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.

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.

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.

Desorting

Examples