generate parentheses

class (object):
    def generateParenthesis(self, n):
        """
        :type n: int
        :rtype: List[str]
        """
        
        res = []
        self.dfs(0, 0, n, [], res)
        return res
        
    def dfs(self, count_left, count_right, n, cur, res):
        if count_right == n:
            res.append("".join(cur))
            return
        if count_right < count_left and count_left < n:
            cur.append("(")
            self.dfs(count_left+1, count_right, n, cur, res)
            cur.pop()
            cur.append(")")
            self.dfs(count_left, count_right+1, n, cur, res)
            cur.pop()
        elif count_right == count_left and count_left < n:
            cur.append("(")
            self.dfs(count_left+1, count_right, n, cur, res)
            cur.pop()
        elif count_right < count_left and count_left == n:
            cur.append(")")
            self.dfs(count_left, count_right+1, n, cur, res)
            cur.pop()