Rearrange to Form an Arithmetic Sequence

Given a list of integers, determine whether it is possible to rearrange the numbers to form an arithmetic sequence. An arithmetic sequence is defined by a constant difference between consecutive terms. In other words, for a sequence \(a_1, a_2, \ldots, a_n\), there exists a constant \(d\) such that for every \(1 \le i < n\), \(a_{i+1} - a_i = d\).

Your task is to read the input from stdin and output to stdout. The first input line contains an integer \(n\) indicating the number of elements, and the second line contains \(n\) space-separated integers. Output YES if the numbers can be rearranged to form an arithmetic sequence, and NO otherwise.

inputFormat

The input is read from stdin and consists of two lines:

• The first line contains a single integer \(n\) ― the number of elements in the list.
• The second line contains \(n\) space-separated integers.

outputFormat

Print a single line to stdout containing YES if the numbers can be rearranged to form an arithmetic sequence; otherwise, print NO.

## sample

3
3 1 2

YES

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