Let $\alpha$ and $\beta$ be two real numbers such that $\alpha+\beta=1$ and $\alpha \beta=-1$. Let $p_n=(\alpha)^n+(\beta)^n, P_{n-1}=11$ and $p_{n+1}=29$ for some integer $n \geq 1$. Then, the value of $p_n^2$ is
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