Strange Sort

2000ms

524288K

Description:

You have a permutation: an array $$$a = [a_1, a_2, \ldots, a_n]$$$ of distinct integers from $$$1$$$ to $$$n$$$. The length of the permutation $$$n$$$ is odd.

Consider the following algorithm of sorting the permutation in increasing order.

A helper procedure of the algorithm, $$$f(i)$$$, takes a single argument $$$i$$$ ($$$1 \le i \le n-1$$$) and does the following. If $$$a_i > a_{i+1}$$$, the values of $$$a_i$$$ and $$$a_{i+1}$$$ are exchanged. Otherwise, the permutation doesn't change.

The algorithm consists of iterations, numbered with consecutive integers starting with $$$1$$$. On the $$$i$$$-th iteration, the algorithm does the following:

if $$$i$$$ is odd, call $$$f(1), f(3), \ldots, f(n - 2)$$$;
if $$$i$$$ is even, call $$$f(2), f(4), \ldots, f(n - 1)$$$.

It can be proven that after a finite number of iterations the permutation will be sorted in increasing order.

After how many iterations will this happen for the first time?

Input:

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^4$$$). Description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$3 \le n \le 2 \cdot 10^5 - 1$$$; $$$n$$$ is odd) — the length of the permutation.

The second line contains $$$n$$$ distinct integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \le a_i \le n$$$) — the permutation itself.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5 - 1$$$.

Output:

For each test case print the number of iterations after which the permutation will become sorted in increasing order for the first time.

If the given permutation is already sorted, print $$$0$$$.

Sample Input:

3
3
3 2 1
7
4 5 7 1 3 2 6
5
1 2 3 4 5

Sample Output:

3
5
0

Note:

In the first test case, the permutation will be changing as follows:

after the $$$1$$$-st iteration: $$$[2, 3, 1]$$$;
after the $$$2$$$-nd iteration: $$$[2, 1, 3]$$$;
after the $$$3$$$-rd iteration: $$$[1, 2, 3]$$$.

In the second test case, the permutation will be changing as follows:

after the $$$1$$$-st iteration: $$$[4, 5, 1, 7, 2, 3, 6]$$$;
after the $$$2$$$-nd iteration: $$$[4, 1, 5, 2, 7, 3, 6]$$$;
after the $$$3$$$-rd iteration: $$$[1, 4, 2, 5, 3, 7, 6]$$$;
after the $$$4$$$-th iteration: $$$[1, 2, 4, 3, 5, 6, 7]$$$;
after the $$$5$$$-th iteration: $$$[1, 2, 3, 4, 5, 6, 7]$$$.

In the third test case, the permutation is already sorted and the answer is $$$0$$$.

Informação

Provedor Codeforces

Código CF1558F