#pragma GCC target("avx2") #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using namespace atcoder; typedef long long ll; #define rep(i, n) for (int i = 0; i < (int)(n); i++) #define repr(i, n) for (int i = (int)(n) - 1; i >= 0; i--) #define repk(i, k, n) for (int i = k; i < (int)(n); i++) #define all(v) v.begin(), v.end() #define mod1 1000000007 #define mod2 998244353 #define mod3 100000007 #define vi vector #define vs vector #define vc vector #define vl vector #define vb vector #define vvi vector> #define vvc vector> #define vvl vector> #define vvb vector> #define vvvi vector>> #define vvvl vector>> #define pii pair #define pil pair #define pli pair #define pll pair #define vpii vector> #define vpll vector> #define vvpii vector>> #define vvpll vector>> using mint = modint998244353; template void debug(T e){ cerr << e << endl; } template void debug(vector &v){ rep(i, v.size()){ cerr << v[i] << " "; } cerr << endl; } template void debug(vector> &v){ rep(i, v.size()){ rep(j, v[i].size()){ cerr << v[i][j] << " "; } cerr << endl; } } template void debug(vector> &v){ rep(i,v.size()){ cerr << v[i].first << " " << v[i].second << endl; } } template void debug(set &st){ for (auto itr = st.begin(); itr != st.end(); itr++){ cerr << *itr << " "; } cerr << endl; } template void debug(multiset &ms){ for (auto itr = ms.begin(); itr != ms.end(); itr++){ cerr << *itr << " "; } cerr << endl; } template void debug(map &mp){ for (auto itr = mp.begin(); itr != mp.end(); itr++){ cerr << itr->first << " " << itr->second << endl; } } void debug_out(){ cerr << endl; } template void debug_out(Head H, Tail... T){ cerr << H << " "; debug_out(T...); } ll my_pow(ll x, ll n, ll mod){ // 繰り返し二乗法.x^nをmodで割った余り. ll ret; if (n == 0){ ret = 1; } else if (n % 2 == 1){ ret = (x * my_pow((x * x) % mod, n / 2, mod)) % mod; } else{ ret = my_pow((x * x) % mod, n / 2, mod); } return ret; } ll inv(ll x, ll mod){ return my_pow(x, mod - 2, mod); } int my_gcd(int a, int b){ int ret = 0; if (a < b){ swap(a, b); } if (b == 0){ ret = a; } else{ ret = my_gcd(b, a % b); } return ret; } vector> matrix_pow(vector> &M, vector &bin, ll N, ll K, ll mod){ //行列累乗を計算する.M^x % modを計算する.ただし,xは陽には引数をとらない. //M: 行列M.bin: n_adic(x, 2, K)(xの2進数表現).N: 行列Mの大きさ.K: 配列binの長さ.mod: (取る場合は)modの値. vector> matrix(N, vector(N)); for (ll i = 0; i < N; i++) { for (ll j = 0; j < N; j++) { matrix[i][j] = M[i][j]; } } vector> ans_old_matrix(N, vector(N)); for (ll i = 0; i < N; i++) { for (ll j = 0; j < N; j++) { if (i == j) ans_old_matrix[i][j] = 1; else ans_old_matrix[i][j] = 0; } } vector> ans_new_matrix(N, vector(N)); for (ll i = 0; i < N; i++) { for (ll j = 0; j < N; j++) { ans_new_matrix[i][j] = 0; } } vector> new_matrix(N, vector(N)); for (ll i = 0; i < N; i++) { for (ll j = 0; j < N; j++) { new_matrix[i][j] = 0; } } for (ll x = 0; x < K; x++) { if (bin[K - 1 - x] == 1) { for (ll i = 0; i < N; i++) { for (ll j = 0; j < N; j++) { for (ll k = 0; k < N; k++) { ans_new_matrix[i][j] = (ans_new_matrix[i][j] + (ans_old_matrix[i][k] * matrix[k][j])) % mod; } } } for (ll i = 0; i < N; i++) { for (ll j = 0; j < N; j++) { ans_old_matrix[i][j] = ans_new_matrix[i][j]; ans_new_matrix[i][j] = 0; } } } for (ll i = 0; i < N; i++) { for (ll j = 0; j < N; j++) { for (ll k = 0; k < N; k++) { new_matrix[i][j] = (new_matrix[i][j] + (matrix[i][k] * matrix[k][j])) % mod; } } } for (ll i = 0; i < N; i++) { for (ll j = 0; j < N; j++) { matrix[i][j] = new_matrix[i][j]; new_matrix[i][j] = 0; } } } return ans_old_matrix; } int main(){ ll T; cin >> T; vector isprime(3000003, true); for (ll i = 2; i <= 3000000; i++){ if (isprime[i]){ for (ll j = 2; j * i <= 3000000; j++){ isprime[i * j] = false; } } } vector sum(3000003, 0); for (ll i = 2; i <= 3000002; i++){ if (isprime[i]) sum[i] = sum[i - 1] + 1; else sum[i] = sum[i - 1]; } while (T--){ ll N; cin >> N; if (isprime[N]){ cout << 'P' << endl; } else{ ll hn = N / 2; // 選べる整数は,2 以上 hn 以下のすべての整数と,hn + 1 以上 N 以下の素数でない数 ll cnt = (hn - 1); cnt += ((N - hn) - sum[N] - sum[hn]); if (cnt % 2 == 0){ cout << 'K' << endl; } else{ cout << 'P' << endl; } } } }