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.Arrays;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Hashtable;
import java.util.Map;
import java.util.Scanner;
import java.util.Set;


public class Main {


    static void solve() {
        Scanner scan = new Scanner(System.in);
        long t = scan.nextLong();

        for (int i = 0; i < t; i++) {
            int n = scan.nextInt();

            scase(n);
        }
    }


    static void solveCase(int t, int x, String s) {

    }

    static void scase(int n) {
        int b = 0;
        int a = 0;
        int goal = n;
        long curr = 0;
        while(curr < goal) {
            while(a<=b) {
                curr = (long) (Math.pow(2, b-a) * Math.pow(3, b));
                if(curr == goal) {
                    System.out.println(b+a);
                    return;
                }
                a++;
            }
            b++;
            a=0;
        }
        System.out.println(-1);
    }


    public static void main(String[] args) {


        solve();
        //        Main m = new Main();
        //        Scanner scan = new Scanner(System.in);

        //        long n = scan.nextLong();
        //        long r = scan.nextLong();
        //        List<Long> list = new ArrayList<>();
        ////        int[] arr = new int[n];
        //        for (long i=0;i<n;i++){
        //            list.add(scan.nextLong());
        //        }
//            System.out.println(ch);
        //        solve(n, arr);
        //        scan.close();
    }


//
//    class Counter extends HashMap<Integer, Integer> {
//        public int get(int k) {
//            return containsKey(k) ? super.get(k) : 0;
//        }
//
//        public void add(int k, int v) {
//            put(k, get(k) + v);
//        }
//    }


//    static class TreeNode {
//        int val;
//        TreeNode left;
//        TreeNode right;
//
//        TreeNode(int x) {
//            val = x;
//        }
//    }

    static class ListNode {
        int val;
        ListNode next;

        ListNode() {
        }

        ListNode(int val) {
            this.val = val;
        }

        ListNode(int val, ListNode next) {
            this.val = val;
            this.next = next;
        }
    }

}