#include #include #include #include using namespace std; // n is even -> yes // n is odd -> p is even and q is odd bool sieve[1000000]; vector primes; bool is_prime(unsigned long long n) { using i64 = long long; using u64 = unsigned long long; using f80 = long double; if (n == 1) return false; if (n == 2) return true; int e = 0; u64 s = n - 1; while (s % 2 == 0) { e++; s /= 2; } auto modmul = [](u64 a, u64 b, u64 m) -> u64 { if (a == 0 || b == 0) return 0; if (a == 1) return b; if (b == 1) return a; u64 q = u64(f80(a) * b / m + 0.5); u64 r = a * b - q * m; return i64(r) < 0 ? r + m : r; }; auto modpow = [modmul](u64 a, u64 b, u64 m) { u64 ret = 1; for (; b > 0; b >>= 1) { if (b & 1) ret = modmul(ret, a, m); a = modmul(a, a, m); } return ret; }; auto check = [&](u64 a) { u64 x = modpow(a, s, n); if (x == 1) return true; for (int i = 0; i < e; i++) { if (x == n - 1) return true; x = modmul(x, x, n); } return false; }; for (int i : {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}) { if (n % i != 0 && !check(i)) return false; } return true; } bool is_square(long long n) { long long s = sqrt(n); return s * s == n; } long long mul(long long a, long long b) { if (a == 0) return 0; if (b == 0) return 0; if (a * b / b != a) return 1.1e18; return a * b; } bool judge(long long n) { if (n <= 3) return false; if (n % 2 == 0) return true; for (int i = 1; n - (1LL << i) >= 3; i++) { long long p = n - (1LL << i); if (is_prime(p)) return true; if (is_square(p) && is_prime(sqrt(p))) return true; for (long long q : primes) { for (long long t = q*q*q; t <= p; t = mul(t, q)) { if (t == p) return true; } } } return false; } int main() { fill(sieve, sieve + 1000000, true); sieve[0] = sieve[1] = false; for (int i = 2; i < 1000000; i++) { if (sieve[i]) { primes.push_back(i); for (int j = i * 2; j < 1000000; j++) { sieve[j] = false; } } } int q; cin >> q; while (q--) { long long n; cin >> n; cout << (judge(n) ? "Yes" : "No") << endl; } }