CSES - Tree Distances II
• Time limit: 1.00 s
• Memory limit: 512 MB
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 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 $b$.

Output

Print $n$ integers: for each node $1,2,\ldots,n$, the sum of the distances.

Constraints
• $1 \le n \le 2 \cdot 10^5$
• $1 \le a,b \le n$
Example

Input:
5 1 2 1 3 3 4 3 5

Output:
6 9 5 8 8