<p>You are given an <code>m x n</code> binary matrix <code>grid</code>.</p>

<p>A row or column is considered <strong>palindromic</strong> if its values read the same forward and backward.</p>

<p>You can <strong>flip</strong> any number of cells in <code>grid</code> from <code>0</code> to <code>1</code>, or from <code>1</code> to <code>0</code>.</p>

<p>Return the <strong>minimum</strong> number of cells that need to be flipped to make <strong>all</strong> rows and columns <strong>palindromic</strong>, and the total number of <code>1</code>&#39;s in <code>grid</code> <strong>divisible</strong> by <code>4</code>.</p>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">grid = [[1,0,0],[0,1,0],[0,0,1]]</span></p>

<p><strong>Output:</strong> <span class="example-io">3</span></p>

<p><strong>Explanation:</strong></p>

<p><img src="https://assets.leetcode.com/uploads/2024/08/01/image.png" style="width: 400px; height: 105px;" /></p>
</div>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">grid = [[0,1],[0,1],[0,0]]</span></p>

<p><strong>Output:</strong> <span class="example-io">2</span></p>

<p><strong>Explanation:</strong></p>

<p><img alt="" src="https://assets.leetcode.com/uploads/2024/07/08/screenshot-from-2024-07-09-01-37-48.png" style="width: 300px; height: 104px;" /></p>
</div>

<p><strong class="example">Example 3:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">grid = [[1],[1]]</span></p>

<p><strong>Output:</strong> <span class="example-io">2</span></p>

<p><strong>Explanation:</strong></p>

<p><img alt="" src="https://assets.leetcode.com/uploads/2024/08/01/screenshot-from-2024-08-01-23-05-26.png" style="width: 200px; height: 70px;" /></p>
</div>

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

<ul>
	<li><code>m == grid.length</code></li>
	<li><code>n == grid[i].length</code></li>
	<li><code>1 &lt;= m * n &lt;= 2 * 10<sup>5</sup></code></li>
	<li><code>0 &lt;= grid[i][j] &lt;= 1</code></li>
</ul>

from typing import List

class Solution:
    def minFlips(self, grid: List[List[int]]) -> int:
        rows = len(grid)
        cols = len(grid[0])
        
        flips = 0
        
        for row in range(rows // 2):
            for col in range(cols // 2):
                values = [
                    grid[row][col],
                    grid[rows - row - 1][col],
                    grid[row][cols - col - 1],
                    grid[rows - row - 1][cols - col - 1]
                ]
                
                ones_count = sum(values)
                
                flips += min(ones_count, 4 - ones_count)
        
        unpaired_flips = 0
        single_one_count = 0
        
        if rows % 2 != 0:
            mid_row = rows // 2
            for col in range(cols // 2):
                if grid[mid_row][col] != grid[mid_row][cols - col - 1]:
                    flips += 1
                    unpaired_flips += 1
                else:
                    if grid[mid_row][col] == 1:
                        single_one_count += 1
        
        if cols % 2 != 0:
            mid_col = cols // 2
            for row in range(rows // 2):
                if grid[row][mid_col] != grid[rows - row - 1][mid_col]:
                    flips += 1
                    unpaired_flips += 1
                else:
                    if grid[row][mid_col] == 1:
                        single_one_count += 1
        
        if rows % 2 != 0 and cols % 2 != 0 and grid[rows // 2][cols // 2] == 1:
            flips += 1
        
        if unpaired_flips == 0 and single_one_count % 2 != 0:
            flips += 2
        
        return flips

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