Alphen has an array of positive integers $$$a$$$ of length $$$n$$$.

Alphen can perform the following operation:

For all $$$i$$$ from $$$1$$$ to $$$n$$$, replace $$$a_i$$$ with $$$\max(0, a_i - 1)$$$.

Alphen will perform the above operation until $$$a$$$ is sorted, that is $$$a$$$ satisfies $$$a_1 \leq a_2 \leq \ldots \leq a_n$$$. How many operations will Alphen perform? Under the constraints of the problem, it can be proven that Alphen will perform a finite number of operations.

Input

Each test contains multiple test cases. The first line of input contains a single integer $$$t$$$ ($$$1 \le t \le 500$$$) — the number of test cases. The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$2 \le n \le 50$$$) — the length of the array $$$a$$$.

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 10 ^ 9$$$) — the elements of the array $$$a$$$.

Output

For each test case, output a single integer — the number of operations that Alphen will perform.

Note

In the first test case, we have $$$a=[1,2,3]$$$. Since $$$a$$$ is already sorted, Alphen will not need to perform any operations. So, the answer is $$$0$$$.

In the second test case, we have $$$a=[2,1,2,1,2]$$$. Since $$$a$$$ is not initially sorted, Alphen will perform one operation to make $$$a=[1,0,1,0,1]$$$. After performing one operation, $$$a$$$ is still not sorted, so Alphen will perform another operation to make $$$a=[0,0,0,0,0]$$$. Since $$$a$$$ is sorted, Alphen will not perform any other operations. Since Alphen has performed two operations in total, the answer is $$$2$$$.

Tales of a Sort

Examples