BALKAN-SL 2007 N5

Let $p \geq 5$ be a prime and let \begin{align*} (p-1)^p +1 = \prod {i=1}^n q_i^{\beta_i} \end{align*} where $q_i$ are primes. Prove, \begin{align*} \sum{i=1}^n q_i \beta_i >p^2 \end{align*}