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.