Path Sum

You are given a tree with n nodes (numbered from 1 to n), node 1 is the root of tree.
Each node has a value say Vi is the value of i'th node.

You have to perform q queries of two types:-
1 i v : change the value of i'th node to v,
2 i   : add all nodes on path from root to i'th node.

Input Format

First line contains single integer n. second line contains n integers v1 v2 v3 .... vn third line contains n-1 integers p2 p3 p4 ... pn here pi is the parent of i'th node fourth line contains single int q q following lines contains queries of type 1 and 2

Output Format

of every query of type 2 print sum of values.

Constraints

1. 1 <= N <= 10^5
2. 1 <= Vi <= 10^4
3. 1 <= q <= 10^4

Example

8
4 7 9 5 2 1 3 5 
1 1 1 4 3 4 1 
7
1 4 3
1 3 8
2 7
1 4 6
1 1 7
2 3
2 4

10
15
13