Divide it!

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.