#P1039D. You Are Given a Tree

    ID: 4390 Type: RemoteJudge 7000ms 512MiB Tried: 0 Accepted: 0 Difficulty: (None) Uploaded By: Tags>data structuresdptrees*2800

You Are Given a Tree

No submission language available for this problem.

Description

A tree is an undirected graph with exactly one simple path between each pair of vertices. We call a set of simple paths $k$-valid if each vertex of the tree belongs to no more than one of these paths (including endpoints) and each path consists of exactly $k$ vertices.

You are given a tree with $n$ vertices. For each $k$ from $1$ to $n$ inclusive find what is the maximum possible size of a $k$-valid set of simple paths.

The first line of the input contains a single integer $n$ ($2 \le n \le 100\,000$) — the number of vertices in the tree.

Then following $n - 1$ lines describe the tree, each of them contains two integers $v$, $u$ ($1 \le v, u \le n$) — endpoints of the corresponding edge.

It is guaranteed, that the given graph is a tree.

Output $n$ numbers, the $i$-th of which is the maximum possible number of paths in an $i$-valid set of paths.

Input

The first line of the input contains a single integer $n$ ($2 \le n \le 100\,000$) — the number of vertices in the tree.

Then following $n - 1$ lines describe the tree, each of them contains two integers $v$, $u$ ($1 \le v, u \le n$) — endpoints of the corresponding edge.

It is guaranteed, that the given graph is a tree.

Output

Output $n$ numbers, the $i$-th of which is the maximum possible number of paths in an $i$-valid set of paths.

Samples

7
1 2
2 3
3 4
4 5
5 6
6 7

7
3
2
1
1
1
1


6
1 2
2 3
2 4
1 5
5 6

6
2
2
1
1
0


Note

One way to achieve the optimal number of paths for the second sample is illustrated in the following picture: