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.*;

public class Main{
  public static boolean isLucky(int n) {
    //Set<Integer> s=new HashSet<>();
    if (n==0) return false;
    while(n!=0){
         if (n%10!=4 && n%10!=7) return false;
         n/=10;
    }
    return true;
  } 
	public static void main(String[] args)throws Exception{
         //StringTokenizer st;//! @ % & * () _ {} # ~ : < > ? "" | ^
         BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
         //StringTokenizer st=new StringTokenizer(br.readLine());
          StringTokenizer st;
          //int a,i=0,b,ans,rem;
         
         
         
         //  int x=Integer.parseInt(st.nextToken());
         

         int t=Integer.parseInt(br.readLine());
         // t=t+1;
        // int f[]=new int[3];
         //int c=t;
         while(t-->0)  {
                  //long n=Long.parseLong(br.readLine());
                  //  st=new StringTokenizer(br.readLine()); 
                  int n=Integer.parseInt(br.readLine());
                  // int t=Integer.parseInt(st.nextToken());
                  //char ch[]=br.readLine().trim().toCharArray();
                  // // //! @ % & * () _ {} # ~ : < > ? "" | ^
                  // String result="";

                  //if (ch[0]>96) ch[0]=(char)(ch[0]-32);
                  // int upper=0,lower=0;
                      int ans=0,two=0,three=0;
                       while(n%3==0){ three++;
                       n/=3; }
                       while(n%2==0){ two++;
                       n/=2; }

                       if(n!=1 || two>three) ans=-1;
                       else{
                           ans=2*three-two;
                       }

                       System.out.println(ans);
                  
                  


                  
       }        

                   

                  
                  //int mmoves=Math.abs(r-2)+Math.abs(c-2);
       // if (isLucky(count)) 
       //     System.out.println("YES");
       //   else  System.out.println("NO");
  
                // for (int i=0;i<ch.length;i++) {
                //      result+=ch[i];
                //   }
       //else  
       // 
         // System.out.println(count++);
	}
}


