class Solution:
    def generateParenthesis(self, n: int) -> List[str]:

        res = []

        def func(Open, Close, result):
            # base case
            if Open == Close == n:
                res.append(result)

            # now we can add an open and close paran
            # to the resulting string under certain cond

            # add a open paran only the limit is not exceeedde
            if Open < n:
                func(Open + 1, Close, result + "(")

            # add a open paran only if the limit is not exceeded
            # and as long as open paran are greater than close
            if Close < n and Open > Close:
                func(Open, Close + 1, result + ")")

            return

        func(0, 0, "")

        return res