Ordered Problem Set

You are running a programming contest with $n$ problems of distinct difficulties. You wish to announce ahead of time that the problems are ordered so that, when they are divided into $k$ sections numbered $1$ through $k$, each with exactly $\frac{n}{k}$ problems, and problem $p$ is assigned to section $\left\lceil \frac{kp}{n} \right\rceil$, then for every pair of sections $i$ and $j$ with $i < j$, every problem in section $i$ is easier than every problem in section $j$. Note that $k$ must be greater than $1$ and be a factor of $n$. However, the problems have already been sent to the printer, so the order cannot be changed. For what values of $k$ would this claim be true?

The first line contains a single integer $n$ ($2 \le n \le 50$), the number of problems. Each of the next $n$ lines contains a single integer $d$ ($1 \le d \le n$), the difficulty of a problem, listed in the order the problems appear in the set. The difficulties are distinct. Difficulty $1$ is the easiest and difficulty $n$ is the hardest.

Output a list of integers, one per line, containing all valid values of $k$ in increasing order. If no valid value exists, output $-1$.