The mode of a list is the element which occurs the most often. For example, the mode of the list [1, 3, 2, 1, 2, 1) is 1. Write a function: def mode_of_list (lat): that takes a list and returns the mode of that list. Your implementation should optimize the average case running time. Analyze the worst-case running time of your code. What data structure could you use to improve the worst case running time? What would be the average case running time of this alternate solution? Include your answers to these questions as comments in your code. Earlier in the summer, you implemented a worst-case linear time algorithm for the two sum problem on a sorted list. This problem asked to find, given a sorted list and a target number, two elements in the list that sum to the target number. Now, write an implementation to solve the same problem for an unsorted list. That is, implement the function: 2 def two_sun(1st, target): that takes as input an unsorted list of numbers 1st and a single number, target, and returns a pair of indexes (as a tuple), indicating the indices in 1st of two numbers whose sum is target. For example, if 1st is the list. [-5, 2, 8, -3, 7, 1], then the call two_sum (1st, -1) should return (1, 3) because 1st [1] 1st [3] is -1. If there is no pair of numbers in 1st that sum to target, then your function should return (None. None).