#include<bits/stdc++.h>

using namespace std;

using int64 = long long;
// const int mod = 1e9 + 7;
const int mod = 31607;

const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;

struct IoSetup {
  IoSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
  }
} iosetup;


template< typename T1, typename T2 >
ostream &operator<<(ostream &os, const pair< T1, T2 > &p) {
  os << p.first << " " << p.second;
  return os;
}

template< typename T1, typename T2 >
istream &operator>>(istream &is, pair< T1, T2 > &p) {
  is >> p.first >> p.second;
  return is;
}

template< typename T >
ostream &operator<<(ostream &os, const vector< T > &v) {
  for(int i = 0; i < (int) v.size(); i++) {
    os << v[i] << (i + 1 != v.size() ? " " : "");
  }
  return os;
}

template< typename T >
istream &operator>>(istream &is, vector< T > &v) {
  for(T &in : v) is >> in;
  return is;
}

template< typename T1, typename T2 >
inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); }

template< typename T1, typename T2 >
inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); }

template< typename T = int64 >
vector< T > make_v(size_t a) {
  return vector< T >(a);
}

template< typename T, typename... Ts >
auto make_v(size_t a, Ts... ts) {
  return vector< decltype(make_v< T >(ts...)) >(a, make_v< T >(ts...));
}

template< typename T, typename V >
typename enable_if< is_class< T >::value == 0 >::type fill_v(T &t, const V &v) {
  t = v;
}

template< typename T, typename V >
typename enable_if< is_class< T >::value != 0 >::type fill_v(T &t, const V &v) {
  for(auto &e : t) fill_v(e, v);
}

template< typename F >
struct FixPoint : F {
  FixPoint(F &&f) : F(forward< F >(f)) {}

  template< typename... Args >
  decltype(auto) operator()(Args &&... args) const {
    return F::operator()(*this, forward< Args >(args)...);
  }
};

template< typename F >
inline decltype(auto) MFP(F &&f) {
  return FixPoint< F >{forward< F >(f)};
}

void beet() {
  int64 X;
  cin >> X;
  int64 Y = X;
  vector< pair< int, int > > d;
  vector< int > p;
  for(int i = 2; i <= 30; i++) {
    bool f = false;
    for(auto j : p) {
      if(i % j == 0) {
        f = true;
        break;
      }
    }
    if(not f) {
      p.emplace_back(i);
      int cnt = 0;
      while(X % i == 0) {
        ++cnt;
        X /= i;
      }
      d.emplace_back(i, cnt);
    }
  }
  int64 mul = 1;
  for(auto &[q, p] : d) {
    mul *= (p + 1);
  }
  int64 ret = infll;
  for(int i = 0; i < d.size(); i++) {
    for(int j = i; j < d.size(); j++) {
      for(int k = j; k < d.size(); k++) {
        for(int l = k; l < d.size(); l++) {

          ++d[i].second;
          ++d[j].second;
          ++d[k].second;
          ++d[l].second;
          int64 mul2 = 1;
          for(auto&[q, p]: d) {
            mul2 *= p + 1;
          }
          if(mul * 2 == mul2) {
            chmin(ret, d[i].first * d[j].first * d[k].first * d[l].first);
          }
          --d[i].second;
          --d[j].second;
          --d[k].second;
          --d[l].second;
        }
        ++d[i].second;
        ++d[j].second;
        ++d[k].second;
        int64 mul2 = 1;
        for(auto&[q, p]: d) {
          mul2 *= p + 1;
        }
        if(mul * 2 == mul2) {
          chmin(ret, d[i].first * d[j].first * d[k].first);
        }
        --d[i].second;
        --d[j].second;
        --d[k].second;
      }

      {
        ++d[i].second;
        ++d[j].second;
        int64 mul2 = 1;
        for(auto&[q, p]: d) {
          mul2 *= p + 1;
        }
        if(mul * 2 == mul2) {
          chmin(ret, d[i].first * d[j].first);
        }
        --d[i].second;
        --d[j].second;
      }
    }
    {
      ++d[i].second;
      int64 mul2 = 1;
      for(auto&[q, p]: d) {
        mul2 *= p + 1;
      }
      if(mul * 2 == mul2) {
        chmin(ret, d[i].first);
      }
      --d[i].second;
    }
  }
  cout << Y * ret << "\n";
}

int main() {
  int T;
  cin >> T;
  while(T--) beet();
}