Hybrid Integers
An integer of the form $p^q q^p$ with prime numbers $p \neq q$ is called a hybrid-integer.
For example, $800 = 2^5 5^2$ is a hybrid-integer.
We define $C(n)$ to be the number of hybrid-integers less than or equal to $n$.
You are given $C(800) = 2$ and $C(800^{800}) = 10790$.
Find $C(800800^{800800})$.