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

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

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

\(1 \le t \le 10\)