Desorting
Description
Call an array $a$ of length $n$ sorted if $a_1 \leq a_2 \leq \ldots \leq a_{n-1} \leq a_n$.
Ntarsis has an array $a$ of length $n$.
He is allowed to perform one type of operation on it (zero or more times):
- Choose an index $i$ ($1 \leq i \leq n-1$).
- Add $1$ to $a_1, a_2, \ldots, a_i$.
- Subtract $1$ from $a_{i+1}, a_{i+2}, \ldots, a_n$.
The values of $a$ can be negative after an operation.
Determine the minimum operations needed to make $a$ not sorted.
Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 100$). The description of the test cases follows.
The first line of each test case contains a single integer $n$ ($2 \leq n \leq 500$) — the length of the array $a$.
The next line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \leq a_i \leq 10^9$) — the values of array $a$.
It is guaranteed that the sum of $n$ across all test cases does not exceed $500$.
Output the minimum number of operations needed to make the array not sorted.
Input
Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 100$). The description of the test cases follows.
The first line of each test case contains a single integer $n$ ($2 \leq n \leq 500$) — the length of the array $a$.
The next line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \leq a_i \leq 10^9$) — the values of array $a$.
It is guaranteed that the sum of $n$ across all test cases does not exceed $500$.
Output
Output the minimum number of operations needed to make the array not sorted.
4
2
1 1
4
1 8 10 13
3
1 3 2
3
1 9 14
1
2
0
3
Note
In the first case, we can perform $1$ operation to make the array not sorted:
- Pick $i = 1$. The array $a$ then becomes $[2, 0]$, which is not sorted.
In the second case, we can perform $2$ operations to make the array not sorted:
- Pick $i = 3$. The array $a$ then becomes $[2, 9, 11, 12]$.
- Pick $i = 3$. The array $a$ then becomes $[3, 10, 12, 11]$, which is not sorted.
It can be proven that $1$ and $2$ operations are the minimal numbers of operations in the first and second test cases, respectively.
In the third case, the array is already not sorted, so we perform $0$ operations.