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F. Dominant Indices
time limit per test
4.5 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

You are given a rooted undirected tree consisting of $$$n$$$ vertices. Vertex $$$1$$$ is the root.

Let's denote a depth array of vertex $$$x$$$ as an infinite sequence $$$[d_{x, 0}, d_{x, 1}, d_{x, 2}, \dots]$$$, where $$$d_{x, i}$$$ is the number of vertices $$$y$$$ such that both conditions hold:

  • $$$x$$$ is an ancestor of $$$y$$$;
  • the simple path from $$$x$$$ to $$$y$$$ traverses exactly $$$i$$$ edges.

The dominant index of a depth array of vertex $$$x$$$ (or, shortly, the dominant index of vertex $$$x$$$) is an index $$$j$$$ such that:

  • for every $$$k < j$$$, $$$d_{x, k} < d_{x, j}$$$;
  • for every $$$k > j$$$, $$$d_{x, k} \le d_{x, j}$$$.

For every vertex in the tree calculate its dominant index.

Input

The first line contains one integer $$$n$$$ ($$$1 \le n \le 10^6$$$) — the number of vertices in a tree.

Then $$$n - 1$$$ lines follow, each containing two integers $$$x$$$ and $$$y$$$ ($$$1 \le x, y \le n$$$, $$$x \ne y$$$). This line denotes an edge of the tree.

It is guaranteed that these edges form a tree.

Output

Output $$$n$$$ numbers. $$$i$$$-th number should be equal to the dominant index of vertex $$$i$$$.

Examples
Input
4
1 2
2 3
3 4
Output
0
0
0
0
Input
4
1 2
1 3
1 4
Output
1
0
0
0
Input
4
1 2
2 3
2 4
Output
2
1
0
0