  It is shown that except in three cases conjugacy classes of classical Weyl
groups $W(B_{n})$ and $W(D_{n})$ are of type ${\rm D}$. This proves that
Nichols algebras of irreducible Yetter-Drinfeld modules over the classical Weyl
groups $\mathbb W_{n}$ (i.e. $H_{n}\rtimes \mathbb{S}_{n}$) are infinite
dimensional, except the class of type $(2, 3),(1^{2}, 3)$ in $\mathbb S_{5}$,
and $(1^{n-2}, 2)$ in $\mathbb S_{n}$ for $n >5$.
