Let $f(n)$ be the number of ways an $n\times n$ square grid can be coloured, each cell either black or white, such that each row and each column contains exactly two black cells.
For example, $f(4)=90$, $f(7)=3110940$ and $f(8)=187530840$.

Let $g(n)$ be the number of colourings in $f(n)$ that are unique up to rotations and reflections.
You are given $g(4)=20$, $g(7)=390816$ and $g(8)=23462347$ giving $g(7)+g(8)=23853163$.

Find $g(7^7)+g(8^8)$. Give your answer modulo $1000000007$.