Can You Form an Arithmetic Progression?

You are given a sequence of n integers. Your task is to determine whether it is possible to rearrange the sequence so that it forms an arithmetic progression.

An arithmetic progression is a sequence where the difference between consecutive terms is constant. In mathematical notation, if the sorted sequence is \(a_1, a_2, \dots, a_n\), then there exists a constant \(d\) such that:

\(a_{i+1} - a_i = d \quad \text{for every } 1 \leq i < n\)

If the sequence can be rearranged to satisfy this condition, print YES; otherwise, print NO.

inputFormat

The input is given via standard input and consists of two lines.

• The first line contains a single integer \(n\) representing the number of elements in the sequence.
• The second line contains \(n\) space-separated integers, which are the elements of the sequence.

outputFormat

Output a single line containing YES if it is possible to rearrange the sequence into an arithmetic progression, or NO otherwise.

5
3 1 5 7 9

YES