"""


A matrix $M$ is called idempotent if $M^2 = M$.
Let $M$ be a three by three matrix : 
$M=\begin{pmatrix} 
  a &amp; b &amp; c\\ 
  d &amp; e &amp; f\\
  g &amp;h &amp;i\\
\end{pmatrix}$.
Let C(n) be the number of  idempotent three by three matrices $M$ with integer elements such that
$ -n \le a,b,c,d,e,f,g,h,i \le n$.

C(1)=164 and C(2)=848.


Find C(200).


"""