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Problem J
Ordinals
The Von Neumann ordinals are a number system. Ordinal numbers can be represented as sets of all numbers less than that number:
\[ \begin{aligned} 0 & = \varnothing & =& \ \{ \} \\ 1 & = \{ 0\} & =& \ \{ \{ \} \} \\ 2 & = \{ 0,1\} & =& \ \{ \{ \} ,\{ \{ \} \} \} \\ 3 & = \{ 0,1,2\} & =& \ \{ \{ \} ,\{ \{ \} \} ,\{ \{ \} ,\{ \{ \} \} \} \} \\ & \vdots \end{aligned} \]Input
Input consists of a single integer $0 \le n \le 8$.
Output
The output is the representation of that number as a set as specified above.
| Sample Input 1 | Sample Output 1 |
|---|---|
0 |
{}
|
| Sample Input 2 | Sample Output 2 |
|---|---|
1 |
{{}}
|
| Sample Input 3 | Sample Output 3 |
|---|---|
2 |
{{},{{}}}
|
