#include "bits/stdc++.h" using namespace std; int q; class Rho { long long int mult(long long int A, long long int B, long long int n) { if (B == 0LL) { return 0; } long long int u = mult(A, B >> 1LL, n); u <<= 1LL; if (u >= n)u %= n; if (B & 1LL)u += A; if (u >= n)u %= n; return u; } long long int f(long long int x, long long int mod) { x %= mod; x = mult(x, x, mod); x += 1; x %= mod; return x; } long long int gcd(long long int a, long long int b) { if (a > b)swap(a, b); while (a) { swap(a, b); a %= b; } return b; } public: long long int find(long long int n) { srand(time(NULL)); long long int x = f(rand() % n, n); long long int y = f(f(x, n), n); while (1) { long long int ab = x - y; if (ab < 0)ab = -ab; long long int gc = gcd(ab, n); if (gc == n)return -1LL; if (gc == 1LL) { x = f(x, n); y = f(f(y, n), n); continue; } return gc; } } }; Rho rrr; bool ok(long long int val, int j) { long long int r = 1; while (j--) { r *= val; if (r > val) { return false; } } if (r > val) { return false; } return true; } long long int sq(long long int w,int j) { if (j == 1) { return w; } if (j == 2) { return sqrt(w); } return -1; } long long int pp(long long int w, int j) { long long int r = 1; while (j--) { r *= w; } return r; } vector primes; vector smallestPrimeFactor; void linearSieve(int n) { if (n < 1) n = 1; if ((int)smallestPrimeFactor.size() >= n + 1) return; int primePiBound = n < 20 ? n - 1 : (int)(n / (log(n * 1.) - 2) + 2); primes.assign(primePiBound + 1, numeric_limits::max()); int P = 0; smallestPrimeFactor.assign(n + 1, 0); smallestPrimeFactor[1] = 1; int n2 = n / 2, n3 = n / 3, n5 = n / 5; if (n >= 2) primes[P++] = 2; if (n >= 3) primes[P++] = 3; for (int q = 2; q <= n; q += 2) smallestPrimeFactor[q] = 2; for (int q = 3; q <= n; q += 6) smallestPrimeFactor[q] = 3; for (int q = 5; q <= n5; q += 2) { if (smallestPrimeFactor[q] == 0) primes[P++] = smallestPrimeFactor[q] = q; int bound = smallestPrimeFactor[q]; for (int i = 2; ; ++i) { int p = primes[i]; if (p > bound) break; int pq = p * q; if (pq > n) break; smallestPrimeFactor[pq] = p; } } for (int q = (n5 + 1) | 1; q <= n; q += 2) { if (smallestPrimeFactor[q] == 0) primes[P++] = smallestPrimeFactor[q] = q; } primes.resize(P); } typedef int FactorsInt; typedef vector > Factors; void primeFactors(FactorsInt x, Factors &out_v) { linearSieve(x); out_v.clear(); while (x != 1) { int p = smallestPrimeFactor[x], k = 0; x /= p, k++; while (x % p == 0) x /= p, k++; out_v.push_back(make_pair(p, k)); } } void divisors(int num, vector &v) { Factors pf; primeFactors(num, pf); queue > stk; stk.push(make_pair(1, 0)); while (!stk.empty()) { pair f = stk.front(); stk.pop(); if (f.second == pf.size()) { continue; } int cur = f.first; stk.push(make_pair(f.first, f.second + 1)); for (int i = 1; i <= pf[f.second].second; i++) { cur *= pf[f.second].first; v.push_back(cur); stk.push(make_pair(cur, f.second + 1)); } } v.push_back(1); } unordered_set s; bool pr[1000002]; bool isprime(long long int val) { for (int i = 0; i < primes.size() && primes[i] * primes[i] <= val; i++) { if (val%primes[i] == 0) { return false; } } return true; } struct Miller { const vector v = { 2 , 7 , 61 }; // < 4,759,123,141 // x^k (mod m) long long modpow(long long x, long long k, long long m) { long long res = 1; while (k) { if (k & 1) { res = res * x % m; } k /= 2; x = x * x % m; } return res; } // check if n is prime bool check(long long n) { if (n < 2) { return false; } long long d = n - 1; long long s = 0; while (d % 2 == 0) { d /= 2; s++; } for (long long a : v) { if (a == n) { return true; } if (modpow(a, d, n) != 1) { bool ok = true; for (long long r = 0; r < s; r++) { if (modpow(a, d * (1LL << r), n) == n - 1) { ok = false; break; } } if (ok) { return false; } } } return true; } }; Miller miller; int main() { linearSieve(1000002); for (int i = 0; i < primes.size(); i++) { pr[primes[i]] = true; long long int val = 1; while (val <= 1000000000000000000LL) { s.insert(val); long long int pp2 = val; val *= primes[i]; if (val / primes[i] != pp2) { break; } } } s.erase(1); cin >> q; while (q--) { long long int n; scanf("%lld", &n); if (n <= 2) { puts("No"); continue; } if (n % 2 == 0LL) { puts("Yes"); continue; } long long int r = 2; bool ok = false; while (r <= n&&r>=0) { long long int rest = n - r; if (rest <= 1) { break; } if (s.count(rest)) { ok = true; break; } for (int j = 2; j >= 1; j--) { long long int k = sq(rest, j); if (k <= 1)continue; if (pp(k, j) == rest) { j = 0; if (k <= 1000000 && pr[k]) { ok = true; break; } else { if (k <= 1000000 && pr[k] == false) { continue; } } if (isprime(k)==false) { continue; } if (k <= 1000000000000LL) { ok = true; break; } if (miller.check(k)) { ok = true; break; } //return 1; } } if (ok) { break; } r *= 2LL; } if (ok) { puts("Yes"); } else { puts("No"); } } return 0; }