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Problems

Brackets (2)

Brackets (2)

Time limit 2 seconds
Memory limit 64 MiB

Print all correct bracket expressions of length n, consisting of round and square brackets.

Input data

One even integer n (1  ≤n14).

Output data

Print each expression on a separate line.

Examples

Input example #1
4
Output example #1
()()
()[]
(())
([])
[]()
[][]
[()]
[[]]