**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 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