Arithmetic Progression Arrangement

You are given an array of n integers. Your task is to determine if it is possible to rearrange the array such that it forms an arithmetic progression.

An arithmetic progression is defined as a sequence in which the difference between consecutive elements is constant. In mathematical terms, a sequence \(a_1, a_2, \dots, a_n\) is an arithmetic progression if there exists a constant \(d\) such that \(a_{i+1} - a_i = d\) for all \(1 \le i < n\). Note that when \(n = 1\), the sequence is trivially considered an arithmetic progression.

Print YES if the array can be rearranged to form an arithmetic progression, otherwise print NO.

inputFormat

The input is read from standard input (stdin) and consists of two lines.

• The first line contains an integer n — the number of elements in the array.
• The second line contains n space-separated integers representing the array.

outputFormat

Output a single line to standard output (stdout) containing YES if the array can be rearranged to form an arithmetic progression, otherwise output NO.

5
3 5 1 7 9

YES