Largest Submatrix With Rearrangements

You are given a binary matrix matrix of size m x n, and you are allowed to rearrange the columns of the matrix in any order.

Return the area of the largest submatrix within matrix where every element of the submatrix is 1 after reordering the columns optimally.

Example 1:

Input: matrix = [
    [0,0,1],
    [1,1,1],
    [1,0,1]
]

Output: 3

Explanation: You can rearrange the columns as shown above.
The largest submatrix of 1s, in bold, has an area of 3.

Example 2:

Input: matrix = [
    [1,1,0],
    [1,0,1]
]

Output: 2

Explanation: Notice that you must rearrange entire columns, and there is no way to make a submatrix of 1s larger than an area of 2.

Constraints:

• 1 <= (matrix.length * matrix[i].length) <= 100,000
• matrix[i][j] is either 0 or 1.

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