B"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 <= q x + y <= q 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 <= q l <= q r <= q 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 <= q x + y <= q 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). 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 <= q n <= q 10^5 ). 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 . For each test case, print the number of pairs of integers (l, r) such that 1 <= q l <= q r <= q 2 cdot n , and you can sort the array under the constraints. In the "...