What is the total number of zeroes in n!?

What is the total number of zeroes in $n!$?

I do not want to know the number of trailing zeroes in $n!$.

Let us take an example to understand what I want to know.

$7! = 5040$. The number of trailing zero in $7!$ is $1$. But the total number of zeroes in $7!$ is $2$.

I would like to know if there is any formula that gives me directly the total number of zeros in $n!$.

Can you help me derive one?