Mainak and Array
Description
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.
- 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.
Input
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 $2000$.
Output
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.
Samples
<div class="test-example-line test-example-line-even test-example-line-0">5</div><div class="test-example-line test-example-line-odd test-example-line-1">6</div><div class="test-example-line test-example-line-odd test-example-line-1">1 3 9 11 5 7</div><div class="test-example-line test-example-line-even test-example-line-2">1</div><div class="test-example-line test-example-line-even test-example-line-2">20</div><div class="test-example-line test-example-line-odd test-example-line-3">3</div><div class="test-example-line test-example-line-odd test-example-line-3">9 99 999</div><div class="test-example-line test-example-line-even test-example-line-4">4</div><div class="test-example-line test-example-line-even test-example-line-4">2 1 8 1</div><div class="test-example-line test-example-line-odd test-example-line-5">3</div><div class="test-example-line test-example-line-odd test-example-line-5">2 1 5</div>
10
0
990
7
4
Note
- 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 $a_n - a_1 = 11 - 1 = 10$.
- In the second testcase, it is optimal to rotate the subarray starting and ending at index $1$ and rotating it by an amount of $2$.
- 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 $8 - 1 = 7$.