Suppose you want to attend as many distinct shows as possible. The list of the shows on that day is released every evening. You do not know what shows will be on sale in the future. Your goal is to design an online algorithm that chooses what shows to attend every day. The algorithm should maximize the number of shows you attend. Please, keep in mind that you do not want to attend the same show twice.

Formally, on day t, your algorithm receives set S_t with the list of shows available on that day. The algorithm may choose a show from the list S_t and buy a ticket to this show. The goal of the algorithm is to maximize the number of distinct shows you attend.

Design a 2-competitive deterministic online algorithm and analyze its performance.