Maximum of Absolute Value Expression
<p>Given two arrays of integers with equal lengths, return the maximum value of:</p>

<p><code>|arr1[i] - arr1[j]| + |arr2[i] - arr2[j]| + |i - j|</code></p>

<p>where the maximum is taken over all <code>0 &lt;= i, j &lt; arr1.length</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> arr1 = [1,2,3,4], arr2 = [-1,4,5,6]
<strong>Output:</strong> 13
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> arr1 = [1,-2,-5,0,10], arr2 = [0,-2,-1,-7,-4]
<strong>Output:</strong> 20
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>2 &lt;= arr1.length == arr2.length &lt;= 40000</code></li>
	<li><code>-10^6 &lt;= arr1[i], arr2[i] &lt;= 10^6</code></li>
</ul>
Array; Math
class Solution:
    def maxAbsValExpr(self, arr1: List[int], arr2: List[int]) -> int:
        dirs = (1, -1, -1, 1, 1)
        ans = -inf
        for a, b in pairwise(dirs):
            mx, mi = -inf, inf
            for i, (x, y) in enumerate(zip(arr1, arr2)):
                mx = max(mx, a * x + b * y + i)
                mi = min(mi, a * x + b * y + i)
                ans = max(ans, mx - mi)
        return ans
