An element 1 in a sequence S of n numbers is called a majority element if it occurs more than 1/2 times in S. This Question asks you to describe two algorithms that decide if the sequence S contains a majority element; if it does, the algorithm returns it; otherwise, the algorithm returns the message "there is no majority element". (1) Show how the majority problem can be solved in O(nlog n) time. Argue why your algorithm is correct and why the running time is O(n logn). (2) Show how the majority problem can be solved in O(n) time. Argue why your algorithm is correct and why the running time is O(n). You are highly encouraged to use any algorithm and any result that was discussed in class. In other words, try to make your algorithms as short as possible by using algorithms discussed in class as "black boxes