// >>> TEMPLATES #include using namespace std; using ll = long long; using ld = long double; using i32 = int32_t; using i64 = int64_t; using u32 = uint32_t; using u64 = uint64_t; #define int ll #define rep(i, n) for (int i = 0; i < (int)(n); i++) #define rep1(i, n) for (int i = 1; i <= (int)(n); i++) #define repR(i, n) for (int i = (int)(n)-1; i >= 0; i--) #define rep1R(i, n) for (int i = (int)(n); i >= 1; i--) #define loop(i, a, B) for (int i = a; i B; i++) #define loopR(i, a, B) for (int i = a; i B; i--) #define all(x) begin(x), end(x) #define allR(x) rbegin(x), rend(x) #define rng(x, l, r) begin(x) + (l), begin(x) + (r) #define pb push_back #define eb emplace_back #define fst first #define snd second template constexpr auto mp(A &&a, B &&b) { return make_pair(forward(a), forward(b)); } template constexpr auto mt(T&&... x) { return make_tuple(forward(x)...); } template auto constexpr inf_ = numeric_limits::max()/2-1; auto constexpr INF32 = inf_; auto constexpr INF64 = inf_; auto constexpr INF = inf_; #ifdef LOCAL #include "debug.hpp" #else #define dump(...) (void)(0) #define say(x) (void)(0) #define debug if (0) #endif template struct pque : priority_queue, Comp> { vector &data() { return this->c; } void clear() { this->c.clear(); } }; template using pque_max = pque>; template using pque_min = pque>; template ::value, int> = 0> ostream& operator<<(ostream& os, T const& a) { bool f = true; for (auto const& x : a) os << (f ? "" : " ") << x, f = false; return os; } template ::value, int> = 0> ostream& operator<<(ostream& os, const T (&a)[N]) { bool f = true; for (auto const& x : a) os << (f ? "" : " ") << x, f = false; return os; } template ())), class = typename enable_if::value>::type> istream& operator>>(istream& is, T &a) { for (auto& x : a) is >> x; return is; } template ostream& operator<<(ostream& os, pair const& p) { return os << p.first << " " << p.second; } template istream& operator>>(istream& is, pair& p) { return is >> p.first >> p.second; } struct IOSetup { IOSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); } } iosetup; template struct FixPoint : private F { constexpr FixPoint(F&& f) : F(forward(f)) {} template constexpr auto operator()(T&&... x) const { return F::operator()(*this, forward(x)...); } }; struct MakeFixPoint { template constexpr auto operator|(F&& f) const { return FixPoint(forward(f)); } }; #define MFP MakeFixPoint()| #define def(name, ...) auto name = MFP [&](auto &&name, __VA_ARGS__) template struct vec_impl { using type = vector::type>; template static type make_v(size_t n, U&&... x) { return type(n, vec_impl::make_v(forward(x)...)); } }; template struct vec_impl { using type = T; static type make_v(T const& x = {}) { return x; } }; template using vec = typename vec_impl::type; template auto make_v(Args&&... args) { return vec_impl::make_v(forward(args)...); } template void quit(T const& x) { cout << x << endl; exit(0); } template constexpr bool chmin(T& x, U const& y) { if (x > (T)y) { x = (T)y; return true; } return false; } template constexpr bool chmax(T& x, U const& y) { if (x < (T)y) { x = (T)y; return true; } return false; } template constexpr auto sumof(It b, It e) { return accumulate(b, e, typename iterator_traits::value_type{}); } template int sz(T const& x) { return x.size(); } template int lbd(C const& v, T const& x) { return lower_bound(begin(v), end(v), x)-begin(v); } template int ubd(C const& v, T const& x) { return upper_bound(begin(v), end(v), x)-begin(v); } constexpr int64_t mod(int64_t x, int64_t m) { assert(m > 0); return (x %= m) < 0 ? x+m : x; } constexpr int64_t div_floor(int64_t x, int64_t y) { assert(y != 0); return x/y - ((x^y) < 0 and x%y); } constexpr int64_t div_ceil(int64_t x, int64_t y) { assert(y != 0); return x/y + ((x^y) > 0 and x%y); } constexpr int dx[] = { 1, 0, -1, 0, 1, -1, -1, 1 }; constexpr int dy[] = { 0, 1, 0, -1, 1, 1, -1, -1 }; constexpr int popcnt(ll