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). The first line of the input contains integer n ( 2 ≤ n ≤ 5·10 4 ) — 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 ≤ 10 6 ) — the values written on each vertex of the tree. The next line contains integer q ( 1 ≤ q ≤ 5·10 4 ) — 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 ≤ 10 6 . 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 that in the query P v u if u lies in subtree of v you must perf