def generateParenthesis(n: int) -> list[str]:
    """
    :type n: int
    :rtype: List[str]
    """
    # Attempted solution
    # stack = []
    # pairs = ""
    # opening_brackets = {'('}
    # closing_brackets = {')'}
    # bracket_pairs = {')': '('}

    # # Create n pairs
    # for i in range(n):
    #     pairs += "()"
    # # print(pairs)
    
    # # Create and filter permutations
    # for pair in permutations(pairs):
    #     parenthesis = "".join(pair)
    #     # print(pair)
    #     # print(parenthesis)
    #     if parenthesis in bracket_pairs.keys():
    #         if not stack or stack[-1] != bracket_pairs[parenthesis]:
    #             print('bad')    

    # Solution
    def dfs(left, right, s):
        print(f'left: {left}')
        print(f'right: {right}')
        print(f's:   {s}')


        # Check if the length of the string is double the size of n
        # Example n=2, s= "(())"
        # Returns the string once 6 characters have been filled out
        if len(s) == n * 2:
            res.append(s)
            return 
        
        # Continuously fills left parenthesis until n
        # Example: n = 2, s = "(", then stops at s="(("
        if left < n:
            # Recursive call to add more to the left
            dfs(left + 1, right, s + '(')

        # Continuously fills right parenthesis until it matches with the left
        # Example: n = 2, s = "(()", then stops at s="(())"
        if right < left:
            # Recursive call to add more to the right
            dfs(left, right + 1, s + ')')

    res = []
    dfs(0, 0, '')
    # print(res)
    return res
generateParenthesis(3)