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

//package codeforces._653;

import java.io.*;
import java.util.StringTokenizer;

public class _653_B {

    public static void main (String[] args) throws Exception {

        String s = "7\n" +
                "1\n" +
                "2\n" +
                "3\n" +
                "12\n" +
                "12345\n" +
                "15116544\n" +
                "387420489";

//        br = new BufferedReader(new StringReader(s));
        br = new BufferedReader(new InputStreamReader(System.in));
        bw = new BufferedWriter(new OutputStreamWriter(System.out));

        rl(); int T = nin();

        test:
        for (int t=0; t<T; ++t) {
            rl(); long n=nlo();
            int c2=0, c3=0;
            while (n%2==0) {
                n/=2; ++c2;
            }
            while (n%3==0) {
                n/=3; ++c3;
            }
            if (n!=1 || c2>c3) {
                bw.write(Long.toString(-1));
                bw.newLine();
                continue test;
            }

            bw.write(Long.toString(c3+(c3-c2)));
            bw.newLine();
        }
        bw.flush();
    }

    static BufferedReader br;
    static BufferedWriter bw;
    static StringTokenizer st;
    static void rl() throws Exception{
        st = new StringTokenizer(br.readLine());
    }
    static long nlo(){
        return Long.parseLong(st.nextToken());
    }
    static int nin(){
        return Integer.parseInt(st.nextToken());
    }
    /*private static void te(){
      }*/
    static double ndo(){
        return Double.parseDouble(st.nextToken());
    }
    static char[] nca(){
        return st.nextToken().toCharArray();
    }
    static String nstr(){
        return st.nextToken();
    }
}