**Generate Parentheses** ========================= **Problem Statement** --------------------- Given a set of balanced parentheses, generate all possible combinations of well-formed parentheses that can be obtained by inserting additional pairs of parentheses around existing ones. **Rules and Constraints** ------------------------- * The generated combinations should only contain valid parentheses (`'('` and `')'`). * The resulting strings must have the same number of open and close parentheses. * No generated string should have any unmatched open or close parentheses. * The order of the parentheses does not matter. **Output Requirements** ------------------------ The solution should return a list of all valid combinations of well-formed parentheses that meet the above constraints. **Notes** ---------- * The input may be an empty string or a string containing balanced parentheses. * The time complexity of the solution should be optimized to handle large inputs efficiently. By following these requirements, you can generate all possible combinations of well-formed parentheses from the input set. ### Example **Input:** {"n":3} **Output:** ["((()))","(()())","(())()","()(())","()()()"]