**Problem Statement:**
Given the required input arguments, write an efficient algorithm to solve the **Next Greater Element** problem. Implement the required logic as specified by standard definitions for this classic algorithmic challenge.
**Hint / Expected Approach:**
Monotonic decreasing stack left-to-right
**Edge Cases to Consider:**
- (1) Strictly decreasing (no next greater)
- (2) Strictly increasing
- (3) Single element