// #pragma comment(linker, "/stack:200000000") #include #include #include namespace suisen { // ! utility template using constraints_t = std::enable_if_t, std::nullptr_t>; template constexpr decltype(auto) constexpr_if(Then&& then, OrElse&& or_else) { if constexpr (cond_v) { return std::forward(then); } else { return std::forward(or_else); } } // ! function template using is_same_as_invoke_result = std::is_same, ReturnType>; template using is_uni_op = is_same_as_invoke_result; template using is_bin_op = is_same_as_invoke_result; template using is_comparator = std::is_same, bool>; // ! integral template >> constexpr int bit_num = std::numeric_limits>::digits; template struct is_nbit { static constexpr bool value = bit_num == n; }; template static constexpr bool is_nbit_v = is_nbit::value; // ? template struct safely_multipliable {}; template <> struct safely_multipliable { using type = long long; }; template <> struct safely_multipliable { using type = __int128_t; }; template <> struct safely_multipliable { using type = float; }; template <> struct safely_multipliable { using type = double; }; template <> struct safely_multipliable { using type = long double; }; template using safely_multipliable_t = typename safely_multipliable::type; } // namespace suisen // ! type aliases using i128 = __int128_t; using u128 = __uint128_t; using ll = long long; using uint = unsigned int; using ull = unsigned long long; template using vec = std::vector; template using vec2 = vec>; template using vec3 = vec>; template using vec4 = vec>; template using pq_greater = std::priority_queue, std::greater>; template using umap = std::unordered_map; // ! macros (capital: internal macro) #define OVERLOAD2(_1,_2,name,...) name #define OVERLOAD3(_1,_2,_3,name,...) name #define OVERLOAD4(_1,_2,_3,_4,name,...) name #define REP4(i,l,r,s) for(std::remove_reference_t>i=(l);i<(r);i+=(s)) #define REP3(i,l,r) REP4(i,l,r,1) #define REP2(i,n) REP3(i,0,n) #define REPINF3(i,l,s) for(std::remove_reference_t>i=(l);;i+=(s)) #define REPINF2(i,l) REPINF3(i,l,1) #define REPINF1(i) REPINF2(i,0) #define RREP4(i,l,r,s) for(std::remove_reference_t>i=(l)+fld((r)-(l)-1,s)*(s);i>=(l);i-=(s)) #define RREP3(i,l,r) RREP4(i,l,r,1) #define RREP2(i,n) RREP3(i,0,n) #define rep(...) OVERLOAD4(__VA_ARGS__, REP4 , REP3 , REP2 )(__VA_ARGS__) #define rrep(...) OVERLOAD4(__VA_ARGS__, RREP4 , RREP3 , RREP2 )(__VA_ARGS__) #define repinf(...) OVERLOAD3(__VA_ARGS__, REPINF3, REPINF2, REPINF1)(__VA_ARGS__) #define CAT_I(a, b) a##b #define CAT(a, b) CAT_I(a, b) #define UNIQVAR(tag) CAT(tag, __LINE__) #define loop(n) for (std::remove_reference_t> UNIQVAR(loop_variable) = n; UNIQVAR(loop_variable) --> 0;) #define all(iterable) (iterable).begin(), (iterable).end() #define input(type, ...) type __VA_ARGS__; read(__VA_ARGS__) // ! I/O utilities // pair template std::ostream& operator<<(std::ostream& out, const std::pair &a) { return out << a.first << ' ' << a.second; } // tuple template std::ostream& operator<<(std::ostream& out, const std::tuple &a) { if constexpr (N >= std::tuple_size_v>) { return out; } else { out << std::get(a); if constexpr (N + 1 < std::tuple_size_v>) { out << ' '; } return operator<<(out, a); } } // vector template std::ostream& operator<<(std::ostream& out, const std::vector &a) { for (auto it = a.begin(); it != a.end();) { out << *it; if (++it != a.end()) out << ' '; } return out; } // array template std::ostream& operator<<(std::ostream& out, const std::array &a) { for (auto it = a.begin(); it != a.end();) { out << *it; if (++it != a.end()) out << ' '; } return out; } inline void print() { std::cout << '\n'; } template inline void print(const Head &head, const Tail &...tails) { std::cout << head; if (sizeof...