Correct bracket sequences#4838

Correct bracket sequences

1 second
64 megabytes
Medium

Given a natural number , output all valid bracket sequences composed of opening parentheses and closing parentheses, arranged in lexicographical order.

Input

The input consists of a single number (n < 12).

Output

Print each valid sequence on a separate line, ensuring that each line ends with a newline character.

Examples

Example 1

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