#define _USE_MATH_DEFINES #include using namespace std; #define FOR(i,m,n) for(int i=(m);i<(n);++i) #define REP(i,n) FOR(i,0,n) #define ALL(v) (v).begin(),(v).end() using ll = long long; constexpr int INF = 0x3f3f3f3f; constexpr long long LINF = 0x3f3f3f3f3f3f3f3fLL; constexpr double EPS = 1e-8; constexpr int MOD = 1000000007; // constexpr int MOD = 998244353; constexpr int DY4[]{1, 0, -1, 0}, DX4[]{0, -1, 0, 1}; constexpr int DY8[]{1, 1, 0, -1, -1, -1, 0, 1}; constexpr int DX8[]{0, -1, -1, -1, 0, 1, 1, 1}; template inline bool chmax(T& a, U b) { return a < b ? (a = b, true) : false; } template inline bool chmin(T& a, U b) { return a > b ? (a = b, true) : false; } struct IOSetup { IOSetup() { std::cin.tie(nullptr); std::ios_base::sync_with_stdio(false); std::cout << fixed << setprecision(20); } } iosetup; std::vector prime_sieve(const int n, const bool get_only_prime) { std::vector smallest_prime_factor(n + 1), prime; std::iota(smallest_prime_factor.begin(), smallest_prime_factor.end(), 0); for (int i = 2; i <= n; ++i) { if (smallest_prime_factor[i] == i) prime.emplace_back(i); for (const int p : prime) { if (i * p > n || p > smallest_prime_factor[i]) break; smallest_prime_factor[i * p] = p; } } return get_only_prime ? prime : smallest_prime_factor; } struct TwoSat { explicit TwoSat(const int n) : n(n), graph(n << 1), rgraph(n << 1), is_visited(n << 1), ids(n << 1) { order.reserve(n << 1); } int negate(const int x) const { return (n + x) % (n << 1); } void add_or(const int x, const int y) { graph[negate(x)].emplace_back(y); graph[negate(y)].emplace_back(x); rgraph[y].emplace_back(negate(x)); rgraph[x].emplace_back(negate(y)); } void add_if(const int x, const int y) { add_or(negate(x), y); } void add_nand(const int x, const int y) { add_or(negate(x), negate(y)); } void set_true(const int x) { add_or(x, x); } void set_false(const int x) { set_true(negate(x)); } std::vector build() { std::fill(is_visited.begin(), is_visited.end(), false); std::fill(ids.begin(), ids.end(), -1); order.clear(); for (int i = 0; i < (n << 1); ++i) { if (!is_visited[i]) dfs(i); } for (int i = (n << 1) - 1, id = 0; i >= 0; --i) { if (ids[order[i]] == -1) rdfs(order[i], id++); } std::vector res(n); for (int i = 0; i < n; ++i) { if (ids[i] == ids[negate(i)]) return {}; res[i] = ids[negate(i)] < ids[i]; } return res; } private: const int n; std::vector> graph, rgraph; std::vector is_visited; std::vector ids, order; void dfs(const int ver) { is_visited[ver] = true; for (const int dst : graph[ver]) { if (!is_visited[dst]) dfs(dst); } order.emplace_back(ver); } void rdfs(const int ver, const int cur_id) { ids[ver] = cur_id; for (const int dst : rgraph[ver]) { if (ids[dst] == -1) rdfs(dst, cur_id); } } }; int main() { const vector is_prime = prime_sieve(10001000, false); int n; cin >> n; vector a(n), b(n); REP(i, n) cin >> a[i] >> b[i]; TwoSat two_sat(n); REP(i, n) REP(j, n) { if (i == j) continue; const int v = stoi(to_string(a[i]) + to_string(a[j])); if (is_prime[v] == v) two_sat.add_if(i, j); } REP(i, n) REP(j, n) { const int v = stoi(to_string(a[i]) + to_string(b[j])); if (is_prime[v] == v) two_sat.add_if(i, two_sat.negate(j)); } REP(i, n) REP(j, n) { const int v = stoi(to_string(b[i]) + to_string(a[j])); if (is_prime[v] == v) two_sat.add_if(two_sat.negate(i), j); } REP(i, n) REP(j, n) { if (i == j) continue; const int v = stoi(to_string(b[i]) + to_string(b[j])); if (is_prime[v] == v) two_sat.add_if(two_sat.negate(i), two_sat.negate(j)); } cout << (two_sat.build().empty() ? "No\n" : "Yes\n"); return 0; }