#if __INCLUDE_LEVEL__ == 0 #include __BASE_FILE__ namespace { using kactl::isprime; constexpr int L = 3'000'000; void solve() { static std::vector v; static std::vector> ds; if (v.empty()) { kactl::eratosthenesSieve(kactl::MAX_PR); v.resize(L + 1); for (const int i : rep1(L)) { v[i] = v[i - 1] + isprime[i]; } ds.resize(L + 1); for (const int d : rep1(L)) { for (int i = d; i <= L; i += d) { ds[i].push_back(d); } } } int n; scan(n); int t = v[n - 1] - v[n / 2]; t = n - t; print("PK"[t & 1]); } } // namespace int main() { std::ios::sync_with_stdio(false); std::cin.tie(nullptr); std::cout << std::setprecision(DBL_DECIMAL_DIG); int t; scan(t); while (t--) { solve(); } } #else // __INCLUDE_LEVEL__ #include // https://github.com/kth-competitive-programming/kactl namespace kactl { using namespace std; #define rep(i, a, b) for (int i = a; i < (b); ++i) typedef long long ll; typedef pair pii; typedef vector vi; const int MAX_PR = 5'000'000; bitset isprime; vi eratosthenesSieve(int lim) { isprime.set(); isprime[0] = isprime[1] = 0; for (int i = 4; i < lim; i += 2) isprime[i] = 0; for (int i = 3; i * i < lim; i += 2) if (isprime[i]) for (int j = i * i; j < lim; j += i * 2) isprime[j] = 0; vi pr; rep(i, 2, lim) if (isprime[i]) pr.push_back(i); return pr; } #undef rep } // namespace kactl template bool chmin(T& x, U&& y) { return y < x && (x = std::forward(y), true); } template bool chmax(T& x, U&& y) { return x < y && (x = std::forward(y), true); } template T inf() { T ret; std::memset(&ret, 0x3f, sizeof(ret)); return ret; } template T inf() { return std::numeric_limits::infinity(); } template concept Range = std::ranges::range && !std::convertible_to; template concept Tuple = std::__is_tuple_like::value && !Range; namespace std { istream& operator>>(istream& is, Range auto&& r) { for (auto&& e : r) { is >> e; } return is; } istream& operator>>(istream& is, Tuple auto&& t) { return apply([&](auto&... xs) -> istream& { return (is >> ... >> xs); }, t); } ostream& operator<<(ostream& os, Range auto&& r) { for (string_view sep = ""; auto&& e : r) { os << exchange(sep, " ") << e; } return os; } ostream& operator<<(ostream& os, Tuple auto&& t) { const auto f = [&](auto&... xs) -> ostream& { [[maybe_unused]] string_view sep = ""; ((os << exchange(sep, " ") << xs), ...); return os; }; return apply(f, t); } } // namespace std void scan(auto&&... xs) { std::cin >> std::tie(xs...); } void print(auto&&... xs) { std::cout << std::tie(xs...) << '\n'; } template class fix { public: explicit fix(F f) : f_(std::move(f)) {} decltype(auto) operator()(auto&&... xs) const { return f_(std::ref(*this), std::forward(xs)...); } private: F f_; }; inline auto rep(int l, int r) { return std::views::iota(std::min(l, r), r); } inline auto rep(int n) { return rep(0, n); } inline auto rep1(int l, int r) { return rep(l, r + 1); } inline auto rep1(int n) { return rep(1, n + 1); } using namespace std::literals; namespace ranges = std::ranges; namespace views = std::views; using i64 = std::int64_t; #endif // __INCLUDE_LEVEL__