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You should use the time limits and constraints to figure out the kind of efficiency class that will pass all test cases in time

Computer Science

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• You should use the time limits and constraints to figure out the kind of efficiency class that will pass all test cases in time.
• You can import from bisect, but please don't add additional import statements.
• You can and should use helper functions to keep your code organized.

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 0) elements from the start of a and then removing some (possibly 0) 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

• 2 <= len(a) <= 500000
• 1 <= a[i] <= 10**9

Time Limit

Your program must finish running on any valid input within 3 seconds.

Sample Input 1

10 6 9 1

Sample Output 1

3

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 6 9, 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

7 7 7

Sample Output 2

0