Tree Distances I

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 line contains an integer $n(1\le n\le 2\cdot 10^5)$ — the number of nodes. The nodes are numbered $1,2,..,n$.

Then there are $n-1$ lines describing the edges. Each line contains two integers $a$ and $b(1\le a,b\le n)$ — there is an edge between nodes $a$ and $b$.

Output

Print $n$ integers: for each node $1,2,..,n$ the maximum distance to another node.

Examples