You are given an m $\times$ n integer matrix grid and an integer limit.

You need to select a subsequence of columns such that for every row i, the absolute difference between the elements in any two consecutive selected columns is at most limit.

Return the maximum number of columns that can be selected.

Constraints:

• $1 \leq$ m $==$ grid.length $\leq 250$

• $1 \leq$ n $==$ grid[i].length $\leq 250$

• $-10^5 \leq$ grid[i][j] $\leq 10^5$

• $0 \leq$ limit $\leq 10^5$

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.