(tails)) std::cout << ' '; print(tails...); } template auto print_all(const Iterable& v, std::string sep = " ", std::string end = "\n") -> decltype(std::cout << *v.begin(), void()) { for (auto it = v.begin(); it != v.end();) { std::cout << *it; if (++it != v.end()) std::cout << sep; } std::cout << end; } // pair template std::istream& operator>>(std::istream& in, std::pair &a) { return in >> a.first >> a.second; } // tuple template std::istream& operator>>(std::istream& in, std::tuple &a) { if constexpr (N >= std::tuple_size_v>) { return in; } else { return operator>>(in >> std::get(a), a); } } // vector template std::istream& operator>>(std::istream& in, std::vector &a) { for (auto it = a.begin(); it != a.end(); ++it) in >> *it; return in; } // array template std::istream& operator>>(std::istream& in, std::array &a) { for (auto it = a.begin(); it != a.end(); ++it) in >> *it; return in; } template void read(Args &...args) { ( std::cin >> ... >> args ); } // ! integral utilities // Returns pow(-1, n) template constexpr inline int pow_m1(T n) { return -(n & 1) | 1; } // Returns pow(-1, n) template <> constexpr inline int pow_m1(bool n) { return -int(n) | 1; } // Returns floor(x / y) template constexpr inline T fld(const T x, const T y) { return (x ^ y) >= 0 ? x / y : (x - (y + pow_m1(y >= 0))) / y; } template constexpr inline T cld(const T x, const T y) { return (x ^ y) <= 0 ? x / y : (x + (y + pow_m1(y >= 0))) / y; } template > = nullptr> constexpr inline int popcount(const T x) { return __builtin_popcount(x); } template > = nullptr> constexpr inline int popcount(const T x) { return __builtin_popcount(x); } template > = nullptr> constexpr inline int popcount(const T x) { return __builtin_popcountll(x); } template > = nullptr> constexpr inline int count_lz(const T x) { return x ? __builtin_clz(x) : suisen::bit_num; } template > = nullptr> constexpr inline int count_lz(const T x) { return x ? __builtin_clz(x) : suisen::bit_num; } template > = nullptr> constexpr inline int count_lz(const T x) { return x ? __builtin_clzll(x) : suisen::bit_num; } template > = nullptr> constexpr inline int count_tz(const T x) { return x ? __builtin_ctz(x) : suisen::bit_num; } template > = nullptr> constexpr inline int count_tz(const T x) { return x ? __builtin_ctz(x) : suisen::bit_num; } template > = nullptr> constexpr inline int count_tz(const T x) { return x ? __builtin_ctzll(x) : suisen::bit_num; } template constexpr inline int floor_log2(const T x) { return suisen::bit_num - 1 - count_lz(x); } template constexpr inline int ceil_log2(const T x) { return floor_log2(x) + ((x & -x) != x); } template constexpr inline int kth_bit(const T x, const unsigned int k) { return (x >> k) & 1; } template constexpr inline int parity(const T x) { return popcount(x) & 1; } struct all_subset { struct all_subset_iter { const int s; int t; constexpr all_subset_iter(int s) : s(s), t(s + 1) {} constexpr auto operator*() const { return t; } constexpr auto operator++() {} constexpr auto operator!=(std::nullptr_t) { return t ? (--t &= s, true) : false; } }; int s; constexpr all_subset(int s) : s(s) {} constexpr auto begin() { return all_subset_iter(s); } constexpr auto end() { return nullptr; } }; // ! container template > = nullptr> auto priqueue_comp(const Comparator comparator) { return std::priority_queue, Comparator>(comparator); } template auto isize(const Iterable &iterable) -> decltype(int(iterable.size())) { return iterable.size(); } template > = nullptr> auto generate_vector(int n, Gen generator) { std::vector v(n); for (int i = 0; i < n; ++i) v[i] = generator(i); return v; } template auto generate_range_vector(T l, T r) { return generate_vector(r - l, [l](int i) { return l + i; }); } template auto generate_range_vector(T n) { return generate_range_vector(0, n); } template void sort_unique_erase(std::vector &a) { std::sort(a.begin(), a.end()); a.erase(std::unique(a.begin(), a.end()), a.end()); } template auto foreach_adjacent_values(InputIterator