#line 1 "main.cpp" #pragma region Macros #include using namespace std; template inline bool chmax(T &a, T b) { if(a < b) { a = b; return 1; } return 0; } template inline bool chmin(T &a, T b) { if(a > b) { a = b; return 1; } return 0; } #ifdef DEBUG template ostream &operator<<(ostream &os, const pair &p) { os << '(' << p.first << ',' << p.second << ')'; return os; } template ostream &operator<<(ostream &os, const vector &v) { os << '{'; for(int i = 0; i < (int)v.size(); i++) { if(i) { os << ','; } os << v[i]; } os << '}'; return os; } void debugg() { cerr << endl; } template void debugg(const T &x, const Args &... args) { cerr << " " << x; debugg(args...); } #define debug(...) \ cerr << __LINE__ << " [" << #__VA_ARGS__ << "]: ", debugg(__VA_ARGS__) #define dump(x) cerr << __LINE__ << " " << #x << " = " << (x) << endl #else #define debug(...) (void(0)) #define dump(x) (void(0)) #endif struct Setup { Setup() { cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(15); } } __Setup; using ll = long long; #define OVERLOAD3(_1, _2, _3, name, ...) name #define ALL(v) (v).begin(), (v).end() #define RALL(v) (v).rbegin(), (v).rend() #define REP1(i, n) for(int i = 0; i < int(n); i++) #define REP2(i, a, b) for(int i = (a); i < int(b); i++) #define REP(...) OVERLOAD3(__VA_ARGS__, REP2, REP1)(__VA_ARGS__) #define UNIQUE(v) sort(ALL(v)), (v).erase(unique(ALL(v)), (v).end()) #define SZ(v) ((int)(v).size()) const int INF = 1 << 30; const ll LLINF = 1LL << 60; constexpr int MOD = 1000000007; constexpr int MOD2 = 998244353; const int dx[4] = {1, 0, -1, 0}; const int dy[4] = {0, 1, 0, -1}; void Case(int i) { cout << "Case #" << i << ": "; } int popcount(int x) { return __builtin_popcount(x); } ll popcount(ll x) { return __builtin_popcountll(x); } #pragma endregion Macros #line 1 "/Users/siro53/kyo-pro/compro_library/math/eratosthenes.hpp" vector eratosthenes(int n) { vector isp(n + 1, true); isp[0] = isp[1] = false; for(int i = 2; i * i <= n; i++) { if(!isp[i]) continue; for(int j = i+i; j <= n; j += i) isp[j] = false; } return isp; } #line 77 "main.cpp" auto isp = eratosthenes(2000000); #include bool check(int a, int b) { string s = to_string(a) + to_string(b); return isp[stoi(s)]; } int main() { int N; cin >> N; vector a(N), b(N); atcoder::two_sat ts(N); // xi = 0 -> a[i] : S, b[i] : T // xi = 1 -> a[i] : T, b[i] : S REP(i, N) { cin >> a[i] >> b[i]; if(check(a[i], b[i]) and check(b[i], a[i])) { cout << "No\n"; return 0; } if(!check(a[i], b[i]) and check(b[i], a[i])) { ts.add_clause(i, 0, i, 0); } else if(check(a[i], b[i]) and !check(b[i], a[i])) { ts.add_clause(i, 1, i, 1); } } REP(i, N) REP(j, i+1, N) { // xi = 0, xj = 0 if(check(a[i], b[j]) or check(a[j], b[i])) { ts.add_clause(i, 1, j, 1); } // xi = 0, xj = 1 if(check(a[i], a[j]) or check(b[j], b[i])) { ts.add_clause(i, 1, j, 0); } // xi = 1, xj = 0 if(check(b[i], b[j]) or check(a[j], a[i])) { ts.add_clause(i, 1, j, 1); } // xi = 1, xj = 1 if(check(b[i], a[j]) or check(b[j], a[i])) { ts.add_clause(i, 0, j, 0); } } auto ans = ts.satisfiable(); cout << (ans ? "Yes" : "No") << endl; }