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.io.*;
public class m2d6 {
    static class InputReader {
        BufferedReader reader;
        StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        String next() { // reads in the next string
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() { // reads in the next int
            return Integer.parseInt(next());
        }

        public long nextLong() { // reads in the next long
            return Long.parseLong(next());
        }

        public double nextDouble() { // reads in the next double
            return Double.parseDouble(next());
        }
    }
    static PrintWriter pw = new PrintWriter(System.out);
    static InputReader r = new InputReader(System.in);

    public static void main(String[] args){
        int t=r.nextInt();
        for(int i=0; i<t; i++){
            int n=r.nextInt();
            if(goodprimes(n) || n==1){
                int count=0;
                while(n>1){
                    if(n%6==0){
                        n/=6;
                    }
                    else{
                        n*=2;
                    }
                    count++;
                }
                pw.println(count);

            }
            else{
                pw.println(-1);
            }
        }
        pw.close();
    }
    static boolean goodprimes(int n){
        HashMap<Integer, Integer> s = new HashMap<>();
        while(n>1){
            for(int i=2; i<= 4; i++){
                if(i==4){
                    return false;
                }
                if(n%i==0){
                    if(s.containsKey(i)){
                        s.put(i, s.get(i)+1);
                    }
                    else{
                        s.put(i,1);
                    }
                    n/= i;
                    break;
                }
            }
        }
        if(s.size() == 1 && s.containsKey(3)){
            return true;
        }
        if(s.size() == 2){
            if(s.containsKey(2) && s.containsKey(3)){
                int a=s.get(2), b=s.get(3);
                if(a<=b){
                    return true;
                }
            }
        }
        return false;
    }
}

