write a go solution for Description:
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<=x+y<=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<=l<=r<=2*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<=x+y<=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<=t<=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<=qn<=q10^5).

The second line contains n integers: the array p_1,p_2,ldots,p_n (1<=p_i<=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<=l<=r<=2*n, and you can sort the array under the constraints.

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.. Output only the code with no comments, explanation, or additional text.