%
% Summer Russian school training informatics camp
% Wednesday, 29 June 2016 
% 
% Problem: Mikhail Ipatov
% Tests: Nikolai Kalinin, Mikhail Ipatov
% Solutions: Nikolai Kalinin
% Idea: Ilya Peresadin
%
\begin{problem}{Tree Partitioning}{\textsl{standard input}}{\textsl{standard output}}{3 seconds}{256 mebibytes}

You are given a tree with $n$ vertices. The $k$-partitioning of the tree is a graph, which 
is made by deleting $k$ edges from the tree.
Size of the $k$-partitioning of the tree is the maximum number of vertices in a component.
The $k$-partitioning with the least size is called the minimum $k$-partitioning of the tree.
For each $k$ from $1$ to $n-1$, you have to find the size of the minimal $k$-partitioning.

\InputFile

The first line contains an integer $n$ "--- the number of vertices in the tree.
The next $n-1$ lines contains two integers $a_i$ and $b_i$ each "--- vertices connected by 
the $i$-th edge.

\OutputFile

Print $n-1$ numbers: sizes of minimum $1$-partitioning, $2$-partitioning, \ldots , $(n-1)$-partitioning.

\Scoring

\SubtaskWithScore{10}

$4 \le n \le 20$

\SubtaskWithScore{20}

$4 \le n \le 1000$

\SubtaskWithScore{20} 

$4 \le n \le 100\,000$ Vertices' degrees are not greater than three. Tree's diameter is not greater than $40$.

\SubtaskWithScore{20}

$4 \le n \le 100\,000$ Vertices' degrees are not greater than three.

\SubtaskWithScore{20}

$4 \le n \le 100\,000$ Tree's diameter is not greater than $40$.

\SubtaskWithScore{10}

$4 \le n \le 100\,000$

\Example

\begin{example}
\exmpfile{001.t}{001.a.t}%
\end{example}


\end{problem}

