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Given that $P(x)$ is a monic fifth-degree polynomial such that

$\begin{aligned} P(1) & = & 1^2 \\ P(2) & = & 2^2 \\ P(3) & = & 3^2 \\ P(4) & = & 4^2 \\ P(5) & = & 5^2,\end{aligned}$

find the value of $P(6)$.

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