#!/usr/bin/env python
# coding=utf-8

"""572. Idempotent matrices
https://projecteuler.net/problem=572

A matrix $M$ is called idempotent if $M^2 = M$.  
Let $M$ be a three by three matrix : $M=\begin{pmatrix} a & b & c\\\ d & e &
f\\\ g &h &i\\\ \end{pmatrix}$.  
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).
"""
