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

//Bismillahi-r-Rahmani-r-RaHIM
import java.util.*;
import java.io.*;
public class Main{
  public static void main(String[] args)throws IOException{
    Scanner sc = new Scanner(System.in);
    long a,b,c,d,e,f,g;
    a = sc.nextLong();
    for(b = 0;b < a;b++){
      c = sc.nextLong();
      if(c == 1){
        System.out.println("0");
      }else if(c % 3 != 0){
        System.out.println("-1");
      }else{
        d = 0;
        while(c >= 3){
          if(c % 6 == 0){
            c = c/6;
            d++;
          }else{
            c = c*2;
            d++;
          }
        }
        if(c == 1){
          System.out.println(d);
        }else{
          System.out.println("-1");
        }
      }
    }
  }
}