#include <iostream>
#include <vector>
#include <algorithm>
#include <array>
#include <iterator>
#include <string>
#include <cctype>
#include <cstring>
#include <cstdlib>
#include <cassert>
#include <cmath>
#include <ctime>
#include <iomanip>
#include <numeric>
#include <stack>
#include <queue>
#include <map>
#include <unordered_map>
#include <set>
#include <unordered_set>
#include <bitset>
#include <random>
#include <utility>
#include <functional>
using namespace std;
const int M = 100;
vector<int> primes;
void calc()
{
	vector<int> isp(M + 1,1);
	for(int i = 2;i <= M;i++)
	{
		if(isp[i])
		{
			primes.push_back(i);
			for(int j = i + i;j <= M;j += i)
			{
				isp[j] = 0;
			}
		}
	}
}
const int K = 11;
void Main()
{
	long long X;
	cin >> X;
	vector<int> ex(K);
	for(int i = 0;i < K;i++)
	{
		long long Y = X;
		while(Y % primes[i] == 0)
		{
			Y /= primes[i];
			ex[i]++;
		}
	}
	long long D = 1;
	for(int i = 0;i < K;i++)
	{
		D *= ex[i] + 1;
	}
	long long ans = (long long)1e18;
	auto dfs = [&](auto dfs,int id,int cur) -> void
	{
		if(id == K)
		{
			long long nD = 1;
			int y = cur;
			for(int i = 0;i < K;i++)
			{
				int e = 0;
				while(y % primes[i] == 0)
				{
					y /= primes[i];
					e++;
				}
				nD *= e + ex[i] + 1;
			}
			if(nD == D * 2)
			{
				ans = min(ans,cur * X);
			}
			return;
		}

		for(int i = 0;;i++)
		{
			dfs(dfs,id + 1,cur);
			cur *= primes[id];
			if(cur > primes[K - 1])
			{
				break;
			}
		}
	};
	dfs(dfs,0,1);
	cout << ans << "\n";
}
int main()
{
	ios::sync_with_stdio(false);
	cin.tie(nullptr);
	calc();
	int tt = 1;
	cin >> tt;
	while(tt--) Main();
}