i); } return ret; } }; #line 2 "Library/C++/geometry/Point.hpp" struct Point{ long long x; long long y; Point(){} Point(long long x, long long y) : x(x), y(y) {} int area(){ if(y < 0){ if(x < 0) return 1; else return 2; } else{ if(x >= 0) return 3; else return 4; } } bool operator<(Point& rhs){ int ap = area(); int aq = rhs.area(); if(ap == aq){ if (x == 0 && y == 0) return true; return x * rhs.y > rhs.x * y; } else{ return ap < aq; } } }; #line 3 "Library/C++/geometry/cross3.hpp" long long cross3(Point &a, Point &b, Point &c){ return (b.x - a.x) * (c.y - a.y) - (b.y - a.y) * (c.x - a.x); } #line 4 "Library/C++/geometry/convexHull.hpp" vector convexHull(vector P, bool multi=true){ sort(P.begin(), P.end(), [](Point &l, Point &r){ if(l.x == r.x) return l.y < r.y; return l.x < r.x; }); vector Q; int n = P.size(); if(multi){ for(auto p:P){ while(Q.size() > 1 && cross3(Q[Q.size() - 1], Q[Q.size() - 2], p) > 0){ Q.pop_back(); } Q.push_back(p); } int t = Q.size(); for(int i = n - 2; i >= 0; i--){ Point p = P[i]; while(Q.size() > t && cross3(Q[Q.size() - 1], Q[Q.size() - 2], p) > 0){ Q.pop_back(); } Q.push_back(p); } } else{ for(auto p:P){ while(Q.size() > 1 && cross3(Q[Q.size() - 1], Q[Q.size() - 2], p) >= 0){ Q.pop_back(); } Q.push_back(p); } int t = Q.size(); for(int i = n - 2; i >= 0; i--){ Point p = P[i]; while(Q.size() > t && cross3(Q[Q.size() - 1], Q[Q.size() - 2], p) >= 0){ Q.pop_back(); } Q.push_back(p); } } Q.pop_back(); return Q; } #line 189 "A.cpp" using ld = long double; void solve(){ INT(n); if(n == 0){ print(1); return; } map mp; vec(ll, X, n); vec(ll, Y, n); fori(i, n){ inp(X[i], Y[i]); mp[(X[i] * 1000000) + Y[i]] = i; } UnionFind UF(n); vector> D; fori(i, -10, 11) fori(j, -10, 11){ if(i == 0 && j == 0) continue; if(i * i + j * j <= 100) D.push_back({i, j}); } fori(i, n){ for(auto tmp:D){ ll x = X[i] + tmp.first; ll y = Y[i] + tmp.second; ll t = (x * 1000000) + y; if(mp.count(t)) UF.unite(i, mp[t]); } } vvec(Point, points, n); fori(i, n){ points[UF.find(i)].push_back({X[i], Y[i]}); } ld ans = 2.0; for(auto &tmp:points){ if(tmp.empty()) continue; if(tmp.size() == 1) continue; auto res = convexHull(tmp, false); int le = len(res); res.insert(res.end(), all(res)); auto dist=[&](int i, int j){ ld dx = res[i].x - res[j].x; ld dy = res[i].y - res[j].y; return sqrt(dx * dx + dy * dy) + 2.0; }; int r = 1; fori(l, le){ while(dist(l, r + 1) > dist(l, r)) r++; chmax(ans, dist(l, r)); } } print(ans); } int main(){ cin.tie(0)->sync_with_stdio(0); cout << fixed << setprecision(12); int t; t = 1; // cin >> t; while(t--) solve(); return 0; }