You are given a sequence $a = (a_1, a_2, \dots, a_N)$ consisting of $N$ integers. You must choose a index $i$ and replace $a_i$ by an integer $k \neq a_i$exactly once. Determine if you can rearrange $a$ to form an arithmetic sequence or not.

Note that $a$ is an arithmetic sequence if and only if all differences between any two consecutive elements are the same.

Input Format

• The first line contains a single integer $T$ — the number of test cases.
• For each testcase:
  • The first line contains one integer $n$ — the length of the sequence.
  • The second line contains $n$ integers $a_1, a_2, ... , a_n$.

Output Format

• For each testcase, output "YES" if the  $a$ can be transformed into an arithmetic sequence. Otherwise, output "NO".

 Constraints

• $1 \leq T \leq 10^4$
• $2 \leq n \leq 10^5$
• $-10^9 \leq a_i \leq 10^9$
• $Sum\; of \; N\;over\;all\;test\;cases\;does\;not\;exceed\;10^6$