Parliament

Time limit1sMemory limit128 MB

Summary

Split N delegates into groups of distinct sizes so that the product of the sizes is maximized, and print the sizes in ascending order.

Level: Medium4 of 10
Topics: Math, Greedy, Combinatorics
Solved: No attempts yet

Problem

A newly convened parliament has $N$ delegates. By the current regulation the delegates must be split into disjoint groups whose sizes are all different, and every day each group sends exactly one of its members to a conciliatory committee. The committee's composition must be different on every day, and the parliament stays in session only as long as this can be done.

Write a program that determines how many delegates each group should contain so that the parliament works for as long as possible.

Input

A single integer $N$ ( $5 \le N \le 1000$ ).

Output

Print the sizes of the groups that let the parliament work for the maximum possible time, on a single line in ascending order and separated by spaces. (This choice of group sizes is uniquely determined.)

Examples3

Example 1
Input
```
7
```
Expected output
```
3 4
```
Example 2
Input
```
5
```
Expected output
```
2 3
```
Example 3
Input
```
6
```
Expected output
```
2 4
```