You are given a rooted tree with \(n\) vertices. Here, \(A\) and \(B\) are playing with the tree. In each turn (starting with \(A\)), each player can select a vertex \(v\) that contains no parent and delete a path with at least two vertices starting from \(v\).
A player loses if he or she cannot make the turn in the game. For each test case, determine who will win.

Input format

The first line contains \(t\) denoting the number of test cases.
The first line of each test case contains \(n\) denoting the number of tree's vertices.
Next \(n-1\) lines of each test case contain \(p_{i}\) that means the \((i+1)^{th}\) vertex's parent is \(p_{i} \).

Output format

For each test case, print \(A\) if \(A\) wins, otherwise print \(B\).

Constraints

\(1 \leq n \leq 5 \times 10^4\)

\(1 \le p_{i} \le i\)

\(1 \le t \le 10\)