As you may know, even recycled problems have their place in programming competitions. This is one such problem.
Let us recall the definitions from Peculiar Function:
You are given an integer K. Your task is to find a set S such that F(S) contains exactly K elements.
Input
An integer K.
Output
The first line of output should contain the number of elements in the set S.
The second line of output should contain the elements of S separated by spaces, in any order.
Constraints
- 1 ≤ K ≤ 1000
- 1 ≤ any value of S ≤ 5000
Sample
| Input | Output | Explanation |
|---|---|---|
| 3 | 2 3 4 | F({3, 4}) contains the following values:
|