Hill Sequence

A sequence $A_1, A_2, \dots, A_N$ of length $N$ is called *good* if any one of the following hold: - The sequence is strictly increasing, or - The sequence is strictly decreasing, or - There exists an index $i\;(1 \lt i \lt N)$ such that: - $A_j \lt A_{j+1}$, for each $1 \le j \lt i$ - $A_j \gt A_{j+1}$, for each $i \le j \lt N$ For example, the sequences $[3, 5, 9]$, $[2, 1]$, $[5, 7,