A13653. Multiply by 2, divide by 6

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.

The first line of the input contains one integer $t$ ( $1 \le t \le 2 \cdot 10^4$ ) — the number of test cases. Then $t$ test cases follow.

The only line of the test case contains one integer $n$ ( $1 \le n \le 10^9$ ).

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 $n$ .

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 $1$ .