<p>You are given a <strong>0-indexed</strong> 2D integer array <code>nums</code>. Initially, your score is <code>0</code>. Perform the following operations until the matrix becomes empty:</p>

<ol>
	<li>From each row in the matrix, select the largest number and remove it. In the case of a tie, it does not matter which number is chosen.</li>
	<li>Identify the highest number amongst all those removed in step 1. Add that number to your <strong>score</strong>.</li>
</ol>

<p>Return <em>the final <strong>score</strong>.</em></p>
<p>&nbsp;</p>
<p><strong>Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [[7,2,1],[6,4,2],[6,5,3],[3,2,1]]
<strong>Output:</strong> 15
<strong>Explanation:</strong> In the first operation, we remove 7, 6, 6, and 3. We then add 7 to our score. Next, we remove 2, 4, 5, and 2. We add 5 to our score. Lastly, we remove 1, 2, 3, and 1. We add 3 to our score. Thus, our final score is 7 + 5 + 3 = 15.
</pre>

<p><strong>Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [[1]]
<strong>Output:</strong> 1
<strong>Explanation:</strong> We remove 1 and add it to the answer. We return 1.</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 300</code></li>
	<li><code>1 &lt;= nums[i].length &lt;= 500</code></li>
	<li><code>0 &lt;= nums[i][j] &lt;= 10<sup>3</sup></code></li>
</ul>

class Solution:
    def matrixSum(self, nums: List[List[int]]) -> int:
        score = 0
        
        while nums:
            # List to store the largest numbers from each row
            max_in_rows = []
            
            for row in nums:
                if row:
                    max_num = max(row)
                    max_in_rows.append(max_num)
                    row.remove(max_num)
            
            # Get the maximum number among the largest numbers from each row
            if max_in_rows:
                score += max(max_in_rows)
            
            # Remove empty rows
            nums = [row for row in nums if row]
        
        return score
1418