CSES Problem Set

# Tree Distances

CSES - Tree DistancesCSES - Tree Distances

 Time limit: 1.00 s Memory limit: 512 MB

You are given a tree that consists 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 that describe 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
• $1 \le n \le 5 \cdot 10^5$
• $1 \le a,b \le n$
Example

Input:
5 1 2 1 3 3 4 3 5

Output:
2 3 2 3 3