Given a connected tree with \(N\) vertices and \(N-1\) edges, you must answer \(M\) queries of the type:

• given three unique vertices \(A\), \(B\), and \(C\), find if there exists a simple path that contains all three vertices.

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

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 vertices in the tree.
  • The next \(N-1\) lines contain 2 space-separated integers, \(u\) and \(v\), indicating that there is an edge between vertices \(u\) & \(v\).
  • The next line contains \(M\) denoting the number of queries.
  • The next \(M\) lines contain 3 unique space-separated integers, \(A\), \(B\), and \(C\).

Output format

For each test case, answer all the \(M\)  queries. For each query print \(\text{Yes}\) if there exists a simple path that contains all three vertices \(A\), \(B\), and \(C\), otherwise print \(\text{No}\). Print answer for each query in a new line.

Constraints

\(1 \leq T \leq 10^5 \\ 3 \leq N \leq 2×10^5 \\ 1≤u,v≤N\\ \\ 1 \leq M \leq 2×10^5\\ 1≤A, B, C≤N\  \\ \text{The sum of all values of N over all test cases doesn't exceed } 2×10^5 \\ \text{The sum of all values of M over all test cases doesn't exceed } 2×10^5\)