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.lang.*;

public class MyTest {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int t;
        long n;
        t = in.nextInt();
        for(int i=1; i<=t; i++){
            n = in.nextInt();
            int count = 0;
            long k = n;
            if(n==2 || n==4 || n==5){
                print(-1);
                continue;
            }
            if(n==1){
                print(0);
                continue;
            }
            if(n==3){
                print(2);
                continue;
            }
            if(n%3!=0 && n%2!=0){
                print(-1);
                continue;
            }
            int m3 = 0;
            int m2 = 0;
            while((k%3==0 || k%2==0) && k>1){
                if(k%3==0){
                    k /= 3;
                    m3++;
                }else{
                    k /= 2;
                    m2++;
                }
            }
            if(k!=1){
                print(-1);
                continue;
            }
            // while(n>1){
            //     if(n%6==0){
            //         n >>= 1;
            //         n /= 3;
            //     }else{
            //         n <<= 1;
            //     }
            //     count++;
            // }
            if(m2 > m3){
                print(-1);
                continue;
            }
            count = m3 + (m3-m2);
            print(count);
        } 

        in.close();
    }

    private static void print(Object obj){
        System.out.println(obj);
    }
} // javac MyTest.java & java MyTest < in