You are given a tree consisting of ~n~ nodes.

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

Input

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

Then there are ~n-1~ lines describing the edges. Each line contains two integers ~a~ and ~b~: there is an edge between nodes ~a~ and ~b~.

Output

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

Constraints

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

Example Input

5
1 2
1 3
3 4
3 5

Example Output

2 3 2 3 3