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Holi And Tree
Tag(s):

Algorithms, Depth-first search, Dp, Dynamic Programming, Dynamic programming, Medium-Hard

Problem
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This Holi you need to color the trees.There is a tree having N nodes with 1 as the root.A valid tree is defined as X-specific:

  • Every node except the leaf node has exactly X children. Here children means immediate children.

enter image description here

Your task is to compute the minimum number of nodes he should remove from the tree to make the tree X-specific. Find this for all X ranging from 1 to N).

Note: You can remove the nodes which are currently leafs in a single step

Constraints

\(1 \le N \le 10^5 \)

Input

The first line contains one integer N .

The next N−1 lines contains two integers u and v denoting that there is an edge between them.

Output

Print N lines containing the answer.

SAMPLE INPUT
6
1 2
1 3
1 4
4 5
4 6
SAMPLE OUTPUT
3
1
2
5
5
5
Explanation

For X=1 remove nodes \(2,3,5\).

For X=2 remove node 2.

For X=3 remove node \(5,6\)

For X=4,5,6 remove all the nodes except root

Time Limit: 1.0 sec(s) for each input file.
Memory Limit: 256 MB
Source Limit: 1024 KB
Marking Scheme: Marks are awarded when all the testcases pass.
Allowed Languages: Bash, C, C++, C++14, Clojure, C#, D, Erlang, F#, Go, Groovy, Haskell, Java, Java 8, JavaScript(Rhino), JavaScript(Node.js), Julia, Kotlin, Lisp, Lisp (SBCL), Lua, Objective-C, OCaml, Octave, Pascal, Perl, PHP, Python, Python 3, R(RScript), Racket, Ruby, Rust, Scala, Swift, Swift-4.1, TypeScript, Visual Basic

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This Problem was Asked in

HackerEarth

Challenge Name

March Easy '18

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