#include <bits/stdc++.h>

using i32 = std::int32_t;
using u32 = std::uint32_t;
using i64 = std::int64_t;
using u64 = std::uint64_t;
using i128 = __int128_t;
using u128 = __uint128_t;
using isize = std::ptrdiff_t;
using usize = std::size_t;

class rep {
    struct Iter {
        usize itr;
        constexpr Iter(const usize pos) noexcept : itr(pos) {}
        constexpr void operator++() noexcept { ++itr; }
        constexpr bool operator!=(const Iter& other) const noexcept { return itr != other.itr; }
        constexpr usize operator*() const noexcept { return itr; }
    };
    const Iter first, last;

  public:
    explicit constexpr rep(const usize first, const usize last) noexcept : first(first), last(std::max(first, last)) {}
    constexpr Iter begin() const noexcept { return first; }
    constexpr Iter end() const noexcept { return last; }
};

template <class T> std::vector<std::pair<T, usize>> factorize(T x) {
    assert(x > 0);
    std::vector<std::pair<T, usize>> ret;
    for (T i = 2; i * i <= x; ++i) {
        if (x % i == 0) {
            ret.emplace_back(i, 0);
            while (x % i == 0) {
                ret.back().second++;
                x /= i;
            }
        }
    }
    if (x > 1) {
        ret.emplace_back(x, 1);
    }
    return ret;
}

template <class T> using Vec = std::vector<T>;

void main_() {
    static std::array<Vec<std::pair<u32, usize>>, 32> fact;
    static bool first = true;
    if (first) {
        for (const u32 i : rep(2, 32)) {
            fact[i] = factorize(i);
        }
        first = false;
    }
    u64 X;
    std::cin >> X;
    for (const auto i : rep(2, 32)) {
        u64 x = 1, y = 1;
        u64 cur = X;
        for (const auto& [p, e] : fact[i]) {
            usize cnt = 0;
            while (cur % p == 0) {
                cnt += 1;
                cur /= p;
            }
            x *= (cnt + e + 1);
            y *= (cnt + 1);
        }
        if (x == 2 * y) {
            std::cout << X * i << '\n';
            return;
        }
    }
}

int main() {
    std::ios_base::sync_with_stdio(false);
    std::cin.tie(nullptr);
    usize cases;
    std::cin >> cases;
    while (cases--) main_();
    return 0;
}