import java.io.*;
import java.util.*;

class Main
{
    public static void main(String args[])throws Exception
    {
        BufferedReader bu=new BufferedReader(new InputStreamReader(System.in));
        StringBuilder sb=new StringBuilder();

        int N=500000,pr[]=new int[N+1],i,j;
        ArrayList<Integer> p=new ArrayList<>();
        for(i=2;i<=N;i++)
        if(pr[i]==0)
        {
            p.add(i);
            for(j=i;j<=N;j+=i) pr[j]=i;
        }

        int t=Integer.parseInt(bu.readLine());
        while(t-->0)
        {
            long n=Long.parseLong(bu.readLine());
            long sm=-1; int fac=1,c;
            HashMap<Integer,Integer> hm=new HashMap<>();

            for(int x:p)
            if(n%x!=0) {sm=x; break;}
            else
            {
                long y=n; c=0;
                while(y%x==0) {y/=x; c++;}
                fac*=c+1;
                hm.put(x,c);
            }

            i=2;
            while(i<sm)
            {
                int x=i,fa2=fac;
                while(x!=1)
                {
                    int cn=0,pri=pr[x];
                    while(x%pri==0) {x/=pri; cn++;}
                    fa2/=hm.getOrDefault(pri,0)+1;
                    fa2*=cn+1+hm.getOrDefault(pri,0);
                }
                //System.out.println(i+" "+fa2);
                if(fa2==2*fac) {sm=i; break;}
                i++;
            }
            sm*=n;
            sb.append(sm+"\n");
        }
        System.out.print(sb);
    }
}