#QTREE7. Query on a tree VII

Query on a tree VII

You are given a tree (an acyclic undirected connected graph) with n nodes. The tree nodes are numbered from 1 to n. Each node has a color, white or black, and a weight. We will ask you to perfrom some instructions of the following form:

  • 0 u: ask for the maximum weight among the nodes which are connected to u, two nodes are connected if all the node on the path from u to v (inclusive u and v) have a same color.
  • 1 u: toggle the color of u(that is, from black to white, or from white to black).
  • 2 u w: change the weight of u to w.

Input

The first line contains a number n denoted how many nodes in the tree(1 ≤ n ≤ 105). The next n-1 lines, each line has two numbers (u, v) describe a edge of the tree(1 ≤ u, v ≤ n). The next 2 lines, each line contains n number, the first line is the initial color of each node(0 or 1), and the second line is the initial weight, let's say Wi, of each node(|Wi| ≤ 109). The next line contains a number m denoted how many operations we are going to process(1 ≤ m ≤ 105). The next m lines, each line describe a operation (t, u) as we mentioned above(0 ≤ t ≤ 2, 1 ≤ un, |w| ≤ 109).

Output

For each query operation, output the corresponding result.

Example

Input 1:
5
5 1 2 1 3 1 4 1 5 0 1 1 1 1 1 2 3 4 5 3 0 1 1 1 0 1
1 2

Output 1:
1 5

Input 2:
7 1 2 1 3 2 4 2 5 3 6 3 7 0 0 0 0 0 0 0 1 2 3 4 5 6 7 4 0 1 1 1 0 2 0 3

Output 2:

7 5 7


Warning: large input/output data,be careful with certain languages