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

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