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 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 n=Integer.parseInt(br.readLine());
         // int pre[]=new int[n];
         // st=new StringTokenizer(br.readLine());
         //  int x=Integer.parseInt(st.nextToken());
         //  pre[0]=x;
         // for (int i=1;i<n ;i++ ) {
         //   x=Integer.parseInt(st.nextToken());
         //   pre[i]=pre[i-1]+x;
         // }

         int t=Integer.parseInt(br.readLine());
         //int c=t;
    while(t-->0){
                 
                  int n=Integer.parseInt(br.readLine());
                 int ans=-1,count=0;
                 int h[]=new int[5];
                 //Map<Integer,Integer> map=new HashMap<Integer,Integer>();
                 for (int i=2;i*i<=n;i++) {
                  count=0;
                  if (i>3) {
                    break;
                  }
                    while(n%i==0){
                      n/=i;
                      h[i]++;
                    }
                 }
                 
                 if (n==1) {
                   ans=0;
                 }
                 else if (n==2) {
                   h[n]++;
                 }
                 else if (n==3) {
                   h[n]++;
                 } 
                 else h[4]=Integer.MIN_VALUE+1000;
                 

                ans=h[3]+h[3]-h[2]+h[4];
                if (ans<0 ||(ans==0 && h[2]>0)) {
                  ans=-1;
                }
                 System.out.println(ans); 
       }
	}
}


