A16145. Desorting

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.

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.