Let $p$ and $p+2$ be prime numbers and let
$\Delta =\left|\begin{array}{ccc}p!& \left(p+1\right)!& \left(p+2\right)!\\ \left(p+1\right)!& \left(p+2\right)!& \left(p+3\right)!\\ \left(p+2\right)!& \left(p+3\right)!& \left(p+4\right)!\end{array}\right|$
Then the sum of the maximum values of $\alpha$ and $\beta$, such that $p^{\alpha }$ and ${\left(p+2\right)}^{\beta }$ divide $\Delta$, is _______.