#include #include #include #include #include #include #include #include namespace nachia{ namespace prime_sieve_explicit_internal{ std::vector isprime = { false }; // a[x] := isprime(2x+1) void CalcIsPrime(int z){ if((int)isprime.size() *2+1 < z+1){ int new_z = isprime.size(); while(new_z*2+1 < z+1) new_z *= 2; z = new_z-1; isprime.resize(z+1, true); for(int i=1; i*(i+1)*2<=z; i++) if(isprime[i]){ for(int j=i*(i+1)*2; j<=z; j+=i*2+1) isprime[j] = false; } } } std::vector prime_list = {2}; int prime_list_max = 0; void CalcPrimeList(int z){ while((int)prime_list.size() < z){ if((int)isprime.size() <= prime_list_max + 1) CalcIsPrime(prime_list_max + 1); for(int p=prime_list_max+1; p<(int)isprime.size(); p++){ if(isprime[p]) prime_list.push_back(p*2+1); } prime_list_max = isprime.size() - 1; } } void CalcPrimeListUntil(int z){ if(prime_list_max < z){ CalcIsPrime(z); for(int p=prime_list_max+1; p<(int)isprime.size(); p++){ if(isprime[p]) prime_list.push_back(p*2+1); } prime_list_max = isprime.size() - 1; } } } bool IsprimeExplicit(int n){ using namespace prime_sieve_explicit_internal; if(n == 2) return true; if(n % 2 == 0) return false; CalcIsPrime(n); return isprime[(n-1)/2]; } int NthPrimeExplicit(int n){ using namespace prime_sieve_explicit_internal; CalcPrimeList(n); return prime_list[n]; } int PrimeCountingExplicit(int n){ using namespace prime_sieve_explicit_internal; if(n < 2) return 0; CalcPrimeListUntil(n); auto res = ::std::upper_bound(prime_list.begin(), prime_list.end(), n) - prime_list.begin(); return (int)res; } // [l, r) ::std::vector SegmentedSieveExplicit(long long l, long long r){ assert(0 <= l); assert(l <= r); long long d = r - l; if(d == 0) return {}; ::std::vector res(d, true); for(long long p=2; p*p<=r; p++) if(IsprimeExplicit(p)){ long long il = (l+p-1)/p, ir = (r+p-1)/p; if(il <= p) il = p; for(long long i=il; i; int main(){ int N; cin >> N; vector A(N); vector B(N); rep(i,N) cin >> A[i] >> B[i]; atcoder::internal::scc_graph scc(N*2); rep(i,N) rep(j,N){ bool prohibit_pp = false; prohibit_pp = prohibit_pp || (B[j].back() != 0 && nachia::IsprimeExplicit(stoi(A[i]+B[j]))); prohibit_pp = prohibit_pp || (B[i].back() != 0 && nachia::IsprimeExplicit(stoi(A[j]+B[i]))); if(prohibit_pp){ scc.add_edge(i, N+j); scc.add_edge(j, N+i); } } rep(i,N) rep(j,N){ bool prohibit_nn = false; prohibit_nn = prohibit_nn || (A[j].back() != 0 && nachia::IsprimeExplicit(stoi(B[i]+A[j]))); prohibit_nn = prohibit_nn || (A[i].back() != 0 && nachia::IsprimeExplicit(stoi(B[j]+A[i]))); if(prohibit_nn){ scc.add_edge(N+i, j); scc.add_edge(N+j, i); } } rep(i,N) rep(j,N) if(i != j){ bool prohibit_pn = false; prohibit_pn = prohibit_pn || (A[j].back() != 0 && nachia::IsprimeExplicit(stoi(A[i]+A[j]))); prohibit_pn = prohibit_pn || (B[i].back() != 0 && nachia::IsprimeExplicit(stoi(B[j]+B[i]))); if(prohibit_pn){ scc.add_edge(i, j); scc.add_edge(N+j, N+i); } } auto G = scc.scc_ids().second; bool ans = true; rep(i,N) if(G[i] == G[N+i]) ans = false; cout << (ans ? "Yes\n" : "No\n"); return 0; } struct ios_do_not_sync{ ios_do_not_sync(){ std::ios::sync_with_stdio(false); std::cin.tie(nullptr); } } ios_do_not_sync_instance;