Tree Distances I

You are given a tree consisting of n nodes. Your task is to determine for each node the maximum distance to another node.

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 maximum distance to another node.

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

2 3 2 3 3