#include "bits/stdc++.h"
//#include "atcoder/all"
using namespace std;
//using namespace atcoder;
//using mint = modint1000000007;
//const int mod = 1000000007;
//using mint = modint998244353;
//const int mod = 998244353;
//const int INF = 1e9;
//const long long LINF = 1e18;
//const bool debug = false;
#define rep(i, n) for (int i = 0; i < (n); ++i)
#define rep2(i,l,r)for(int i=(l);i<(r);++i)
#define rrep(i, n) for (int i = (n-1); i >= 0; --i)
#define rrep2(i,l,r)for(int i=(r-1);i>=(l);--i)
#define all(x) (x).begin(),(x).end()
#define allR(x) (x).rbegin(),(x).rend()
#define endl "\n"
#define P pair<int,int>
template<typename A, typename B> inline bool chmax(A & a, const B & b) { if (a < b) { a = b; return true; } return false; }
template<typename A, typename B> inline bool chmin(A & a, const B & b) { if (a > b) { a = b; return true; } return false; }
//約数の個数
vector<long long>p = { 2,3,5,7,11,13,17,19,23,29,31 };
long long calc(long long n) {
	long long ret = 1;
	rep(i, p.size()) {
		long long c = 0;
		while (0==n%p[i]) {
			c++;
			n /= p[i];
		}
		ret *= c + 1;
	}
	return ret;
}
int main() {
	ios::sync_with_stdio(false);
	cin.tie(nullptr);
	int t; cin >> t;
	while (t--) {
		long long x; cin >> x;
		long long idx;
		rep(i, p.size()) {
			if (0 != x % p[i]) {
				idx = i;
				break;
			}
		}
		long long xc = calc(x);
		rep2(i, 2, p[idx] + 1) {
			long long yc = xc;
			rep(j, p.size()) {
				long long c = 0;
				long long copyx = x;
				while (0 == copyx % p[j]) {
					c++;
					copyx /= p[j];
				}
				yc /= c + 1;
				long long copyi = i;
				while (0 == copyi % p[j]) {
					c++;
					copyi /= p[j];
				}
				yc *= c + 1;
			}
			if (yc == xc * 2) {
				cout << x * i << endl;
				break;
			}
		}
	}
	return 0;
}