Largest Rectangle in a Plot

You are given a plot represented as a matrix of characters. Each cell is either . (free land) or # (tree). Your task is to find the area of the largest rectangular region that is completely free of trees. In other words, find the maximum area rectangle consisting solely of . characters.

The area of a rectangle is computed by $\text{width} \times \text{height}$.

inputFormat

The first line of the input contains two integers n and m representing the number of rows and columns of the matrix, respectively.

The next n lines each contain a string of length m consisting only of the characters . and #.

Note: Input is read from standard input (stdin).

outputFormat

Output a single integer which is the area of the largest rectangle that can be formed by contiguous cells containing . (free land) only. The output should be written to standard output (stdout).

4 4
..#.
....
.#..
....

6