Problem Statement

The sacred tree in niuez's town is home to tree fairies.
When a "tri-butree" is placed on a vertex of a tree, the fairies nearby gather at that vertex.
niuez decided to play with this.

There is an undirected tree with $N$ vertices numbered from $0$ to $N-1$ and $N-1$ edges, where the $i \ (0 \leq i < N-1)$-th edge has endpoints $u_i$ and $v_i$.
Also, there are $A_i$ fairies on vertex $i \ (0 \leq i \le N - 1)$.
Fairies stay only on vertices, and they have the habit that when a "tri-butree" is placed on a vertex at distance $2$ or less from the vertex where they are staying, they move to the vertex where the "tri-butree" was placed.
After moving, the fairies stay on the destination vertex.
Here, the distance between a pair of vertices $a, b$ is defined as the number of edges on the path between $a, b$.
Process the following $Q$ ${\rm query}$ in order.

• $x$

  • Place a "tri-butree" on vertex $x$. Then, find the number of fairies on vertex $x$.

Input

$N$
$u_0 \  v_0$
$\cdots$
$u_{N-2} \  v_{N-2}$
$A_0 \  A_1 \ \cdots \  A_{N-1}$
$Q$
$x_0$
$\cdots$
$x_{Q-1}$

• $2 \leq N \leq 10^5$
• $0 \leq u_i, v_i < N$
  • $u_i \neq v_i$
  • $(u_i, v_i) = (u_j, v_j) \Leftrightarrow i = j$
• $0 \leq A_i \leq 10^5$
• $1 \leq Q \leq 10^5$
• $0 \leq x_i < N$
• All input values are integers.

Output

Output $Q$ lines. On the $i$-th line, output the answer to the $i$-th ${\rm query}$ as an integer.

Sample

10
0 1
0 2
1 3
1 4
2 5
2 6
3 7
3 8
4 9
0 1 2 3 4 5 6 7 8 9
3
1
4
0

34
34
45