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.BufferedReader;
    import java.io.IOException;
    import java.io.InputStreamReader;
    import java.util.Arrays;
    import java.util.Random;
    import java.util.StringTokenizer;
     
    public class A {
        public static void main(String[] args) {
			FastScanner fs = new FastScanner();
			int cases = fs.nextInt();
			while(cases-- > 0){
				int n = fs.nextInt();
				int i,j;
				i=2;
				int two=0,three=0;
				while(n%i==0) {
					
						two++;
						n=n/2;
				}
				i++;
				while(n%i==0) {
					three++;
					n=n/3;
				}
				//System.out.println(two+"\n"+three);
				if(n>1 || two>three){
					System.out.println("-1");
				}else{
					int count = three-two;
					count += three;
					System.out.println(count);
				}
			}
        }
        
     
        static void ruffle_sort(int arr[]){
            Random r = new Random();
            int n = arr.length;
            for (int i = 0; i < n; i++) {
                int oi = r.nextInt(n);
                int temp = arr[i];
                arr[i] = arr[oi];
                arr[oi] = temp;
            }
            Arrays.sort(arr);
        }
     
    static class FastScanner {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st=new StringTokenizer("");
        public String next() {
            while (!st.hasMoreElements())
                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());
		}
    }
}
