#include <algorithm>
#include <cassert>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <iostream>
#include <tuple>
#include <vector>
#include <map>
#include <set>
#include <queue>
#include <ranges>
#include <iomanip>
using namespace std;
using ll = long long;

auto range(int n) { return views::iota(0, n); }

template<class T, class U> ostream& operator<<(ostream& os, const pair<T, U>& p){ return os << "{" << p.first << ", " << p.second << "}"; }
template<typename T> ostream& operator<<(ostream& os, const vector<T>& obj) { os << "{"; for (const auto& e : obj) os << e << ", "; return os << "}"; }
template<typename T> ostream& operator<<(ostream& os, const set<T>& obj) { os << "set{"; for (const auto& e : obj) os << e << ", "; return os << "}"; }
template<typename T, typename U> ostream& operator<<(ostream& os, const map<T, U>& obj) { os << "map{"; for (const auto& e : obj) os << e << ", "; return os << "}"; }

#ifdef ONLINE_JUDGE
#define dump(expr) ;
#else
#define dump(expr) { cerr << "\033[33m#L" << __LINE__ << ": " << expr << "\033[39m" << endl; }
#endif

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

ll prod(vector<ll> ve) {
  ll z = 1;
  for (auto e : ve) z *= e + 1;
  return z;
}

ll ans = 1LL << 60;
bool go(vector<ll> ve, int idx, ll prod0, ll target) {
  ll curr = prod(ve);
  if (curr > target) return false;

  if (idx == (int)vp.size()) {
    if (curr == target) {
      dump(ve << " " << prod0);
      ans = min(prod0, ans);
    }
    return true;
  }

  while (go(ve, idx + 1, prod0, target)) {
    ve[idx]++;
    prod0 *= vp[idx];
  }
  return true;
}

ll solve() {
  ll x; cin >> x;

  ll s = 1;
  vector<ll> ve;
  for (auto p : vp) {
    ll e = 0;
    for (ll y = x; y % p == 0; y /= p) e++, s *= p;
    ve.push_back(e);
  }

  ll t = 2 * prod(ve);

  ans = 1LL << 60;
  go(ve, 0, s, t);

  return x / s * ans;
}

int main() {
  cout << fixed << setprecision(12);
  int T; cin >> T;
  while (T--) cout << solve() << endl;
}