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`

**Example 1:**

Input:matrix = [[0,0,1],[1,1,1],[1,0,1]]Output:4Explanation: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:3Explanation: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:2Explanation:Notice that you must rearrange entire columns, and there is no way to make a submatrix of 1s larger than an area of 2.

**Example 4:**

Input:matrix = [[0,0],[0,0]]Output:0Explanation:As there are no 1s, no submatrix of 1s can be formed and the area is 0.

**Constraints:**

`m == matrix.length`

`n == matrix[i].length`

`1 <= m * n <= 10`

^{5}`matrix[i][j]`

is`0`

or`1`

.

class Solution {
public int largestSubmatrix(int[][] matrix) {
}
}