Alice was given a tree containing $N$ vertices, numbered $1,...,N$, by her dad as a present. The tree is rooted at vertex $1$ and has $N - 1$ edges. Alice made an interesting task with the tree, can you solve it? 

For every edge in the tree, Alice wrote either an opening bracket $($, or a closing bracket $)$, and now she wants you to answer some queries. She will ask $Q$ queries, and for each query she wants you to check if the brackets on the edges in the path from $u$ to $v$ listed in order forms a balanced bracket sequence. 

For each query your program should output "YES" (without quotes) if the path from $u$ to $v$ forms a balanced bracket sequence and "NO" (without quotes) otherwise. 

A balanced bracket sequence is a string of just brackets that produces a correct mathematical expression when specific numbers and mathematical operations are added to it.

NOTE: In your output YES/NO should be in all uppercase. 

INPUT FORMAT

The first line of the input contains an integer $N$ ($1 <= N <= 10^5$) - the number of vertices. 

This is followed by $N - 1$ lines, each containing an integer, $p_{j}$ ($1 <= p_{j} < j$), and a character $c_{j}$ - the parent of vertex $j$, and the type of bracket on the edge going from $p_{j}$ to $j$. The value of $j$ runs through all values from $2$ to $n$ inclusive. It is guaranteed that each set of input data has a correct hanged tree with a root at the vertex $1$.

The next line contains an integer, $Q$ $(1 <= Q <= 10^5)$ - the number of queries. 

The following $Q$ lines contain two integers $u$ ($1 <= u <= n$), and $v$ ($1 <= v <= n$), $u \neq v$ - denoting the start and end of a path that needs to be checked. 

OUTPUT FORMAT 

You should answer all Q queries, hence the output should contain Q lines containing either a string YES or NO.