Imagine a network of $N$ points connected by $N-1$ lines, forming a tree-like structure. Every point has a number assigned to it, given as an array $Arr$ of size $N$. Now, you need to answer $Q$ queries. In each query, you're asked to do the following:

1. Pick any number from $0$ to $X$ (inclusive). Let's refer to this number $α$.
2. Temporarily change each point's number to the Bitwise XOR result of that point's initial value and $α$.
3. After the above modification, determine the maximum value that can be obtained by performing a Bitwise XOR operation on all numbers on points that lie on the simple path between points $A$ and $B$ (including $A$ & $B$).

Note: A simple path is a path in a tree that does not have repeating points.

Input Format:

• The first line contains a single integer $T$, which denotes the number of test cases.
• For each test case:
  • The first line contains $N$ denoting the number of points.
  • The following $N-1$ lines contain 2 space-separated integers, $U$ & $V$ indicating that there is a link between points $U$ & $V$ 
  • The second line contains $N$ space-separated integers, denoting the numbers assigned to every point.
  • The next line contains $Q$ denoting the number of queries.
  • The next $Q$ lines contain 3 space-separated integers, $X$, $A$ and $B$.

Output Format:

For each test case, answer all the $Q$ queries. For each query, print in a new line the maximum Bitwise XOR result of all the numbers on points that lie on the simple path between points $A$ and $B$ (inclusive) for each query that you can get after choosing a number $α$, which lies between $0$ & $X$ (inclusive), and each points value has been temporarily modified to Bitwise XOR result of the initial value of that point and $α$.

Constraints:

$1 \leq T \leq 10^5 \\ 3 \leq N \leq 10^5 \\ 0 ≤ Arr[i] ≤ 10^{9}\ ∀\ i∈[1,N] \\ 1≤U, V≤N\\ 1≤Q≤10^5\\ 0≤X≤10^9 \\ 1≤A, B≤N \\ \text{The sum of all values of N over all test cases doesn't exceed } 10^6 \\ \text{The sum of all values of Q over all test cases doesn't exceed } 10^6$