// clang-format off #include #include #include #include #include #include #include #include #include namespace atcoder { namespace internal { template struct simple_queue { std::vector payload; int pos = 0; void reserve(int n) { payload.reserve(n); } int size() const { return int(payload.size()) - pos; } bool empty() const { return pos == int(payload.size()); } void push(const T& t) { payload.push_back(t); } T& front() { return payload[pos]; } void clear() { payload.clear(); pos = 0; } void pop() { pos++; } }; } // namespace internal } // namespace atcoder namespace atcoder { template struct mf_graph { public: mf_graph() : _n(0) {} mf_graph(int n) : _n(n), g(n) {} int add_edge(int from, int to, Cap cap) { assert(0 <= from && from < _n); assert(0 <= to && to < _n); assert(0 <= cap); int m = int(pos.size()); pos.push_back({from, int(g[from].size())}); int from_id = int(g[from].size()); int to_id = int(g[to].size()); if (from == to) to_id++; g[from].push_back(_edge{to, to_id, cap}); g[to].push_back(_edge{from, from_id, 0}); return m; } struct edge { int from, to; Cap cap, flow; }; edge get_edge(int i) { int m = int(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}; } std::vector edges() { int m = int(pos.size()); std::vector result; for (int i = 0; i < m; i++) { result.push_back(get_edge(i)); } return result; } void change_edge(int i, Cap new_cap, Cap new_flow) { int m = int(pos.size()); assert(0 <= i && i < m); assert(0 <= new_flow && new_flow <= new_cap); auto& _e = g[pos[i].first][pos[i].second]; auto& _re = g[_e.to][_e.rev]; _e.cap = new_cap - new_flow; _re.cap = new_flow; } Cap flow(int s, int t) { return flow(s, t, std::numeric_limits::max()); } Cap flow(int s, int t, Cap flow_limit) { assert(0 <= s && s < _n); assert(0 <= t && t < _n); assert(s != t); 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()) { int 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; Cap res = 0; int level_v = level[v]; for (int& i = iter[v]; i < int(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) return res; } level[v] = _n; return res; }; Cap flow = 0; while (flow < flow_limit) { bfs(); if (level[t] == -1) break; std::fill(iter.begin(), iter.end(), 0); Cap f = dfs(dfs, t, flow_limit - flow); if (!f) break; flow += f; } return flow; } std::vector min_cut(int s) { std::vector visited(_n); internal::simple_queue que; que.push(s); while (!que.empty()) { int p = que.front(); que.pop(); visited[p] = true; for (auto e : g[p]) { if (e.cap && !visited[e.to]) { visited[e.to] = true; que.push(e.to); } } } return visited; } private: int _n; struct _edge { int to, rev; Cap cap; }; std::vector> pos; std::vector> g; }; } // namespace atcoder #define mp make_pair #define fst first #define snd second #define forn(i,n) for (int i = 0; i < int(n); i++) #define forn1(i,n) for (int i = 1; i <= int(n); i++) #define popcnt __builtin_popcountll #define ffs __builtin_ffsll #define ctz __builtin_ctzll #define clz __builtin_clz #define clzll __builtin_clzll #define all(a) (a).begin(), (a).end() using namespace std; using namespace __gnu_pbds; using uint = unsigned int; using ll = long long; using ull = unsigned long long; using pii = pair; using pli = pair; using pil = pair; using pll = pair; template using vec = vector; using vi = vec; using vl = vec; template using que = queue; template using deq = deque; template using ordered_set = tree, rb_tree_tag, tree_order_statistics_node_update>; template using ordered_map = tree, rb_tree_tag, tree_order_statistics_node_update>; template T id(T b) {return b;}; template void chmax(T &x, T y) {if (x < y) x = y;} template void chmin(T &x, T y) {if (x > y) x = y;} template bool contains(S &s, K k) { return s.find(k) != s.end(); } template bool getf(T flag, size_t i) { return (flag>>i) & 1; } template T setf(T flag, size_t i) { return flag | (T(1)< T unsetf(T flag, size_t i) { return flag & ~(T(1)<> n; auto ball = [](int i) { return i; }; auto rule = [&](int i) { return i + n; }; int s = 2 * n; int t = s + 1; atcoder::mf_graph g(t + 1); forn(i, n) { int a, b; cin >> a >> b; a--, b--; g.add_edge(ball(a), rule(i), 1); g.add_edge(ball(b), rule(i), 1); } forn(i, n) { g.add_edge(s, ball(i), 1); g.add_edge(rule(i), t, 1); } if (g.flow(s, t) < n) { cout << "No\n"; return 0; } vi ans(n); for (auto e : g.edges()) { if (e.flow == 1 and n <= e.to and e.to < 2 * n) { ans[e.to - n] = e.from + 1; } } cout << "Yes\n"; for (auto x : ans) { cout << x << "\n"; } return 0; }