A15290 | Mainak and Array

Mainak has an array $a_1, a_2, \ldots, a_n$ of $n$ positive integers. He will do the following operation to this array exactly once:

- Pick a subsegment of this array and cyclically rotate it by any amount.

Formally, he can do the following exactly once:- Pick two integers $l$ and $r$ , such that $1 \le l \le r \le n$ , and any positive integer $k$ .
- Repeat this $k$ times: set $a_l=a_{l+1}, a_{l+1}=a_{l+2}, \ldots, a_{r-1}=a_r, a_r=a_l$ (all changes happen at the same time).

Mainak wants to maximize the value of $(a_n - a_1)$ after exactly one such operation. Determine the maximum value of $(a_n - a_1)$ that he can obtain.

Each test contains multiple test cases. The first line contains a single integer $t$ ( $1 \le t \le 50$ ) — the number of test cases. Description of the test cases follows.

The first line of each test case contains a single integer $n$ ( $1 \le n \le 2000$ ).

The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $1 \le a_i \le 999$ ).

It is guaranteed that the sum of $n$ over all test cases does not exceed $2000$ .

For each test case, output a single integer — the maximum value of $(a_n - a_1)$ that Mainak can obtain by doing the operation exactly once.