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.StringTokenizer;

public class Solution {


    public static void main( String[] args ) throws IOException {
//        System.setIn(new FileInputStream("input.txt"));
//        System.setOut(new PrintStream(new FileOutputStream("output.txt")));

        Scanner cin = new Scanner( System.in );
        int t = cin.nextInt();
        StringBuilder sb = new StringBuilder();
        for ( int i = 0; i < t; i++ ) {
            int n = cin.nextInt();
            int ans = 0;
            if ( n==1 ) {
                sb.append( 0 ).append( "\n" );
                continue;
            }
            if ( n % 3 != 0 ) {
                sb.append( -1 ).append( "\n" );
                continue;
            }

            while ( true ) {
                ans++;

                if ( n % 6 == 0 ) {
                    n/=6;
                    if ( n==1 ) break;
                    if ( n % 3 != 0 ) {
                        ans = -1;
                        break;
                    }
                }
                else {
                    n *= 2;
                }

            }
            sb.append( ans ).append( "\n" );
        }
        System.out.println(sb.toString());
    }

    static class Scanner {
        BufferedReader br = new BufferedReader( new InputStreamReader( System.in ) );
        StringTokenizer st = new StringTokenizer( "" );

        public Scanner( InputStream in ) {

        }

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

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

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

        public int[] readArray( int n ) {
            int[] a = new int[ n ];
            for ( int i = 0; i < n; i++ ) {
                a[ i ] = nextInt();
            }
            return a;
        }

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

    }
}
