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 perform 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 ≤ u ≤ n, |w| ≤ 10⁹).

Output

For each query operation, output the corresponding result.

Example

Input 1:
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
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