#define LOCAL #include using namespace std; #pragma region Macros typedef long long ll; typedef __int128_t i128; typedef unsigned int uint; typedef unsigned long long ull; #define ALL(x) (x).begin(), (x).end() template istream& operator>>(istream& is, vector& v) { for (T& x : v) is >> x; return is; } template ostream& operator<<(ostream& os, const vector& v) { for (int i = 0; i < (int)v.size(); i++) { os << v[i] << (i + 1 == (int)v.size() ? "" : " "); } return os; } template ostream& operator<<(ostream& os, const pair& p) { os << '(' << p.first << ',' << p.second << ')'; return os; } template ostream& operator<<(ostream& os, const map& m) { os << '{'; for (auto itr = m.begin(); itr != m.end();) { os << '(' << itr->first << ',' << itr->second << ')'; if (++itr != m.end()) os << ','; } os << '}'; return os; } template ostream& operator<<(ostream& os, const unordered_map& m) { os << '{'; for (auto itr = m.begin(); itr != m.end();) { os << '(' << itr->first << ',' << itr->second << ')'; if (++itr != m.end()) os << ','; } os << '}'; return os; } template ostream& operator<<(ostream& os, const set& s) { os << '{'; for (auto itr = s.begin(); itr != s.end();) { os << *itr; if (++itr != s.end()) os << ','; } os << '}'; return os; } template ostream& operator<<(ostream& os, const multiset& s) { os << '{'; for (auto itr = s.begin(); itr != s.end();) { os << *itr; if (++itr != s.end()) os << ','; } os << '}'; return os; } template ostream& operator<<(ostream& os, const unordered_set& s) { os << '{'; for (auto itr = s.begin(); itr != s.end();) { os << *itr; if (++itr != s.end()) os << ','; } os << '}'; return os; } template ostream& operator<<(ostream& os, const deque& v) { for (int i = 0; i < (int)v.size(); i++) { os << v[i] << (i + 1 == (int)v.size() ? "" : " "); } return os; } template void print_tuple(ostream&, const T&) {} template void print_tuple(ostream& os, const T& t) { if (i) os << ','; os << get(t); print_tuple(os, t); } template ostream& operator<<(ostream& os, const tuple& t) { os << '{'; print_tuple<0, tuple, Args...>(os, t); return os << '}'; } void debug_out() { cerr << '\n'; } template void debug_out(Head&& head, Tail&&... tail) { cerr << head; if (sizeof...(Tail) > 0) cerr << ", "; debug_out(move(tail)...); } #ifdef LOCAL #define debug(...) \ cerr << " "; \ cerr << #__VA_ARGS__ << " :[" << __LINE__ << ":" << __FUNCTION__ << "]" << '\n'; \ cerr << " "; \ debug_out(__VA_ARGS__) #else #define debug(...) 42 #endif template T gcd(T x, T y) { return y != 0 ? gcd(y, x % y) : x; } template T lcm(T x, T y) { return x / gcd(x, y) * y; } int topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); } int topbit(long long t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); } int botbit(signed a) { return a == 0 ? 32 : __builtin_ctz(a); } int botbit(long long a) { return a == 0 ? 64 : __builtin_ctzll(a); } int popcount(signed t) { return __builtin_popcount(t); } int popcount(long long t) { return __builtin_popcountll(t); } bool ispow2(int i) { return i && (i & -i) == i; } template T ceil(T x, T y) { assert(y >= 1); return (x > 0 ? (x + y - 1) / y : x / y); } template T floor(T x, T y) { assert(y >= 1); return (x > 0 ? x / y : (x - y + 1) / y); } template inline bool chmin(T1& a, T2 b) { if (a > b) { a = b; return true; } return false; } template inline bool chmax(T1& a, T2 b) { if (a < b) { a = b; return true; } return false; } #pragma endregion #include #include #include template struct EulerianTrail { std::vector>> G; EulerianTrail(int n) : G(n), n(n), m(0), deg(n, 0), used_vertex(n, false) {} void add_edge(int u, int v) { assert(0 <= u and u < n); assert(0 <= v and v < n); edges.emplace_back(u, v); used_edge.emplace_back(false); G[u].emplace_back(v, m); deg[u]++; if (directed) deg[v]--; else { G[v].emplace_back(u, m); deg[v]++; } m++; } std::vector> solve() { if (directed) { if (std::count_if(deg.begin(), deg.end(), [](int x) { return x != 0; })) return {}; } else { if (std::count_if(deg.begin(), deg.end(), [](int x) { return (x & 1) != 0; })) return {}; } std::vector> res; for (int i = 0; i < n; i++) { if (G[i].empty() or used_vertex[i]) continue; res.emplace_back(go(i)); } return res; } std::vector> solve_semi() { checked_vertex.assign(n, false); std::vector> res; for (int i = 0; i < n; i++) { if (checked_vertex[i]) continue; int s = -1, t = -1; if (!dfs(i, s, t)) return {}; res.emplace_back(go(s >= 0 ? s : i)); if (res.back().empty()) res.pop_back(); } return res; } std::pair operator[](int k) const { return edges[k]; } private: int n, m; std::vector deg; std::vector> edges; std::vector used_vertex, used_edge, checked_vertex; bool dfs(int v, int& s, int& t) { checked_vertex[v] = true; if (directed) { if (deg[v] < -1 or 1 < deg[v]) return false; if (deg[v] == 1) { if (s >= 0) return false; s = v; } } else { if (deg[v] & 1) { if (s == -1) s = v; else if (t == -1) t = v; else return false; } } for (const auto& e : G[v]) { int u = e.first; if (checked_vertex[u]) continue; if (!dfs(u, s, t)) return false; } return true; } std::vector go(int s) { std::vector> st; std::vector order; st.emplace_back(s, -1); while (!st.empty()) { int v = st.back().first; used_vertex[v] = true; if (G[v].empty()) { order.emplace_back(st.back().second); st.pop_back(); } else { auto e = G[v].back(); G[v].pop_back(); if (used_edge[e.second]) continue; used_edge[e.second] = true; st.emplace_back(e); } } order.pop_back(); reverse(order.begin(), order.end()); return order; } }; /** * @brief Eulerian Trail * @docs docs/graph/EulerianTrail.md */ const int INF = 1e9; const long long IINF = 1e18; const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1}; const char dir[4] = {'D', 'R', 'U', 'L'}; const long long MOD = 1000000007; // const long long MOD = 998244353; int main() { cin.tie(0); ios::sync_with_stdio(false); int N, M; cin >> N >> M; EulerianTrail ET(N); for (int i = 0; i < M; i++) { int a, b; cin >> a >> b; ET.add_edge(a, b); } cout << (ET.solve_semi().size() == 1 ? "YES" : "NO") << '\n'; return 0; }