/* #region Head */ // #include #include #include #include #include // assert.h #include // math.h #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using ll = long long; using ull = unsigned long long; using ld = long double; using pll = pair; template using vc = vector; template using vvc = vc>; using vll = vc; using vvll = vvc; using vld = vc; using vvld = vvc; using vs = vc; using vvs = vvc; template using um = unordered_map; template using pq = priority_queue; template using pqa = priority_queue, greater>; template using us = unordered_set; #define TREP(T, i, m, n) for (T i = (m), i##_len = (T)(n); i < i##_len; ++(i)) #define TREPM(T, i, m, n) for (T i = (m), i##_max = (T)(n); i <= i##_max; ++(i)) #define TREPR(T, i, m, n) for (T i = (m), i##_min = (T)(n); i >= i##_min; --(i)) #define TREPD(T, i, m, n, d) \ for (T i = (m), i##_len = (T)(n); i < i##_len; i += (d)) #define TREPMD(T, i, m, n, d) \ for (T i = (m), i##_max = (T)(n); i <= i##_max; i += (d)) #define REP(i, m, n) for (ll i = (m), i##_len = (ll)(n); i < i##_len; ++(i)) #define REPM(i, m, n) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; ++(i)) #define REPR(i, m, n) for (ll i = (m), i##_min = (ll)(n); i >= i##_min; --(i)) #define REPD(i, m, n, d) \ for (ll i = (m), i##_len = (ll)(n); i < i##_len; i += (d)) #define REPMD(i, m, n, d) \ for (ll i = (m), i##_max = (ll)(n); i <= i##_max; i += (d)) #define REPI(itr, ds) for (auto itr = ds.begin(); itr != ds.end(); itr++) #define REPIR(itr, ds) for (auto itr = ds.rbegin(); itr != ds.rend(); itr++) #define ALL(x) begin(x), end(x) #define SIZE(x) ((ll)(x).size()) #define ISIZE(x) ((int)(x).size()) #define PERM(c) \ sort(ALL(c)); \ for (bool c##p = 1; c##p; c##p = next_permutation(ALL(c))) #define UNIQ(v) v.erase(unique(ALL(v)), v.end()); #define CEIL(a, b) (((a) + (b)-1) / (b)) #define endl '\n' constexpr ll INF = 1'010'000'000'000'000'017LL; constexpr int IINF = 1'000'000'007LL; constexpr ll MOD = 1'000'000'007LL; // 1e9 + 7 // constexpr ll MOD = 998244353; constexpr ld EPS = 1e-12; constexpr ld PI = 3.14159265358979323846; // 前方宣言 template istream &operator>>(istream &is, vc &vec); template ostream &operator<<(ostream &os, const vc &vec); template ostream &operator>>(ostream &os, const vc &vec); template istream &operator>>(istream &is, array &arr); template ostream &operator<<(ostream &os, const array &arr); template ostream &operator>>(ostream &os, const array &arr); template istream &operator>>(istream &is, pair &pair_var); template ostream &operator<<(ostream &os, const pair &pair_var); template ostream &out_iter(ostream &os, const T &map_var); template ostream &operator<<(ostream &os, const map &map_var); template ostream &operator<<(ostream &os, const um &map_var); template ostream &operator<<(ostream &os, const set &set_var); template ostream &operator<<(ostream &os, const us &set_var); template ostream &operator<<(ostream &os, const pq &pq_var); template ostream &operator<<(ostream &os, const queue &queue_var); template ostream &operator<<(ostream &os, const stack &stk_var); template istream &operator>>(istream &is, vc &vec) { // vector 入力 for (T &x : vec) is >> x; return is; } template ostream &operator<<(ostream &os, const vc &vec) { // vector 出力 (for dump) os << "{"; REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "" : ", "); os << "}"; return os; } template ostream &operator>>(ostream &os, const vc &vec) { // vector 出力 (inline) REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "\n" : " "); return os; } template istream &operator>>(istream &is, array &arr) { // array 入力 REP(i, 0, SIZE(arr)) is >> arr[i]; return is; } template ostream &operator<<(ostream &os, const array &arr) { // array 出力 (for dump) os << "{"; REP(i, 0, SIZE(arr)) os << arr[i] << (i == i_len - 1 ? "" : ", "); os << "}"; return os; } template istream &operator>>(istream &is, pair &pair_var) { // pair 入力 is >> pair_var.first >> pair_var.second; return is; } template ostream &operator<<(ostream &os, const pair &pair_var) { // pair 出力 os << "(" << pair_var.first << ", " << pair_var.second << ")"; return os; } // map, um, set, us 出力 template ostream &out_iter(ostream &os, const T &map_var) { os << "{"; REPI(itr, map_var) { os << *itr; auto itrcp = itr; if (++itrcp != map_var.end()) os << ", "; } return os << "}"; } template ostream &operator<<(ostream &os, const map &map_var) { return out_iter(os, map_var); } template ostream &operator<<(ostream &os, const um &map_var) { os << "{"; REPI(itr, map_var) { auto [key, value] = *itr; os << "(" << key << ", " << value << ")"; auto itrcp = itr; if (++itrcp != map_var.end()) os << ", "; } os << "}"; return os; } template ostream &operator<<(ostream &os, const set &set_var) { return out_iter(os, set_var); } template ostream &operator<<(ostream &os, const us &set_var) { return out_iter(os, set_var); } template ostream &operator<<(ostream &os, const pq &pq_var) { pq pq_cp(pq_var); os << "{"; if (!pq_cp.empty()) { os << pq_cp.top(), pq_cp.pop(); while (!pq_cp.empty()) os << ", " << pq_cp.top(), pq_cp.pop(); } return os << "}"; } // tuple 出力 template ostream &operator<<(ostream &os, tuple &a) { if constexpr (N < std::tuple_size_v>) { os << get(a); if constexpr (N + 1 < std::tuple_size_v>) { os << ' '; } else if constexpr (end_line) { os << '\n'; } return operator<< (os, a); } return os; } template void print_tuple(tuple &a) { operator<< <0, true>(std::cout, a); } void pprint() { std::cout << endl; } template void pprint(Head &&head, Tail &&...tail) { std::cout << head; if (sizeof...(Tail) > 0) std::cout << ' '; pprint(move(tail)...); } // dump #define DUMPOUT cerr void dump_func() { DUMPOUT << endl; } template void dump_func(Head &&head, Tail &&...tail) { DUMPOUT << head; if (sizeof...(Tail) > 0) DUMPOUT << ", "; dump_func(move(tail)...); } // chmax (更新「される」かもしれない値が前) template > bool chmax(T &xmax, const U &x, Comp comp = {}) { if (comp(xmax, x)) { xmax = x; return true; } return false; } // chmin (更新「される」かもしれない値が前) template > bool chmin(T &xmin, const U &x, Comp comp = {}) { if (comp(x, xmin)) { xmin = x; return true; } return false; } // ローカル用 #ifndef ONLINE_JUDGE #define DEBUG_ #endif #ifndef MYLOCAL #undef DEBUG_ #endif #ifdef DEBUG_ #define DEB #define dump(...) \ DUMPOUT << " " << string(#__VA_ARGS__) << ": " \ << "[" << to_string(__LINE__) << ":" << __FUNCTION__ << "]" \ << endl \ << " ", \ dump_func(__VA_ARGS__) #else #define DEB if (false) #define dump(...) #endif #define VAR(type, ...) \ type __VA_ARGS__; \ assert((std::cin >> __VA_ARGS__)); template istream &operator,(istream &is, T &rhs) { return is >> rhs; } template ostream &operator,(ostream &os, const T &rhs) { return os << ' ' << rhs; } struct AtCoderInitialize { static constexpr int IOS_PREC = 15; static constexpr bool AUTOFLUSH = false; AtCoderInitialize() { ios_base::sync_with_stdio(false), std::cin.tie(nullptr), std::cout.tie(nullptr); std::cout << fixed << setprecision(IOS_PREC); if (AUTOFLUSH) std::cout << unitbuf; } } ATCODER_INITIALIZE; void Yn(bool p) { std::cout << (p ? "Yes" : "No") << endl; } void YN(bool p) { std::cout << (p ? "YES" : "NO") << endl; } template constexpr void operator--(vc &v, int) noexcept { for (int i = 0; i < ISIZE(v); ++i) v[i]--; } template constexpr void operator++(vc &v, int) noexcept { for (int i = 0; i < ISIZE(v); ++i) v[i]++; } /* #endregion */ // #include // using namespace atcoder; /* #region rho */ // ミラーラビン素数判定法とロー法 - ジョイジョイジョイ // http://joisino.hatenablog.com/entry/2017/08/03/210000 // ポラード・ロー素因数分解法(Pollard's rho algorithm) PKU 2447とか. - おろログ // http://orolog.hatenablog.jp/entry/20100804/1280943541 /* #region miller */ // ミラー・ラビン素数判定法クラス template class Miller { const vc> bases = { {2, 3}, {2, 299417}, {2, 7, 61}, // < 4,759,123,141 {15, 176006322, 4221622697ull}, {2, 2570940, 211991001, 3749873356ull}, {2, 2570940, 880937, 610386380, 4130785767ull}, {2, 325, 9375, 28178, 450775, 9780504, 1795265022ull}}; // x^k (mod m) を返す inline T modpow(T x, T k, const T &m) { T res = 1; while (k) { if (k & 1) res = res * x % m; k /= 2; x = x * x % m; } return res; } // 合成数とわかったら true を返す inline bool is_composite(T n, T a, T s, T d) { if (a == n) return false; if (modpow(a, d, n) != 1) { // a^d mod n != 1 bool composite = true; // for (T r = 0; r < s; ++r) { // [0, s) // の範囲の全ての r について // if (modpow(a, d * ((T)1ull << r), n) == n - 1) { // a^(2^r * // d) mod n != -1 じゃない // composite = false; // break; // } // } a = modpow(a, d, n); if (a == n - 1) return false; // 合成数とは言い切れない for (T r = 1; r < s; ++r) { a = (a * a) % n; // pprint("aa", a); if (a == n - 1) { // a^(2^r * d) mod n != -1 じゃない // dump(n, a, s, d, n - 1); composite = false; break; } } return composite; } return false; // 合成数とは言い切れない } public: // n が素数かどうか判定する bool is_probably_prime(const T &n) { if (n < 2) return false; if (!(n & 1)) return n == 2; if (n <= 8) return true; // base 選択 int x = (n < 1373653ll) ? 0 : // (n < 19471033ll) ? 1 : // (n < 4759123141ll) ? 2 : // (n < 154639673381ll) ? 3 : // (n < 47636622961201ll) ? 4 : // (n < 3770579582154547ll) ? 5 : 6; // // n-1 を 2 の冪乗で割って,2^s * d の形にする T d = n - 1; T s = 0; while (d % 2 == 0) { d /= 2; s++; } // dump(x); for (const T &a : bases[x]) { // [1, n-1] から a を選ぶ if (is_composite(n, a, s, d)) { // dump(n, a, s, d); return false; // 合成数なら false を返す } } return true; // probably prime } }; /* #endregion */ // ポラード・ロー素因数分解法クラス template class Rho { mt19937 mt; Miller miller; T c; // 乱数生成 inline T f(T x, T n) { return ((((x % n) * (x % n)) % n) + (c % n)) % n; } // 合成数 n の自明でない素因数を 1 つ見つける.失敗した場合は -1 を返す. inline T get_factor(T n) { if (n == 4) return 2; c = (T)mt() % n; T x = (T)mt() % n; T y = x; T d = 1; while (d == 1) { x = f(x, n); y = f(f(y, n), n); d = std::gcd(std::abs(x - y), n); } if (d == n) return -1; return d; } public: // コンストラクタ Rho() { mt.seed(clock()); } // n を素因数分解する vc decompose(T n) { if (n <= 1) return {}; if (miller.is_probably_prime(n)) return {n}; // 素数を弾く T res = -1; while (res == -1) res = get_factor(n); vc fa = decompose(res); if (SIZE(fa) >= 4 || (SIZE(fa) >= 3 and (n / res >= 2))) { fa.push_back(n / res); return fa; } vc fb = decompose(n / res); fa.insert(fa.end(), fb.begin(), fb.end()); return fa; } }; /* #endregion */ // Problem void solve() { VAR(ll, q); vll a(q); cin >> a; Rho<> rho; REP(i, 0, q) { vll ans = rho.decompose(a[i]); Yn(SIZE(ans) == 3); } } // entry point int main() { solve(); return 0; }