#include #pragma GCC optimize("Ofast") #define _GLIBCXX_DEBUG using namespace std; using std::cout; using std::cin; using std::endl; using ll=long long; using ld=long double; ll ILL=2167167167167167167; const int INF=2100000000; const ll mod=998244353; #define rep(i,a) for (ll i=0;i using _pq = priority_queue, greater>; template ll LB(vector &v,T a){return lower_bound(v.begin(),v.end(),a)-v.begin();} template ll UB(vector &v,T a){return upper_bound(v.begin(),v.end(),a)-v.begin();} template bool chmin(T &a,const T &b){if(a>b){a=b;return 1;}else return 0;} template bool chmax(T &a,const T &b){if(a void So(vector &v) {sort(v.begin(),v.end());} template void Sore(vector &v) {sort(v.begin(),v.end(),[](T x,T y){return x>y;});} void yneos(bool a){if(a) cout<<"Yes\n"; else cout<<"No\n";} template void vec_out(vector &p){for(int i=0;i<(int)(p.size());i++){if(i) cout<<" ";cout<> G; std::vector> G_rev; int size; SCC(int n):G(n),G_rev(n),size(n){} int add_ver(){ G.push_back({}); G_rev.push_back({}); size++; return size-1; } void add_edge(int from,int to){ assert(0<=to&&to &order,std::vector &seen,int ind,int &now){ if(seen[ind]!=0) return; seen[ind]=-1; for(auto x:G[ind]){ dfs1(order,seen,x,now); } order[now]=ind; now++; } void dfs2(std::vector &seen,int ind,int rank){ if(seen[ind]!=-1) return; seen[ind]=rank; for(auto x:G_rev[ind]){ dfs2(seen,x,rank); } } std::vector> tp_sort(){ std::vector seen(size,0),order(size); int now=0; for(int i=0;i=0;i--){ if(seen[order[i]]==-1){ dfs2(seen,order[i],now); now++; } } std::vector> ans(now); for(int i=0;i for_two_sat(){ std::vector seen(size,0),order(size); int now=0; for(int i=0;i=0;i--){ if(seen[order[i]]==-1){ dfs2(seen,order[i],now); now++; } } return seen; } }; struct two_SAT{ po167::SCC graph; std::vector ans; bool exists=false; int size; two_SAT(int n):graph(2*n),ans(n),size(n){} void add_clause(int i,bool f,int j,bool g){ graph.add_edge(i*2+(!f),j*2+(g)); graph.add_edge(j*2+(!g),i*2+(f)); } void one_true_in_group(std::vector> &p){ int ind; for(int i=0;i<(int)(p.size())-1;i++){ ind=graph.add_ver(); graph.add_ver(); ind/=2; add_clause(ind,1,p[i].first,p[i].second^1); add_clause(ind,0,p[i+1].first,p[i+1].second^1); if(i){ add_clause(ind-1,0,ind,1); } ans.push_back(false); size++; } } bool build(){ auto rank=graph.for_two_sat(); exists=true; for(int i=0;i Eratosthenes(long long a){ if(a<2) return {}; vector p(a+1),ans; p[0]=1,p[1]=1; long long k=2; while(k*k<=a){ if(p[k]==0){ ans.push_back(k); for(long long i=2;i*k<=a;i++){ p[i*k]=1; } } k++; } while(k<=a){ if(p[k]==0) ans.push_back(k); k++; } return p; } auto table=Eratosthenes(1e6+10); bool prime(int a){ return (table[a]==0); } void solve(); // oddloop int main() { ios::sync_with_stdio(false); cin.tie(nullptr); int t=1; //cin>>t; rep(i,t) solve(); } void solve(){ int N; cin>>N; vector> p(N,vector(2)); rep(i,N) cin>>p[i][0]>>p[i][1]; two_SAT T(N); rep(i,N){ if(prime(unite(p[i][0],p[i][1]))) T.add_clause(i,1,i,1); if(prime(unite(p[i][1],p[i][0]))) T.add_clause(i,0,i,0); } rep(i,N) rep(j,i){ rep(k,2) rep(l,2){ if(prime(unite(p[i][k],p[j][l]))){ T.add_clause(i,k^1,j,l); } if(prime(unite(p[j][k],p[i][l]))){ T.add_clause(j,k^1,i,l); } } } bool ans=T.build(); yneos(ans); }