#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
long long calc(long long n) {
	vector<long long> x;
	for (long long i = 2; i*i <= n; i++) {
		int c = 0;
		while (n%i == 0) { // 素数で割り切れなくなるまで割っていく
			c++;//割った個数を配列に足す
			n /= i;
		}
		if (0 != c) x.push_back(c);
		if (1 == n) break;
	}
	if (1 != n) x.push_back(1);

	long long nAns = 1;
	for (long long n = 0; n < x.size(); ++n) nAns *= x[n] + 1;
	return nAns;
}
vector<long long>p = { 2,3,5,7,11,13,17,19,23,29,31 };
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;
				int copyx = x;
				while (0 == copyx % p[j]) {
					c++;
					copyx /= p[j];
				}
				yc /= c + 1;
				int 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;
}