#include <iostream>
#include <vector>
#include <string>
#include <algorithm>
using namespace std;
using ll = long long;
using ull = unsigned long long;
#define rep(i,n) for(int i=0; i<(n); i++) 

vector<ll> P = { 2,3,5,7,11,13,17,19,23,29,31,37 };

ll divcnt(const vector<ll>& pp){
  ll ans = 1;
  for(auto a : pp) ans *= a+1;
  return ans;
}
vector<ll> multdiv(const vector<ll>& v, int x){
  auto res = v;
  rep(i,P.size()){
    while(x%P[i] == 0){ x /= P[i]; res[i]++; }
  }
  return move(res);
}



int main(){
  int T; cin >> T;
  while(T--){
    ll V; cin >> V;
    vector<ll> D(P.size());
    ll v = V;
    rep(i,P.size()){
      while(v%P[i] == 0){ v /= P[i]; D[i]++; }
    }
    ll divcnt0 = divcnt(D);
    ll ans = 0;
    for(int m=2; m<=37; m++){
      if(divcnt(multdiv(D,m)) == divcnt0 * 2){
        ans = V * m;
        break;
      }
    }
    cout << ans << "\n";
  }
  return 0;
}

struct ios_do_not_sync{
  ios_do_not_sync(){
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
  }
} ios_do_not_sync_instance;