You are given an integer $n$. You can perform any of the following operations with this number an arbitrary (possibly, zero) number of times: 1. Replace $n$ with $\frac{n}{2}$ if $n$ is divisible by $2$; 2. Replace $n$ with $\frac{2n}{3}$ if $n$ is divisible by $3$; 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.