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.util.ArrayList;
import java.util.Scanner;
import java.util.Stack;
import java.util.stream.IntStream;

public class Main {
    public static boolean IsSorted(int []arr,int index) {
        for (int i = 1; i <= index; i++) {
            if(arr[i]<arr[i-1]){
                return false;
            }
        }
        return true;
    }
    public static Integer[] sorter(int []x) {
        ArrayList<Integer> sorted=new ArrayList<>();
        sorted.add(0, x[0]);
    for (int i = 1; i < x.length; i++) {
        boolean added=false;
        for (int j = 0; j < sorted.size(); j++) {
            if(x[i]<=sorted.get(j)){
                sorted.add(j, x[i]);
                added=true;
                break;
            }
        }
        if(!added)sorted.add(x[i]);
    }        
        
        return sorted.toArray(new Integer [0]);
    }
    public static Integer[] sorter(Integer []x) {
        ArrayList<Integer> sorted=new ArrayList<>();
        sorted.add(0, x[0]);
    for (int i = 1; i < x.length; i++) {
        boolean added=false;
        for (int j = 0; j < sorted.size(); j++) {
            if(x[i]<=sorted.get(j)){//ascending
                sorted.add(j, x[i]);
                added=true;
                break;
            }
        }
        if(!added)sorted.add(x[i]);
    }        
        
        return sorted.toArray(new Integer [0]);
    }
    public static int methos(int n) {
        int no_of2=0;
        while(n%2==0){
            n=n/2;
            no_of2++;
        }
        double log=Math.log10(n)/Math.log10(3);
        if(log%1!=0 || no_of2>log)
        {
            return -1;            
        }
        return (int) (2 * log - no_of2);
    }

    public static void main(String[] args) {
        Scanner obj = new Scanner(System.in);
        int test=obj.nextInt();
        while(test-->0){
        int n=obj.nextInt();
       System.out.println(methos(n));
        }
    }
}