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.

- In the first test case, we can rotate the subarray from index $3$ to index $6$ by an amount of $2$ (i.e. choose $l = 3$ , $r = 6$ and $k = 2$ ) to get the optimal array: $$$$[1, 3, \underline{9, 11, 5, 7}] \longrightarrow [1, 3, \underline{5, 7, 9, 11}] $$ So the answer is $a\_n - a\_1 = 11 - 1 = 10$ .</li><li> In the second testcase, it is optimal to rotate the subarray starting and ending at index $1$ and rotating it by an amount of $2$ .</li><li> In the fourth testcase, it is optimal to rotate the subarray starting from index $1$ to index $4$ and rotating it by an amount of $3$ . So the answer is $8 - 1 = 7$$$.