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.*;
import java.io.*;

public class Mul2div6 {
    public static void main(String[] arg) {
        Scanner scan = new Scanner(System.in);
        
        int t = scan.nextInt();
        
        for(int i=0; i<t; i++) {
            int n = scan.nextInt();
            int count2 = 0;
            while(n%2==0){
                n = n/2;
                count2++;
            }
            int count3 = 0;
            while(n%3==0) {
                n = n/3;
                count3++;
            }
            if(n!=1) {
                System.out.println(-1);
            }
            else{
                if(count2==count3){
                    System.out.println(count3);
                }
                else if(count2>count3){
                    System.out.println(-1);
                }
                else{
                    System.out.println(count3-count2+count3);
                }
            }
        }
    }
}

            // int limit = 4*n;
            // int move = 0;
            // while(n!=1 && n<limit) {
            //     if(n%6==0) {
            //         n = n/6;
            //     }
            //     else{
            //         n = n*2;
            //     }
            //     move++;
            //     // System.out.println(n);
            // }
            // if(n>=limit) {
            //     System.out.println(-1);
            // }
            // else{
            //     System.out.println(move);
            // }