You start from the top floor. At each step, you can go either diagonally down to the left or diagonally down to the right. This way you can form a route from the top of the pyramid to its base. Note that there are multiple routes that end somewhere in the base of the pyramid. Your goal is to maximize the sum of the integers on any route. Design and analyze an efficient algorithm to compute the maximum sum on any route from the top to the base of the pyramid.