- Time limit: 1.00 s
- Memory limit: 512 MB
You are given a tree consisting of nodes.
Your task is to determine for each node the maximum distance to another node.
Input
The first input line contains an integer : the number of nodes. The nodes are numbered .
Then there are lines describing the edges. Each line contains two integers and : there is an edge between nodes and .
Output
Print integers: for each node , the maximum distance to another node.
Constraints
Example
Input:
5 1 2 1 3 3 4 3 5
Output:
2 3 2 3 3