Maximal Rectangle in a Binary Matrix

Given a binary matrix filled with 0's and 1's, your task is to find the largest rectangle containing only 1's and return its area.

The rectangle must be axis-aligned (i.e., its sides are parallel to the matrix edges). Use an efficient algorithm to solve the problem.

Hint: You can solve this problem by leveraging the Largest Rectangle in Histogram approach.

Example:

Input:
4 5
1 0 1 0 0
1 0 1 1 1
1 1 1 1 1
1 0 0 1 0
Output:
6

</p>

inputFormat

The first line of input contains two integers n and m representing the number of rows and columns in the binary matrix, respectively. The following n lines each contain m space-separated integers (either 0 or 1), representing the matrix.

For example:

4 5
1 0 1 0 0
1 0 1 1 1
1 1 1 1 1
1 0 0 1 0

outputFormat

Output a single integer representing the area of the largest rectangle containing only 1's.

For example:

6

## sample

4 5
1 0 1 0 0
1 0 1 1 1
1 1 1 1 1
1 0 0 1 0

6