#include using namespace std; #define repd(i,a,b) for (ll i=(a);i<(b);i++) #define rep(i,n) repd(i,0,n) #define all(x) (x).begin(),(x).end() template inline bool chmin(T& a, T b) { if (a > b) { a = b; return true; } return false; } template inline bool chmax(T& a, T b) { if (a < b) { a = b; return true; } return false; } typedef long long ll; typedef pair P; typedef vector vec; using Graph = vector>; const long long INF = 1LL<<60; const long long MOD = 1000000007; //https://nyaannyaan.github.io/library/math/two-sat.hpp.html namespace TwoSatImpl { namespace internal { template struct csr { vector start; vector elist; csr(int n, const vector>& edges) : start(n + 1), elist(edges.size()) { for (auto e : edges) { start[e.first + 1]++; } for (int i = 1; i <= n; i++) { start[i] += start[i - 1]; } auto counter = start; for (auto e : edges) { elist[counter[e.first]++] = e.second; } } }; struct scc_graph { public: scc_graph(int n) : _n(n) {} int num_vertices() { return _n; } void add_edge(int from, int to) { edges.push_back({from, {to}}); } pair> scc_ids() { auto g = csr(_n, edges); int now_ord = 0, group_num = 0; vector visited, low(_n), ord(_n, -1), ids(_n); visited.reserve(_n); auto dfs = [&](auto self, int v) -> void { low[v] = ord[v] = now_ord++; visited.push_back(v); for (int i = g.start[v]; i < g.start[v + 1]; i++) { auto to = g.elist[i].to; if (ord[to] == -1) { self(self, to); low[v] = min(low[v], low[to]); } else { low[v] = min(low[v], ord[to]); } } if (low[v] == ord[v]) { while (true) { int u = visited.back(); visited.pop_back(); ord[u] = _n; ids[u] = group_num; if (u == v) break; } group_num++; } }; for (int i = 0; i < _n; i++) { if (ord[i] == -1) dfs(dfs, i); } for (auto& x : ids) { x = group_num - 1 - x; } return {group_num, ids}; } vector> scc() { auto ids = scc_ids(); int group_num = ids.first; vector counts(group_num); for (auto x : ids.second) counts[x]++; vector> groups(ids.first); for (int i = 0; i < group_num; i++) { groups[i].reserve(counts[i]); } for (int i = 0; i < _n; i++) { groups[ids.second[i]].push_back(i); } return groups; } void add_node_size(int m) { _n += m; } int size() { return _n; } private: int _n; struct edge { int to; }; vector> edges; }; } // namespace internal struct two_sat { public: two_sat() : _n(0), built(false), scc(0) {} two_sat(int n) : _n(n), built(false), scc(2 * n) {} int add_var() { scc.add_node_size(2); return _n++; } // (not i) は ~i で渡す void add_clause(int i, int j) { i = max(2 * i, -1 - 2 * i); j = max(2 * j, -1 - 2 * j); assert(0 <= i && i < 2 * _n); assert(0 <= j && j < 2 * _n); scc.add_edge(i, j ^ 1); scc.add_edge(j, i ^ 1); } void if_then(int i, int j) { add_clause(~i, j); } void set_val(int i) { add_clause(i, i); } // (not i) は ~i で渡す void at_most_one(const vector& nodes) { if ((int)nodes.size() <= 1) return; int cur = ~nodes[0]; for (int i = 2; i < (int)nodes.size(); i++) { int nxt = add_var(), n_i = ~nodes[i]; add_clause(cur, n_i); add_clause(cur, nxt); add_clause(n_i, nxt); cur = ~nxt; } add_clause(cur, ~nodes[1]); } bool satisfiable() { _answer.resize(_n); built = true; auto id = scc.scc_ids().second; for (int i = 0; i < _n; i++) { if (id[2 * i] == id[2 * i + 1]) { _answer.clear(); return false; } _answer[i] = id[2 * i] < id[2 * i + 1]; } return true; } vector answer() { if (!built) satisfiable(); return _answer; } private: int _n; vector _answer; bool built; internal::scc_graph scc; }; } // namespace TwoSatImpl using TwoSatImpl::two_sat; // Sieve of Eratosthenes // https://youtu.be/UTVg7wzMWQc?t=2774 struct Sieve { int n; vector f, primes; Sieve(int n=1):n(n), f(n+1) { f[0] = f[1] = -1; for (ll i = 2; i <= n; ++i) { if (f[i]) continue; primes.push_back(i); f[i] = i; for (ll j = i*i; j <= n; j += i) { if (!f[j]) f[j] = i; } } } bool isPrime(int x) { return f[x] == x;} vector factorList(int x) { vector res; while (x != 1) { res.push_back(f[x]); x /= f[x]; } return res; } vector

factor(int x) { vector fl = factorList(x); if (fl.size() == 0) return {}; vector

res(1, P(fl[0], 0)); for (int p : fl) { if (res.back().first == p) { res.back().second++; } else { res.emplace_back(p, 1); } } return res; } vector> factor(ll x) { vector> res; for (int p : primes) { int y = 0; while (x%p == 0) x /= p, ++y; if (y != 0) res.emplace_back(p,y); } if (x != 1) res.emplace_back(x,1); return res; } }sieve(999999); int main() { ios::sync_with_stdio(false); cin.tie(0); ll n;cin>>n; vec a(n),b(n); rep(i,n){ cin>>a[i]>>b[i]; } auto f=[&](ll x,ll y){ int res=0; ll now=1; while(y){ res+=now*(y%10); y/=10; now*=10; } while(x){ res+=now*(x%10); x/=10; now*=10; } return res; }; bool ans=1; two_sat ts(n); rep(i,n)repd(j,i,n){ if(i==j){ ll cnt=0; if(sieve.isPrime(f(a[i],b[i]))){ cnt++; ts.set_val(~i); } if(sieve.isPrime(f(b[i],a[i]))){ cnt++; ts.set_val(i); } if(cnt==2)ans=0; continue; } if(sieve.isPrime(f(a[i],a[j]))||sieve.isPrime(f(b[j],b[i]))){ ts.add_clause(~i,j); } if(sieve.isPrime(f(a[i],b[j]))||sieve.isPrime(f(a[j],b[i]))){ ts.add_clause(~i,~j); } if(sieve.isPrime(f(b[i],a[j]))||sieve.isPrime(f(b[j],a[i]))){ ts.add_clause(i,j); } if(sieve.isPrime(f(b[i],b[j]))||sieve.isPrime(f(a[j],a[i]))){ ts.add_clause(i,~j); } } if(!ts.satisfiable())ans=0; if(ans)cout<<"Yes"<