<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>

class Solution:
    def maxAbsValExpr(self, arr1: List[int], arr2: List[int]) -> int:
        minA = minB = minC = minD = math.inf
        maxA = maxB = maxC = maxD = -math.inf

        for i, (num1, num2) in enumerate(zip(arr1, arr2)):
            minA = min(minA, i + num1 + num2)
            maxA = max(maxA, i + num1 + num2)
            minB = min(minB, i + num1 - num2)
            maxB = max(maxB, i + num1 - num2)
            minC = min(minC, i - num1 + num2)
            maxC = max(maxC, i - num1 + num2)
            minD = min(minD, i - num1 - num2)
            maxD = max(maxD, i - num1 - num2)
        
        return max(maxA - minA, maxB - minB,
                   maxC - minC, maxD - minD)
24000