Once upon the time, there was one restaurant with only one boss, one chef, and one wok. The restaurant

$$Uji Jin Hall$$ is famous for its variety of delicious fried rice dishes. After cooking each dish, the chef

must wash the wok. During the busy noon hours, the restaurant owner wants to increase throughput by

reducing the wok washing time. The owner suggests that the chef can skip washing the wok if cooking

the same type of fried rice consecutively.

To maintain the restaurant$$s reputation and customer satisfaction, orders must be fulfilled in the order

they were placed. However, the chef can skip some orders to maximize efficiency.

There are T minutes available at noon. Assume that cooking any dish takes A minutes and washing

the wok takes B minutes. Given a sequence of N orders in chronological order $($all the orders are placed

before noon$),$ how many dishes can the restaurant serve within the available time? Devise an algorithm

to solve this problem. Give a correctness proof and analyze the running time.