Consider a Permutation \(P\) of length \(N\).

Let us define an operation on \(P\) as follows:

For example

Let initially \(P = [2\ 3\ 1] \)

So, \(P[1] = 2, P[2] = 3, P[3] = 1\)

After \(1\) operation:

\(P[1]\) becomes \(P[P[1]] = P[2] = 3\)

\(P[2]\) becomes \(P[P[2]] = P[3] = 1\)

\(P[3]\) becomes \(P[P[3]] = P[1] = 2\)

So, \(P\) becomes \([3\ 1\ 2]\)

You need to find the minimum number of operations after which \(P\) becomes an Identity Permutation.

Output \(-1\) if not possible.

Note

Input Format

The First line contains an integer \(T\) representing the number of test cases.
Each test case contains an integer \(N\) representing the size of permutation \(P\).
Next line contains \(N\) space seperated integers representing the permutation \(P\).

Output Format

For each test case, Print the minimum number of operations as asked, output \(-1\) if not possible.

Constraints