You are given an integer n. In one move, you can either multiply n by two or divide n by 6 (if it is divisible by 6 without the remainder).

Your task is to find the minimum number of moves needed to obtain 1 from n or determine if it's impossible to do that.

You have to answer t independent test cases.

Input

The first line of the input contains one integer t (1 ≤ t ≤ 2 ⋅ 10^4) — the number of test cases. Then t test cases follow. 

The only line of the test case contains one integer n (1 ≤ n ≤ 10^9).

Output

For each test case, print the answer — the minimum number of moves needed to obtain 1 from n if it's possible to do that or -1 if it's impossible to obtain 1 from n.

Example

Input


7
1
2
3
12
12345
15116544
387420489


Output


0
-1
2
-1
-1
12
36

Note

Consider the sixth test case of the example. The answer can be obtained by the following sequence of moves from the given integer 15116544:

  1. Divide by 6 and get 2519424; 
  2. divide by 6 and get 419904; 
  3. divide by 6 and get 69984; 
  4. divide by 6 and get 11664; 
  5. multiply by 2 and get 23328; 
  6. divide by 6 and get 3888; 
  7. divide by 6 and get 648; 
  8. divide by 6 and get 108; 
  9. multiply by 2 and get 216; 
  10. divide by 6 and get 36; 
  11. divide by 6 and get 6; 
  12. divide by 6 and get 1. 
1
999838675

-1

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

public class comp2 {
    static int inp=0;
    public static void main(String[] args) throws IOException {
//        Scanner scan=new Scanner(System.in);
//        int cases=Integer.parseInt(scan.nextLine());
//        for(int i=0; i<cases; i++){
//            StringTokenizer st=new StringTokenizer(scan.nextLine());
//            //k mod x= y, k%x=y
//            int x=Integer.parseInt(st.nextToken());
//            int y=Integer.parseInt(st.nextToken());
//            int n=Integer.parseInt(st.nextToken());
//            int t=n/x;
//            for(int j=0; j<200; j++){
//                if((t-j)*x+y<=n){
//                    System.out.println((t-j)*x+y);
//                    break;
//                }
//            }
//        }
        Scanner scan=new Scanner(System.in);
        int cases=Integer.parseInt(scan.nextLine());
        for(int i=0; i<cases; i++){
            int x=Integer.parseInt(scan.nextLine());
            int a=x/2;
            int b=x/3;
            if(x==1){
                System.out.println(0);
            }else if(a*b==0 || x/(a*b)!=1 || a>b){
                System.out.println("-1");
            }else{
                System.out.println(b-a+((b-a)*2)/6);
            }
        }
    }
//    public static int twos(int n){
//        int count=0;
//        int g=n;
//        while(g%2==0){
//            count++;
//            g=g/2;
//        }
//        int inp=g;
//        return count;
//
//    }
//    public static int threes(int n){
//        int count=0;
//        int g=n;
//        while(g%3==0){
//            count++;
//            g=g/2;
//        }
//        if(g!=1){
//            return -1;
//        }
//        return count;
//    }
}