**Time limit:**1.00 s**Memory limit:**512 MB

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`