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

<p>A <strong>move</strong> consists of choosing any row or column and toggling each value in that row or column (i.e., changing all <code>0</code>&#39;s to <code>1</code>&#39;s, and all <code>1</code>&#39;s to <code>0</code>&#39;s).</p>

<p>Every row of the matrix is interpreted as a binary number, and the <strong>score</strong> of the matrix is the sum of these numbers.</p>

<p>Return <em>the highest possible <strong>score</strong> after making any number of <strong>moves</strong> (including zero moves)</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/07/23/lc-toogle1.jpg" style="width: 500px; height: 299px;" />
<pre>
<strong>Input:</strong> grid = [[0,0,1,1],[1,0,1,0],[1,1,0,0]]
<strong>Output:</strong> 39
<strong>Explanation:</strong> 0b1111 + 0b1001 + 0b1111 = 15 + 9 + 15 = 39
</pre>

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

<pre>
<strong>Input:</strong> grid = [[0]]
<strong>Output:</strong> 1
</pre>

<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;= 20</code></li>
	<li><code>grid[i][j]</code> is either <code>0</code> or <code>1</code>.</li>
</ul>

class Solution:
    def matrixScore(self, A: List[List[int]]) -> int:
        rows, cols = len(A), len(A[0])
        
        # Step 1: Ensure the first column is all 1s
        for i in range(rows):
            if A[i][0] == 0:
                # Flip the entire row
                A[i] = [1 - A[i][j] for j in range(cols)]
        
        # Step 2: For each remaining column, if more than half of the rows have 0, flip the column
        for j in range(1, cols):
            count_one = sum(A[i][j] for i in range(rows))
            if count_one < rows / 2:
                # Flip the column
                for i in range(rows):
                    A[i][j] = 1 - A[i][j]
        
        # Calculate the final score
        score = 0
        for row in A:
            row_value = int(''.join(map(str, row)), 2)
            score += row_value
        
        return score

16600