//オイラー路(グラフの全ての辺をちょうど1回ずつ通るパス)の検出 //計算量 O(E+V) //verified with //https://codeforces.com/contest/1361/problem/C //https://yukicoder.me/submissions/591125 #include using namespace std; struct io_setup{ io_setup(){ ios_base::sync_with_stdio(false); cin.tie(NULL); cout << fixed << setprecision(15); } } io_setup; struct Union_Find_Tree{ vector data; const int n; Union_Find_Tree(int n) : data(n, -1), n(n) {} int root(int x){ if(data[x] < 0) return x; return data[x] = root(data[x]); } int operator [] (int i) {return root(i);} bool unite(int x, int y){ x = root(x), y = root(y); if(x == y) return false; if(data[x] > data[y]) swap(x, y); data[x] += data[y], data[y] = x; return true; } int size(int x) {return -data[root(x)];} bool same(int x, int y) {return root(x) == root(y);} void clear() {fill(begin(data), end(data), -1);} }; template struct Eulerian_Trail{ struct edge{ int to, id; edge(int to, int id) : to(to), id(id) {} }; vector> es; vector> list; vector used_e, used_v; vector deg; const int n; int m; Eulerian_Trail(int n) : es(n), used_v(n), deg(n), n(n), m(0) {} void add_edge(int from, int to){ list.emplace_back(from, to), es[from].emplace_back(to, m); if(directed) deg[from]++, deg[to]--; else es[to].emplace_back(from, m), deg[from]++, deg[to]++; m++; } pair get_edge(int id) {return list[id];} vector trace(int s){ stack st; vector ret; st.emplace(s, -1); while(!st.empty()){ int now = st.top().to; used_v[now] = true; if(es[now].empty()){ ret.push_back(st.top().id); st.pop(); } else{ auto e = es[now].back(); es[now].pop_back(); if(used_e[e.id]) continue; used_e[e.id] = true, st.push(e); } } ret.pop_back(); reverse(begin(ret), end(ret)); return ret; } vector> eulerian_trail(){ vector> ret; fill(begin(used_v), end(used_v), false); if(directed){ for(auto &e: deg) if(e != 0) return {}; } else{ for(auto &e: deg) if(e&1) return {}; } used_e.assign(m, false); for(int i = 0; i < n; i++){ if(es[i].empty() || used_v[i]) continue; ret.push_back(trace(i)); } return ret; } vector> semi_eulerian_trail(){ Union_Find_Tree uf(n); for(auto &e: list) uf.unite(e.first, e.second); vector> group(n); for(int i = 0; i < n; i++){ group[uf[i]].emplace_back(i); } vector> ret; used_e.assign(m, false); for(auto &vs: group){ if(vs.empty()) continue; int s = -1, t = -1; if(directed){ for(auto &u: vs){ if(abs(deg[u]) > 1) return {}; else if(deg[u] == 1){ if(s != -1) return {}; s = u; } } } else{ for(auto &u: vs){ if(deg[u]&1){ if(s == -1) s = u; else if(t == -1) t = u; else return {}; } } } ret.push_back(trace(s == -1? vs.front() : s)); if(ret.back().empty()) ret.pop_back(); } return ret; } }; int main(){ int V, E; cin >> V >> E; Eulerian_Trail G(V); while(E--){ int u, v; cin >> u >> v; G.add_edge(u, v); } cout << (G.semi_eulerian_trail().size() == 1? "YES" : "NO") << '\n'; }