#include #define endl '\n' #define int long long #define lint long long #define pii pair #define FOR(i,a,b) for(int i=(a);i<(b);++i) #define REP(i,n) FOR(i,0,n) #define ALL(v) (v).begin(),(v).end() #define SZ(v) ((int)v.size()) #define ZERO(a) memset(a,0,sizeof(a)) #define MINUS(a) memset(a,0xff,sizeof(a)) #define MINF(a) memset(a,0x3f,sizeof(a)) #define POW(n) (1LL<<(n)) #define POPCNT(n) (__builtin_popcount(n)) #define IN(i,a,b) (a <= i && i <= b) using namespace std; template inline bool CHMIN(T& a,T b) { if(a>b) { a=b; return 1; } return 0; } template inline bool CHMAX(T& a,T b) { if(a inline void SORT(T& a) { sort(ALL(a)); } template inline void REV(T& a) { reverse(ALL(a)); } template inline void UNI(T& a) { sort(ALL(a)); a.erase(unique(ALL(a)),a.end()); } template inline T LB(vector& v, T a) { return *lower_bound(ALL(v),a); } template inline int LBP(vector& v, T a) { return lower_bound(ALL(v),a) - v.begin(); } template inline T UB(vector& v, T a) { return *upper_bound(ALL(v),a); } template inline int UBP(vector& v, T a) { return upper_bound(ALL(v),a) - v.begin(); } template ostream& operator<< (ostream& os, const pair& p) { os << p.first << " " << p.second; return os; } template istream& operator>> (istream& is, pair& p) { is >> p.first >> p.second; return is; } template ostream& operator<< (ostream& os, const vector& v) { REP(i,v.size()) { if (i) os << " "; os << v[i]; } return os; } template istream& operator>> (istream& is, vector& v) { for(T& in : v) is >> in; return is; } template vector make_v(size_t a) { return vector(a); } template auto make_v(size_t a, Ts... ts) { return vector(ts...))>(a,make_v(ts...)); } template typename enable_if::value == 0>::type fill_v(T &t, const V &v) { t = v; } template typename enable_if::value != 0>::type fill_v(T &t, const V &v) { for(auto &e : t) fill_v(e,v); } const lint MOD = 1000000007; const lint INF = 0x3f3f3f3f3f3f3f3f; const double EPS = 1e-10; // ミラーラビン素数判定法 struct MillerRabin { mt19937_64 mt; MillerRabin() { mt.seed(chrono::steady_clock::now().time_since_epoch().count()); } // a^n (mod m) int mod_pow(__int128_t a, int n, int m) { a %= m; if (a < 0) a += m; __int128_t res = !!a; while (n > 0) { if (n & 1) res = res * a % m; a = a * a % m; n >>= 1; } return res; } // 素数判定 bool is_prime(int n, int k = 10) { if (n == 2) return true; if (n < 2 || !(n & 1)) return false; int d = n - 1; while (!(d & 1)) { d >>= 1; } uniform_int_distribution dist(1, n - 1); for (int i = 0; i < k; ++i) { int a = dist(mt); int t = d; int y = mod_pow(a, t, n); while (t != n - 1 && y != 1 && y != n - 1) { y = mod_pow(y, 2, n); t <<= 1; } if (y != n - 1 && !(t & 1)) return false; } return true; } }; // ポラード・ロー素因数分解法 struct Rho { using P = pair; mt19937_64 mt; MillerRabin mr; Rho() { mt.seed(chrono::steady_clock::now().time_since_epoch().count()); } inline long long f(__int128_t x, long long c, long long n) { return (x * x % n + c) % n; } long long rho(long long n) { if (!(n & 1)) return 2; long long c = mt() % n; long long x = mt() % n; long long y = x; long long d = 1; while (d == 1) { x = f(x, c, n); y = f(f(y, c, n), c, n); d = __gcd(abs(x - y), n); } if (d == n) return -1; return d; } vector

prime_factor(long long n) { if (n <= 1) return {}; if (mr.is_prime(n)) return {P(n, 1)}; long long p = -1; while (p < 0 || !mr.is_prime(p)) { p = rho(n); } long long num = 0; while (n % p == 0) { num++; n /= p; } vector

pf = prime_factor(n); pf.emplace_back(p, num); return pf; } }; void _main() { int Q; cin >> Q; Rho rho; REP(i, Q) { int N; cin >> N; if (N <= 2) { cout << "No" << endl; } else if (N % 2 == 0) { cout << "Yes" << endl; } else { bool no = true; for (int j = 2; j < N; j <<= 1) { auto pf = rho.prime_factor(N - j); if (pf.size() == 1) { no = false; break; } } cout << (no ? "No" : "Yes") << endl; } } } signed main(signed argc, char **argv) { if (argc > 1) { if (strchr(argv[1], 'i')) freopen("input.txt", "r", stdin); if (strchr(argv[1], 'o')) freopen("output.txt", "w", stdout); } cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(10); _main(); return 0; }