#include using namespace std; using ll = long long; #ifdef MY_DEBUG #define dbg(var) debug_out(#var, "=", var) #define dbgm(...) debug_out(__VA_ARGS__) #else #define dbg(...) #define dbgm(...) #endif void debug_out(); template void debug_out(Head, Tail...); template bool chmax(T&, const T&); template bool chmin(T&, const T&); template T pwr(T, ll); template T squ(T x) { return x * x; } ll fact(ll); ll comb(ll, ll); ll ctoll(char); char lltoc(ll); bool flg(ll b, ll i) { return ((b) >> (i)) & 1LL; } // flg(0b010, 1LL) -> true const ll LINF = (ll)4e18 + 7; const double EPS = 1e-9; const int MAX_DUBUG_SIZE = 10; unordered_set prime_set(const int N) { vector is_prime(N + 1); for (int i = 0; i <= N; i++) { is_prime[i] = true; } unordered_set P; for (int i = 2; i <= N; i++) { if (is_prime[i]) { for (int j = 2 * i; j <= N; j += i) { is_prime[j] = false; } P.insert(i); } } return P; } // エラトステネスの篩による素数列挙 // 計算量:O(N log log N) vector prime_vector(ll N) { vector is_prime(N + 1, true); is_prime[0] = is_prime[1] = false; vector res; for (ll i = 2; i <= N; i++) { if (is_prime[i]) { for (ll j = 2 * i; j <= N; j += i) { is_prime[j] = false; } res.push_back(i); } } for (auto&& x : res) { x *= 2; } return res; } /* 使い方 vector pv = prime_vector(100); // pv = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, ... } */ auto ps = prime_set(3000000); auto pv = prime_vector(3000000); void solve([[maybe_unused]] int test) { ll n; cin >> n; dbg(pv); if (ps.contains(n)) { cout << 'P' << endl; } else { auto itr1 = upper_bound(pv.begin(), pv.end(), n); // set, mapは map.lower_bound(探したい数字) ll idx1 = itr1 - pv.begin(); // x <= a[idx] となる最小のidx, 存在しない場合は idx = ssize(a) auto itr2 = lower_bound(pv.begin(), pv.end(), 2 * n); // set, mapは map.lower_bound(探したい数字) ll idx2 = itr2 - pv.begin(); // x <= a[idx] となる最小のidx, 存在しない場合は idx = ssize(a) ll ans = (n - 2) - (idx2 - idx1); dbg(test); dbg(n); dbg(ans); dbg(idx1); dbg(idx2); dbg('\n'); if (ans % 2 == 0) { cout << 'P' << endl; } else { cout << 'K' << endl; } } } int main() { cin.tie(nullptr), ios::sync_with_stdio(false); cout << fixed << setprecision(12), cerr << fixed << setprecision(12); int testcase_size = 1; cin >> testcase_size; for (int _t = 0; _t < testcase_size; _t++) { solve(_t); } } /* -----------------------------------MY_FUNCTIONS------------------------------------ */ template ostream& operator<<(ostream& os, const pair& pp); template ostream& operator<<(ostream& os, const vector& V); template ostream& operator<<(ostream& os, const vector>& VV); template ostream& operator<<(ostream& os, const vector>>& VVV); template ostream& operator<<(ostream& os, const set& SS); template ostream& operator<<(ostream& os, const map& MM); void debug_out(); void debug_out_vl(vector V); void debug_out_vvl(vector> VV); template void debug_out(Head H, Tail... T); template ostream& operator<<(ostream& os, const pair& pp) { return os << "{" << pp.first << "," << pp.second << "}"; } template ostream& operator<<(ostream& os, const vector& V) { if (V.empty()) return os << "[]"; os << "["; for (ll i = 0; i < (ll)V.size(); i++) { os << V[i] << (i == int(V.size() - 1) ? "]" : ","); } return os; } template ostream& operator<<(ostream& os, const vector>& VV) { if (VV.empty()) return os << "[[]]"; os << "[" << endl; for (auto&& V : VV) { os << V << endl; } os << "]"; return os; } template ostream& operator<<(ostream& os, const vector>>& VVV) { if (VVV.empty()) return os << "[[[]]]"; os << "[" << endl; int cnt = 0; for (auto&& VV : VVV) { os << cnt++ << VV << endl << endl; } os << "]"; return os; } template ostream& operator<<(ostream& os, const set& SS) { if (SS.empty()) return os << "[]"; os << "["; auto ii = SS.begin(); for (; ii != SS.end(); ii++) os << *ii << (ii == prev(SS.end()) ? "]" : ","); return os; } template ostream& operator<<(ostream& os, const map& MM) { if (MM.empty()) return os << "[{:}]"; os << "["; auto ii = MM.begin(); for (; ii != MM.end(); ii++) os << "{" << ii->first << ":" << ii->second << "}" << (ii == prev(MM.end()) ? "]" : ","); return os; } void debug_out() { cerr << endl; } void debug_out_vl(vector V) { const int MAX_SIZE = min((int)V.size(), MAX_DUBUG_SIZE); cerr << "\033[33m"; if (V.empty()) { cerr << "[]" << endl; return; } cerr << "["; for (int i = 0; i < MAX_SIZE; i++) { if (V[i] == LINF) cerr << "INF"; else cerr << V[i]; if (i == (int)V.size() - 1) cerr << "]" << endl; else if (i == MAX_DUBUG_SIZE - 1) cerr << ",..." << endl; else cerr << ","; } return; } void debug_out_vvl(vector> VV) { cerr << "\033[33m"; if (VV.empty()) { cerr << "[[]]" << endl; return; } cerr << "[" << endl; int MAX_ROW = min((int)VV.size(), MAX_DUBUG_SIZE); for (int i = 0; i < MAX_ROW; i++) { const int MAX_COLUMN = min((int)VV[i].size(), MAX_DUBUG_SIZE); if (VV[i].empty()) { cerr << "[]" << endl; continue; } cerr << "["; for (int j = 0; j < MAX_COLUMN; j++) { if (VV[i][j] == LINF) cerr << "INF"; else cerr << VV[i][j]; if (j == (int)VV[i].size() - 1) cerr << "]" << endl; else if (j == MAX_DUBUG_SIZE - 1) cerr << ",..." << endl; else cerr << ","; } if (i != (int)VV.size() - 1 and i == MAX_DUBUG_SIZE - 1) { cerr << ":\n:\033[m" << endl; return; } } cerr << "]\033[m" << endl; return; } template void debug_out(Head H, Tail... T) { if constexpr (std::is_same_v>) { debug_out_vl(H); } else if constexpr (std::is_same_v>>) { debug_out_vvl(H); } else { cerr << "\033[33m" << H << "\033[m "; } debug_out(T...); } template bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } return false; } template bool chmin(T& a, const T& b) { if (b < a) { a = b; return true; } return false; } template T pwr(T x, ll n) { T res = 1; for (int i = 0; i < n; i++) { res *= x; } return res; } ll fact(ll n) { ll res = 1; for (ll i = 1; i <= n; i++) res *= i; return res; } ll comb(ll n, ll r) { // comb(60, 30)までオーバーフローなし ll res = 1; for (int i = 1; i <= r; i++) { res *= n--; res /= i; } return res; } ll ctoll(char c) { if (c < '0' or '9' < c) { cerr << "\n\033[33m ctoll に '0'~'9' 以外の文字が入りました.\033[m\n" << endl; } return ll(c - '0'); } char lltoc(ll n) { if (n < 0 or 9 < n) { cerr << "\n\033[33m lltoc に 0 ~ 9 以外の数字が入りました.\033[m\n" << endl; } return char(n + '0'); }