Can you help me solve the following algorithm problem? Please show me how the permutation work:

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Output all correct parentheses sequences of length N in lexicographic order.

A correct parentheses sequence is defined as follows:

"()" is a correct parentheses sequence.

If S is a correct parentheses sequence, then "(S)" is also a correct parentheses sequence.

If S and T are correct parentheses sequences, then ST (the concatenation of S and T) is also a correct parentheses sequence.

All other strings are not correct parentheses sequences.

For example, "()", "()(())", and "()()()()" are correct parentheses sequences, while ")(", ")))()(((", and "((((a))))" are not.

Note that "(" comes before ")" in lexicographic order.