You are given a $0$ indexed $2$D integer array nums. You begin with a score of $0$.

Repeat the following process until the matrix is empty:

1. From each row, select and remove the element with the highest value. If there is a tie, any one of the highest elements may be removed.

2. Determine the maximum value among all elements removed in this step.

3. Add this maximum value to your score.

Return the final score after all elements are removed from nums.

Constraints:

• $1 \leq$ nums.length $\leq 300$

• $1 \leq$ nums[i].length $\leq 500$

• $0 \leq$ nums[i][j] $\leq 10^3$

Input: nums = [[4,9,2,9],[8,1,7,3],[6,5,0,4]]-List[List[int]]
Output: 24-int
Explanation: In each round, remove the highest remaining element from every row, take the maximum among the removed elements, and add it to the score. Repeating until the matrix is empty gives a final score of 24.

Input: nums = [[0,0],[0,0],[0,0]]-List[List[int]]
Output: 0-int
Explanation: Every removed element is 0, so the maximum added in every round is 0 and the final score remains 0.

Input: nums = [[12,3,8]]-List[List[int]]
Output: 23-int
Explanation: Since there is one row, each round removes its largest remaining element. The score is 12 + 8 + 3 = 23.

Input: nums = [[1000],[7],[42],[999]]-List[List[int]]
Output: 1000-int
Explanation: Each row contains one element, so all elements are removed in one round. The maximum removed value is 1000, giving a final score of 1000.

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.