Hopf Algebras of Dimension $pq$

Let $H$ be a non-semisimple Hopf algebra with antipode $S$ of dimension $pq$ over an algebraically closed field of characteristic 0 where $p\le q$ are odd primes. We prove that $\text{Tr}(S^{2p})=p^{2}d$ where $d\equiv pq(\mathrm{m}\mathrm{o}\mathrm{d}4)$. As a consequence, if $p,q$ are twin primes, then any Hopf algebra of dimension $pq$ is semisimple.