// #pragma once

// C
#include <cassert>
#include <cctype>
#include <cfloat>
#include <ciso646>
#include <climits>
#include <csetjmp>
#include <cstdarg>
#include <cstddef>
#include <cstdlib>
#include <cstdint>

// C++
#include <bitset>
#include <complex>
#include <algorithm>
#include <bitset>
#include <functional>
#include <iterator>
#include <limits>
#include <memory>
#include <new>
#include <numeric>
#include <typeinfo>
#include <utility>
#include <array>
#include <atomic>
#include <initializer_list>
#include <ratio>
#include <scoped_allocator>
#include <tuple>
#include <typeindex>
#include <type_traits>

#if _HAS_CXX17
#include <any>
// #include <execution>
#include <optional>
#include <variant>
#include <string_view>
#endif

#if _HAS_CXX20
#include <bit>
#include <compare>
#include <concepts>
#include <numbers>
#include <ranges>
#include <span>
#include <source_location>
#include <version>
#endif

#if _HAS_CXX23
#include <expected>
#include <stdatomic.h>
#if __cpp_impl_coroutine
#include <coroutine>
#endif
#endif

// C
#include <cassert>
#include <cctype>
#include <cerrno>
#include <cfloat>
#include <ciso646>
#include <climits>
#include <clocale>
#include <cmath>
#include <csetjmp>
#include <csignal>
#include <cstdarg>
#include <cstddef>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <cwchar>
#include <cwctype>
#include <ccomplex>
#include <cfenv>
#include <cinttypes>
// #include <cstdalign>
#include <cstdbool>
#include <cstdint>
#include <ctgmath>
#include <cuchar>

// C++
#include <complex>
#include <deque>
#include <exception>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iosfwd>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <locale>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <stdexcept>
#include <streambuf>
#include <string>
#include <typeinfo>
#include <utility>
#include <valarray>
#include <vector>
#include <array>
#include <atomic>
#include <chrono>
#include <codecvt>
#include <condition_variable>
#include <forward_list>
#include <future>
#include <initializer_list>
#include <mutex>
#include <random>
#include <ratio>
#include <regex>
#include <scoped_allocator>
#include <system_error>
#include <thread>
#include <tuple>
#include <typeindex>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <shared_mutex>

#if _HAS_CXX17
#include <any>
#include <charconv>
// #include <execution>
#include <filesystem>
#include <optional>
#include <memory_resource>
#include <variant>
#endif

#if _HAS_CXX20
#include <barrier>
#include <bit>
#include <compare>
#include <concepts>
#include <format>
#include <latch>
#include <numbers>
#include <ranges>
#include <span>
#include <stop_token>
#include <semaphore>
#include <source_location>
#include <syncstream>
#include <version>
#endif

#if _HAS_CXX23
#include <expected>
#include <spanstream>
#if __has_include(<stacktrace>)
#include <stacktrace>
#endif
#include <stdatomic.h>
#include <stdfloat>
#endif
using i64 = long long;
using u64 = unsigned long long;

// https://github.com/Heltion/debug.h/blob/main/debug.h

template <class T, size_t size = std::tuple_size<T>::value> std::string to_debug(T, std::string s = "") requires(not std::ranges::range<T>);
std::string to_debug(auto x) requires requires(std::ostream& os) { os << x; } { return static_cast<std::ostringstream>(std::ostringstream() << x).str(); }
std::string to_debug(std::ranges::range auto x, std::string s = "") requires(not std::is_same_v<decltype(x), std::string>) {
    for (auto xi : x) { s += ", " + to_debug(xi); }
    return "[" + s.substr(s.empty() ? 0 : 2) + "]";
}
template <class T, size_t size> std::string to_debug(T x, std::string s) requires(not std::ranges::range<T>) {
    [&]<size_t... I>(std::index_sequence<I...>) { ((s += ", " + to_debug(get<I>(x))), ...); }(std::make_index_sequence<size>());
    return "(" + s.substr(s.empty() ? 0 : 2) + ")";
}

#define debug(...) std::cerr << __FILE__ ":" << __LINE__ << ": (" #__VA_ARGS__ ") = " << to_debug(std::tuple(__VA_ARGS__)) << "\n"

std::vector<int> minp, primes;

void sieve(int n) {
    minp.assign(n + 1, 0);
    primes.clear();
    
    for (int i = 2; i <= n; i++) {
        if (minp[i] == 0) {
            minp[i] = i;
            primes.push_back(i);
        }
        
        for (auto p : primes) {
            if (i * p > n) {
                break;
            }
            minp[i * p] = p;
            if (p == minp[i]) {
                break;
            }
        }
    }
}

constexpr int N = 30000;
std::vector<long double> ln(N + 1), dp(N + 1);

void solve() {
    int n;
    std::cin >> n;

    std::cout << std::fixed << std::setprecision(8);

    std::cout << dp[n] << '\n';

}

int main() {
    std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
    
    sieve(N);
    for(int i = 1; i <= N; i ++ ) {
        ln[i] = std::log(i);
    }
    
    for(auto e : primes) {
        auto _dp = dp;
        for(int i = e; i <= N; i *= i) {
            for(int j = i; j <= N; j ++ ) {
                dp[j] = std::max(dp[j], _dp[j - i] + ln[i]);
            }
        }
        std::vector<long double>().swap(_dp);
    }
    
    int T = 1;
    std::cin >> T;
    while(T -- ) {
        solve();
    }
    return 0;
}