#include #define rep(i,a,b) for(int i=a;i=b;i--) #define fore(i,a) for(auto &i:a) #pragma GCC optimize ("-O3") using namespace std; void _main(); int main() { cin.tie(0); ios::sync_with_stdio(false); _main(); } //--------------------------------------------------------------------------------------------------- #ifdef _MSC_VER #pragma push_macro("long") #undef long #ifdef _WIN32 inline unsigned int __builtin_ctz(unsigned int x) { unsigned long r; _BitScanForward(&r, x); return r; } inline unsigned int __builtin_clz(unsigned int x) { unsigned long r; _BitScanReverse(&r, x); return 31 - r; } inline unsigned int __builtin_ffs(unsigned int x) { unsigned long r; return _BitScanForward(&r, x) ? r + 1 : 0; } inline unsigned int __builtin_popcount(unsigned int x) { return __popcnt(x); } inline unsigned int hidword(unsigned long long x) { return static_cast(x >> 32); } inline unsigned int lodword(unsigned long long x) { return static_cast(x & 0xFFFFFFFF); } inline unsigned long long __builtin_ctzll(unsigned long long x) { return lodword(x) ? __builtin_ctz(lodword(x)) : __builtin_ctz(hidword(x)) + 32; } inline unsigned long long __builtin_clzll(unsigned long long x) { return hidword(x) ? __builtin_clz(hidword(x)) : __builtin_clz(lodword(x)) + 32; } inline unsigned long long __builtin_ffsll(unsigned long long x) { return lodword(x) ? __builtin_ffs(lodword(x)) : hidword(x) ? __builtin_ffs(hidword(x)) + 32 : 0; } inline unsigned long long __builtin_popcountll(unsigned long long x) { return __builtin_popcount(lodword(x)) + __builtin_popcount(hidword(x)); } #endif // _WIN32 #pragma pop_macro("long") #endif // _MSC_VER typedef long long ll; typedef __int128 int128_t; //typedef ll int128_t; int128_t powmod(int128_t x, int128_t y, int128_t p) { // O(log y) assert(0 <= x and x < p); assert(0 <= y); int128_t z = 1; for (int128_t i = 1; i <= y; i <<= 1) { if (y & i) z = z * x % p; x = x * x % p; } return z; } int K = 10; int getrand(int l, int r) { // [l, r] static uint32_t y = time(NULL); y ^= (y << 13); y ^= (y >> 17); y ^= (y << 5); return y % (r - l + 1) + l; } ll getrandll(ll l, ll r) { // [l,r] ll a = getrand(0, 999999999); ll b = getrand(0, 999999999); ll x = a * 1000000000LL + b; assert(0 <= x); return x % (r - l + 1) + l; } bool isprime(ll v, int loop = 50) { ll d = v - 1; int s = 0, i, j; if (v <= 1) return false; if (v == 2) return true; if (v % 2 == 0) return false; while (d % 2 == 0) d /= 2, s++; rep(i, 0, loop) { ll a = getrandll(1, v - 1); ll r = powmod(a, d, v); if (r == 1 || r == v - 1) continue; int j; for (j = 0; j < s; j++) { r = powmod(r, 2, v); if (r == v - 1) break; } if (j == s) return false; } return true; } /*---------------------------------------------------------------------------------------------------             ∧_∧       ∧_∧  (´<_` )  Welcome to My Coding Space!      ( ´_ゝ`) /  ⌒i     /   \    | |     /   / ̄ ̄ ̄ ̄/  |   __(__ニつ/  _/ .| .|____      \/____/ (u ⊃ ---------------------------------------------------------------------------------------------------*/ typedef long long ll; typedef long double ld; #define INF 1LL<<60 ld lginf = -1; inline ll mul(ll a, ll b) { if (a == 0 or b == 0) return 0; if (a*b < a or a*b < b) return INF; return a*b; } inline ll fastpow(ll x, ll n) { ll ret = 1; while (0 < n) { if ((n % 2) == 0) x = mul(x,x), n >>= 1; else ret = mul(ret,x), --n; } return ret; } ll N; #define INF 1LL<<60 #define yes "Yes" #define no "No" //--------------------------------------------------------------------------------------------------- int isprimePow(ll n) { int k = 1; int up = n; if (isprime(n)) return 1; for (ll q = 2; q < n; q *= 2) { ll ok = k == 1 ? n : expl(logl(n + 1) / k) + 1e-6; if (fastpow(ok, k) == n and isprime(ok)) return 1; k++; up = ok; } return 0; } //--------------------------------------------------------------------------------------------------- string solve() { cin >> N; if (N <= 2) return no; if (N % 2 == 0) { if (4 <= N) return yes; else return no; } for (ll q = 2; q < N; q *= 2) if (isprimePow(N - q)) return yes; return no; } //--------------------------------------------------------------------------------------------------- void _main() { int Q; cin >> Q; rep(q, 0, Q) printf("%s\n", solve().c_str()); }