#pragma GCC optimize ("O3") #include using namespace std; using ll = long long int; #define all(v) (v).begin(),(v).end() #define repeat(cnt,l) for(typename remove_const::type>::type cnt={};(cnt)<(l);++(cnt)) #define rrepeat(cnt,l) for(auto cnt=(l)-1;0<=(cnt);--(cnt)) #define iterate(cnt,b,e) for(auto cnt=(b);(cnt)!=(e);++(cnt)) #define diterate(cnt,b,e) for(auto cnt=(b);(cnt)!=(e);--(cnt)) const long long MD = 1000000007ll; const long double PI = 3.1415926535897932384626433832795L; template inline ostream& operator <<(ostream &o, const pair p) { o << '(' << p.first << ':' << p.second << ')'; return o; } template inline T& chmax(T& to, const T& val) { return to = max(to, val); } template inline T& chmin(T& to, const T& val) { return to = min(to, val); } void bye(string s, int code = 0) { cout << s << endl; exit(code); } mt19937_64 randdev(8901016); template::value>::type* = nullptr> inline T rand(T l, T h, Random& rand = randdev) { return uniform_int_distribution(l, h)(rand); } template::value>::type* = nullptr> inline T rand(T l, T h, Random& rand = randdev) { return uniform_real_distribution(l, h)(rand); }template static ostream& operator<<(ostream& o, const std::vector& v) { o << "[ "; for(const auto& e : v) o< struct MyRangeFormat{ I b,e; MyRangeFormat(I _b, I _e):b(_b),e(_e){} }; template static ostream& operator<<(ostream& o, const MyRangeFormat& f) { o << "[ "; iterate(i,f.b,f.e) o<<*i<<' '; return o << ']'; } template struct MyMatrixFormat{ const I& p; long long n, m; MyMatrixFormat(const I& _p, long long _n, long long _m):p(_p),n(_n),m(_m){} }; template static ostream& operator<<(ostream& o, const MyMatrixFormat& f) { o<<'\n'; repeat(i,(f.n)) { repeat(j,f.m) o<(m,m+w)) #define FMTR(b,e) (MyRangeFormat(b,e)) #define FMTV(v) FMTR(v.begin(),v.end()) #define FMTM(m,h,w) (MyMatrixFormat(m,h,w)) #if defined(_WIN32) || defined(_WIN64) #define getc_x _getc_nolock #define putc_x _putc_nolock #elif defined(__GNUC__) #define getc_x getc_unlocked #define putc_x putc_unlocked #else #define getc_x getc #define putc_x putc #endif class MaiScanner { FILE* fp_; constexpr bool isvisiblechar(char c) noexcept { return (0x21<=(c)&&(c)<=0x7E); } public: inline MaiScanner(FILE* fp):fp_(fp){} template void input_integer(T& var) noexcept { var = 0; T sign = 1; int cc = getc_x(fp_); for (; cc < '0' || '9' < cc; cc = getc_x(fp_)) if (cc == '-') sign = -1; for (; '0' <= cc && cc <= '9'; cc = getc_x(fp_)) var = (var << 3) + (var << 1) + cc - '0'; var = var * sign; } inline int c() noexcept { return getc_x(fp_); } template::value, nullptr_t>::type = nullptr> inline MaiScanner& operator>>(T& var) noexcept { input_integer(var); return *this; } inline MaiScanner& operator>>(string& var) { int cc = getc_x(fp_); for (; !isvisiblechar(cc); cc = getc_x(fp_)); for (; isvisiblechar(cc); cc = getc_x(fp_)) var.push_back(cc); return *this; } template inline void in(IT begin, IT end) { for (auto it = begin; it != end; ++it) *this >> *it; } }; class MaiPrinter { FILE* fp_; public: inline MaiPrinter(FILE* fp):fp_(fp){} template void output_integer(T var) noexcept { if (var == 0) { putc_x('0', fp_); return; } if (var < 0) putc_x('-', fp_), var = -var; char stack[32]; int stack_p = 0; while (var) stack[stack_p++] = '0' + (var % 10), var /= 10; while (stack_p) putc_x(stack[--stack_p], fp_); } inline MaiPrinter& operator<<(char c) noexcept { putc_x(c, fp_); return *this; } template::value, nullptr_t>::type = nullptr> inline MaiPrinter& operator<<(T var) noexcept { output_integer(var); return *this; } inline MaiPrinter& operator<<(char* str_p) noexcept { while (*str_p) putc_x(*(str_p++), fp_); return *this; } inline MaiPrinter& operator<<(const string& str) { const char* p = str.c_str(); const char* l = p + str.size(); while (p < l) putc_x(*p++, fp_); return *this; } template void join(IT begin, IT end, char sep = ' ') { for (bool b = 0; begin != end; ++begin, b = 1) b ? *this << sep << *begin : *this << *begin; } }; MaiScanner scanner(stdin); MaiPrinter printer(stdout); class GraphE { public: using W_T = int; struct Edge { int u, v; W_T value; Edge(int from = 0, int to = 0, W_T value = 0) : u(from), v(to), value(value) {} inline int to(int _v) const { return _v == v ? u : v; } }; size_t n; vector> vertex_to; vector edges; explicit GraphE(int n = 1) : n(n), vertex_to(n) {} inline size_t size() const noexcept { return n; } void resize(size_t _n) { vertex_to.resize(n = _n); } void connect(int from, int to, W_T val = 0) { vertex_to[(size_t)from].push_back((int)edges.size()); vertex_to[(size_t)to].push_back((int)edges.size()); edges.emplace_back(from, to, val); } void connect(vector&& es) { edges = move(es); for (int i = 0; (size_t)i < edges.size(); ++i) { vertex_to[edges[i].u].push_back(i); vertex_to[edges[i].v].push_back(i); } } }; // int N; GraphE graph; // map, vector>> edges; // [(u,v)] = [](index, select) bool painted[100010]; // unused void update(int u, int v, int p){ // LOG << u << "<->" << v <<" : " << p; if (u > v) swap(u, v); for (auto& vv : edges[make_pair(u,v)]) { if (vv.second == -1) { vv.second = p; break; } } painted[p] = true; } bool vis1[100010]; int dfs(int i, vector& g){ int a = 0; g.push_back(i); vis1[i] = true; for (auto ei : graph.vertex_to[i]) { auto to = graph.edges[ei].to(i); if (vis1[to]) continue; a += dfs(to, g); } return a + 1; } void greedy(int i) { pair best{MD, -9}; for (auto ei : graph.vertex_to[i]) { auto& e = graph.edges[ei]; auto to = e.to(i); if (!e.value) { if (painted[to]) { e.value = true; update(i, to, i); return; } chmin(best, pair{graph.vertex_to[to].size(), ei}); } } auto& e = graph.edges[best.second]; e.value = true; update(i, e.to(i), i); } // bool vis2[100010]; // void paint(int i) { // LOG << i; // vis2[i] = true; // for (auto ei : graph.vertex_to[i]) { // auto& e = graph.edges[ei]; // auto to = e.to(i); // if (!e.value) { // LOG << e.u << ' ' << e.v << " - " << i << ' ' << to; // e.value = true; // if (!painted[i]) { // update(i, to, i); // } else if (!painted[to]) { // update(i, to, to); // } else { // LOG << FMTA(painted, N); // LOG << "?"; // } // paint(to); // } // } // return; // } int main() { scanner >> N; graph.resize(N); repeat(i, N) { int a, b; scanner >> a >> b; --a; --b; if (a > b) swap(a, b); graph.connect(a, b); edges[make_pair(a,b)].push_back(make_pair(i, -1)); } repeat(i, N) { if (vis1[i]) { if (!painted[i]) cerr << "!!!"; continue; } vector group; int n = dfs(i, group); int m = 0; priority_queue> vq; for (auto v : group) { int s = graph.vertex_to[v].size(); m += s; vq.emplace(-s, v); } m /= 2; if (n != m) { bye("No"); } while (!vq.empty()) { auto p = vq.top(); vq.pop(); greedy(p.second); } } vector sel(N); for (auto& kv : edges) { for (auto p : kv.second) { sel[p.first] = p.second + 1; } } printer << "Yes\n"; printer.join(all(sel), '\n'); return 0; }