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.util.ArrayList;
import java.math.BigInteger; 
 
public class Main{   
     static class Pair{
     int x;
     int y;
       Pair(){
       
       }
       Pair(int x,int y){
       this.x=x;
       this.y=y;
       }
     }
    
 
    public static void main(String[] args)
    {
    Scanner param = new Scanner(System.in);
    
    int end=param.nextInt();
    c:while(end-->0)
    {   
        

      long x=param.nextLong();
      int count=0;
      if(x==1){System.out.println(0);
      continue c;}
      
      while(x%6==0)
      {
          count++;
          x/=6;
      }
      if(x%3!=0)
      {
          System.out.println(-1);
          continue c;
      }
      while(x!=1)
      {
          x*=2;
          count++;
          x/=6;
          count++;
          if(x%3!=0&&x!=1)
          {
              System.out.println(-1);
              continue c;
          }
          
      }
      System.out.println(count);
      
}
}
}
