//#define _GLIBCXX_DEBUG #include using namespace std; #define endl '\n' #define lfs cout<= (ll)(n); i--) using ll = long long; using ld = long double; const ll MOD1 = 1e9+7; const ll MOD9 = 998244353; const ll INF = 1e18; using P = pair; template using PQ = priority_queue; template using QP = priority_queue,greater>; templatebool chmin(T1 &a,T2 b){if(a>b){a=b;return true;}else return false;} templatebool chmax(T1 &a,T2 b){if(avoid ans(bool x,T1 y,T2 z){if(x)cout<void anss(T1 x,T2 y,T3 z){ans(x!=y,x,z);}; templatevoid debug(const T &v,ll h,ll w,string sv=" "){for(ll i=0;ivoid debug(const T &v,ll n,string sv=" "){if(n!=0)cout<void debug(const vector&v){debug(v,v.size());} templatevoid debug(const vector>&v){for(auto &vv:v)debug(vv,vv.size());} templatevoid debug(stack st){while(!st.empty()){cout<void debug(queue st){while(!st.empty()){cout<void debug(deque st){while(!st.empty()){cout<void debug(PQ st){while(!st.empty()){cout<void debug(QP st){while(!st.empty()){cout<void debug(const set&v){for(auto z:v)cout<void debug(const multiset&v){for(auto z:v)cout<void debug(const array &a){for(auto z:a)cout<void debug(const map&v){for(auto z:v)cout<<"["<vector>vec(ll x, ll y, T w){vector>v(x,vector(y,w));return v;} ll gcd(ll x,ll y){ll r;while(y!=0&&(r=x%y)!=0){x=y;y=r;}return y==0?x:y;} vectordx={1,-1,0,0,1,1,-1,-1};vectordy={0,0,1,-1,1,-1,1,-1}; templatevector make_v(size_t a,T b){return vector(a,b);} templateauto make_v(size_t a,Ts... ts){return vector(a,make_v(ts...));} templateostream &operator<<(ostream &os, const pair&p){return os << p.first << " " << p.second;} templateostream &operator<<(ostream &os, const vector &v){for(auto &z:v)os << z << " ";cout<<"|"; return os;} templatevoid rearrange(vector&ord, vector&v){ auto tmp = v; for(int i=0;ivoid rearrange(vector&ord,Head&& head, Tail&&... tail){ rearrange(ord, head); rearrange(ord, tail...); } template vector ascend(const vector&v){ vectorord(v.size());iota(ord.begin(),ord.end(),0); sort(ord.begin(),ord.end(),[&](int i,int j){return make_pair(v[i],i) vector descend(const vector&v){ vectorord(v.size());iota(ord.begin(),ord.end(),0); sort(ord.begin(),ord.end(),[&](int i,int j){return make_pair(v[i],-i)>make_pair(v[j],-j);}); return ord; } template vector inv_perm(const vector&ord){ vectorinv(ord.size()); for(int i=0;i0);return n>=0?n/div:(n-div+1)/div;} ll CEIL(ll n,ll div){assert(div>0);return n>=0?(n+div-1)/div:n/div;} ll digitsum(ll n){ll ret=0;while(n){ret+=n%10;n/=10;}return ret;} ll modulo(ll n,ll d){return (n%d+d)%d;}; templateT min(const vector&v){return *min_element(v.begin(),v.end());} templateT max(const vector&v){return *max_element(v.begin(),v.end());} templateT acc(const vector&v){return accumulate(v.begin(),v.end(),T(0));}; templateT reverse(const T &v){return T(v.rbegin(),v.rend());}; //mt19937 mt(chrono::steady_clock::now().time_since_epoch().count()); int popcount(ll x){return __builtin_popcountll(x);}; int poplow(ll x){return __builtin_ctzll(x);}; int pophigh(ll x){return 63 - __builtin_clzll(x);}; templateT poll(queue &q){auto ret=q.front();q.pop();return ret;}; templateT poll(priority_queue &q){auto ret=q.top();q.pop();return ret;}; templateT poll(QP &q){auto ret=q.top();q.pop();return ret;}; templateT poll(stack &s){auto ret=s.top();s.pop();return ret;}; ll MULT(ll x,ll y){if(LLONG_MAX/x<=y)return LLONG_MAX;return x*y;} ll POW2(ll x, ll