Arithmetic Progression Rearrangement

You are given a sequence of integers. Your task is to determine whether the sequence can be rearranged to form an arithmetic progression.

An arithmetic progression is a sequence where the difference between consecutive elements is constant. In other words, after sorting the sequence, it should satisfy:

$$a_{i+1} - a_i = d \quad \text{for all } 1 \leq i < n $$

If the sequence can be rearranged into such a progression, output YES; otherwise, output NO.

Note: You need to read the input from standard input and print the output to standard output.

inputFormat

The first line of the input contains a single integer T (T ≥ 1) — the number of test cases. The description of the test cases follows.

For each test case:

• The first line contains an integer N (N ≥ 2) — the number of elements in the sequence.
• The second line contains N space-separated integers representing the sequence.

outputFormat

For each test case, print a single line containing YES if the sequence can be rearranged to form an arithmetic progression, or NO otherwise.

## sample

3
3
3 1 2
4
2 4 1 3
4
1 2 4 5

YES
YES
NO

</p>