<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:
        max_a = max_b = max_c = max_d = float("-inf")
        min_a = min_b = min_c = min_d = float("inf")

        for i in range(len(arr1)):
            a = arr1[i] + arr2[i] + i
            b = arr1[i] - arr2[i] + i
            c = arr1[i] + arr2[i] - i
            d = arr1[i] - arr2[i] - i

            if a > max_a: max_a = a
            if b > max_b: max_b = b
            if c > max_c: max_c = c
            if d > max_d: max_d = d

            if a < min_a: min_a = a
            if b < min_b: min_b = b
            if c < min_c: min_c = c
            if d < min_d: min_d = d
            
        return max(max_a - min_a, max_b - min_b, max_c - min_c, max_d - min_d)

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