Problem Statement

Start City has $N$ towns and $N - 1$ roads.
Road $i$ connects town $A_i$ and town $B_i$ bidirectionally, and it is possible to travel between any $2$ towns by following some roads.

Now, at night in Start City, ghosts appear in $M$ towns $V_1, \cdots, V_M$.

Each ghost casts an area spell and
plays pranks on all towns reachable from the town where it appeared by following $0$ or $1$ roads.

Cleaning up after the pranks is a lot of work, so it was decided to perform an exorcism.
When an exorcism is performed in town $v$ ($1 \le v \le N$),
a spell is cast that annihilates the ghosts that appeared in towns reachable from town $v$ by following $0$ or $1$ roads.
Ghosts hit by this spell can no longer play pranks on any town.

The exorcism is hard work, so it can be performed only $1$ time. Therefore, the choice of the town in which to perform it is an important matter.
For each of $v = 1, 2, \cdots, N$, find the number of towns on which pranks are played if the exorcism is performed in town $v$.

Input

$N$
$A_1$ $B_1$
$\cdots$
$A_{N-1}$ $B_{N-1}$
$M$
$V_1 \dots V_M$

• All inputs are integers
• It is possible to reach any $2$ towns from each other by following some roads
• $2 \le N \le 200000$
• $1 \le A_i \le N, 1 \le B_i \le N$
• $1 \le M \le N$
• $1 \le V_1 \lt V_2 \lt \cdots \lt V_M \le N$

Output

On line $i$ ($1 \le i \le N$), output the number of towns on which pranks are played if the exorcism is performed in town $i$.

Sample

6
1 2
2 3
3 4
3 5
5 6
3
2 3 6

5
2
2
5
3
5