HMMT 2012 A8

Let $x_{1}=y_{1}=x_{2}=y_{2}=1$, then for $n \geq 3$ let $x_{n}=x_{n-1} y_{n-2}+x_{n-2} y_{n-1}$ and $y_{n}=y_{n-1} y_{n-2}-$ $x_{n-1} x_{n-2}$. What are the last two digits of $\left|x_{2012}\right|$ ?