What could this limit be?

Calculus Level 4

\[\Large \lim_{n \to \infty} \left(\frac {n!}{n^n} \right)^\frac 1n = \ ? \]

\[1/e\] Limit does not exist \[\pi\] \[1\] \[\frac{\pi}{2}\] \[0\] \[e\] \[\frac{\pi}{4}\]