#include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using namespace atcoder; #define ll long long #define INF 1000000 using std::cout; using std::endl; using std::chrono::duration_cast; using std::chrono::milliseconds; using std::chrono::seconds; using std::chrono::system_clock; //namespace atcoder { ostream& operator<<(ostream& os,vector& a){ for(int i:a){ os< ans(200010,-1); struct _edge { ll to, rev; ll cap; ll index; }; template struct mf_graph { public: mf_graph() : _n(0) {} mf_graph(ll n) : _n(n), g(n) {} ll add_edge(ll from, ll to, Cap cap,ll index) { assert(0 <= from && from < _n); assert(0 <= to && to < _n); assert(0 <= cap); ll m = (long long)pos.size(); pos.push_back({from, (long long)g[from].size()}); ll from_id = (long long)g[from].size(); ll to_id = (long long)g[to].size(); if (from == to) to_id++; g[from].push_back(_edge{to, to_id, cap, index}); g[to].push_back(_edge{from, from_id, 0, index}); return m; } struct edge { ll from, to; Cap cap, flow; }; edge get_edge(ll i) { ll m = (long long)pos.size(); assert(0 <= i && i < m); auto _e = g[pos[i].first][pos[i].second]; auto _re = g[_e.to][_e.rev]; return edge{pos[i].first, _e.to, _e.cap + _re.cap, _re.cap}; } Cap flow(ll s, ll t) { return flow(s, t, std::numeric_limits::max()); } Cap flow(ll s, ll t, Cap flow_limit) { assert(0 <= s && s < _n); assert(0 <= t && t < _n); assert(s != t); time_t flow_start=time(NULL); std::vector level(_n), iter(_n); internal::simple_queue que; auto bfs = [&]() { std::fill(level.begin(), level.end(), -1); level[s] = 0; que.clear(); que.push(s); while (!que.empty()) { ll v = que.front(); que.pop(); for (auto e : g[v]) { if (e.cap == 0 || level[e.to] >= 0) continue; level[e.to] = level[v] + 1; if (e.to == t) return; que.push(e.to); } } }; auto dfs = [&](auto self, int v, Cap up) { if (v == s) return up; if (time(NULL)-flow_start>1.8){ cout<<"No\n"; exit(0); } Cap res = 0; ll level_v = level[v]; for (long long& i = iter[v]; i < (long long)g[v].size(); i++) { _edge& e = g[v][i]; if (level_v <= level[e.to] || g[e.to][e.rev].cap == 0) continue; Cap d = self(self, e.to, std::min(up - res, g[e.to][e.rev].cap)); if (d <= 0) continue; g[v][i].cap += d; g[e.to][e.rev].cap -= d; res += d; if (res == up) break; } return res; }; Cap flow = 0; while (flow < flow_limit) { bfs(); if (level[t] == -1) break; std::fill(iter.begin(), iter.end(), 0); while (flow < flow_limit) { Cap f = dfs(dfs, t, flow_limit - flow); if (!f) break; flow += f; } } return flow; } //private: ll _n; std::vector> pos; std::vector> g; }; ostream& operator<<(ostream& os,const _edge& a){ return os<(system_clock::now().time_since_epoch()).count(); ll N,A,B; cin>>N; mf_graph F(2*N+2); dsu uf(N); vector had_edge(N); for(ll i=0;i>A>>B; A--;B--; uf.merge(A,B); had_edge.at(A)++; had_edge.at(B)++; F.add_edge(2*N,i,1,-1); F.add_edge(i,N+A,1,i); if(A!=B)F.add_edge(i,N+B,1,i); F.add_edge(N+i,2*N+1,1,-1); } auto g=uf.groups(); for(auto i:g){ ll cnt=0; for(ll j:i){ cnt+=had_edge.at(j); } cnt/=2; if(cnt!=(ll)i.size()){ cout<<"No\n"; return 0; } } ll cnt=F.flow(2*N,2*N+1); if(cnt!=N){ cout<<"No\n"; return 0; } //ここから構築 cout<<"Yes\n"; for(ll i=N;i<2*N;i++){ ll s=F.g.at(i).size(); for(ll j=0;j(system_clock::now().time_since_epoch()).count(); cerr<<"time:"<