You are given a tree consisting of $n$ nodes.
Your task is to determine for each node the maximum distance to another node.
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 $b$ .
Print $n$ integers: for each node $1,2,\ldots,n$ , the maximum distance to another node.