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.io.*;

public class B{
	private static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	private static BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
	
	public static void main (String[] args) throws java.lang.Exception{
		int t = Integer.parseInt(br.readLine());
		while(t-- > 0){
			int n = Integer.parseInt(br.readLine());
			if(n==1){
				bw.write("0");
				bw.newLine();
				continue;
			}
		    if(n==3){
				bw.write("2");
				bw.newLine();
				continue;
			}
			if(n==6){
				bw.write("1");
				bw.newLine();
				continue;
			}
			if(n<6){
				bw.write("-1");
				bw.newLine();
				continue;
			}
			int c3 = 0, c2 = 0;
			while(n%3==0){
				c3++;
				n /= 3;
			}
			while(n%2==0){
				c2++;
				n /= 2;
			}
			if(n!=1 || c2>c3){
				bw.write("-1");
				bw.newLine();
			}else{
				int ans = c3 - c2;
				ans += c3;
				bw.write(ans + "");
				bw.newLine();
			}
		}
		bw.flush();
	}
}
