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:

$$V X$$: Find the longest length prefix that is common in the binary representation of $$V$$ and the binary representation of node value of any of the ancestors of node $$X$$ including node $$X$$ itself. Also, the binary representation should be of length $$62$$ and of the order from Most Significant Bit to Least Significant Bit.

Find 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 $$v$$.
The prefix of a binary representation is defined as a contiguous set of bits from the starting of the representation.

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 $$A$$.
- Next $$N - 1$$ lines contain two space-separated integers $$u v$$ denoting an edge between node $$u$$ and $$v$$.
- The next line contains an integer $$Q$$.
- Next $$Q$$ lines contain two space-separated integers $$V X$$ denoting the query.

Output format

For each test case, print $$Q$$ space-separated integers denoting the longest length common prefix for $$Q$$ queries. Print the output for each test case in a new line.

Constraints

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