Find all elements x in S4 such that x^4 = e.

(e is the identity)

Cycle notation is advised.

**The attempt at a solution**

I know there are 4 elements in this (1 2 3 4). And I feel like I need to find the order of S which can be found by finding the number of cycles.

Suppose S is a finite group with x elements, then x^n = e for all x in S. That's my start. not sure where to go from there.