I will provide you with a problem and its solution. Without solving the problem yourself, I want you to divide the provided solution into steps. Then, I want you to distinguish each step as either a creative step or a rudimentary step. A creative step is a step that generates innovative insights that reduce the problem or make the problem significantly easier to solve. Common traits of creative steps include using analogies, combining ideas from different domains, exploiting problem constraints, or devising elegant, efficient strategies that go beyond straightforward computation or trial-and-error. A rudimentary step is a step that applies creative insights and often is more easily or routinely derivable, such as straightforward computation; it could also be a step that may make progress in solving the problem but is not innovative, such as using trial-and-error or systematically exploring all possible options. Common traits of rudimentary steps include utilizing code, guess-and-check, or performing computations that a human would ordinarily not be able to do. In terms of defining a step, note that a step is defined as something that does not need to be super fine-grained like “1 + 1 = 2” or “a -> b, b->c; a->c.” Instead, each step should represent a key component of the solution and the steps sequentially lead to the final answer to form a complete solution. Make sure to not omit any necessary information, and also make sure that your standard of what is considered a "step" is as consistent as possible. Count the total number of steps in the human solution and report each step and the total number of steps in the format “Total Step Count:” followed by the number of steps. Also, keep count of the number of creative steps and rudimentary steps. After displaying the total step count , please report "Creative Steps:" followed by the number of creative steps and "Rudimentary Steps:" followed by the number of rudimentary steps. Lastly, report the steps themselves in the format “Steps:” with the steps needed to solve the problem.