You are given a tree with $$$n$$$ nodes numbered from $$$1$$$ to $$$n$$$, along with an array of size $$$n$$$. The value of $$$i$$$-th node is $$$a_{i}$$$. There are $$$q$$$ queries. In each query, you are given 2 nodes numbered as $$$x$$$ and $$$y$$$.

Consider the path from the node numbered as $$$x$$$ to the node numbered as $$$y$$$. Let the path be represented by $$$x = p_0, p_1, p_2, \ldots, p_r = y$$$, where $$$p_i$$$ are the intermediate nodes. Compute the sum of $$$a_{p_i}\oplus i$$$ for each $$$i$$$ such that $$$0 \le i \le r$$$ where $$$\oplus$$$ is the XOR operator.

More formally, compute $$$$$$\sum_{i =0}^{r} a_{p_i}\oplus i$$$$$$.

Input

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases. Each test case contains several sets of input data.

The first line of each set of input data contains a single integer $$$n$$$ ($$$1 \le n \le 5 \cdot 10^5$$$) — the number of nodes.

The next $$$n-1$$$ lines of each set of input data contain $$$2$$$ integers, $$$u$$$ and $$$v$$$ representing an edge between the node numbered $$$u$$$ and the node numbered $$$v$$$. It is guaranteed that $$$u \ne v$$$ and that the edges form a tree.

The next line of each set of input data contains $$$n$$$ integers, $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \le a_i \le 5 \cdot 10^5$$$) — values of the nodes.

The next line contains a single integer $$$q$$$ ($$$1 \le q \le 10^5$$$) — the number of queries.

The next $$$q$$$ lines describe the queries. The $$$i$$$-th query contains $$$2$$$ integers $$$x$$$ and $$$y$$$ ($$$1 \le x,y \le n$$$) denoting the starting and the ending node of the path.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$5 \cdot 10^5$$$ and sum of $$$q$$$ over all test cases does not exceed $$$10^5$$$.

Output

For each query, output a single number — the sum from the problem statement.

Your Loss

Examples