On this assignment, efficiency concerns are more important than on previous assignments. For this reason, we have provided time limits for each question. To pass a test case, your program must produce the correct output (as always) but also finish within the time limit. Some solutions, while correct, may not be fast enough. Solving the problem with such a solution, though, is far from a waste of time: it has the possibility of receiving up to 70 percent of the points, it is a good step toward understanding how the problem can be solved, and it may help you progress to a faster solution! Q1: Assignment Difficulty Dan has a list of problems suitable for Assignment 4. The difficulties of these problems are stored in a list of integers a. The i-th problem's difficulty is represented by a[i] (the higher the integer, the more difficult the problem). Dan is too busy eating saltines to worry about Assignment 4 decisions, so he asks Michael the TA to select at least two problems from the list for the assignment. Since there are many possible subsets of the problems to consider and Michael has a life, he decides to consider only sublists (definition follows) of the list of problems. To make grading the assignment easier, Michael wants to pick problems that don't vary too much in difficulty. What is the smallest difference between the difficulties of the most difficult selected problem and the least difficult selected problem he can achieve by selecting a sublist of length at least 2 of the original list of problems? Definition: A sublist of a list a is any list you can obtain by removing some (possibly o) elements from the start of a and then removing some (possibly o) elements from the end of it. (It's like the definition of segment from lecture.). Filename Your filename for this question must be q1.py. Input The input consists of a single line containing the integers in the list a, separated by single spaces. Output Print a single integer indicating the smallest difference in difficulties Michael can achieve. Constraints Time Limit 2 <1en (a) <= 500000 • 1 <= a[i] <= 10**9 Your Sample Input 1 program must finish running on any valid input within 3 seconds. 10 6 9 1 3 Sample Output 1 Sample 1 Explanation • If Michael selects all of the problems, the maximum difficulty would be 10 and the minimum difficulty would be 1. In this case, the difference he wants to minimize would be 9. • If he selects the sublist 69, the maximum and minimum difficulties would be 9 and 6 respectively and the difference would be 3. • Note that he can't select 10 9, as that's not a sublist of a. Sample Input 2 0 777 Sample Output 2