## Inequality with primes

Let $a$ be a positive integer and $q_i,i=1,2..,n$; $n\ge2$ distinct primes

Prove or disprove:

If $\prod_{i=1}^{n}q_i = 3^a-2$

then $\prod_{i=1}^{n}(q_i-1) > \frac{2}{3}3^{a}$