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.Scanner;

public class mmddd {
	public static int[] th(int a) {
		int count =0;
	  int f[] =new int[2];
		while(a !=1) {
			if(a%2 ==0) {
				a =a/2;
				count =count+1;
			}
			else {
				break;
			}
		}if(a !=1) {
			int e =ty(a);
		f[0] =count;
		f[1] =e;
		}
		else {
			f[0] =0;
			f[1] =1;
		}
		return f;
	}
	public static int  ty(int a) {
		int count=0;
		int s=0;
		if(a !=1) {
			while(a !=1) {
				if(a%3 ==0) {
					a =a/3;
					count =count+1;
				}
				else {
					break;
				}
			}
		}if(a ==1) {
		return count;
	}
		else {
			return s;}
		}
	

	public static void main(String[] args) {
		Scanner sc =new Scanner(System.in);
		int a =sc.nextInt();
		for(int j=0;j<a;j++) {
			int b =sc.nextInt();
			int d[] =th(b);
			
				if(d[1] !=0 && d[1]>=d[0] && b!=1 && b!=2){
					int w =d[1] -d[0];
					int g =d[1] +w;
					System.out.println(g+" ");
				}
				else if(b ==1) {
					System.out.println(0+" ");
				}
				else if(b ==2) {
					System.out.println(-1+" ");
				}
				else {
					System.out.println(-1+" ");
				}
				
					
				}
			}

}
