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 X {

	public static void main(String[] args) {
		FastScanner in=new FastScanner();
		PrintWriter out=new PrintWriter(System.out);
		int t=in.nextInt();
		while(t-->0){
		   
		    long n=in.nextLong();
		    long two=0,three=0,other=0;
		    long temp=n;
		   
		        while(n%2==0){
		            n/=2;
		           two++;
		        }
		    while(n%3==0){
		            n/=3;
		           three++;
		        }
		        
		    if(n!=1){ other++;
		    }
		    if(other>0||three<two) out.println(-1);
		    else out.println(three-two+three);
		}
		out.close();
	}
	
	static class Node {
		ArrayList<Node> adj=new ArrayList<>();
		int number, degree, index;
		int removeSpot;
		boolean added=false;
		public Node(int index, int number) {
			this.index=index;
			this.number=number;
		}
	}
	
	static class Edge implements Comparable<Edge> {
		Node a, b;
		int index;
		
		public Edge(Node a, Node b, int index) {
			this.a=a;
			this.b=b;
			this.index=index;
		}

		int val() {
			return Math.min(a.removeSpot, b.removeSpot);
		}
		
		public int compareTo(Edge o) {
			return Integer.compare(val(), o.val());
		}
	}

	static void sort(int[] a) {
		ArrayList<Integer> l=new ArrayList<>();
		for (int i:a) l.add(i);
		Collections.sort(l);
		for (int i=0; i<a.length; i++) a[i]=l.get(i);
	}
	
	static class FastScanner {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer("");
		String next() {
			while (!st.hasMoreTokens())
				try {
					st=new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			return st.nextToken();
		}
		
		int nextInt() {
			return Integer.parseInt(next());
		}
		int[] readArray(int n) {
			int[] a=new int[n];
			for (int i=0; i<n; i++) a[i]=nextInt();
			return a;
		}
		long nextLong() {
			return Long.parseLong(next());
		}
	}

	
}
