Divide it!
Description
You are given an integer $n$.
You can perform any of the following operations with this number an arbitrary (possibly, zero) number of times:
- Replace $n$ with $\frac{n}{2}$ if $n$ is divisible by $2$;
- Replace $n$ with $\frac{2n}{3}$ if $n$ is divisible by $3$;
- Replace $n$ with $\frac{4n}{5}$ if $n$ is divisible by $5$.
For example, you can replace $30$ with $15$ using the first operation, with $20$ using the second operation or with $24$ using the third operation.
Your task is to find the minimum number of moves required to obtain $1$ from $n$ or say that it is impossible to do it.
You have to answer $q$ independent queries.
The first line of the input contains one integer $q$ ($1 \le q \le 1000$) — the number of queries.
The next $q$ lines contain the queries. For each query you are given the integer number $n$ ($1 \le n \le 10^{18}$).
Print the answer for each query on a new line. If it is impossible to obtain $1$ from $n$, print -1. Otherwise, print the minimum number of moves required to do it.
Input
The first line of the input contains one integer $q$ ($1 \le q \le 1000$) — the number of queries.
The next $q$ lines contain the queries. For each query you are given the integer number $n$ ($1 \le n \le 10^{18}$).
Output
Print the answer for each query on a new line. If it is impossible to obtain $1$ from $n$, print -1. Otherwise, print the minimum number of moves required to do it.
Samples
7
1
10
25
30
14
27
1000000000000000000
0
4
6
6
-1
6
72