#line 1 "A.cpp" #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__))); #define endl "\n" #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__) #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 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 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 T sum(vector &A){ T tot = 0; for(auto a:A) tot += a; return tot; } #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 117 "A.cpp" void solve(){ INT(n); vec(ll, X, n); vec(ll, Y, n); vec(ll, T, n); fori(i, n) inp(X[i], Y[i], T[i]); vector>> edges; fori(i, n) fori(j, i + 1, n){ if(T[i] != T[j]){ ll d1 = X[i] * X[i] + Y[i] * Y[i]; ll d2 = X[j] * X[j] + Y[j] * Y[j]; if(d2 > d1) swap(d1, d2); if(d1 == d2){ edges.push_back({0, {i, j}}); continue; } ll a = d1, b = d2; ll l = -1; ll r = a + b; auto ok=[&](ll c){ return 4 * a * b >= (c - a - b) * (c - a - b); }; while(r - l > 1){ ll c = (l + r) / 2; if(ok(c)){ r = c; } else l = c; } edges.push_back({r, {i, j}}); } else{ ll dx = X[j] - X[i]; ll dy = Y[j] - Y[i]; ll d = dx * dx + dy * dy; edges.push_back({d, {i, j}}); } } UnionFind UF(n); sort(all(edges)); for(auto tmp:edges){ UF.unite(tmp.second.first, tmp.second.second); if(UF.same(0, n - 1)){ print(tmp.first); break; } } } int main(){ cin.tie(0)->sync_with_stdio(0); int t; t = 1; // cin >> t; while(t--) solve(); return 0; }