(i) Let $d \equiv 2$ or $3 \bmod 4$. Show that $(p)$ remains prime in $\mathcal{O}_{\mathbb{Q}(\sqrt{d})}$ if and only if $x^{2}-d$ is irreducible $\bmod p$.

(ii) Factorise $(2)$, (3) in $\mathcal{O}_{K}$, when $K=\mathbb{Q}(\sqrt{-14})$. Compute the class group of $K$.