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 Main {
    public static void main(String[] args) {
        
        Scanner sc = new Scanner(System.in);
        
        int t = sc.nextInt();
        
        while(t-- > 0) {
            int n = sc.nextInt();
            int count2 = 0;
            int count3 = 0;
            
            boolean possible = true;
            
            while(n>0) {
                if(n == 1) {
                    break;  
                } else if(n%2 == 0) {
                    count2++;
                    n/=2;
                } else if(n%3 == 0) {
                    count3++;
                    n/=3;
                } else {
                    possible = false;
                    break;
                }
            }
            
            if(possible) {
                int b = count3;
                int a = b - count2;
                
                if(a <0 || b <0) {
                    System.out.println(-1);
                } else {
                    System.out.println(a+b);
                }
            } else {
                System.out.println(-1);
            }
        }
    }
}