$x^6 + x^3 + x^3y + y = 147^{157}$

$x^3 + x^3y + y^2 + y + z^9 = 157^{147}$

Let $n$ be the number of solutions for the above system. i.e. if $x=a, y=b, z=c$ is a solution then the number of solutions is incremented by 1. Give your answer as first six digits of $(n+e)^{134}$.