— What is my mission?

— To count graph diameters.

You and Your Submission

A tree is a connected undirected graph without cycles. A weighted tree has a weight assigned to each edge. The degree of a vertex is the number of edges connected to this vertex.

You are given a weighted tree with $$$n$$$ vertices, each edge has a weight of $$$1$$$. Let $$$L$$$ be the set of vertices with degree equal to $$$1$$$.

You have to answer $$$q$$$ independent queries. In the $$$i$$$-th query:

You are given a positive integer $$$x_i$$$.
For all $$$u,v \in L$$$ such that $$$u \lt v$$$, add edge $$$(u, v)$$$ with weight $$$x_i$$$ to the graph (initially the given tree).
Find the diameter of the resulting graph.

The diameter of a graph is equal to $$$\max\limits_{1 \le u \lt v \le n}{\operatorname{d}(u, v)}$$$, where $$$\operatorname{d}(u, v)$$$ is the length of the shortest path between vertex $$$u$$$ and vertex $$$v$$$.

Input

The first line contains a single integer $$$n$$$ ($$$3 \le n \le 10^6$$$).

The second line contains $$$n - 1$$$ integers $$$p_2,p_3,\ldots,p_n$$$ ($$$1 \le p_i \lt i$$$) indicating that there is an edge between vertices $$$i$$$ and $$$p_i$$$. It is guaranteed that the given edges form a tree.

The third line contains a single integer $$$q$$$ ($$$1 \le q \le 10$$$).

The fourth line contains $$$q$$$ integers $$$x_1,x_2,\ldots,x_q$$$ ($$$1 \le x_i \le n$$$). All $$$x_i$$$ are distinct.

Output

Print $$$q$$$ integers in a single line — the answers to the queries.

Note

The graph in the first test after adding the edges:

$\text{[math]}$

Triameter

Examples