Let the coefficient of $x^r$ in the expansion of
$$
\begin{aligned}
& (x+3)^{n-1}+(x+3)^{n-2}(x+2)+ \\
& (x+3)^{n-3}(x+2)^2+\cdots \cdots+(x+2)^{n-1}
\end{aligned}
$$
be $\alpha_r$. If $\sum_{r=0}^n \alpha_r=\beta^n-\gamma^n, \beta, \gamma \in N$, then the value of $\beta^2+\gamma^2$ equals
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