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.HashMap;
import java.util.Map;
import java.util.StringTokenizer;

public class Solution2 {

    public static void main(String[] args) throws Exception {
        int tc = scan.nextInt();
        for (int i = 0; i < tc; i++) {
            solve();
        }
        out.close();
    }


    private static void solve() {
        int n = scan.nextInt();
        int res = solve(n, new HashMap<>());
        out.println(res == Integer.MAX_VALUE ? -1 : res);
    }

    static int solve(int n, Map<Integer, Integer> cache) {
        if (n == 1) return 0;
        if (n % 3 != 0) {
            return Integer.MAX_VALUE;
        }
        if (cache.containsKey(n)) return cache.get(n);
        int output = Integer.MAX_VALUE;
        if (n % 6 == 0) {
            output = Math.min(output, solve(n / 6, cache));
        }
        output = Math.min(output, solve(n * 2, cache));
        if (output < Integer.MAX_VALUE) {
            output++;
        }
        cache.put(n, output);
        return output;
    }

    //-----------PrintWriter for faster output---------------------------------
    public static PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));

    public static MyScanner scan = new MyScanner();

    //-----------MyScanner class for faster input----------
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

    }
    //--------------------------------------------------------

}