<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>

from typing import List

class Solution:
    def maxAbsValExpr(self, arr1: List[int], arr2: List[int]) -> int:
        max_value = 0
        n = len(arr1)
        
        # Consider all four combinations of signs
        for sign1 in [1, -1]:
            for sign2 in [1, -1]:
                max_val = float('-inf')
                min_val = float('inf')
                
                for i in range(n):
                    # Calculate the expression value for the current combination of signs
                    value = sign1 * arr1[i] + sign2 * arr2[i] + i
                    max_val = max(max_val, value)
                    min_val = min(min_val, value)
                
                # Update the maximum value found
                max_value = max(max_value, max_val - min_val)
        
        return max_value
23400