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.Scanner;

public class Code
{
    static public long gcd(long j,long k)
    {
        if(j%k==0)
        {
            return k;
        }
        return gcd(k,j%k);
    }
    static boolean isPowerOfTwo(int n) 
    { 
        if(n==0) 
            return false; 
        return (int)(Math.ceil((Math.log(n) / Math.log(2)))) ==  (int)(Math.floor(((Math.log(n) / Math.log(2))))); 
    } 
    public static int divisors(int n)
    {
        int cnt=0;
        for (int i = 3; i <= Math.sqrt(n); i = i + 2)
        {
            while (n % i == 0)
            {
                cnt++;
                n = n/i;
                if(cnt==2) break;
            }
        if(cnt==2) 
            break;
        }
        if(n>2)cnt++;
        return cnt; 
    }

    public static void main(String[] args)
    {
        Scanner sc = new Scanner(System.in);
        int t = sc.nextInt();
        while(t-->0)
        {
            int n = sc.nextInt();
            long cnt = 0;
            while(n>1)
            {if(n%6==0){n/=6;cnt++;}
             else if(n%3==0&&n%2!=0){n*=2;cnt++;}
             else{cnt = -1;break;}}
            System.out.println(cnt);
        }
    }
}