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

$1 \leq n \leq 5 \times 10^4$

$1 \le p_{i} \le i$

$1 \le t \le 10$