Problem B
Neumann

There are many ways to define the natural numbers. One of the more famous ones is John von Neumann’s definition. In his definition we first define $0$ as the empty set $\varnothing $. Next we define the successor of a number $x$ as $x \cup \{ x\} $. The axiom of infinity then guarantees the existence of a set that contains $0$ and all its successors. But the finer details of this logic isn’t what this problem is about. The only thing we ask of here is to print some natural numbers. Most programming languages do this by printing out the numbers in base $10$. But we’re going to do things properly here and print according to this definition.

Note that the elements of a set are not internally ordered, but since all sets in this problem correspond to numbers the elements of a set should be printed in increasing order. For example $\{ \} $ should be printed before $\{ \{ \} \} $ since the first set corresponds to $0$ and the other one corresponds to $1$.

Input

The input contains a single line with a single natural number $0 \leq n \leq 20$.

Output

Print out $n$ as a set using Neumann’s definition as described above.

0

{}

1

{{}}

2

{{},{{}}}