// yukicoder: No.577 Prime Powerful Numbers // 2019.5.16 bal4u #include #include #include typedef long long ll; typedef unsigned long long ull; // 高速入力(入力データ数が少ないので、使わなくても問題なさそう) #if 1 #define gc() getchar_unlocked() #define pc(c) putchar_unlocked(c) #else #define gc() getchar() #define pc(c) putchar(c) #endif ll in() { ll n = 0; int c = gc(); while (isspace(c)) c = gc(); do n = 10 * n + (c & 0xf); while ((c = gc()) >= '0'); return n; } void outs(char *s) { while (*s) pc(*s++); } // 数値のハッシュ関数。素数のべき乗を登録しておく #define HASHSIZ 19997 ll hash[HASHSIZ+5], *hashend = hash + HASHSIZ; int lookup(ll n) { ll *p = hash + (int)(n % HASHSIZ); while (*p) { if (*p == n) return 1; if (++p == hashend) p = hash; } return 0; } void insert(ll n) { ll *p = hash + (int)(n % HASHSIZ); while (*p) { if (*p == n) return; if (++p == hashend) p = hash; } *p = n; } #define INF 1000000000000000000LL // 10^18 int ptbl[] = { 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 0 }; int yes[11] = {0,0,0,0,1,1,1,1,1,1,1}; char *msg[] = { "No\n", "Yes\n" }; void init() { int i, b; ll a; for (i = 0; b = ptbl[i]; i++) { a = b; while (a > 0 && a < INF) insert(a), a *= b; } } //// ラビン素数テスト #define mulmod128(a,b,n) ((__int128_t)a*b % n) ull powmod(ull a, ull k, ull n) { ull bit = 0x2000000000000000LL, p = 1; while (bit) { if (p > 1) p = mulmod128(p, p, n); if (k & bit) p = mulmod128(p, a, n); bit >>= 1; } return p; } unsigned xorshift(int id) { static unsigned y = 2463534242; y = y ^ (y << 13), y = y ^ (y >> 17), y = y ^ (y << 5); return y; } ull gcd(ull a, ull b) { ull r; while (b != 0) r = a % b, a = b, b = r; return a; } int suspect(ull n) { int i, j, b; ull t, u, x; u = n-1, t = 0; while ((u & 1) == 0) u >>= 1, t++; for (j = 0; j < 6; j++) { do b = xorshift(j) % n; while (gcd(b, n) > 1); x = powmod(b, u, n); if (x == 1 || x == n-1) continue; for (i = 1; i < t; i++) { x = mulmod128(x, x, n); if (x == 1) return 0; if (x == n-1) break; } if (i == t) return 0; } return 1; } int miller_rabin(ull n) { if (n <= 1) return 0; if (n == 2 || n == 3) return 1; if ((n & 1) == 0) return 0; return suspect(n); } int main() { int i, Q; ll N, a; init(); Q = (int)in(); while (Q--) { N = in(); if (N <= 10) outs(msg[yes[N]]); else if ((N & 1) == 0) outs(msg[1]); else { for (i = 1; i <= 59; i++) { a = N - (1LL << i); if (a <= 0) { i = 60; break; } if (lookup(a)) break; if (miller_rabin(a)) break; } outs(msg[i <= 59]); } } return 0; }