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); } }