LogiQuest

218. Generate Parentheses

MediumBacktracking

Print all valid combinations of n pairs of parentheses in lexicographic order ('(' < ')'), one per line.

Input format

A single integer n.

Output format

The valid strings.

Example 1

Input

3

Output

((()))
(()())
(())()
()(())
()()()

Example 2

Input

1

Output

()

Constraints

1 ≤ n ≤ 8

Read input from standard input and print the answer to standard output. Your code is judged against 4 test cases, most of them hidden.

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