Limit involving a bounded sequence and a sine term

Let $\{a_n\}_{n\ge1}$ be a sequence of real numbers such that $|a_n|\le\sqrt n$, $n=1,2,…$. Then

$$\lim_{n\to\infty}\left\{e^{\frac{a_n}n}+\sqrt n\sin\left(\sqrt{\frac2n}\right)\right\}$$

is equal to ____________