Tree Distances II

You are given a tree consisting of $n$ nodes.

Your task is to determine for each node the sum of the distances from the node to all other nodes.

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 sum of the distances.

Examples