#include using namespace std; #define overload3(_1, _2, _3, name, ...) name #define rep1(n) for (decltype(n) _tmp = 0; _tmp < (n); _tmp++) #define rep2(i, n) for (decltype(n) i = 0; i < (n); i++) #define rep3(i, a, b) for (decltype(b) i = a; i < (b); i++) #define rep(...) overload3(__VA_ARGS__, rep3, rep2, rep1)(__VA_ARGS__) #if __has_include() #include #else #define dbg(...) (void(0)) #endif struct IOSetup { IOSetup() noexcept { ios::sync_with_stdio(false); cin.tie(nullptr); cout << fixed << setprecision(10); cerr << fixed << setprecision(10); } } iosetup; template void drop(const T &x) { cout << x << "\n"; exit(0); } template bool chmax(T &a, const T &b) { return a < b and (a = b, true); } template bool chmin(T &a, const T &b) { return a > b and (a = b, true); } using i64 = long long; using f64 = long double; #include using Bint = boost::multiprecision::cpp_int; /** * @brief Union Find * @note a.k.a DSU; Disjoint Set Union */ struct UnionFind { vector parents_or_size; UnionFind(int size_): parents_or_size(size_, -1) {} bool unite(int u, int v) { u = root(u), v = root(v); if (u == v) return false; if (parents_or_size[u] > parents_or_size[v]) swap(u, v); parents_or_size[u] += parents_or_size[v]; parents_or_size[v] = u; return true; } int root(int k) { return parents_or_size[k] < 0 ? k : parents_or_size[k] = root(parents_or_size[k]); } int size(int k) { return -parents_or_size[root(k)]; } bool same(int u, int v) { return root(u) == root(v); } vector> groups() { size_t n = parents_or_size.size(); vector> ret(n); rep(i, n) ret[root(i)].emplace_back(i); ret.erase(remove_if(begin(ret), end(ret), [&](const vector &v) { return v.empty(); })); return ret; } }; /** * @brief Kruskal's Algorithm * @note Solve MST; Minimum Spanning Tree in $O(|E|log|E)$. * @note The sum of the weights of the edges can be obtained from * ```accumulate(begin(ret), end(ret), 0, [](T acc, auto e) { return acc + get<2>(e); })```. * @return Set of edges by vector> */ template vector> kruskal(vector>> const &graph) { using Edge = tuple; vector edges{}; size_t n = size(graph); if (n == 1) return {}; rep(i, n) for (const auto &[j, cost]: graph[i]) edges.emplace_back(Edge{i, j, cost}); sort(begin(edges), end(edges), [](Edge a, Edge b) { return get<2>(a) < get<2>(b); }); UnionFind uf(n); vector ret{}; for (const auto &[u, v, cost]: edges) { if (not uf.same(u, v)) { ret.emplace_back(Edge{u, v, cost}); uf.unite(u, v); } if (size(ret) == n - 1) break; } return ret; } int main() { size_t n; cin >> n; vector graph(n, vector>{}); rep(n * (n - 1) / 2) { size_t a, b; Bint c; cin >> a >> b >> c; graph[--a].emplace_back(pair{--b, c}); graph[b].emplace_back(pair{a, c}); } auto edges = kruskal(graph); Bint ans = get<2>(edges.front()); for (const auto &[a, b, c]: edges) chmax(ans, c); cout << ans << "\n"; }