Quite large

Let $f(x) = 9x+2$ and $g(x) = 25x+6$ . Find the sum of all possible constant terms of all functions that are compositions of the functions $f$ and $g$ in which $f$ and $g$ each appear exactly 4 times.

For example, a composition of $f$ and $g$ in which $f$ and $g$ each appear exactly 2 times could be $f(f(g(g(x))))$ or $f(g(f(g(x))))$ .

Also note that the constant term of a function $h$ is equal to $h(0)$ .