You are given a tree consisting of $n$ nodes. Your task is to determine for each node the maximum distance to another node. \InputFile 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 $b$. \OutputFile Print $n$ integers: for each node $1, 2, .., n$ the maximum distance to another node. \includegraphics{https://static.eolymp.com/content/b8/b8edde7cu167n2498j70b6fogc.gif}