#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using lint = long long; using pint = pair; using plint = pair; struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_; #define ALL(x) (x).begin(), (x).end() #define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i=i##_begin_;i--) #define REP(i, n) FOR(i,0,n) #define IREP(i, n) IFOR(i,0,n) template void ndarray(vector& vec, const V& val, int len) { vec.assign(len, val); } template void ndarray(vector& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); } template bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; } template bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; } int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); } template pair operator+(const pair &l, const pair &r) { return make_pair(l.first + r.first, l.second + r.second); } template pair operator-(const pair &l, const pair &r) { return make_pair(l.first - r.first, l.second - r.second); } template vector sort_unique(vector vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; } template int arglb(const std::vector &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); } template int argub(const std::vector &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); } template istream &operator>>(istream &is, vector &vec) { for (auto &v : vec) is >> v; return is; } template ostream &operator<<(ostream &os, const vector &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; } template ostream &operator<<(ostream &os, const array &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; } #if __cplusplus >= 201703L template istream &operator>>(istream &is, tuple &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; } template ostream &operator<<(ostream &os, const tuple &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; } #endif template ostream &operator<<(ostream &os, const deque &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; } template ostream &operator<<(ostream &os, const set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const pair &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; } template ostream &operator<<(ostream &os, const map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } #ifdef HITONANODE_LOCAL const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m"; #define dbg(x) cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl #define dbgif(cond, x) ((cond) ? cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl : cerr) #else #define dbg(x) (x) #define dbgif(cond, x) 0 #endif // Bipartite matching of undirected bipartite graph (Hopcroft-Karp) // // Comprexity: O(EsqrtV) // 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::queue q; for (int i = 0; i < V; i++) { if (!color[i] and !used[i]) { q.emplace(i), dist[i] = 0; } } while (!q.empty()) { int now = q.front(); q.pop(); for (auto nxt : to[now]) { int c = match[nxt]; if (c >= 0 and dist[c] == -1) { q.emplace(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::queue q; q.emplace(root); while (!q.empty()) { int now = q.front(), c = color[now]; q.pop(); for (auto nxt : to[now]) if (color[nxt] == -1) color[nxt] = !c, q.emplace(nxt); else if (color[nxt] == c) return false; } return true; } int solve() { for (int i = 0; i < V; i++) if (color[i] == -1) { if (!_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; } friend std::ostream &operator<<(std::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] << "),"; } os << '}'; return os; } }; int main() { int N; cin >> N; BipartiteMatching bm(N * 2); REP(i, N) { int a, b; cin >> a >> b; a--, b--; bm.add_edge(i, a + N); bm.add_edge(i, b + N); } auto ret = bm.solve(); if (ret < N) { puts("No"); return 0; } cout << "Yes\n"; REP(i, N) cout << bm.match[i] + 1 << '\n'; }