Balanced Tree Node Query

You are given a tree with n nodes. Each node has an associated integer value. The tree is provided as an undirected graph with n-1 edges. The tree is rooted at node 1, and for each node, its children are assigned as follows: when performing a DFS from the root, the first encountered child becomes the left child and the second becomes the right child. (Any extra children beyond two are ignored.)

A node is considered balanced if the sum of values in its left subtree equals the sum of values in its right subtree. Formally, if for a node u we let S_L(u) be the sum of values in the left subtree and S_R(u) be the sum in the right subtree, then u is balanced if:

$$ S_L(u) = S_R(u) $$

You will be given several queries. Each query is a node index, and for each query, you must determine whether the queried node is balanced.

inputFormat

The input is given in stdin and has the following format:

n
v1 v2 ... vn
u1 v1
u2 v2
... (n-1 lines of edges)
q
q1 q2 ... qq

Here:

• n is the number of nodes.
• The next line contains n integers representing the values of the nodes 1 through n.
• Each of the next n-1 lines contains two integers representing an undirected edge between two nodes.
• q is the number of queries.
• The last line contains q integers, each an index of a node to be queried.

outputFormat

For each query, print a line containing either YES if the queried node is balanced, or NO if it is not.

The output should be written to stdout.

## sample

5
1 2 3 4 5
1 2
1 3
3 4
3 5
2
3 2

NO
YES

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