#include // #pragma GCC optimize("Ofast") // #pragma GCC optimize("unroll-loops") // #pragma GCC target("sse,sse2,sse3,ssse3,sse4,fma,abm,mmx,avx,avx2") #define rep(i, n) for (int i = 0; i < (int)(n); i++) #define rrep(i, n) for (int i = (int)(n - 1); i >= 0; i--) #define all(x) (x).begin(), (x).end() #define sz(x) int(x.size()) #define yn(joken) cout<<((joken) ? "Yes" : "No")<<"\n" #define YN(joken) cout<<((joken) ? "YES" : "NO")<<"\n" using namespace std; using ll = long long; using vi = vector; using vl = vector; using vs = vector; using vc = vector; using vd = vector; using vld = vector; using vvi = vector>; using vvl = vector>; using vvs = vector>; using vvc = vector>; using vvd = vector>; using vvld = vector>; using vvvi = vector>>; using vvvl = vector>>; using vvvvi = vector>>>; using vvvvl = vector>>>; using pii = pair; using pll = pair; const int INF = 1e9; const ll LINF = 2e18; template bool chmax(T& a, const T& b) { if (a < b) { a = b; return 1; } return 0; } template bool chmin(T& a, const T& b) { if (b < a) { a = b; return 1; } return 0; } bool ispow2(int i) { return i && (i & -i) == i; } bool ispow2(ll i) { return i && (i & -i) == i; } template vector make_vec(size_t a) { return vector(a); } template auto make_vec(size_t a, Ts... ts) { return vector(ts...))>(a, make_vec(ts...)); } template istream& operator>>(istream& is, vector& v) { for (int i = 0; i < int(v.size()); i++) { is >> v[i]; } return is; } template ostream& operator<<(ostream& os, const vector& v) { for (int i = 0; i < int(v.size()); i++) { os << v[i]; if (i < int(v.size()) - 1) os << ' '; } return os; } static uint32_t RandXor(){ static uint32_t x=123456789; static uint32_t y=362436069; static uint32_t z=521288629; static uint32_t w=88675123; uint32_t t; t=x^(x<<11); x=y; y=z; z=w; return w=(w^(w>>19))^(t^(t>>8)); } static double Rand01(){ return (RandXor()+0.5)*(1.0/UINT_MAX); } struct sieve{ vector is_prime; vector min_factor,primes; sieve(int N): is_prime(N+1,true),min_factor(N+1,-1){ is_prime[1]=false; min_factor[1]=1; for(int i=2;i<=N;i++){ if(!is_prime[i]) continue; primes.push_back(i); min_factor[i]=i; for(int j=i;j<=N;j+=i){ is_prime[j]=false; if(min_factor[j]==-1) min_factor[j]=i; } } } vector> factorize(int n){ vector> ret; while(n>1){ int p=min_factor[n]; int e=0; while(n%p==0){ e++; n/=p; } ret.emplace_back(p,e); } return ret; } }; template struct Edge{ int from, to; T cost; int idx; Edge() = default; Edge(int from, int to, T cost = 1, int idx = -1) : from(from), to(to), cost(cost), idx(idx) {} operator int() const { return to; } }; template struct Graph{ vector>> g; int es; Graph() = default; explicit Graph(int n) : g(n), es(0) {} size_t size() const{ return g.size(); } void add_directed_edge(int from, int to, T cost = 1){ g[from].emplace_back(from, to, cost, es++); } void add_edge(int from, int to, T cost = 1){ g[from].emplace_back(from, to, cost, es); g[to].emplace_back(to, from, cost, es++); } void read(int M, int padding = -1, bool weighted = false, bool directed = false){ for (int i = 0; i < M; i++){ int a, b; cin >> a >> b; a += padding; b += padding; T c = T(1); if (weighted) cin >> c; if (directed) add_directed_edge(a, b, c); else add_edge(a, b, c); } } inline vector> &operator[](const int &k){ return g[k]; } inline const vector> &operator[](const int &k) const{ return g[k]; } }; template using Edges = vector>; template struct StronglyConnectedComponent{ private: G g; const int V; int cnt; vector in,low; stack st; void dfs(const int v,int &time){ in[v]=time; low[v]=time; time++; st.push(v); for(auto nv:g[v]){ if(in[nv]<0){ dfs(nv,time); low[v]=min(low[v],low[nv]); } else if(rev[nv]<0){ low[v]=min(low[v],in[nv]); } } if(in[v]==low[v]){ while(true){ const int u=st.top(); st.pop(); rev[u]=cnt; if(u==v) break; } cnt++; } } public: vector> members; vector rev; StronglyConnectedComponent(G &_g): g(_g),V(_g.size()),cnt(0),in(_g.size(),-1),low(_g.size()), rev(_g.size(),-1){ int time=0; for(int i=0;i>N; vs A(N),B(N); rep(i,N) cin>>A[i]>>B[i]; sieve SE(1000000); vi P(1000000); for(auto p:SE.primes) P[p]++; if(N==1){ string s1=A[0]+B[0],s2=B[0]+A[0]; yn(!P[stoi(s1)] || !P[stoi(s2)]); } Graph G(2*N); rep(i,N){ rep(j,i){ // S,T string s1=A[i]+A[j],t1=B[j]+B[i]; if(P[stoi(s1)] || P[stoi(t1)]){ G.add_directed_edge(i,j); G.add_directed_edge(j+N,i+N); } // S,S string s2=A[i]+B[j],t2=A[j]+B[i]; if(P[stoi(s2)] || P[stoi(t2)]){ G.add_directed_edge(i,j+N); G.add_directed_edge(j,i+N); } // T,T string s3=B[i]+A[j],t3=B[j]+A[i]; if(P[stoi(s3)] || P[stoi(t3)]){ G.add_directed_edge(i+N,j); G.add_directed_edge(j+N,i); } // T,S string s4=B[i]+B[j],t4=A[j]+A[i]; if(P[stoi(s4)] || P[stoi(t4)]){ G.add_directed_edge(i+N,j+N); G.add_directed_edge(j,i); } } } rep(i,N){ string s1=A[i]+B[i]; if(P[stoi(s1)]){ rep(j,N){ if(i==j) continue; G.add_directed_edge(j,i+N); G.add_directed_edge(j+N,i+N); G.add_directed_edge(i,j); G.add_directed_edge(i,j+N); } } string s2=B[i]+A[i]; if(P[stoi(s2)]){ rep(j,N){ if(i==j) continue; G.add_directed_edge(j,i); G.add_directed_edge(j+N,i); G.add_directed_edge(i+N,j); G.add_directed_edge(i+N,j+N); } } } StronglyConnectedComponent> SCC(G); vi num(2*N); auto mem=SCC.members; rep(i,sz(mem)) for(auto v:mem[i]) num[v]=i; bool flg=true; rep(i,N) if(num[i]==num[i+N]) flg=false; yn(flg); } int main(){ cin.tie(nullptr); ios::sync_with_stdio(false); solve(); }