Divide it!
描述
给你一个整数 n。
你可以对这个数进行任意次数（可能为零）的以下操作之一：
- 如果 n 能被 2 整除，则将 n 替换为 n/2；
- 如果 n 能被 3 整除，则将 n 替换为 2n/3；
- 如果 n 能被 5 整除，则将 n 替换为 4n/5。
例如，你可以使用第一种操作将 30 替换为 15，使用第二种操作将 30 替换为 20，或者使用第三种操作将 30 替换为 24。
你的任务是找到从 n 得到 1 所需的最小移动次数，或者判断无法实现。
你需要回答 q 个独立的查询。
输入
输入的第一行包含一个整数 q（1 ≤ q ≤ 1000）——查询的数量。
接下来 q 行包含查询。对于每个查询，你会给出一个整数 n（1 ≤ n ≤ 10^18）。
输出
对于每个查询，打印答案在一行中。如果无法从 n 得到 1，则打印 -1。否则，请打印所需的最小移动次数。
示例
7
1
10
25
30
14
27
1000000000000000000
0
4
6
6
-1
6
72
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