#include #define REP_(i, a_, b_, a, b, ...) \ for (int i = (a), END_##i = (b); i < END_##i; ++i) #define REP(i, ...) REP_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__) #define ALL(x) std::begin(x), std::end(x) using i64 = long long; template inline bool chmax(T &a, U b) { return a < b and ((a = std::move(b)), true); } template inline bool chmin(T &a, U b) { return a > b and ((a = std::move(b)), true); } template inline int ssize(const T &a) { return (int) std::size(a); } template std::istream &operator>>(std::istream &is, std::vector &a) { for (auto &x: a) is >> x; return is; } template std::ostream &operator<<(std::ostream &os, const std::pair &a) { return os << "(" << a.first << ", " << a.second << ")"; } template std::ostream &print_seq(const Container &a, std::string_view sep = " ", std::string_view ends = "\n", std::ostream &os = std::cout) { auto b = std::begin(a), e = std::end(a); for (auto it = std::begin(a); it != e; ++it) { if (it != b) os << sep; os << *it; } return os << ends; } template struct is_iterable : std::false_type {}; template struct is_iterable())), decltype(std::end(std::declval()))>> : std::true_type { }; template::value && !std::is_same::value && !std::is_same::value>> std::ostream &operator<<(std::ostream &os, const T &a) { return print_seq(a, ", ", "", (os << "{")) << "}"; } void print() { std::cout << "\n"; } template void print(const T &x) { std::cout << x << "\n"; } template void print(const Head &head, Tail... tail) { std::cout << head << " "; print(tail...); } struct Input { template operator T() const { T x; std::cin >> x; return x; } } in; #ifdef MY_DEBUG #include "debug_dump.hpp" #else #define DUMP(...) #endif using namespace std; struct PrimeSieve { std::vector spf; // smallest prime factors table. std::vector primes; explicit PrimeSieve(int n) : spf(n + 1) { // O(n) for (int i = 2; i <= n; ++i) { if (spf[i] == 0) { spf[i] = i; primes.push_back(i); } for (const auto &p: primes) { if (i * p > n or p > spf[i]) break; spf[i * p] = p; } } } inline bool is_prime(int n) const { return spf[n] == n; } // Möbius function. int moebius(int n) const { assert(0 < n and n < int(spf.size())); int res = 1; while (n > 1) { const int p = spf[n]; n /= p; if (n % p == 0) return 0; res *= -1; } return res; } }; template i64 bisect(i64 true_x, i64 false_x, F pred) { static_assert(std::is_invocable_r_v, "F must be: i64 -> bool"); assert(std::max(true_x, false_x) <= std::numeric_limits::max() / 2); // To allow negative values, use floor_div() in the loop. assert(true_x >= -1 and false_x >= -1); using u64 = unsigned long long; while (std::abs(true_x - false_x) > 1) { i64 mid = ((u64) true_x + (u64) false_x) / 2; if (pred(mid)) { true_x = std::move(mid); } else { false_x = std::move(mid); } } return true_x; } #include using i128 = boost::multiprecision::checked_int128_t; auto main() -> int { ios_base::sync_with_stdio(false), cin.tie(nullptr); const PrimeSieve sieve(64); auto f = [&](i64 x) -> i64 { i64 cnt = 0; for (i64 i = 2; i < 64; ++i) { const int mu = sieve.moebius(i); if (mu == 0) continue; i64 ymax = bisect(1, x + 1, [&](i64 y) -> bool { i128 yp = 1; REP(j, i) { yp *= y; if (yp > x) return false; } return yp <= x; }); cnt += -mu * (ymax - 1); } return cnt + 1; }; auto solve = [&]() -> i64 { const i64 K = in; return bisect(K * K, 0LL, [&](i64 x) { return f(x) >= K; }); }; const int t = in; REP(test_case, t) { auto ans = solve(); print(ans); } }