k){ll ret=1,mul=x;while(k){if(mul==LLONG_MAX)return LLONG_MAX;if(k&1)ret=MULT(ret,mul);mul=MULT(mul,mul);k>>=1;}return ret;} ll POW(ll x, ll k){ll ret=1;for(int i=0;i struct edge { int to; T cost; int id; edge():id(-1){}; edge(int to, T cost = 1, int id = -1):to(to), cost(cost), id(id){} operator int() const { return to; } }; template using Graph = vector>>; template Graphrevgraph(const Graph &g){ Graphret(g.size()); for(int i=0;i Graph readGraph(int n,int m,int indexed=1,bool directed=false,bool weighted=false){ Graph ret(n); for(int es = 0; es < m; es++){ int u,v; T w=1; cin>>u>>v;u-=indexed,v-=indexed; if(weighted)cin>>w; ret[u].emplace_back(v,w,es); if(!directed)ret[v].emplace_back(u,w,es); } return ret; } template Graph readParent(int n,int indexed=1,bool directed=true){ Graphret(n); for(int i=1;i>p; p-=indexed; ret[p].emplace_back(i); if(!directed)ret[i].emplace_back(p); } return ret; } #line 2 "graph/bipartite_matching.hpp" #include #include #include // Bipartite matching of undirected bipartite graph (Hopcroft-Karp) // https://ei1333.github.io/luzhiled/snippets/graph/hopcroft-karp.html // Comprexity: O((V + E)sqrtV) // int solve(): enumerate maximum number of matching / return -1 (if graph is not bipartite) struct BipartiteMatching { int V; std::vector> to; // Adjacency list std::vector dist; // dist[i] = (Distance from i'th node) std::vector match; // match[i] = (Partner of i'th node) or -1 (No parter) std::vector used, vv; std::vector color; // color of each node(checking bipartition): 0/1/-1(not determined) BipartiteMatching() = default; BipartiteMatching(int V_) : V(V_), to(V_), match(V_, -1), used(V_), color(V_, -1) {} void add_edge(int u, int v) { assert(u >= 0 and u < V and v >= 0 and v < V and u != v); to[u].push_back(v); to[v].push_back(u); } void _bfs() { dist.assign(V, -1); std::vector q; int lq = 0; for (int i = 0; i < V; i++) { if (!color[i] and !used[i]) q.push_back(i), dist[i] = 0; } while (lq < int(q.size())) { int now = q[lq++]; for (auto nxt : to[now]) { int c = match[nxt]; if (c >= 0 and dist[c] == -1) q.push_back(c), dist[c] = dist[now] + 1; } } } bool _dfs(int now) { vv[now] = true; for (auto nxt : to[now]) { int c = match[nxt]; if (c < 0 or (!vv[c] and dist[c] == dist[now] + 1 and _dfs(c))) { match[nxt] = now, match[now] = nxt; used[now] = true; return true; } } return false; } bool _color_bfs(int root) { color[root] = 0; std::vector q{root}; int lq = 0; while (lq < int(q.size())) { int now = q[lq++], c = color[now]; for (auto nxt : to[now]) { if (color[nxt] == -1) { color[nxt] = !c, q.push_back(nxt); } else if (color[nxt] == c) { return false; } } } return true; } int solve() { for (int i = 0; i < V; i++) { if (color[i] == -1 and !_color_bfs(i)) return -1; } int ret = 0; while (true) { _bfs(); vv.assign(V, false); int flow = 0; for (int i = 0; i < V; i++) { if (!color[i] and !used[i] and _dfs(i)) flow++; } if (!flow) break; ret += flow; } return ret; } template friend OStream &operator<<(OStream &os, const BipartiteMatching &bm) { os << "{N=" << bm.V << ':'; for (int i = 0; i < bm.V; i++) { if (bm.match[i] > i) os << '(' << i << '-' << bm.match[i] << "),"; } return os << '}'; } }; #line 2 "graph/strongly_connected_components.hpp" #include #line 5 "graph/strongly_connected_components.hpp" // CUT begin // Directed graph library to find strongly connected components (強連結成分分解) // 