You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in c++17.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```cpp
<your code here>
```

Execution time limit: 2.0 seconds
Memory limit: 256.0 MB

# Problem
Fox has found an array $$$p_1, p_2, \ldots, p_n$$$, that is a permutation of length $$$n^\dagger$$$ of the numbers $$$1, 2, \ldots, n$$$. She wants to sort the elements in increasing order. Cat wants to help her — he is able to swap any two numbers $$$x$$$ and $$$y$$$ in the array, but only if $$$l \leq x + y \leq r$$$ (note that the constraint is imposed on the values of the elements, not their positions). He can make such swaps any number of times.

They don't know the numbers $$$l$$$, $$$r$$$ yet, they only know that it's true that $$$1 \leq l \leq r \leq 2 \cdot n$$$.

You are given the number $$$n$$$ and the array $$$p_1, p_2, \ldots, p_n$$$. Determine how many pairs $$$(l, r)$$$ satisfying the conditions are there such that you can sort the permutation if you can only swap two number $$$(x, y)$$$ such that $$$l \leq x + y \leq r$$$ (arbitrary number of times, possibly $$$0$$$).

$$$^\dagger$$$ A permutation of length $$$n$$$ is an array consisting of $$$n$$$ distinct integers from $$$1$$$ to $$$n$$$ in arbitrary order. For example, $$$[2,3,1,5,4]$$$ is a permutation, but $$$[1,2,2]$$$ is not a permutation ($$$2$$$ appears twice in the array), and $$$[1,3,4]$$$ is also not a permutation ($$$n=3$$$ but there is $$$4$$$ in the array).

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

Description of each test case consists of two lines. The first line contains one integer $$$n$$$ ($$$1 \leq n \leq 10^5$$$).

The second line contains $$$n$$$ integers: the array $$$p_1, p_2, \ldots, p_n$$$ ($$$1 \le p_i \le n$$$). It is guaranteed that this array is a permutation of length $$$n$$$.

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

## Output Format
For each test case, print the number of pairs of integers $$$(l, r)$$$ such that $$$1 \leq l \leq r \leq 2 \cdot n$$$, and you can sort the array under the constraints.

## Examples
```input
7
2
2 1
3
3 1 2
4
3 2 1 4
5
5 3 1 2 4
5
1 2 3 4 5
6
3 2 1 5 4 6
6
1 3 2 4 5 6
```
```output
6
11
23
29
55
46
58
```

## Note
In the first example, we need to be able to swap $$$1$$$ and $$$2$$$, so we must be able to swap numbers with sum $$$3$$$. There are exactly $$$6$$$ pairs satisfying the condition: $$$(1, 3), (2, 3), (3, 3), (1, 4), (2, 4)$$$ and $$$(3, 4)$$$, so the answer is $$$6$$$.

In the second example, the $$$11$$$ pairs satisfying the condition are $$$(1, 4), (1, 5), (1, 6), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6), (4, 5)$$$ and $$$(4, 6)$$$. For example, if we pick the pair $$$(3, 4)$$$ we can first swap the numbers $$$1$$$ and $$$2$$$ and then the numbers $$$1$$$ and $$$3$$$, after this, the permutation is sorted.

Now solve the problem and return the code.