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.

Examples

Example 1

Input:  matrix = [[0,0,1],[1,1,1],[1,0,1]]
Output: 4

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

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

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
• 1 <= m * n <= 10⁵
• matrix[i][j] is either 0 or 1.