Maximal Forest Rectangle

You are given a grid of r rows and c columns. Each cell of the grid contains a character. A cell marked with 'F' represents a forest tile, while any other character represents a non-forest tile.

Your task is to compute the area of the largest rectangle (aligned with the grid) that can be formed using only forest tiles. In other words, you should find the maximal number of contiguous cells forming a rectangle, all of which are 'F'.

The problem can also be described using the following formula in LaTeX:

\( \text{Max Area} = \max_{\substack{1 \leq i \leq j \leq r \ 1 \leq k \leq l \leq c}} \{(j-i+1) \times (l-k+1) \ \text{ such that every cell } (p,q)\ in\ [i,j]\times[k,l]\ is\ 'F'\} \)

Note that the rectangle must be contiguous and aligned with the grid rows and columns.

inputFormat

The input is read from stdin and has the following format:

• The first line contains two space-separated integers r and c, where r is the number of rows and c is the number of columns.
• This is followed by r lines, each containing a string of length c representing a row of the grid.

outputFormat

Output to stdout a single integer, which is the area of the largest rectangle composed entirely of forest tiles ('F').

3 3
WFW
FWF
FFF

3