782. Parenthesis Generation

0

Medium

Given an integer 'n', generate all possible combinations of 'n' pairs of balanced parentheses. The output strings should be printed in ascending order, with '(' having a higher value than ')'.

Input Format

A single line containing an integer 'n'.

Output Format

Print the balanced parentheses strings, with each solution on a new line.

Example

Input

2

Output

()() (())

Constraints

1<=n<=11
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