#include #include using namespace std; using namespace atcoder; #define overload4(_1, _2, _3, _4, name, ...) name #define rep1(n) for(int i = 0; i < (int)(n); ++i) #define rep2(i, n) for(int i = 0; i < (int)(n); ++i) #define rep3(i, a, b) for(int i = (a); i < (int)(b); ++i) #define rep4(i, a, b, c) for(int i = (a); i < (int)(b); i += (c)) #define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__) #define rrep(i,n) for(int i = (int)(n) - 1; i >= 0; --i) #define ALL(a) (a).begin(), (a).end() #define Sort(a) (sort((a).begin(), (a).end())) #define RSort(a) (sort((a).rbegin(), (a).rend())) #define UNIQUE(a) (a.erase(unique((a).begin(), (a).end()), (a).end())) typedef long long int ll; typedef unsigned long long ul; typedef long double ld; typedef vector vi; typedef vector vll; typedef vector vc; typedef vector vst; typedef vector vd; typedef vector vld; typedef pair P; template long long sum(const T& a){ return accumulate(a.begin(), a.end(), 0LL); } template auto min(const T& a){ return *min_element(a.begin(), a.end()); } template auto max(const T& a){ return *max_element(a.begin(), a.end()); } const long long MINF = 0x7fffffffffff; const long long INF = 0x1fffffffffffffff; const long long MOD = 998244353; const long double EPS = 1e-9; const long double PI = acos(-1); template inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; } template inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; } template istream &operator>>(istream &is, pair &p){ is >> p.first >> p.second; return is; } template ostream &operator<<(ostream &os, const pair &p){ os << "(" << p.first << ", " << p.second << ")"; return os; } template istream &operator>>(istream &is, vector &v){ for(T &in : v) is >> in; return is; } template ostream &operator<<(ostream &os, const vector &v){ for(int i = 0; i < (int) v.size(); ++i){ os << v[i] << (i + 1 != (int) v.size() ? " " : ""); } return os; } template ostream &operator<<(ostream &os, const map &mp){ for(auto &[key, val] : mp){ os << key << ":" << val << " "; } return os; } template ostream &operator<<(ostream &os, const set &st){ auto itr = st.begin(); for(int i = 0; i < (int)st.size(); ++i){ os << *itr << (i + 1 != (int)st.size() ? " " : ""); itr++; } return os; } template ostream &operator<<(ostream &os, const multiset &st){ auto itr = st.begin(); for(int i = 0; i < (int)st.size(); ++i){ os << *itr << (i + 1 != (int)st.size() ? " " : ""); itr++; } return os; } template ostream &operator<<(ostream &os, queue q){ while(q.size()){ os << q.front() << " "; q.pop(); } return os; } template ostream &operator<<(ostream &os, deque q){ while(q.size()){ os << q.front() << " "; q.pop_front(); } return os; } template ostream &operator<<(ostream &os, stack st){ while(st.size()){ os << st.top() << " "; st.pop(); } return os; } template ostream &operator<<(ostream &os, priority_queue pq){ while(pq.size()){ os << pq.top() << " "; pq.pop(); } return os; } template inline T vin(T& vec, U n) { vec.resize(n); for(int i = 0; i < (int) n; ++i) cin >> vec[i]; return vec; } template inline void vout(T vec, string s = "\n"){ for(auto x : vec) cout << x << s; } template void in(T&... a){ (cin >> ... >> a); } void out(){ cout << '\n'; } template void out(const T& a, const Ts&... b){ cout << a; (cout << ... << (cout << ' ', b)); cout << '\n'; } template void inGraph(vector>& G, U n, U m, bool directed = false){ G.resize(n); for(int i = 0; i < m; ++i){ int a, b; cin >> a >> b; a--, b--; G[a].push_back(b); if(!directed) G[b].push_back(a); } } template struct Rerooting{ struct edge{ int from, to, idx, rev_idx; }; int n, root; vector> edges; vector visited; vector> out; vector reverse_edge; vector ans; function merge; E e; function put_edge; function put_vertex; Rerooting(int _n, const function &_merge, const E &_e, const function &_put_edge, const function &_put_vertex) : n(_n), merge(_merge), e(_e), put_edge(_put_edge), put_vertex(_put_vertex){ edges.resize(n); } private: V dfs(int v){ visited[v]++; E val = e; for(auto &p : edges[v]){ if(visited[p.to] > 0 && p.to != edges[v].back().to){ swap(p, edges[v].back()); } if(visited[p.to] > 0) continue; E nval = put_edge(dfs(p.to), p.idx); out[v].emplace_back(nval); val = merge(val, nval); } return put_vertex(val, v); } void bfs(int v){ int siz = out[v].size(); vector left(siz + 1), right(siz + 1); left[0] = e, right[siz] = e; for(int i = 0; i < siz; i++){ left[i + 1] = merge(left[i], out[v][i]); } for(int i = siz - 1; i >= 0; i--){ right[i] = merge(out[v][i], right[i + 1]); } for(int i = 0; i < siz; i++){ reverse_edge[edges[v][i].to] = put_edge(put_vertex(merge(merge(left[i], right[i + 1]), reverse_edge[v]), v), edges[v][i].rev_idx); bfs(edges[v][i].to); } ans[v] = put_vertex(merge(left[siz], reverse_edge[v]), v); } public: void add_edge(int u, int v, int idx1, int idx2){ edges[u].push_back({u, v, idx1, idx2}); edges[v].push_back({v, u, idx2, idx1}); } V build(int v = 0){ root = v; out.resize(n); visited.assign(n, 0); return dfs(root); } vector reroot(){ reverse_edge.resize(n); reverse_edge[root] = e; ans.resize(n); bfs(root); return ans; } }; ll n; void input(){ in(n); } // ll solve_sub(ll x){ // auto dfs = [&](auto &self, ll curr, ll prev) -> vll { // vll dp(2); // dp[1] = 1; // for(auto x : G[curr]){ // if(x == prev) continue; // vll ndp = self(self, x, curr); // dp[0] += max(ndp[0], ndp[1]); // dp[1] += ndp[0]; // } // return dp; // }; // vll dp = dfs(dfs, x, -1); // return dp[1]; // } void solve(){ using T = vll; auto merge = [&](T x, T y){ T res = {x[0] + y[0], x[1] + y[1]}; return res; }; auto put_edge = [&](T x, int i){ T res = {max(x[0], x[1]), x[0]}; return res; }; auto put_vertex = [&](T e, int v){ T res = {e[0], e[1] + 1}; return res; }; T e = {0LL, 0LL}; Rerooting G(n, merge, e, put_edge, put_vertex); rep(i, n - 1){ ll a, b; in(a, b); a--, b--; G.add_edge(a, b, i, i); } G.build(); ll ans = INF; for(auto x : G.reroot()){ chmin(ans, x[1]); } out(ans); } int main(){ ios::sync_with_stdio(false); cin.tie(nullptr); cout << fixed << setprecision(20); input(); solve(); }