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# Maximum Absolute Difference

Problem Description

You are given an array of N integers, A1, A2 ,..., AN. Return maximum value of f(i, j) for all 1 ≤ i, j ≤ N. f(i, j) is defined as |A[i] - A[j]| + |i - j|, where |x| denotes absolute value of x.

Problem Constraints
1 <= |A| <= 105
-109 <= Ai <= 109

Input Format
The first argument is an integer array A.

Output Format
Return an integer equal to the maximum value of f(i, j)

Example Input
A = [1, 3, -1]

Example Output
5

Example Explanation
Given A = [1, 3, -1],
f(1, 1) = f(2, 2) = f(3, 3) = 0
f(1, 2) = f(2, 1) = |1 - 3| + |1 - 2| = 3
f(1, 3) = f(3, 1) = |1 - (-1)| + |1 - 3| = 4
f(2, 3) = f(3, 2) = |3 - (-1)| + |2 - 3| = 5
The maximum value is 5, which is of f(2, 3)

NOTE: You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified. Still have a question? Checkout Sample Codes for more details.
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## Discussion

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