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CSES Problem Set

Tree Distances II


Task | Statistics


CSES - Tree Distances II

Time limit:1.00 s Memory limit:512 MB

You are given a tree that consists 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 that describe 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
Example

Input:
5
1 2
1 3
3 4
3 5


Output:
6 9 5 8 8