x) { return __builtin_popcountll(x); } mt19937_64 seed_{random_device{}()}; template Int rand(Int a, Int b) { return uniform_int_distribution(a, b)(seed_); } i64 irand(i64 a, i64 b) { return rand(a, b); } // [a, b] u64 urand(u64 a, u64 b) { return rand(a, b); } // template void shuffle(It l, It r) { shuffle(l, r, seed_); } template vector &operator--(vector &v) { for (T &x : v) --x; return v; } template vector &operator++(vector &v) { for (T &x : v) ++x; return v; } // <<< // >>> bfs #ifndef EDGE_INFO #define EDGE_INFO constexpr int dest(int v) { return v; } template ().to)> constexpr int dest(E const& e) { return e.to; } constexpr int cost(int) { return 1; } template ().cost)> constexpr auto cost(E const& e) { return e.cost; } template using cost_t = decltype(cost(declval())); #endif template vector bfs(vector> const& g, int s, int inf) { vector d(g.size(), inf); queue q; d[s] = 0; q.push(s); while (q.size()) { int x = q.front(); q.pop(); for (auto const& e : g[x]) { const int y = dest(e); if (chmin(d[y], d[x]+1)) q.push(y); } } return d; } // <<< // >>> Dinic template struct Dinic { static constexpr Flow INF = numeric_limits::max(); static constexpr Flow EPS = 1e-10; // struct Edge { int32_t to, rev, id; Flow cap; Edge(int to, int rev, int id, Flow cap) : to(to), rev(rev), id(id), cap(cap) {} }; vector> g; vector> es; vector level, iter; int V, E, s, t; Dinic(int V = 0) : g(V), V(V), E(0), s(-1), t(-1) {} void add_edge(int from, int to, Flow cap) { assert(0 <= from); assert(from < V); assert(0 <= to); assert(to < V); assert(cap >= 0); es.emplace_back(from, g[from].size()); g[from].emplace_back(to, g[to].size(), E, cap); g[to].emplace_back(from, g[from].size()-1, E, 0); E++; } struct edge_t { int32_t from, to; Flow flow, cap; }; Edge& internal_edge(int id) { assert(0 <= id); assert(id < (int)es.size()); int from, idx; tie(from, idx) = es[id]; return g[from][idx]; } edge_t edge(int id) const { assert(0 <= id); assert(id < (int)es.size()); int32_t from, idx; tie(from, idx) = es[id]; auto const& e = g[from][idx]; auto const& r = g[e.to][e.rev]; return { from, e.to, r.cap, e.cap+r.cap }; } vector edges() const { vector ret(E); rep (id, E) ret[id] = edge(id); return ret; } bool bfs() { level.assign(V, -1); queue q; level[s] = 0; q.push(s); while (q.size() && level[t] < 0) { int x = q.front(); q.pop(); for (auto const& e : g[x]) { if (e.cap > EPS && level[e.to] < 0) { level[e.to] = level[x] + 1; q.push(e.to); } } } return level[t] >= 0; } Flow dfs(int x, Flow f = INF) { if (x == t) return f; Flow res = 0; for (auto &i = iter[x]; i < int(g[x].size()); ++i) { auto &e = g[x][i]; if (e.cap > EPS && level[x] < level[e.to]) { Flow d = dfs(e.to, min(f, e.cap)); e.cap -= d; g[e.to][e.rev].cap += d; res += d; f -= d; if (f == 0) break; } } return res; } Flow max_flow(int s, int t) { assert(0 <= s); assert(s < V); assert(0 <= t); assert(t < V); this-> s = s; this->t = t; Flow flow = 0; while (bfs()) { iter.assign(V, 0); for (Flow f = 0; (f = dfs(s)); flow += f) {} } return flow; } #ifdef LOCAL friend string to_s(Dinic d) { string ret = "\n"; ret += "V = " + to_s(d.V) + ", E = " + to_s(d.E) + "\n"; ret += "s = " + to_s(d.s) + ", t = " + to_s(d.t) + "\n"; for (auto const& p : d.es) { auto const& e = d.g[p.first][p.second]; auto const& r = d.g[e.to][e.rev]; ret += to_s(e.id) + " : "; ret += to_s(p.first) + "->" + to_s(e.to) + " : "; ret += to_s(r.cap) + "/" + to_s(e.cap+r.cap) + "\n"; } return ret; } #endif }; // <<< int32_t main() { int n; cin >> n; vector> g(n); rep (i, n-1) { int x, y; cin >> x >> y; --x, --y; g[x].eb(y); g[y].eb(x); } auto dep = bfs(g, 0, INF); Dinic dinic(n+2); const int S = n, T = n+1; rep (x, n) { if (dep[x] % 2 == 0) { dinic.add_edge(S, x, 1); } else { dinic.add_edge(x, T, 1); } } rep (x, n) for (int y : g[x]) { if (dep[x] % 2 == 0) { dinic.add_edge(x, y, 1); } else { dinic.add_edge(y, x, 1); } } cout << dinic.max_flow(S, T) << '\n'; }