#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); } 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; } int is_primesmall(uint32_t n){ const uint32_t ps[] = {3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97}; int lb = -1; int ub = sizeof(ps)/sizeof(ps[0]); while(ub - lb > 1){ int m = (lb + ub)/2; if(ps[m] == n) return 1; if(ps[m] < n) lb = m; else ub = m; } return 0; } int is_prime32(uint32_t n){ static const uint32_t as32[] = {2, 7, 61}; int i, j, r; uint32_t d; r = __builtin_ctz(n-1); d = (n-1) >> 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 < 100) return is_primesmall(n); if(n < (1LL << 32)) return is_prime32(n); return is_prime64(n); } uint64_t gcd64(uint64_t x, uint64_t y){ if(x == 0 || y == 0) return x^y; int bx = __builtin_ctzll(x); int by = __builtin_ctzll(y); int k = (bx < by) ? bx : by; x >>= bx; y >>= by; while(x!=y){ if(x < y){ y -= x; y >>= __builtin_ctzll(y); } else { x -= y; x >>= __builtin_ctzll(x); } } return x << k; } int is_power64(uint64_t n, uint64_t p){ int i; uint64_t a[49]; uint64_t x; a[0] = p; a[1] = p * p; for(i=1; a[i] <= n && a[i] > a[i-1]; i++){ a[i+1] = a[i] * a[i]; } /* if(a[--i] == n) return 1; while(i){ if(n % a[i]) return 0; n /= a[i]; while(i > 0 && n < a[--i]) ; } */ x = a[--i]; if(x == n) return 1; for(--i; i>=0;--i){ uint64_t y = x * a[i]; if(y == n) return 1; else if(y < x) return 0; else if(y < n) x = y; } return 0; } uint64_t is_primepower64(uint64_t n){ uint64_t i; if(n <= 1) return 0; if(!(n&(n-1))) return 2; if(!(n&1)) return 0; //return is_prime64(n); uint64_t s, m, r2, one; m = ex_gcd(n); one = -1UL % n + 1; r2 = (uint128_t) (int128_t) -1 % n + 1; uint64_t y = 2; uint64_t x = one << 1; if(x >= n) x -= n; uint64_t in = MR((uint128_t)modpow64(x, n, m, n), m, n); uint64_t inmi = in >= y ? in - y : in + n - y; uint64_t p = gcd64(inmi, n); //fprintf(stderr, "%ld\n", p); return is_prime(p) && is_power64(n, p); // return is_prime64(p); } int main(){ int i, q; scanf("%d", &q); for(i=0;i=n) puts("No"); else puts("Yes"); } } return 0; }