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Problem
Editorial
Analytics

You are given a tree containing $N$ nodes(numbered from $1$ to $N$) and each node has a value associated with it. We define 'special value' of any graph as the maximum absolute difference of values of any two nodes such that there exists a path between them. Now you are given $N-1$ integers denoting that you have to delete ith edge at the ith step and find the 'special value' of the graph thus formed.

INPUT:

First line constains an integer $N$-number of nodes.
Next $N-1$ lines contains two integers $u$ $v$ denoting that there is a bidirectional edge between node $u$ and $v$
Next line contains $N$ integers ith of which is the value of node i.
Next $N-1$ lines contains an integer $x$ where the ith line denotes the index of the edge to be deleted at ith step.

Note: Every edge will be deleted exactly once.

OUTPUT:
Print $N-1$ lines where ith line should contain the 'special value' of the graph formed after deleting the edges of first i steps.

CONTRAINTS:
1 <= $N$ <= 105
0 <= value of each node <=109
1 <= $u$ , $v$ <= $N$
1 <= $x$ <= $N-1$

SAMPLE INPUT
3
1 2
2 3
1 2 3
2
1
SAMPLE OUTPUT
1
0

Explanation

In the 1st  first step edge between node number 2 and 3 is deleted so the maximum difference of values is between node number 1 and 2 which is 1.

After deleting edge between node 1 and 2 no two nodes are connected hence answer is 0.

Time Limit: 1.0 sec(s) for each input file.
Memory Limit: 256 MB
Source Limit: 1024 KB

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