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.io.*;
import java.util.*;
import java.math.*;
     
public class Main{
	public static void main(String[] args) throws Exception {
	IO io = new IO();
	PrintWriter out = new PrintWriter(System.out);
	Solver sr = new Solver();
	sr.solve(io,out);
	out.flush();
	out.close();
    	}

	static class Solver
	{
	   void solve(IO io, PrintWriter out)
        {
            int t = io.nextInt();
            while(t-->0)
            {
                long n = io.nextInt();
                int c1=0, c2=0;
                while(n%6==0){
                    n/=6;
                    c1++;
                }
                
                while(n%3==0){
                    n/=3;
                    c2++;
                }
                if(n==1)
                    out.println(c1+2*c2);
                else
                    out.println("-1");
            }
	    }
	}
	//Special thanks to Petr (on codeforces) who inspired me to implement IO class!
	static class IO
	{
    	private static final int BUF_SIZE = 2048;
        BufferedReader br;
        private IO() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }
        private boolean isSpace(char c) {
            return c == '\n' || c == '\r' || c == ' ';
        }
        String next() {
            try {
                StringBuilder sb = new StringBuilder();
                int r;
                while ((r = br.read()) != -1 && isSpace((char) r));
                if (r == -1) {
                    return null;
                }
                sb.append((char) r);
                while ((r = br.read()) != -1 && !isSpace((char) r)) {
                    sb.append((char) r);
                }
                return sb.toString();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return null;
        }
        int nextInt() {
            return Integer.parseInt(next());
        }
        long nextLong() {
            return Long.parseLong(next());
        }
        double nextDouble() {
            return Double.parseDouble(next());
        }
	}
}
/*12339
0
15
54306
999999995
185
999999998*/