Given a rooted tree with $1$ as the root, the parent of node $i$ is $p_i$, and its color is $col_i$, where $col_i \in \{0, 1\}$.

Alice and Bob play a game on this tree. They take turns making moves, with Alice going first. In each turn, a player chooses a node $x$ such that $x=1$ or $p_x$ has already been removed, and removes $x$.

If the color of the last removed node is $0$, Alice wins; otherwise, Bob wins. Both players play optimally to win.

Given $T$ test cases, determine the winner for each case.

Input

The first line contains a positive integer $T$, representing the number of test cases. The format for each test case is as follows:

• The first line contains a positive integer $n$.
• The second line contains $n-1$ positive integers $p_2, p_3, \dots, p_n$.
• The third line contains $n$ non-negative integers $col_1, col_2, \dots, col_n$.

Output

For each test case, output a single line containing Alice or Bob, indicating the winner.

Constraints

This problem uses subtask-based testing.

For all test cases, it is guaranteed that $1 \le T \le 10000$, $1 \le \sum n \le 5 \times 10^5$, $1 \le p_i < i$, and $0 \le col_i \le 1$.

Subtask $1$ ($20$ pts): Guaranteed $T=1, n \le 20$.

Subtask $2$ ($30$ pts): Guaranteed that for all $i$, $i=1 \lor p_i=1 \lor p_{p_i}=1$.

Subtask $3$ ($20$ pts): Guaranteed that for all $i$, either $i$ is a leaf or the size of the subtree rooted at $i$ is even.

Subtask $4$ ($30$ pts): No additional restrictions.

Examples

Input 1

3
2
1
1 0
5
1 2 2 1
0 0 0 1 0
8
1 2 2 2 1 6 1
1 0 0 0 1 0 1 0

Output 1

Alice
Bob
Alice