Print all valid bracket expressions of length N, consisting of parentheses and square brackets.
Input
The first line contains a single number N. \(1 <= N <= 14\), N is even.
Output
Each expression is displayed on a separate line.
Examples
| # |
Input |
Output |
| 1 |
2 |
()
[]
|
| 2 |
4 |
(())
[[]]
[()]
()[]
[]()
()()
([])
[][]
|