<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>either</strong> all rows <strong>palindromic</strong> or all columns <strong>palindromic</strong>.</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],[0,0,0],[0,0,1]]</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/2024/07/07/screenshot-from-2024-07-08-00-20-10.png" style="width: 420px; height: 108px;" /></p>

<p>Flipping the highlighted cells makes all the rows palindromic.</p>
</div>

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

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

<p><strong>Output:</strong> <span class="example-io">1</span></p>

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

<p><img alt="" src="https://assets.leetcode.com/uploads/2024/07/07/screenshot-from-2024-07-08-00-31-23.png" style="width: 300px; height: 100px;" /></p>

<p>Flipping the highlighted cell makes all the columns palindromic.</p>
</div>

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

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

<p><strong>Output:</strong> <span class="example-io">0</span></p>

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

<p>All rows are already palindromic.</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>

class Solution:
    def minFlips(self, grid: List[List[int]]) -> int:
        m = len(grid)
        n = len(grid[0])
        
        def min_flips_to_make_palindromic(line):
            flips = 0
            for i in range(len(line) // 2):
                if line[i] != line[-i-1]:
                    flips += 1
            return flips
        
        # Calculate the minimum flips to make all rows palindromic
        row_flips = sum(min_flips_to_make_palindromic(row) for row in grid)
        
        # Calculate the minimum flips to make all columns palindromic
        column_flips = 0
        for col in range(n):
            column = [grid[row][col] for row in range(m)]
            column_flips += min_flips_to_make_palindromic(column)
        
        return min(row_flips, column_flips)

            
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