Conjugacy classes and finite $p$-groups

Let $G$ be a finite $p$-group, where $p$ is a prime number, and $a\in G$. Denote by $\text{Cl}(a)=\{ga{g}^{-1}\mid g\in G\}$ the conjugacy class of $a$ in $G$. Assume that $\mathrm{\mid }\text{Cl}(a)\mathrm{\mid }=p^n$. Then $\Cl(a)\Cl(a^{-1})={xy\mid x\in \Cl(a), y\in \Cl(a^{-1})}$istheunionofatleast$n(p-1)+1$ distinct conjugacy classes of $G$.