Let $L$ be a language over an alphabet $\Sigma$. The equivalence relation $\sim_{L}$ on the set $\Sigma^{\ast }$ of finite strings over $\Sigma$ is defined by $u \sim_{L} v$ if and only if for all $w \in \Sigma^{\ast }$ it is the case that $u w \in L$ if and only if $v w \in L$.
Suppose that $\Sigma=\{a, b\}$ and $L$ is the language determined by the regular expression $a ^\ast b(a \mid b)$. Number of $\sim_{L}$-equivalence classes for this $L$ is ________
