Problem Statement

Given is a tree with N vertices. The vertices are numbered $1,2,\ldots ,N$, and the i-th edge is an undirected edge connecting Vertices u_i and v_i.
For each integer i$,(1 \leq i \leq N), find \sum_{j=1}^{N}dis(i,j)$.
Here, dis(i,j) denotes the minimum number of edges that must be traversed to go from Vertex i to Vertex j.

Input

Input is given from Standard Input in the following format:
N
u_1 v_1
u_2 v_2
$\vdots$
u_{N-1} v_{N-1}

Output

Print N lines.
The i-th line should contain $\sum_{j=1}^{N}dis(i,j)$.

Constraints

• $2 \leq N \leq 2 \times 10^5$
• $1 \leq u_i < v_i \leq N$
• The given graph is a tree.
• All values in input are integers.

Sample Input 1

3
1 2
2 3

Sample Output 1

3
2
3

We have:
dis(1,1)+dis(1,2)+dis(1,3)=0+1+2=3,
dis(2,1)+dis(2,2)+dis(2,3)=1+0+1=2,
dis(3,1)+dis(3,2)+dis(3,3)=2+1+0=3.

Sample Input 2

2
1 2

Sample Output 2

1
1

Sample Input 3

6
1 6
1 5
1 3
1 4
1 2

Sample Output 3

5
9
9
9
9
9

见题面 Input 部分

见题面 Output 部分