0-indexed directed graph // Complexity: O(V + E) struct DirectedGraphSCC { int V; // # of Vertices std::vector> to, from; std::vector used; // Only true/false std::vector vs; std::vector cmp; int scc_num = -1; DirectedGraphSCC(int V = 0) : V(V), to(V), from(V), cmp(V) {} void _dfs(int v) { used[v] = true; for (auto t : to[v]) if (!used[t]) _dfs(t); vs.push_back(v); } void _rdfs(int v, int k) { used[v] = true; cmp[v] = k; for (auto t : from[v]) if (!used[t]) _rdfs(t, k); } void add_edge(int from_, int to_) { assert(from_ >= 0 and from_ < V and to_ >= 0 and to_ < V); to[from_].push_back(to_); from[to_].push_back(from_); } // Detect strongly connected components and return # of them. // Also, assign each vertex `v` the scc id `cmp[v]` (0-indexed) int FindStronglyConnectedComponents() { used.assign(V, false); vs.clear(); for (int v = 0; v < V; v++) if (!used[v]) _dfs(v); used.assign(V, false); scc_num = 0; for (int i = (int)vs.size() - 1; i >= 0; i--) if (!used[vs[i]]) _rdfs(vs[i], scc_num++); return scc_num; } // Find and output the vertices that form a closed cycle. // output: {v_1, ..., v_C}, where C is the length of cycle, // {} if there's NO cycle (graph is DAG) int _c, _init; std::vector _ret_cycle; bool _dfs_detectcycle(int now, bool b0) { if (now == _init and b0) return true; for (auto nxt : to[now]) if (cmp[nxt] == _c and !used[nxt]) { _ret_cycle.emplace_back(nxt), used[nxt] = 1; if (_dfs_detectcycle(nxt, true)) return true; _ret_cycle.pop_back(); } return false; } std::vector DetectCycle() { int ns = FindStronglyConnectedComponents(); if (ns == V) return {}; std::vector cnt(ns); for (auto x : cmp) cnt[x]++; _c = std::find_if(cnt.begin(), cnt.end(), [](int x) { return x > 1; }) - cnt.begin(); _init = std::find(cmp.begin(), cmp.end(), _c) - cmp.begin(); used.assign(V, false); _ret_cycle.clear(); _dfs_detectcycle(_init, false); return _ret_cycle; } // After calling `FindStronglyConnectedComponents()`, generate a new graph by uniting all // vertices belonging to the same component(The resultant graph is DAG). DirectedGraphSCC GenerateTopologicalGraph() { DirectedGraphSCC newgraph(scc_num); for (int s = 0; s < V; s++) for (auto t : to[s]) { if (cmp[s] != cmp[t]) newgraph.add_edge(cmp[s], cmp[t]); } return newgraph; } }; // 2-SAT solver: Find a solution for `(Ai v Aj) ^ (Ak v Al) ^ ... = true` // - `nb_sat_vars`: Number of variables // - Considering a graph with `2 * nb_sat_vars` vertices // - Vertices [0, nb_sat_vars) means `Ai` // - vertices [nb_sat_vars, 2 * nb_sat_vars) means `not Ai` struct SATSolver : DirectedGraphSCC { int nb_sat_vars; std::vector solution; SATSolver(int nb_variables = 0) : DirectedGraphSCC(nb_variables * 2), nb_sat_vars(nb_variables), solution(nb_sat_vars) {} void add_x_or_y_constraint(bool is_x_true, int x, bool is_y_true, int y) { assert(x >= 0 and x < nb_sat_vars); assert(y >= 0 and y < nb_sat_vars); if (!is_x_true) x += nb_sat_vars; if (!is_y_true) y += nb_sat_vars; add_edge((x + nb_sat_vars) % (nb_sat_vars * 2), y); add_edge((y + nb_sat_vars) % (nb_sat_vars * 2), x); } // Solve the 2-SAT problem. If no solution exists, return `false`. // Otherwise, dump one solution to `solution` and return `true`. bool run() { FindStronglyConnectedComponents(); for (int i = 0; i < nb_sat_vars; i++) { if (cmp[i] == cmp[i + nb_sat_vars]) return false; solution[i] = cmp[i] > cmp[i + nb_sat_vars]; } return true; } }; #line 5 "graph/dulmage_mendelsohn_decomposition.hpp" #include #line 7 "graph/dulmage_mendelsohn_decomposition.hpp" // Dulmage–Mendelsohn (DM) decomposition (DM 分解) // return: [(W+0, W-0), (W+1,W-1),...,(W+(k+1), W-(k+1))] // : sequence of pair (left vetrices, right vertices) // - |W+0| < |W-0| or both empty // - |W+i| = |W-i| (i = 1, ..., k) // - |W+(k+1)| > |W-(k+1)| or both empty // - W is topologically sorted // Example: // (2, 2, [(0,0), (0,1), (1,0)]) => [([],[]),([0,],[1,]),([1,],[0,]),([],[]),] // Complexity: O(N + (N + M) sqrt(N)) // Verified: https://yukicoder.me/problems/no/1615 std::vector, std::vector>> dulmage_mendelsohn(int L, int R, const std::vector> &edges) { for (auto p : edges) { assert(0 <= p.first and p.first < L); assert(0 <= p.second and p.second < R); } BipartiteMatching bm(L + R); for (auto p : edges) bm.add_edge(p.first, L + p.second); bm.solve(); DirectedGraphSCC scc(L + R); for (auto p : edges) scc.add_edge(p.first, L + p.second); for (int l = 0; l < L; ++l) { if (bm.match[l] >= L) scc.add_edge(bm.match[l], l); } int nscc = scc.FindStronglyConnectedComponents(); std::vector cmp_map(nscc, -2); std::vector vis(L + R); std::vector st; for (int c = 0; c < 2; ++c) { std::vector> to(L + R); auto color = [&L](int x) { return x >= L; }; for (auto p : edges) { int u = p.first, v = L + p.second; if (color(u) != c) std::swap(u, v); to[u].push_back(v); if (bm.match[u] == v) to[v].push_back(u); } for (int i = 0; i < L + R; ++i) { if (bm.match[i] >= 0 or color(i) != c or vis[i]) continue; vis[i] = 1, st = {i}; while (!st.empty()) { int now = st.back(); cmp_map[scc.cmp[now]] = c - 1; st.pop_back(); for (int nxt : to[now]) { if (!vis[nxt]) vis[nxt] = 1, st.push_back(nxt); } } } } int nset = 1; for (int n = 0; n < nscc; ++n) { if (cmp_map[n] == -2) cmp_map[n] = nset++; } for (auto &x : cmp_map) { if (x == -1) x = nset; } nset++; std::vector, std::vector>> groups(nset); for (int l = 0; l < L; ++l) { if (bm.match[l] < 0) continue; int c = cmp_map[scc.cmp[l]]; groups[c].first.push_back(l); groups[c].second.push_back(bm.match[l] - L); } for (int l = 0; l < L; ++l) { if (bm.match[l] >= 0) continue; int c = cmp_map[scc.cmp[l]]; groups[c].first.push_back(l); } for (int r = 0; r < R; ++r) { if (bm.match[L + r] >= 0) continue; int c = cmp_map[scc.cmp[L + r]]; groups[c].second.push_back(r); } return groups; } template vectornibu_graph(const Graph&g){ int n=g.size(); vectort(n,-1); queueque; for(ll i=0;i(); } } } return t; } template vector>>>nibu_graph_con(const Graph&g){ int n=g.size(); vector>>>v; vectort(n,-1); queueque; for(ll i=0;i>(2)); t[i]=0; while(!que.empty()){ auto p=que.front();que.pop(); v.back().second[t[p]].push_back(p); for(auto e:g[p]){ if(t[e.to]==-1){ que.push(e.to); t[e.to]=t[p]^e.cost; } else if(t[p]!=t[e.to]^e.cost)v.back().first=false; } } } return v; } int main(){ cin.tie(nullptr); ios_base::sync_with_stdio(false); ll res=0,buf=0; bool judge = true; ll n;cin>>n; auto g=readGraph(n,n-1); auto t=nibu_graph(g); int L=0,R=0; vectoridx(n); vector>edges; rep(i,0,n){ if(t[i]==0)idx[i]=L++; else idx[i]=R++; } rep(i,0,n){ for(auto to:g[i]){ if(t[i]==0){ edges.EB(idx[i],idx[to]); } } } auto dm=dulmage_mendelsohn(L,R,edges); ll ret=n; for(auto z:dm)ret-=min(z.fi.size(),z.se.size()); ll mx=0; for(auto z:dm)chmax(mx,abs((ll)z.fi.size()-(ll)z.se.size())); cout<