<p>You are given a binary matrix <code>matrix</code> of size <code>m x n</code>, and you are allowed to rearrange the <strong>columns</strong> of the <code>matrix</code> in any order.</p> <p>Return <em>the area of the largest submatrix within </em><code>matrix</code><em> where <strong>every</strong> element of the submatrix is </em><code>1</code><em> after reordering the columns optimally.</em></p> <p> </p> <p><strong class="example">Example 1:</strong></p> <img alt="" src="https://assets.leetcode.com/uploads/2020/12/29/screenshot-2020-12-30-at-40536-pm.png" style="width: 500px; height: 240px;" /> <pre> <strong>Input:</strong> matrix = [[0,0,1],[1,1,1],[1,0,1]] <strong>Output:</strong> 4 <strong>Explanation:</strong> You can rearrange the columns as shown above. The largest submatrix of 1s, in bold, has an area of 4. </pre> <p><strong class="example">Example 2:</strong></p> <img alt="" src="https://assets.leetcode.com/uploads/2020/12/29/screenshot-2020-12-30-at-40852-pm.png" style="width: 500px; height: 62px;" /> <pre> <strong>Input:</strong> matrix = [[1,0,1,0,1]] <strong>Output:</strong> 3 <strong>Explanation:</strong> You can rearrange the columns as shown above. The largest submatrix of 1s, in bold, has an area of 3. </pre> <p><strong class="example">Example 3:</strong></p> <pre> <strong>Input:</strong> matrix = [[1,1,0],[1,0,1]] <strong>Output:</strong> 2 <strong>Explanation:</strong> Notice that you must rearrange entire columns, and there is no way to make a submatrix of 1s larger than an area of 2. </pre> <p> </p> <p><strong>Constraints:</strong></p> <ul> <li><code>m == matrix.length</code></li> <li><code>n == matrix[i].length</code></li> <li><code>1 <= m * n <= 10<sup>5</sup></code></li> <li><code>matrix[i][j]</code> is either <code>0</code> or <code>1</code>.</li> </ul>