You have a root tree containing n vertexes. Let's number the tree vertexes with integers from 1 to n. The tree root is in the vertex 1.

Each vertex (except fot the tree root) v has a direct ancestor p_v. Also each vertex v has its integer value s_v.

Your task is to perform following queries:

P v u (u ≠ v). If u isn't in subtree of v, you must perform the assignment p_v = u. Otherwise you must perform assignment p_u = v. Note that after this query the graph continues to be a tree consisting of n vertexes.
V v t. Perform assignment s_v = t.

Your task is following. Before starting performing queries and after each query you have to calculate expected value written on the lowest common ancestor of two equiprobably selected vertices i and j. Here lowest common ancestor of i and j is the deepest vertex that lies on the both of the path from the root to vertex i and the path from the root to vertex j. Please note that the vertices i and j can be the same (in this case their lowest common ancestor coincides with them).

Input

The first line of the input contains integer n (2 ≤ n ≤ 5·10⁴) — the number of the tree vertexes.

The second line contains n - 1 integer p₂, p₃, ..., p_n (1 ≤ p_i ≤ n) — the description of the tree edges. It is guaranteed that those numbers form a tree.

The third line contains n integers — s₁, s₂, ... s_n (0 ≤ s_i ≤ 10⁶) — the values written on each vertex of the tree.

The next line contains integer q (1 ≤ q ≤ 5·10⁴) — the number of queries. Each of the following q lines contains the description of the query in the format described in the statement. It is guaranteed that query arguments u and v lie between 1 and n. It is guaranteed that argument t in the queries of type V meets limits 0 ≤ t ≤ 10⁶.

Output

Print q + 1 number — the corresponding expected values. Your answer will be considered correct if its absolute or relative error doesn't exceed 10^- 9.

Note

Note that in the query P v u if u lies in subtree of v you must perform assignment p_u = v. An example of such case is the last query in the sample.

ELCA

Examples