CSES - Tree Distances I
  • Time limit: 1.00 s
  • Memory limit: 512 MB

You are given a tree consisting of nn nodes.

Your task is to determine for each node the maximum distance to another node.

Input

The first input line contains an integer nn: the number of nodes. The nodes are numbered 1,2,,n1,2,\ldots,n.

Then there are n1n-1 lines describing the edges. Each line contains two integers aa and bb: there is an edge between nodes aa and bb.

Output

Print nn integers: for each node 1,2,,n1,2,\ldots,n, the maximum distance to another node.

Constraints

  • 1n21051 \le n \le 2 \cdot 10^5
  • 1a,bn1 \le a,b \le n

Example

Input:

5
1 2
1 3
3 4
3 5

Output:

2 3 2 3 3