# 1727. Largest Submatrix With Rearrangements

<https://leetcode.com/problems/largest-submatrix-with-rearrangements>

## Description

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:**

![](https://assets.leetcode.com/uploads/2020/12/29/screenshot-2020-12-30-at-40536-pm.png)

```
**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:**

![](https://assets.leetcode.com/uploads/2020/12/29/screenshot-2020-12-30-at-40852-pm.png)

```
**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.
```

**Example 4:**

```
**Input:** matrix = [[0,0],[0,0]]
**Output:** 0
**Explanation:** 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 <= 105`
* `matrix[i][j]` is `0` or `1`.

## ac

```java
```