<p>You are given an <code>n x n</code> integer <code>matrix</code>. You can do the following operation <strong>any</strong> number of times:</p>

<ul>
	<li>Choose any two <strong>adjacent</strong> elements of <code>matrix</code> and <strong>multiply</strong> each of them by <code>-1</code>.</li>
</ul>

<p>Two elements are considered <strong>adjacent</strong> if and only if they share a <strong>border</strong>.</p>

<p>Your goal is to <strong>maximize</strong> the summation of the matrix&#39;s elements. Return <em>the <strong>maximum</strong> sum of the matrix&#39;s elements using the operation mentioned above.</em></p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/07/16/pc79-q2ex1.png" style="width: 401px; height: 81px;" />
<pre>
<strong>Input:</strong> matrix = [[1,-1],[-1,1]]
<strong>Output:</strong> 4
<b>Explanation:</b> We can follow the following steps to reach sum equals 4:
- Multiply the 2 elements in the first row by -1.
- Multiply the 2 elements in the first column by -1.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/07/16/pc79-q2ex2.png" style="width: 321px; height: 121px;" />
<pre>
<strong>Input:</strong> matrix = [[1,2,3],[-1,-2,-3],[1,2,3]]
<strong>Output:</strong> 16
<b>Explanation:</b> We can follow the following step to reach sum equals 16:
- Multiply the 2 last elements in the second row by -1.
</pre>

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

<ul>
	<li><code>n == matrix.length == matrix[i].length</code></li>
	<li><code>2 &lt;= n &lt;= 250</code></li>
	<li><code>-10<sup>5</sup> &lt;= matrix[i][j] &lt;= 10<sup>5</sup></code></li>
</ul>

import math
class Solution:
    
    def fun(self, a):
        n = len(a)
        min_e = 0
        count_n = 0
        count_z = 0
        min_p = math.inf
        s = 0
        for i in range(n):
            for j in range(n):
                p = a[i][j]
                s += abs(p)
                if p == 0:
                    count_z += 1
                elif p < 0:
                    count_n += 1
                    if min_e == 0:
                        min_e = p
                    elif p > min_e:
                        min_e = p
                    else:
                        pass
                else:
                    if p < min_p:
                        min_p = p

        if count_z > 0:
            return s
        if count_n % 2 == 1:
            if abs(min_p) < abs(min_e):
                s -= 2*min_p
            else:
                s += 2*min_e
        return s    
                    
    def maxMatrixSum(self, matrix: List[List[int]]) -> int:
        return self.fun(matrix)
702