first, InputIterator last, BiConsumer f) -> decltype(f(*first++, *last), void()) { if (first != last) for (auto itr = first, itl = itr++; itr != last; itl = itr++) f(*itl, *itr); } template auto foreach_adjacent_values(Container c, BiConsumer f) -> decltype(c.begin(), c.end(), void()){ foreach_adjacent_values(c.begin(), c.end(), f); } // ! other utilities // x <- min(x, y). returns true iff `x` has chenged. template inline bool chmin(T &x, const T &y) { if (y >= x) return false; x = y; return true; } // x <- max(x, y). returns true iff `x` has chenged. template inline bool chmax(T &x, const T &y) { if (y <= x) return false; x = y; return true; } namespace suisen {} using namespace suisen; using namespace std; struct io_setup { io_setup(int precision = 20) { std::ios::sync_with_stdio(false); std::cin.tie(nullptr); std::cout << std::fixed << std::setprecision(precision); } } io_setup_{}; // ! code from here #include #include #include namespace atcoder { // Implement (union by size) + (path compression) // Reference: // Zvi Galil and Giuseppe F. Italiano, // Data structures and algorithms for disjoint set union problems struct dsu { public: dsu() : _n(0) {} explicit dsu(int n) : _n(n), parent_or_size(n, -1) {} int merge(int a, int b) { assert(0 <= a && a < _n); assert(0 <= b && b < _n); int x = leader(a), y = leader(b); if (x == y) return x; if (-parent_or_size[x] < -parent_or_size[y]) std::swap(x, y); parent_or_size[x] += parent_or_size[y]; parent_or_size[y] = x; return x; } bool same(int a, int b) { assert(0 <= a && a < _n); assert(0 <= b && b < _n); return leader(a) == leader(b); } int leader(int a) { assert(0 <= a && a < _n); if (parent_or_size[a] < 0) return a; return parent_or_size[a] = leader(parent_or_size[a]); } int size(int a) { assert(0 <= a && a < _n); return -parent_or_size[leader(a)]; } std::vector> groups() { std::vector leader_buf(_n), group_size(_n); for (int i = 0; i < _n; i++) { leader_buf[i] = leader(i); group_size[leader_buf[i]]++; } std::vector> result(_n); for (int i = 0; i < _n; i++) { result[i].reserve(group_size[i]); } for (int i = 0; i < _n; i++) { result[leader_buf[i]].push_back(i); } result.erase( std::remove_if(result.begin(), result.end(), [&](const std::vector& v) { return v.empty(); }), result.end()); return result; } private: int _n; // root node: -1 * component size // otherwise: parent std::vector parent_or_size; }; } // namespace atcoder int main() { input(int, n); vector>> g(n); int d = 0; loop(n - 1) { input(int, u, v, w); --u, --v; g[u].emplace_back(v, w); g[v].emplace_back(u, w); chmax(d, w); } auto f = [&](int x) { atcoder::dsu uf(n); rep(u, n) { for (const auto& [v, w] : g[u]) { if (w <= x) uf.merge(u, v); } } auto groups = uf.groups(); const int c = groups.size(); vector ids(n); rep(i, c) { for (auto v : groups[i]) ids[v] = i; } vector deg(c, 0); rep(u, n) { for (const auto& [v, w] : g[u]) { if (u >= v or w <= x) continue; int ui = ids[u], vi = ids[v]; ++deg[ui]; ++deg[vi]; } } if (*max_element(all(deg)) > 2) { return false; } int si = -1, ti = -1; rep(i, c) { if (deg[i] == 1) { (si < 0 ? si : ti) = i; } } int s = -1, t = -1; rep(u, n) { for (const auto& [v, w] : g[u]) { if (w <= x) continue; int ui = ids[u]; if (ui == si) s = u; if (ui == ti) t = u; } } vector path; vector weights; auto dfs = [&](auto dfs, int cur, int par, int weight) -> bool { path.push_back(cur); weights.push_back(weight); if (cur == t) return true; for (const auto& [nxt, w] : g[cur]) { if (nxt != par and dfs(dfs, nxt, cur, w)) return true; } path.pop_back(); weights.pop_back(); return false; }; dfs(dfs, s, -1, numeric_limits::max()); int min_weight = *min_element(all(weights)); rep(u, n) { for (const auto &[v, w] : g[u]) { if (w - min_weight > x) return false; } } return true; }; int l = -1, r = d; while (r - l > 1) { int m = (l + r) >> 1; (f(m) ? r : l) = m; } print(r); return 0; }