using System;
using static System.Console;
using System.Linq;
using System.Collections.Generic;

class Program
{
    static int NN => int.Parse(ReadLine());
    static int[] NList => ReadLine().Split().Select(int.Parse).ToArray();
    public static void Main()
    {
        Solve();
    }
    static void Solve()
    {
        var t = NN;
        var ans = new long[t];
        for (var u = 0; u < t; ++u)
        {
            var x = long.Parse(ReadLine());
            ans[u] = Mul(x);
        }
        WriteLine(string.Join("\n", ans));
    }
    static long Mul(long x)
    {
        var plist = new int[] { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31 };
        var countb = Enumerable.Repeat(1, plist.Length).ToArray();
        for (var i = 0; i < plist.Length; ++i)
        {
            var xi = x;
            while (xi % plist[i] == 0)
            {
                ++countb[i];
                xi /= plist[i];
            }
        }
        var allb = 1;
        foreach (var c in countb) allb *= c;
        for (var m = 2; m <= 31; ++m)
        {
            var count = (int[]) countb.Clone();
            var tmp = m;
            for (var i = 0; i < plist.Length; ++i)
            {
                while (tmp % plist[i] == 0)
                {
                    ++count[i];
                    tmp /= plist[i];
                }
            }
            var all = 1;
            foreach (var c in count) all *= c;
            if (allb * 2 == all) return x * m;
        }
        return -1;
    }
}