You are given an undirected tree with $$N$$ nodes rooted at node 1. Every node has a value $$A[i]$$ assigned to it. You are required to answer $$Q$$ queries of the following type:

$$U V X$$
- Select a subtree with $$U$$ as the root node and subtree with $$V$$ as the root node and swap their positions. That is, detach both the subtrees and swap their positions.
- If node $$U$$ is an ancestor of node $$V$$ or node $$V$$ is an ancestor of node $$U$$, the above Swap operation is not performed.
- Find the sum of node values present in the subtree rooted at node $$X$$.
- If the Swap operation is performed, then redo this operation. That is, swap the subtree with $$U$$ as the root node and subtree with $$V$$ as the root node.

Determine the required answer for $$Q$$ queries.

Note

Assume 1-based indexing.
A node $$u$$ is said to be an ancestor of node $$v$$ if node $$u$$ lies on a simple path between the root and node $$v$$.
Here, Redo means re-doing the operation performed.

Input format

The first line contains a single integer $$T$$ that denotes the number of test cases.
For each test case:
- The first line contains an integer $$N$$.
- The second line contains $$N$$ space-separated integers denoting array $$A$$.
- The next $$N - 1$$ line contains two space-separated integers $$u v$$ denoting an edge between node $$u$$ and $$v$$.
- The next line contains an integer $$Q$$.
- The next $$Q$$ lines contain three space-separated integers $$U V X$$ denoting the query.

Output format

For each test case, print $$Q$$ space-separated integers denoting the sum of node values present in the subtree rooted at node $$X$$ after the swap operation is performed. Print the output for each test case in a new line.

Constraints

\(1 \le T \le 10 \\ 1 \le N, Q \le 10^5 \\ 1 \le A[i] \le 10^9 \\ 1 \le U, V, X \le N\)