F. Almost Same Distancetime limit per test5 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputLet G be a simple graph. Let W be a non-empty subset of vertices. Then W is almost-k-uniform if for each pair of distinct vertices u,v \in W the distance between u and v is either k or k+1.You are given a tree on n vertices. For each i between 1 and n, find the maximum size of an almost-i-uniform set.InputThe first line contains a single integer n (2 \leq n \leq 5 \cdot 10^5) – the number of vertices of the tree.Then n-1 lines follows, the i-th of which consisting of two space separated integers u_i, v_i (1 \leq u_i, v_i \leq n) meaning that there is an edge between vertices u_i and v_i. It is guaranteed that the given graph is tree. OutputOutput a single line containing n space separated integers a_i, where a_i is the maximum size of an almost-i-uniform set.ExamplesInput
5
1 2
1 3
1 4
4 5
Output
4 3 2 1 1
Input
6
1 2
1 3
1 4
4 5
4 6
Output
4 4 2 1 1 1
NoteConsider the first example.   The only maximum almost-1-uniform set is \{1, 2, 3, 4\}.  One of the maximum almost-2-uniform sets is or \{2, 3, 5\}, another one is \{2, 3, 4\}.  A maximum almost-3-uniform set is any pair of vertices on distance 3.  Any single vertex is an almost-k-uniform set for k \geq 1. In the second sample there is an almost-2-uniform set of size 4, and that is \{2, 3, 5, 6\}.
5
1 2
1 3
1 4
4 5

4 3 2 1 1 
['dfs and similar', 'graphs', '*2900']