#include <iostream>
#include <algorithm>
#include <utility>
#include <string>
#include <vector>
#include <set>
#include <stack>
#include <queue>
#include <map>
#include <math.h>
#include <string.h>
#include <iomanip>
#include <numeric>
#include <cstdlib>
#include <cstdint>
#include <cmath>
#include <functional>
#include <limits>
#include <cassert>
#include <bitset>
#include <chrono>
#include <random>
#include <memory>
 
/* macro */
 
#define rep(i, a, n) for (int i = (int)(a); i < (int)(n); i++)
#define rrep(i, a, n) for (int i = ((int)(n-1)); i >= (int)(a); i--)
#define Rep(i, a, n) for (i64 i = (i64)(a); i< (i64)(n); i++)
#define RRep(i, a, n) for (i64 i = ((i64)(n-i64(1))); i>=(i64)(a); i--)
#define all(v) (v).begin(),(v).end()
#define rall(v) (v).rbegin(),(v).rend()
 
/* macro end */
 
/* template */
 
namespace ebi {
 
#ifdef LOCAL
#define debug(...)                                                    \
    std::cerr << "LINE: " << __LINE__ << "  [" << #__VA_ARGS__ << "]:", \
        debug_out(__VA_ARGS__)
#else
#define debug(...)
#endif
 
void debug_out() { std::cerr << std::endl; }
 
template <typename Head, typename... Tail>
void debug_out(Head h, Tail... t) {
    std::cerr << " " << h;
    if (sizeof...(t) > 0) std::cout << " :";
    debug_out(t...);
}
 
template <typename T1, typename T2>
std::ostream& operator<<(std::ostream& os, std::pair<T1, T2> pa) {
    return os << pa.first << " " << pa.second;
}
 
template <typename T>
std::ostream& operator<<(std::ostream& os, std::vector<T> vec) {
    for (std::size_t i = 0; i < vec.size(); i++) os << vec[i] << (i + 1 == vec.size() ? "" : " ");
    return os;
}
 
using size_t = std::size_t;
using i64 = long long;
using u64 = unsigned long long;
 
template<class T> void fill(std::vector<T> &v) { for(T &e: v) std::cin >> e; }
 
template <class T>
inline bool chmin(T &a, T b) {
    if (a > b){
        a = b;
        return true;
    }
    return false;
}
 
template <class T>
inline bool chmax(T &a, T b) {
    if (a < b){
        a = b;
        return true;
    }
    return false;
}
 
template <class T>
T gcd(T a, T b){
    if( b==0 ) return a;
    else return gcd(b, a%b);
}
 
template <class T>
T lcm(T a, T b) {
    return (a*b)/gcd(a,b);
}
 
template<class T>
T Pow(T x, i64 n) {
    T res = 1;
    while(n>0){
        if(n&1) res = res *x;
        x = x*x;
        n>>=1;
    }
    return res;
}
 
template<class T>
T scan() {
    T val;
    std::cin >> val;
    return val;
}
 
constexpr i64 LNF = std::numeric_limits<i64>::max()/4;
 
constexpr int INF = std::numeric_limits<int>::max()/4;
 
const long double PI = acos(-1);
 
const std::vector<int> dy = {1,0,-1,0,1,1,-1,-1};
const std::vector<int> dx = {0,1,0,-1,1,-1,1,-1};
 
}
 
/* template end */


namespace ebi {

using ld = long double;

using P = std::pair<int,int>;

const int p[] = {2,3,5,7,11,13,17,19,23,29,31};

void main_() {
    i64 x;
    std::cin >> x;
    std::vector<int> ret(11,0);
    i64 y = x;
    rep(i,0,11) {
        while(y % p[i] == 0) {
            y /= p[i];
            ret[i]++;
        }
    }
    rep(i,1,32) {
        int val = i;
        std::vector<i64> tmp(2,1), l(11,0);
        rep(j,0,11) {
            while(val % p[j] == 0) {
                val /= p[j];
                l[j]++;
            }
            tmp[0] *= ret[j] + 1;
            tmp[1] *= ret[j] + l[j] + 1;
        }
        if(tmp[0]*2 == tmp[1]) {
            std::cout << x * i << '\n';
            return;
        }
    }
    assert(false);
}
 
}

 
int main() {
    std::cout << std::fixed << std::setprecision(15);
    std::cin.tie(nullptr);
    std::ios::sync_with_stdio(false);
    int t;
    std::cin >> t;
    while(t--) {
        ebi::main_();
    }
    return 0;
}