1727 - Largest Submatrix With Rearrangements.

Medium

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: 4

Explanation: You can rearrange the columns as shown above. The largest submatrix of 1s, in bold, has an area of 4.

Example 2:

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

Output: 3

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

Example 3:

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:

• m == matrix.length

• n == matrix[i].length

• <code>1 <= m * n <= 10⁵</code>

• matrix[i][j] is either 0 or 1.