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 $|x_{2012}|?$

Let's think step by step and output the final answer within \boxed{}.
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