Prove: $\lim _{n\to \infty }\left(\sqrt[n]{\frac{n!}{n^n}}\right)=\frac{1}{e}$

Question

Prove: $\lim _{n\to \infty }\left(\sqrt[n]{\frac{n!}{n^n}}\right)=\frac{1}{e}$

I tried to do some algebraic manipulations and squeeze it but couldn't get further.

Any help appreciated.