#include #include #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); } static inline uint64_t mulmod64(uint64_t x, uint64_t y, uint64_t m, uint64_t n){ return MR((uint128_t) x*y, m, n); } int jacobi(int64_t a, uint64_t n){ uint64_t t; int j = 1; while(a){ if(a<0){ a = -a; if((n&3)==3) j = -j; } int ba = __builtin_ctzll(a); a >>= ba; if(((n&7)==3||(n&7)==5) && (ba&1)) j = -j; if((a&n&3)==3) j = -j; t = a; a = n; n = t; a %= n; if(a>n/2) a-=n; } return n == 1 ? j : 0; } static inline uint64_t addmod64(uint64_t x, uint64_t y, uint64_t n){ return x + y >= n ? x + y - n : x + y; } static inline uint64_t submod64(uint64_t x, uint64_t y, uint64_t n){ return x >= y ? x - y : x - y + 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::vector vec_pp; const int maxp = 7130; //const int maxp = 1<<16; //const int maxp = 2642246; int sieve_p[maxp/2]; void make_set_pp(){ std::set set_pp; uint32_t i; for(i=3;i(set_pp.begin(), set_pp.end()); } 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(const uint64_t n){ const uint64_t one = -1ULL % n + 1; const uint64_t r2 = (uint128_t) (int128_t) -1 % n + 1; const uint64_t m = ex_gcd(n); { uint64_t d = (n-1) << __builtin_clzll(n-1); uint64_t t = one << 1; if(t >= n) t -= n; for(d<<=1;d;d<<=1){ t = mulmod64(t, t, m, n); if(d>>63){ t <<= 1; if(t>=n) t -= n; } } if(t != one){ uint64_t x = (n-1) & -(n-1); uint64_t mone = n - one; for(x>>=1;t!=mone;x>>=1){ if(x == 0) return 0; t = mulmod64(t, t, m, n); // if(t == one) return 0; } } } { int64_t D = 5; int i; for(i=0;jacobi(D, n) != -1 && i<64;i++){ if(i==32){ uint32_t k = round(sqrtl(n)); if(k*k == n) return 0; } if(i&1) D -= 2; else D += 2; D = -D; } // if(i==64) puts("ERROR"); uint64_t Q = RM(D < 0 ? (1-D)/4%n : n - (D-1)/4%n, r2, m, n); uint64_t u, v, Qn; uint64_t k = (n+1) << __builtin_clzll(n+1); u = one; v = one; Qn = Q; D %= (int64_t) n; D = RM(D < 0 ? n+D : D, r2, m, n); for(k<<=1;k;k<<=1){ u = mulmod64(u,v,m,n); v = submod64(mulmod64(v,v,m,n), addmod64(Qn, Qn, n), n); Qn = mulmod64(Qn, Qn, m, n); if(k>>63){ uint64_t uu = addmod64(u, v, n); if(uu&1) uu += n; uu >>= 1; v = addmod64(mulmod64(D,u,m,n), v, n); if(v&1) v += n; v >>= 1; u = uu; Qn = mulmod64(Qn, Q, m, n); } } if(u == 0 || v == 0) return 1; uint64_t x = (n+1) & ~n; for(x>>=1;x;x>>=1){ u = mulmod64(u,v,m,n); v = submod64(mulmod64(v,v,m,n), addmod64(Qn, Qn, n), n); if(v == 0) return 1; Qn = mulmod64(Qn, Qn, m, n); } } return 0; } int is_prime(uint64_t n){ if(n <= 1) return 0; if(n <= 3) return 1; if(!(n & 1)) return 0; if(n < (1LL << 32)) return is_prime32(n); return is_prime64(n); } uint32_t is_square(uint64_t n){ if((0xfffdffeffdfefdecULL >> (n & 0x3F)) & 1) return 0; uint32_t k = round(sqrt(n)); if(k * k == n) return k; else return 0; } uint32_t is_cubic(uint64_t n){ if((0xfffffffff7fffefcULL >> (n & 0x3F)) & 1) return 0; uint32_t k = round(cbrt(n)); if(k * k * k == n) return k; else return 0; } int is_oddprimepower64(uint64_t n){ if(n == 1) return 0; if(std::binary_search(vec_pp.begin(), vec_pp.end(), n)) return 1; uint32_t k = is_square(n); if(k){ n = k; k = is_square(n); if(k) return is_prime(k); else return is_prime(n); } k = is_cubic(n); if(k) return is_prime(k); return is_prime(n); } int main(){ int i, q; make_set_pp(); scanf("%d", &q); for(i=0;i=n) puts("No"); else puts("Yes"); } } return 0; }