There are many ways to order a list of integers from 1 to n. For example, if \( n = 3\), the list could be : \([3\; 1\; 2]\).

But there is a special way to create another list from the given list of integers. In this list, position of integer i is the \(i-th\) number in the given list. So following this rule, the given list will be written as: \([2\; 3\; 1]\). This list is called inverse list. Now there exists some list whose inverse list is identical. For example, inverse list of \([1\; 2\; 3]\) is same as given list. Given a list of integers you have to determine whether the list is inverse or not.

The input contains several test cases. The first line is the number of test cases t \((1 <= t <= 100)\) . The first line of each test case contains an integer \(n \;(1 <= n <= 100000)\). Then a list of the integers 1 to n follows in the next line.