E. ELCA
time limit per test
8 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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.

• 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 p 2, p 3, ..., 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 — s 1, s 2, ... 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.

Examples
Input
51 2 2 11 2 3 4 55P 3 4P 4 5V 2 3P 5 2P 1 4
Output
1.6400000001.8000000002.2800000002.3200000002.8000000001.840000000
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.