You are given an m $ imes$ n integer matrix points with indices starting at $0$. You want to maximize the total score obtained from the matrix.

To accumulate score, you must choose exactly one cell from each row. Choosing the cell at coordinate (r, c) adds points[r][c] to your score.

However, your score decreases if you choose a cell that is far from the cell chosen in the previous row. For every two adjacent rows r and r $+ 1$ (where $0 \leq$ r $< m -$ $1$), choosing cells at (r, c1) and (r $+ 1$, c2) subtracts $|$c1 $-$ c2$|$ from your score.

Return the maximum score you can achieve.

Constraints:

• m $==$ points.length

• n $==$ points[r].length

• $1 \leq$ m, n $\leq 10^5$

• $1 \leq$ m $ imes$ n $\leq 10^5$

• $0 \leq$ points[r][c] $\leq 10^5$

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.