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문제

Every day each of Farmer John's N (1 <= N <= 100,000) cows conveniently numbered 1..N move from the barn to her private pasture. The pastures are organized as a tree, with the barn being on pasture 1. Exactly N-1 cow unidirectional paths connect the pastures; directly connected pastures have exactly one path. Path i connects pastures A_i and B_i (1 <= A_i <= N; 1 <= B_i <= N).

Cow i has a private pasture P_i (1 <= P_i <= N). The barn's small door lets only one cow exit at a time; and the patient cows wait until their predecessor arrives at her private pasture. First cow 1 exits and moves to pasture P_1. Then cow 2 exits and goes to pasture P_2, and so on.

While cow i walks to P_i she might or might not pass through a pasture that already contains an eating cow. When a cow is present in a pasture, cow i walks slower than usual to prevent annoying her friend.

Consider the following pasture network, where the number between parentheses indicates the pastures' owner.

1 (3)
/ \
(1) 4   3 (5)
/ \
(2) 2   5 (4)

First, cow 1 walks to her pasture:

1 (3)
/ \
[1] 4*  3 (5)
/ \
(2) 2   5 (4)

When cow 2 moves to her pasture, she first passes into the barn's pasture, pasture 1. Then she sneaks around cow 1 in pasture 4 before arriving at her own pasture.

1 (3)
/ \
[1] 4*  3 (5)
/ \
[2] 2*  5 (4)

Cow 3 doesn't get far at all -- she lounges in the barn's pasture, #1.

1* [3]
/ \
[1] 4*  3 (5)
/ \
[2] 2*  5 (4)

Cow 4 must slow for pasture 1 and 4 on her way to pasture 5:

1* [3]
/ \
[1] 4*  3 (5)
/ \
[2] 2*  5* [4]

Cow 5 slows for cow 3 in pasture 1 and then enters her own private pasture:

1* [3]
/ \
[1] 4*  3*[5]
/ \
[2] 2*  5* [4]

FJ would like to know how many times each cow has to slow down.

입력

• Line 1: Line 1 contains a single integer: N
• Lines 2..N: Line i+1 contains two space-separated integers: A_i and B_i
• Lines N+1..N+N: line N+i contains a single integer: P_i

출력

• Lines 1..N: Line i contains the number of times cow i has to slow down.

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

0
1
0
2
1