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C. Min Max Sort

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou are given a permutation $$$p$$$ of length $$$n$$$ (a permutation of length $$$n$$$ is an array of length $$$n$$$ in which each integer from $$$1$$$ to $$$n$$$ occurs exactly once).

You can perform the following operation any number of times (possibly zero):

- choose two different elements $$$x$$$ and $$$y$$$ and erase them from the permutation;
- insert the minimum of $$$x$$$ and $$$y$$$ into the permutation in such a way that it becomes the first element;
- insert the maximum of $$$x$$$ and $$$y$$$ into the permutation in such a way that it becomes the last element.

For example, if $$$p = [1, 5, 4, 2, 3]$$$ and we want to apply the operation to the elements $$$3$$$ and $$$5$$$, then after the first step of the operation, the permutation becomes $$$p = [1, 4, 2]$$$; and after we insert the elements, it becomes $$$p = [3, 1, 4, 2, 5]$$$.

Your task is to calculate the minimum number of operations described above to sort the permutation $$$p$$$ in ascending order (i. e. transform $$$p$$$ so that $$$p_1 < p_2 < \dots < p_n$$$).

Input

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases.

The first line of the test case contains a single integer $$$n$$$ ($$$1 \le n \le 2 \cdot 10^5$$$) — the number of elements in the permutation.

The second line of the test case contains $$$n$$$ distinct integers from $$$1$$$ to $$$n$$$ — the given permutation $$$p$$$.

The sum of $$$n$$$ over all test cases doesn't exceed $$$2 \cdot 10^5$$$.

Output

For each test case, output a single integer — the minimum number of operations described above to sort the array $$$p$$$ in ascending order.

Example

Input

451 5 4 2 331 2 342 1 4 365 2 4 1 6 3

Output

2 0 1 3

Note

In the first example, you can proceed as follows:

- in the permutation $$$p = [1, 5, 4, 2, 3]$$$, let's choose the elements $$$4$$$ and $$$2$$$, then, after applying the operation, the permutation becomes $$$p = [2, 1, 5, 3, 4]$$$;
- in the permutation $$$p = [2, 1, 5, 3, 4]$$$, let's choose the elements $$$1$$$ and $$$5$$$, then, after applying operation, the permutation becomes $$$p = [1, 2, 3, 4, 5]$$$.

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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