#include <iostream>
#include <algorithm>
#include <iomanip>
#include <vector>
#include <queue>
#include <set>
#include <map>
#include <tuple>
#include <cmath>
#include <numeric>
#include <functional>
#include <cassert>

#define debug_value(x) cerr << "line" << __LINE__ << ":<" << __func__ << ">:" << #x << "=" << x << endl;
#define debug(x) cerr << "line" << __LINE__ << ":<" << __func__ << ">:" << x << endl;

template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }

using namespace std;
typedef long long ll;

vector<int> primes = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31};
vector<vector<int>> vs;

void dfs(int prod, int i, vector<int> &v){
    if(!v.empty()){
        vs.push_back(v);
    }
    for(int j = i; j < primes.size(); j++){
        if(prod*primes[j] <= 31) {
            v.push_back(primes[j]);
            dfs(prod*primes[j], j, v);
            v.pop_back();
        }
    }
}

void init(){
    vector<int> v;
    dfs(1, 0, v);
}

bool ok(ll x, vector<int> v){
    ll y = x;
    set<int> st;
    for(int p: v) {
        y *= p;
        st.insert(p);
    }
    ll a = 1;
    ll b = 1;
    for(int p: st){
        int cnt_x = 0, cnt_y = 0;
        while(x%p == 0){
            x /= p;
            cnt_x++;
        }
        while(y%p == 0){
            y /= p;
            cnt_y++;
        }
        a *= cnt_x+1;
        b *= cnt_y+1;
    }
    return a*2 == b;
}

void solve(){
    ll x; cin >> x;
    int ans = 100;
    for(auto v: vs){
        if(ok(x, v)){
            int prod = accumulate(v.begin(), v.end(), 1, [](int a, int b){ return a*b; });
            chmin(ans, prod);
        }
    }
    cout << ans*x << endl;

}

int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout << setprecision(10) << fixed;
    init();
    int t; cin >> t;
    while(t--) solve();
}