You are given an m $ imes$ n binary matrix matrix and an integer numSelect, which represents the number of distinct columns you must select.

A row is considered covered if all indices j where matrix[i][j] $= 1$ are among the chosen columns. In other words, a row is covered if every cell in that row containing a $1$ belongs to the selected set of columns.

Return the maximum number of rows that can be covered by choosing exactly numSelect distinct columns.

Constraints:

• m $==$ matrix.length

• n $==$ matrix[i].length

• $1 \leq$ m, n $\leq 12$

• matrix[i][j] is either $0$ or $1$.

• $1 \leq$ numSelect $\leq$ n

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.