Maximum Rectangle Area of 'X'

You are given an N x M grid, where each cell contains either the character X or .. Your task is to find the area of the largest rectangular sub-grid that contains only the character X.

The area of a sub-grid is defined as the number of cells in that rectangle. If there is no rectangle filled entirely with X, then the answer is 0.

Mathematical formulation:

Let f(i, j) denote the height of consecutive X's in column j ending at row i. Then the problem reduces to finding the maximum area in the histogram of heights for each row. The largest area for a given histogram is given by:

\[ \max_{1 \leq i \leq N} \left( \text{max_area}(\{f(i,1), f(i,2), \dots, f(i,M)\}) \right) \]

inputFormat

The input is given via standard input (stdin) in the following format:

1. The first line contains two space-separated integers N and M, representing the number of rows and columns respectively.
2. The next N lines each contain a string of length M, where each character is either X or ..

outputFormat

Output a single integer to standard output (stdout), which is the area of the largest rectangular sub-grid that contains only X.

4 5
X.X.X
XX..X
XXXX.
XXX.X

6