Consider a three dimensional grid of cubes. An amoeba in cube $(x,y,z)$ can divide itself into three amoebas to occupy the cubes $(x+1,y,z)$, $(x,y+1,z)$ and $(x,y,z+1)$, provided these cubes are empty.

Originally there is only one amoeba in the cube $(0,0,0)$. After $N$ divisions there will be $2N+1$ amoebas arranged in the grid. An arrangement may be reached in several different ways but it is only counted once. Let $D(N)$ be the number of different possible arrangements after $N$ divisions.

For example, $D(2)=3$, $D(10)=44499$, $D(20)=9204559704$ and the last nine digits of $D(100)$ are $780166455$.

Find $D(10000)$, enter the last nine digits as your answer.