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Problem D
Ordered Problem Set

You are running a programming contest that features n problems of distinct difficulties. You wish to announce ahead of time that the problems are ordered in such a way that, if the problems are divided into k sections numbered 1 through k, each with exactly nk problems, and problem p is assigned to section kpn, 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, you have just sent your problems to the printer so the order cannot be changed. For what values of k would this claim be true?

Input

The first line of input contains a single integer n (2n50), which is the number of problems.

Each of the next n lines contains a single integer d (1dn). These are the difficulties for the problems in the order that they appear in the problem set. The difficulties are distinct. The problem with difficulty 1 is the easiest problem and the problem with difficulty n is the hardest problem.

Output

Output a list of integers, one per line. The integers are all valid values of k in increasing order. If no such values exist, output 1.

Sample Input 1 Sample Output 1
6
1
3
2
4
5
6
2
Sample Input 2 Sample Output 2
6
1
2
3
4
5
6
2
3
6
Sample Input 3 Sample Output 3
6
6
5
4
3
2
1
-1
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