Tree Distances I

Input

The first line contains an integer n~(1 \le n \le 2 \cdot 10^5) — the number of vertices in the tree. The vertices are numbered from $1$ to $n$.

The next n - 1 lines describe the edges: each line contains two integers $a$ and b~(1 \le a, b \le n), indicating that there is an edge between vertices $a$ and $b$.

Output

Print $n$ integers. For each vertex from $1$ to $n$, print the maximum distance to any other vertex in the tree.

Examples