CF482E.ELCA

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).

你有一棵包含 $n$ 个顶点的有根树。我们将树的顶点编号为 $1$ 到 $n$，其中根节点位于顶点 $1$。

每个顶点（除根节点外）$v$ 都有一个直接父节点 $p_v$。此外，每个顶点 $v$ 还有一个整数值 $s_v$。

你需要执行以下两类查询：

• P v u（其中 $u \ne v$）。若 $u$ 不在 $v$ 的子树中，则执行赋值操作 $p_v = u$；否则执行赋值操作 $p_u = v$。注意：执行该查询后，图仍是一棵包含 $n$ 个顶点的树。
• V v t。执行赋值操作 $s_v = t$。

你的任务如下：在开始执行查询之前，以及每次查询执行完毕之后，你都需要计算：随机等概率地选取两个顶点 $i$ 和 $j$（允许 $i = j$），它们的最近公共祖先（LCA）上所写数值的期望值。此处，$i$ 与 $j$ 的最近公共祖先定义为同时位于从根到顶点 $i$ 的路径、以及从根到顶点 $j$ 的路径上的深度最大的顶点。请注意，当 $i = j$ 时，其最近公共祖先即为 $i$（或 $j$）自身。

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.

输入的第一行包含一个整数 $ n $（$ 2 \leq n \leq 5 \cdot 10^4 $）——树的顶点数量。

第二行包含 $ n-1 $ 个整数 $ p_2, p_3, \dots, p_n $（$ 1 \leq p_i \leq n $）——树的边的描述。保证这些数字构成一棵树。

第三行包含 $ n $ 个整数——$ s_1, s_2, \dots, s_n $（$ 0 \leq s_i \leq 10^6 $）——树中每个顶点上所写的数值。

接下来一行包含一个整数 $ q $（$ 1 \leq q \leq 5 \cdot 10^4 $）——查询的数量。随后的 $ q $ 行每行包含一个按题面所述格式描述的查询。保证查询中的参数 $ u $ 和 $ v $ 均在 $ 1 $ 到 $ n $ 之间。保证类型为 V 的查询中的参数 $ t $ 满足限制 $ 0 \leq t \leq 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.

输出 $q + 1$ 个数——对应的期望值。若你的答案的绝对或相对误差不超过 $10^{-9}$，则视为正确。

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.

注意，在查询 $P_{v\,u}$ 中，如果 $u$ 位于 $v$ 的子树中，则必须执行赋值操作 $p_u = v$。样例中的最后一个查询即为这种情况的一个示例。