Let \( p \) and \( p+2 \) be prime numbers and let \[ \Delta=\left|\begin{array}{ccc} p ! & (p+1...

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Let \( p \) and \( p+2 \) be prime numbers and let
\[
\Delta=\left|\begin{array}{ccc}
p ! & (p+1) ! & (p+2) \\
(p+1) ! & (p+2) ! & (p+3) ! \\
(p+2) ! & (p+3) ! & (p+4) !
\end{array}\right|
\]
Such that \( p^{\alpha} \) and \( (p+2)^{\beta} \) divide \( \Delta \), then the sum of the maximum values of \( \alpha \) and \( \beta \).
(a) 0
(b) 1
(c) 2
(d) 4
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