Zero Total in a Compound Poisson Batch Model

Let $N\sim\mathrm{Poisson}(3)$ and let the i.i.d. batch sizes $B_i$ satisfy \[ P(B_i=0)=0.2,\quad P(B_i=1)=0.5,\quad P(B_i=2)=0.3. \] If $S=\sum_{i=1}^N B_i$, compute $P(S=0)$ using the PGF.