You are given a binary matrix matrix of dimensions m $ imes$ n. You are permitted to rearrange the columns of matrix in any order.

Return the area of the largest submatrix consisting entirely of $1$’s after reordering the columns.

Constraints:

• m == matrix.length

• n == matrix[i].length

• $1 \leq$ m * n $\leq 10^5$

• matrix[i][j] is either $0$ or $1$.

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.