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

Prove or disprove:

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

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