Description
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 iff 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.
Sample Input
51 2
1 3
1 4
1 5
0 1 1 1 1
1 2 3 4 5
3
0 1
1 1
0 1
Sample Output
15
