Problem Statement

You are given a tree with $N$ vertices numbered $1,2,\dots ,N$. For $i=1,2,\dots ,N-1$, the $i$-th edge connects vertex $u_i$ and vertex $v_i$.

For each $v=1,2,\dots ,N$, find the number of vertices whose distance from vertex $v$ is $2$.

Constraints

• All input values are integers.
• $2\le N\le 3\times 10^5$
• $1\le u_i,v_i\le N\ (1\le i\le N-1)$
• The given graph is a tree.

Input

$N$
$u_1$ $v_1$
$\vdots$
$u_{N-1}$ $v_{N-1}$

Output

Print $N$ lines. On the $v$-th line, print the number of vertices whose distance from vertex $v$ is $2$.

Sample

5
1 2
2 3
3 4
3 5

1
2
1
2
2

2
1 2

0
0

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

4
3
3
2
2
2
1
1
1
1