#include #include #include #include typedef __int128 int128_t; typedef unsigned __int128 uint128_t; uint64_t ex_gcd(uint64_t y){ int i; uint64_t u, v; u = 1; v = 0; uint64_t x = 1LL<<63; for(i=0;i<64;i++){ if(u&1){ u = (u + y) / 2; v = v/2 + x; } else { u >>= 1; v >>= 1; } } return v; } static inline uint64_t MR(uint128_t x, uint64_t m, uint64_t n){ uint64_t z = ((uint128_t) ((uint64_t) x * m) * n + x) >> 64; return z < n ? z : z - n; } static inline uint64_t RM(uint64_t x, uint64_t r2, uint64_t m, uint64_t n){ return MR((uint128_t) r2 * x, m, n); } // k > 0 static inline uint64_t modpow64(uint64_t a, uint64_t k, uint64_t m, uint64_t n){ uint64_t r; for(r=a,--k;k;k/=2){ if(k&1) r = MR((uint128_t)r*a, m, n); a = MR((uint128_t) a*a, m, n); } return r; } static inline uint32_t modpow32(uint32_t a, uint32_t k, uint32_t n){ uint32_t r; for(r=1;k;k/=2){ if(k&1) r = (uint64_t)r*a%n; a = (uint64_t) a*a%n; } return r; } std::set set_pp; const int maxp = 7130; //const int maxp = 1<<16; //const int maxp = 2642246; int sieve_p[maxp/2]; void make_set_pp(){ uint32_t i; for(i=3;i> r; for(i=0;i<3;i++){ uint32_t a = as32[i] % n; if(a == 0) return 1; uint32_t t = modpow32(a, d, n); if(t == 1) continue; for(j=0;t!=n-1;j++){ if(j == r-1) return 0; t = (uint64_t) t * t % n; if(t == 1) return 0; } } return 1; } int is_prime64(uint64_t n){ static const uint64_t as64[] = {2, 325, 9375, 28178, 450775, 9780504, 1795265022}; int i, j, r; uint64_t d, one, mone, r2, m; if(n < (1LL << 32)) return is_prime32(n); r = __builtin_ctzll(n-1); d = (n-1) >> r; m = ex_gcd(n); one = -1ULL % n + 1; mone = n - one; r2 = (uint128_t) (int128_t) -1 % n + 1; for(i=0;i<7;i++){ uint64_t a = RM(as64[i], r2, m, n); if(a == 0) return 1; uint64_t t = modpow64(a, d, m, n); if(t == one) continue; for(j=0;t!=mone;j++){ if(j == r-1) return 0; t = MR((uint128_t) t * t, m, n); // if(t == one) return 0; } } return 1; } int is_prime(uint64_t n){ if(n <= 1) return 0; if(n <= 3) return 1; if(!(n & 1)) return 0; // if(n < 128) return is_primesmall(n); if(n < (1LL << 32)) return is_prime32(n); return is_prime64(n); } uint64_t is_oddprimepower64(uint64_t n){ if(n == 1) return 0; if(set_pp.count(n)) return 1; uint32_t k = round(sqrt(n)); if(k*k==n){ n = k; k = round(sqrt(n)); if(k*k == n) return is_prime(k); else return is_prime(n); } k = round(cbrt(n)); if(k*k*k==n) return is_prime(k); return is_prime(n); } int main(){ int i, q; make_set_pp(); /* for(uint64_t x: set_pp){ printf("%lu\n", x); } printf("%u\n", set_pp.size()); return 0; */ scanf("%d", &q); for(i=0;i=n) puts("No"); else puts("Yes"); } } return 0; }